diff --git a/.gitignore b/.gitignore index 747d42e..8165e4c 100644 --- a/.gitignore +++ b/.gitignore @@ -1,3 +1,6 @@ +# backup files +*~ + # ---> TeX ## Core latex/pdflatex auxiliary files: *.aux diff --git a/Makefile b/Makefile new file mode 100644 index 0000000..4c290d3 --- /dev/null +++ b/Makefile @@ -0,0 +1,200 @@ +TEXBASE=nonlinearbaseline +BIBFILE=references.bib +REBUTTALBASE= + +TEXFILE=$(TEXBASE).tex +PDFFILE=$(TEXBASE).pdf +TXTFILE=$(TEXBASE).txt + +PDFFIGURES=$(shell sed -n -e '/^[^%].*includegraphics/{s/^.*includegraphics.*{\([^}]*\)}.*/\1.pdf/;p}' $(TEXFILE)) + +PT=$(wildcard *.py) +PYTHONFILES=$(filter-out plotstyle.py, $(PT)) +PYTHONPDFFILES=$(PYTHONFILES:.py=.pdf) + +REVISION=e3814a1be539f9424c17b7bd7ef45a8826a9f1e2 + +ifdef REBUTTALBASE +REBUTTALTEXFILE=$(REBUTTALBASE).tex +REBUTTALPDFFILE=$(REBUTTALBASE).pdf +endif +REBUTTALREVISION= + +# all ########################################################### +ifdef REBUTTALBASE +all: bib rebuttalbib +else +all: bib +endif + +# python ######################################################### +plots: $(PYTHONPDFFILES) +$(PYTHONPDFFILES): %.pdf: %.py plotstyle.py + python3 $< + +watchplots : + while true; do ! make -q plots && make plots; sleep 0.5; done + + +# compile manuscript ################################################# +bib: $(TEXBASE).bbl +$(TEXBASE).bbl: $(TEXFILE) $(BIBFILE) + lualatex $(TEXFILE) + bibtex $(TEXBASE) + lualatex $(TEXFILE) + lualatex $(TEXFILE) + lualatex $(TEXFILE) + @echo + @echo "BibTeX log:" + @sed -n -e '1,/You.ve used/p' $(TEXBASE).blg + +pdf: $(PDFFILE) +$(PDFFILE) : $(TEXFILE) + lualatex -interaction=scrollmode $< | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && lualatex -interaction=scrollmode $< || true + +again : + lualatex $(TEXFILE) + +# watch files ####################################################### +watchpdf : + while true; do ! make -s -q pdf && make pdf; sleep 0.5; done + + +# make diffs ######################################################## +diff : + #latexdiff-git -r $(REVISION) --pdf $(TEXFILE) + latexdiff-git -r $(REVISION) $(TEXFILE) + -lualatex $(TEXBASE)-diff$(REVISION) + -bibtex $(TEXBASE)-diff$(REVISION) + -lualatex $(TEXBASE)-diff$(REVISION) + -lualatex $(TEXBASE)-diff$(REVISION) + -lualatex $(TEXBASE)-diff$(REVISION) + mv $(TEXBASE)-diff$(REVISION).pdf $(TEXBASE)-diff.pdf + mv $(TEXBASE)-diff$(REVISION).tex $(TEXBASE)-diff.tex + mv $(TEXBASE)-diff$(REVISION).bbl $(TEXBASE)-diff.bbl + rm $(TEXBASE)-diff$(REVISION).* + + +# convert to txt file ################################################ +txt: $(PDFFILE) + #dvi2tty -w 132 -v 500000 -e-60 -q $(DVIFILE) | sed -n -e '/\cL/,+2!p' > $(TXTFILE) + pdftotext -nopgbrk $(PDFFILE) - | fold -s > $(TXTFILE) + +# convert to rtf file ################################################ +rtf : + latex2rtf $(TEXFILE) + +# remove all fancy commands from the tex file: +simplify : + sed -e '/overall style/,/page style/d; /setdoublespacing/,+1d; /usepackage.*caption/s/{\(.*\)}/\1/; /figure placement/,/^%/d; /ifthenelse.*nofigs/,/#1/d; /begin{multicols}/d; /end{multicols}/d; /begin{keywords}/,/end{keywords}/d; /begin{contributions}/,/end{contributions}/d; /figurecaptions/d; /linenomath/d; s/captionc/caption/' $(TEXFILE) | perl -00 -lpe 's/\\showfigure{((\s|.)*?)}/$$1/' > $(TEXBASE)-simplified.tex + +# statistics ######################################################### +stats: $(PDFFILE) +# use \pagestyle{empty} and don't include any pictures! + pdftotext -nopgbrk $(PDFFILE) - | fold -s > tmp.txt + @echo + @echo " words: " `wc -w tmp.txt 2> /dev/null | cut -d ' ' -f 1` + @echo "characters: " `wc -c tmp.txt 2> /dev/null | cut -d ' ' -f 1` + rm tmp.txt + +# rebuttal ########################################################## +ifdef REBUTTALBASE +rebuttalbib: $(REBUTTALBASE).bbl +$(REBUTTALBASE).bbl: $(REBUTTALTEXFILE) $(BIBFILE) + lualatex $(REBUTTALTEXFILE) + bibtex $(REBUTTALBASE) + lualatex $(REBUTTALTEXFILE) + lualatex $(REBUTTALTEXFILE) + lualatex $(REBUTTALTEXFILE) + @echo + @echo "BibTeX log:" + @sed -n -e '1,/You.ve used/p' $(REBUTTALBASE).blg + +rebuttal: $(REBUTTALPDFFILE) +$(REBUTTALPDFFILE) : $(REBUTTALTEXFILE) + lualatex -interaction=scrollmode $< | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && lualatex -interaction=scrollmode $< || true + +watchrebuttal : + while true; do ! make -q rebuttal && make rebuttal; sleep 0.5; done + +rebuttaldiff : + latexdiff-git -r $(REBUTTALREVISION) --append-textcmd="response,issue" --pdf $(REBUTTALTEXFILE) + mv $(REBUTTALBASE)-diff$(REBUTTALREVISION).pdf $(REBUTTALBASE)-diff.pdf + rm $(REBUTTALBASE)-diff$(REBUTTALREVISION).* +endif + +# git ############################################################## +pull : + git pull origin master + +ifdef REBUTTALBASE + +edit : pull + emacs $(TEXFILE) $(BIBFILE) $(REBUTTALTEXFILE) Makefile & + sleep 1 + okular $(REBUTTALPDFFILE) $(PDFFILE) & + +prepare : pull bib diffrev rebuttalbib rebuttaldiff + +else + +edit : pull + emacs $(TEXFILE) $(BIBFILE) Makefile & + sleep 1 + okular $(PDFFILE) & + +prepare : pull bib diffrev + +endif + +push : prepare + git commit -a + git push origin master + +# convert figures to png files ####################################### +figures: + ./latexfigures2png $(TEXFILE) + +# convert pdf figures to eps ######################################### +epsfigures: + #for i in $(PDFFIGURES); do echo $$i; rm -f $${i%.pdf}.eps; pdftops -level3 -eps $$i $${i%.pdf}.eps; done + for i in $(PDFFIGURES); do echo $$i; rm -f $${i%.pdf}.eps; gs -q -dNOCACHE -dNOPAUSE -dBATCH -dSAFER -sDEVICE=epswrite -sOutputFile=$${i%.pdf}.eps $$i; done + +# clean up ############################################################ + +clean: + rm -rf auto *~ *.aux *.blg *.bbl *.dvi *.log *.out *.fff *.ttt $(PDFFIGURES) __pycache__ + +cleanall: clean + rm -f $(PDFFILE) figure-??.png + +# help ################################################################ +help : + @echo -e \ + "make pdf: make the pdf file of the paper.\n"\ + "make bib: run bibtex and make the pdf file of the paper.\n"\ + "make again: run pdflatex and make the pdf file of the paper,\n"\ + " no matter whether you changed the .tex file or not.\n"\ + "make watchpdf: make the pdf file of the paper\n"\ + " whenever the tex file is modified.\n"\ + "make diff: make a diff file against the specified revision (REVISION variable)\n"\ + "make txt: make a plain text version of the paper ($(TXTFILE)).\n"\ + "make rtf: convert the paper ($(TXTFILE)) to rtf format.\n"\ + "make simplify: strip all fancy commands from the paper ($(TXTFILE))\n"\ + "make stats: print number of words and characters.\n"\ + "make rebuttalbib: run bibtex and make the pdf file of the rebuttal.\n"\ + "make rebuttal: make the pdf file of the rebuttal.\n"\ + "make watchrebuttal: make the pdf file of the rebuttal\n"\ + " whenever the tex file is modified.\n"\ + "make rebuttaldiff: make a diff file of the rebuttal against the specified revision\n"\ + " (REBUTTALREVISION variable).\n"\ + "make pull: pull from the git repository.\n"\ + "make edit: pull and open emacs and okular with te relevant files.\n"\ + "make prepare: pull and make the pdfs and diffs of the manuscript and the rebuttal.\n"\ + "make push: prepare, commit, and push to the git repository.\n"\ + "make figures : convert all figures to png files.\n"\ + "make epsfigures: convert all included pdf figures to eps files.\n"\ + "make clean: remove all intermediate files,\n"\ + " just leave the source files and the final .pdf files.\n"\ + "make cleanup: remove all intermediate files as well as\n"\ + " the final .pdf files.\n"\ diff --git a/journalsabbrv.bib b/journalsabbrv.bib new file mode 100644 index 0000000..a3dfa8a --- /dev/null +++ b/journalsabbrv.bib @@ -0,0 +1,129 @@ +@STRING( ActaPhysiolScand = "Acta Physiol Scand" ) +@STRING( AmZool = "Am Zool" ) +@STRING( AnnNYAcadSci = "Ann NY Acad Sci" ) +@STRING( AnimBehav = "Anim Behav" ) +@STRING( AnimBiol = "Anim Biol" ) +@STRING( AnnuRevNeurosci = "Annu Rev Neurosci" ) +@STRING( AnnuRevPhysiol = "Annu Rev Physiol" ) +@STRING( AnnuRevPsychol = "Annu Rev Psychol" ) +@STRING( BehavBrainSci = "Behav Brain Sci" ) +@STRING( BehavBrainRes = "Behav Brain Res" ) +@STRING( BehavEcol = "Behav Ecol" ) +@STRING( BehavEcolSociobiol = "Behav Ecol Sociobiol" ) +@STRING( BiolBull = "Biol Bull" ) +@STRING( BiolCell = "Biol Cell" ) +@STRING( BiolCons = "Biological Conservation" ) +@STRING( BiolCybern = "Biol Cybern" ) +@STRING( BiolLett = "Biol Lett" ) +@STRING( BiolRev = "Biol Rev" ) +@STRING( Biometrika = "Biometrika" ) +@STRING( BiophysJ = "Biophys J" ) +@STRING( Biosystems = "Biosyst" ) +@STRING( BrainBehavEvol = "Brain Behav Evol" ) +@STRING( BrainRes = "Brain Res" ) +@STRING( BrainResRev = "Brain Res Rev" ) +@STRING( BrainResBull = "Brain Res Bull" ) +@STRING( BrainResCognBrainRes = "Brain Res Cogn Brain Res" ) +@STRING( BullMathBiol = "Bull Math Biol" ) +@STRING( CanJZool = "Can J Zool" ) +@STRING( CellTissueRes = "Cell Tissue Res" ) +@STRING( CerebCortex = "Cereb Cortex" ) +@STRING{ CompBiochemPhysiol = "Comp Biochem Physiol"} +@STRING( CurrBiol = "Curr Biol" ) +@STRING( CurrOpinNeurobiol = "Curr Opin Neurobiol" ) +@STRING( eLife = "eLife" ) +@STRING( eNeuro = "eNeuro" ) +@STRING( EuropBiophysJ = "Europ Biophys J" ) +@STRING( EuroJNeurosci = "Euro J Neurosci" ) +@STRING( ExpBrainRes = "Exp Brain Res" ) +@STRING( FluctNoiseLett = "Fluct Noise Lett" ) +@STRING( FrontComputNeurosci = "Front Comput Neurosci" ) +@STRING( FrontNeuroInform = "Front Neuroinform" ) +@STRING( FrontPsychol = "Front Psychol" ) +@STRING( HearRes = "Hear Res" ) +@STRING( Hippocampus = "Hippocampus" ) +@STRING( HormBehav = "Horm Behav" ) +@STRING( IEEETNN = "IEEE TNN" ) +@STRING( IEEETransInfTechBiomed = "IEEE Trans Inf Tech Biomed" ) +@STRING( IntegrCompBiol = "Integr Comp Biol" ) +@STRING( IntJBifChaos = "Int J Bif Chaos" ) +@STRING( IntJInsMorpholEmbryol = "Int J Ins Morphol Embryol" ) +@STRING( IntJNeuralSyst = "Int J Neural Syst" ) +@STRING( JAcoustSocAm = "J Acoust Soc Am" ) +@STRING( JAnimEcol = "J Anim Ecol" ) +@STRING( JARO = "JARO" ) +@STRING( JBiolChem = "J Biol Chem" ) +@STRING( JCellBiol = "J Cell Biol" ) +@STRING( JChemNeuroanat = "J Chem Neuroanat" ) +@STRING( JCompNeurol = "J Comp Neurol" ) +@STRING( JCompPhysiol = "J Comp Physiol" ) +@STRING( JCompPhysiolA = "J Comp Physiol A" ) +@STRING( JCompPhysiolB = "J Comp Physiol B" ) +@STRING( JComputNeurosci = "J Comput Neurosci" ) +@STRING( JEvolBiol = "J Evol Biol" ) +@STRING( JExpBiol = "J Exp Biol" ) +@STRING( JExpZool = "J Exp Zool" ) +@STRING( JFishBiol = "J Fish Biol" ) +@STRING( JGenPhysiol = "J Gen Physiol" ) +@STRING( JInsectBehav = "J Insect Behav" ) +@STRING( JInsectPhysiol = "J Insect Physiol" ) +@STRING( JMathBiol = "J Math Biol" ) +@STRING( JMembrBiol = "J Membr Biol" ) +@STRING( JMorph = "J Morph" ) +@STRING( JNeuralEng = "J Neural Eng " ) +@STRING( JNeurocytol = "J Neurocytol" ) +@STRING( JNeuroGenetics = "J Neuro Genetics" ) +@STRING( JNeurophysiol = "J Neurophysiol" ) +@STRING( JNeurosci = "J Neurosci" ) +@STRING( JNeurosciMethods = "J Neurosci Methods" ) +@STRING( JOSA = "J Opt Soc Am A" ) +@STRING( JPharmacolExpTher = "J Pharmaco Exp Ther" ) +@STRING( JPhysiol = "J Physiol" ) +@STRING( JPhysiolParis = "J Physiol Paris" ) +@STRING{ JPlanktonRes = "J Plankton Res" } +@STRING( JpnJPhysiol = "Jpn J Physiol" ) +@STRING( JStatPhys = "J Stat Phys" ) +@STRING( JTheorBiol = "J Theor Biol" ) +@STRING( JVis = "J Vis" ) +@STRING( MathBiosci = "Math Biosci" ) +@STRING( MicroscResTech = "Microsc Res Tech" ) +@STRING( NatNeurosci = "Nat Neurosci" ) +@STRING( Nature = "Nature" ) +@STRING( NatCommun = "Nat Commun" ) +@STRING( NatRevNeurosci = "Nat Rev Neurosci" ) +@STRING( Naturforsch = "Naturforsch" ) +@STRING( Naturwissenschaften = "Naturwissenschaften" ) +@STRING( Network = "Network Comput Neural Syst" ) +@STRING( NeuralComput = "Neural Comput" ) +@STRING( NeuralNetw = "Neural Netw" ) +@STRING( Neurocomput = "Neurocomput" ) +@STRING( Neuron = "Neuron" ) +@STRING( NeuroReport = "NeuroReport" ) +@STRING( Neuroscience = "Neurosci" ) +@STRING( NeurosciLett = "Neurosci Lett" ) +@STRING( NeurosciRes = "Neurosci Res" ) +@STRING( PflugersArch = {Pflugers Arch} ) +@STRING( PLoSBiol = "PLoS Biol" ) +@STRING( PLoSComputBiol = "PLoS Comput Biol" ) +@STRING( PLoSONE = "PLoS ONE" ) +@STRING( PNAS = "Proc Natl Acad Sci" ) +@STRING( PhilTransRSocLondBBiolSci = "Phil Trans R Soc Lond B Biol Sci" ) +@STRING( PhysicaD = "Physica D" ) +@STRING( PhysiolRep = "Physiol Rep" ) +@STRING( PhysiolRev = "Physiol Rev" ) +@STRING( PhysRep = "Phys Rep" ) +@STRING( PhysRevA = "Phys Rev A" ) +@STRING( PhysRevE = "Phys Rev E" ) +@STRING( PhysRevLett = "Phys Rev Lett" ) +@STRING( ProcRSocLondBBiolSci = "Proc R Soc Lond B Biol Sci" ) +@STRING( ProcSPIE = "Proc SPIE" ) +@STRING( ProgBrainRes = "Prog Brain Res" ) +@STRING( ProgRetinEyeRes = "Prog Retin Eye Res" ) +@STRING( Science = "Science" ) +@STRING( SIAMJApplMath = "SIAM J Appl Math" ) +@STRING( TheorPopulBiol = "Theor Popul Biol" ) +@STRING{ TICS = "Trends Cog Sci"} +@STRING( TIEE = "Trends Ecol Evol" ) +@STRING( TINS = "Trends Neurosci" ) +@STRING( VisNeurosci = "Vis Neurosci" ) +@STRING( VisionRes = "Vision Res" ) diff --git a/nonlinearbaseline.tex b/nonlinearbaseline.tex new file mode 100644 index 0000000..3774829 --- /dev/null +++ b/nonlinearbaseline.tex @@ -0,0 +1,897 @@ +\documentclass[10pt,letterpaper]{article} + +\title{Spike generation in electroreceptor afferents introduces additional spectral response components by weakly nonlinear interactions} + +%\title{Weakly nonlinear interactions of the spike generator introduce additional spectral response components in electroreceptor afferents} + +\author{Alexandra Barayeu\textsuperscript{1}, + Maria Schlungbaum\textsuperscript{2,3}, + Benjamin Lindner\textsuperscript{2,3}, + Jan Grewe\textsuperscript{1}, + Jan Benda\textsuperscript{1, 4, $\dagger$}} + +\date{\normalsize + \textsuperscript{1} Institute for Neurobiology, Eberhard Karls Universit\"at T\"ubingen, Germany\\ + \textsuperscript{2} Bernstein Center for Computational Neuroscience Berlin, Berlin, Germany\\ + \textsuperscript{3} Department of Physics, Humboldt University Berlin, Berlin, Germany\\ + \textsuperscript{4} Bernstein Center for Computational Neuroscience Tübingen, Germany\\ + \textsuperscript{$\dagger$} corresponding author: \url{jan.benda@uni-tuebingen.de}} + +\newcommand{\runningtitle}{} + +%%%%% overall style %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +% number the lines: +\newcommand{\setlinenumbers}{false} + +% use double spacing: +\newcommand{\setdoublespacing}{false} + +% show authors: +\newcommand{\showauthors}{true} + +% show keywords: +\newcommand{\showkeywords}{true} + +% show author contributions: +\newcommand{\showcontributions}{true} + +% figures and captions at end: +\newcommand{\figsatend}{false} + +% remove images from figures: +\newcommand{\nofigs}{false} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%% line numbering, spacing, authors, keywords %%%%%%%%%%%%%%%%%%%%%%%%%%%% +\usepackage{ifthen} + +\usepackage[nointegrals]{wasysym} + +\ifthenelse{\boolean{\setlinenumbers}}{% +\usepackage{lineno}\linenumbers}% +{\newenvironment{linenomath}{}{}} + +\ifthenelse{\boolean{\setdoublespacing}}{% +\usepackage{setspace}\doublespacing}{} + +\ifthenelse{\boolean{\showauthors}}{}{\author{}\date{}} + +\usepackage[inline]{enumitem} +\newenvironment{keywords}% +{\paragraph{Keywords}\begin{itemize*}[label={},itemjoin={~$|$\ },afterlabel={}]}% +{\end{itemize*}\par} +\usepackage{comment} +\ifthenelse{\boolean{\showkeywords}}{}{\excludecomment{keywords}} + +\newenvironment{contributions}{\section{Author contributions}}{\par} +\ifthenelse{\boolean{\showcontributions}}{}{\excludecomment{contributions}} + + +%%%%% page style %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\usepackage[left=25mm,right=25mm,top=25mm,bottom=25mm]{geometry} +\pagestyle{myheadings} +\markright{\runningtitle} + +%%%%% language %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\usepackage[english]{babel} + +%%%%% fonts %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%\usepackage{pslatex} % nice font for pdf file + +%%%%% section style %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\usepackage[sf,bf,it,big,clearempty]{titlesec} +\usepackage{titling} +\renewcommand{\maketitlehooka}{\sffamily\bfseries} +\renewcommand{\maketitlehookb}{\rmfamily\mdseries} +\setcounter{secnumdepth}{-1} + +%%%%% math %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\usepackage{amsmath} +%\usepackage{lualatex-math} + +\usepackage{iftex} + +% LuaTeX-spezifischen Code nur ausführen, wenn LuaTeX verwendet wird +\ifluatex + \usepackage{lualatex-math} +\fi + +%%%%% units %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\usepackage[mediumspace,mediumqspace,Gray]{SIunits} % \ohm, \micro + +%%%%% graphics %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\usepackage{xcolor} +%\pagecolor{white} +\usepackage{graphicx} +\usepackage{tabularx} +\newcommand{\trh}{\rule[-1ex]{0pt}{3.5ex}} +\newcommand{\trt}{\rule{0pt}{2.5ex}} + +\newcolumntype{L}[1]{>{\raggedright\let\newline\\\arraybackslash\hspace{0pt}}m{#1}} +\newcolumntype{C}[1]{>{\centering\let\newline\\\arraybackslash\hspace{0pt}}m{#1}} +\newcolumntype{R}[1]{>{\raggedleft\let\newline\\\arraybackslash\hspace{0pt}}m{#1}} + +%%%%% figures %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +% captions: +\ifthenelse{\boolean{\setdoublespacing}}{% +\usepackage[format=plain,singlelinecheck=off,labelfont=bf,font={small,sf,doublespacing}]{caption}}% +{\usepackage[format=plain,singlelinecheck=off,labelfont=bf,font={small,sf}]{caption}} + +% put caption on separate float: +\newcommand{\breakfloat}{\end{figure}\begin{figure}[t]} + +% references to panels of a figure within the caption: +\newcommand{\figitem}[2][]{\ifthenelse{\equal{#1}{}}{\textsf{\bfseries #2}}{\textsf{\bfseries #2}}$_{\sf #1}$} +% references to panels of a figure within the text: +\newcommand{\panel}[2][]{\ifthenelse{\equal{#1}{}}{\textsf{#2}}{\textsf{#2}$_{\sf #1}$}} +% references to figures: +\newcommand{\fref}[1]{\textup{\ref{#1}}} +\newcommand{\subfref}[2]{\textup{\ref{#1}}\,\panel{#2}} +% references to figures in normal text: +\newcommand{\fig}{fig.} +\newcommand{\Fig}{Fig.} +\newcommand{\figs}{figs.} +\newcommand{\Figs}{Figs.} +\newcommand{\figref}[1]{\fig~\fref{#1}} +\newcommand{\Figref}[1]{\Fig~\fref{#1}} +\newcommand{\figsref}[1]{\figs~\fref{#1}} +\newcommand{\Figsref}[1]{\Figs~\fref{#1}} +\newcommand{\subfigref}[2]{\fig~\subfref{#1}{#2}} +\newcommand{\Subfigref}[2]{\Fig~\subfref{#1}{#2}} +\newcommand{\subfigsref}[2]{\figs~\subfref{#1}{#2}} +\newcommand{\Subfigsref}[2]{\Figs~\subfref{#1}{#2}} +% references to figures within brackets: +\newcommand{\figb}{fig.} +\newcommand{\Figb}{Fig.} +\newcommand{\figsb}{figs.} +\newcommand{\Figsb}{Figs.} +\newcommand{\figrefb}[1]{\figb~\fref{#1}} +\newcommand{\Figrefb}[1]{\Figb~\fref{#1}} +\newcommand{\figsrefb}[1]{\figsb~\fref{#1}} +\newcommand{\Figsrefb}[1]{\Figsb~\fref{#1}} +\newcommand{\subfigrefb}[2]{\figb~\subfref{#1}{#2}} +\newcommand{\Subfigrefb}[2]{\Figb~\subfref{#1}{#2}} +\newcommand{\subfigsrefb}[2]{\figsb~\subfref{#1}{#2}} +\newcommand{\Subfigsrefb}[2]{\Figsb~\subfref{#1}{#2}} + +% figure placement: +\ifthenelse{\boolean{\figsatend}}{% +\setcounter{topnumber}{10}% +\setcounter{totalnumber}{10}% +\renewcommand{\textfraction}{0.0}% +\renewcommand{\topfraction}{1.0}% +\renewcommand{\floatpagefraction}{0.0}% +\usepackage[nolists,markers,figuresonly]{endfloat}% +\ifthenelse{\boolean{\nofigs}}{\renewcommand{\efloatseparator}{\mbox{}}}{}% +\newcommand{\figurecaptions}{\pagestyle{empty}\clearpage\processdelayedfloats\renewcommand{\figureplace}{}}}% +{\setcounter{topnumber}{1}% +\setcounter{totalnumber}{2}% +\renewcommand{\textfraction}{0.2}% +\renewcommand{\topfraction}{0.8}% +\renewcommand{\floatpagefraction}{0.7}% +\newcommand{\figurecaptions}{}% +} +\newcommand*{\captionc}[1]{\captionof{figure}{#1}} + +% no images in figures: +\ifthenelse{\boolean{\nofigs}}{% +\newcommand{\showfigure}[1]{}}% +{\newcommand{\showfigure}[1]{#1}} + +% bibliography ---------------------------------- +\usepackage[round,colon]{natbib} +\renewcommand{\bibsection}{\section{References}} +\setlength{\bibsep}{0pt} +\setlength{\bibhang}{1.5em} +\bibliographystyle{jneurosci} + +\usepackage[breaklinks=true,colorlinks=true,citecolor=blue!30!black,urlcolor=blue!30!black,linkcolor=blue!30!black]{hyperref} + +%%%%% tables %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% references to tables: +\newcommand{\tref}[1]{\textup{\ref{#1}}} +% references to tables in normal text: +\newcommand{\tab}{Tab.} +\newcommand{\Tab}{Table} +\newcommand{\tabs}{Tabs.} +\newcommand{\Tabs}{Tables} +\newcommand{\tabref}[1]{\tab~\tref{#1}} +\newcommand{\Tabref}[1]{\Tab~\tref{#1}} +\newcommand{\tabsref}[1]{\tabs~\tref{#1}} +\newcommand{\Tabsref}[1]{\Tabs~\tref{#1}} +% references to tables within the bracketed text: +\newcommand{\tabb}{Tab.} +\newcommand{\tabsb}{Tab.} +\newcommand{\tabrefb}[1]{\tabb~\tref{#1}} +\newcommand{\tabsrefb}[1]{\tabsb~\tref{#1}} + +%%%%% equation references %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\renewcommand{\eqref}[1]{(\ref{#1})} +\newcommand{\eqnref}[1]{Eq.~\eqref{#1}} +\newcommand{\eqnsref}[1]{Eqs.~\eqref{#1}} + +%%%%% species names %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\newcommand{\Lepto}{\emph{Apteronotus leptorhynchus}} +\newcommand{\lepto}{\emph{A. leptorhynchus}} +\newcommand{\Eigen}{\emph{Eigenmannia virescens}} +\newcommand{\eigen}{\emph{E. virescens}} + +%%%%% notes %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 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+\newcommand{\bcsumehalf}{\ensuremath{\bcsum{}=f_{\rm{EOD}}/2}}%sum + +\newcommand{\bcdiffb}{\ensuremath{\bcdiff{}=\fbasesolid{}}}%diff of both beat frequencies +\newcommand{\bcdiffbc}{\ensuremath{\bcdiff{}=\fbasecorr{}}}%diff of both beat frequencies +\newcommand{\bcdiffe}{\ensuremath{\bcdif{}f=f_{\rm{EOD}}}}%diff of both +\newcommand{\bcdiffehalf}{\ensuremath{\bcdiff{}=f_{\rm{EOD}}/2}}%diff of both + +\newcommand{\burstcorr}{\ensuremath{{Corrected}}} +\newcommand{\cvbasecorr}{CV\ensuremath{_{BaseCorrected}}} +\newcommand{\cv}{CV\ensuremath{_{Base}}}%\cvbasecorr{} +\newcommand{\nli}{PNL\ensuremath{(\fbase{})}}%Fr$_{Burst}$ +\newcommand{\nlicorr}{PNL\ensuremath{(\fbasecorr{}})}%Fr$_{Burst}$ +\newcommand{\suscept}{$|\chi_{2}|$} +\newcommand{\susceptf}{$|\chi_{2}|(f_1, f_2)$} +\newcommand{\frcolor}{pink lines} + +\newcommand{\rec}{\ensuremath{\rm{R}}}%{\ensuremath{con_{R}}} +\newcommand{\rif}{\ensuremath{\rm{RIF}}} +\newcommand{\ri}{\ensuremath{\rm{RI}}}%sum +\newcommand{\rf}{\ensuremath{\rm{RF}}}%sum +\newcommand{\withfemale}{\rm{ROC}\ensuremath{\rm{_{Female}}}}%sum \textit{ +\newcommand{\wofemale}{\rm{ROC}\ensuremath{\rm{_{NoFemale}}}}%sum +\newcommand{\dwithfemale}{\rm{\ensuremath{\auc_{Female}}}}%sum CV\ensuremath{_{BaseCorrected}} +\newcommand{\dwofemale}{\rm{\ensuremath{\auc_{NoFemale}}}}%sum +\newcommand{\fp}{\ensuremath{\rm{FP}}}%sum +\newcommand{\cd}{\ensuremath{\rm{CD}}}%sum + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{document} + +\maketitle + +%\paragraph{Short title:} +%\paragraph{Corresponding author:}Jan Grewe, E-mail: jan.grewe@uni-tuebingen.de +%\paragraph{Conflict of interest:}The authors declare no conflict of interest. +%\paragraph{Author Contributions:} All authors designed the study and discussed the results. AB performed the data analyses and modeling, AB and JG drafted the paper, all authors discussed and revised the manuscript. + +\begin{keywords} +\item second-order susceptibility +\item electric fish +\item nonlinear coding +\end{keywords} + +% Please keep the abstract below 300 words +\section{Abstract} +Neuronal processing is inherently nonlinear --- spiking thresholds or rectification at synapses is essential to neuronal computations. Nevertheless, linear response theory has been instrumental in understanding, for example, the impact of noise or neuronal synchrony on signal transmission, or the emergence of oscillatory activity, but is valid only at low stimulus amplitudes or large levels of intrinsic noise. At higher signal-to-noise ratios, however, nonlinear response components become relevant. Theoretical results for leaky integrate-and-fire neurons in the weakly nonlinear regime suggest strong responses at the sum of two input frequencies if these frequencies or their sum match the neuron's baseline firing rate. +We here analyze nonlinear responses in two types of primary electroreceptor afferents, the P-units of the active and the ampullary cells of the passive electrosensory system of the wave-type electric fish \textit{Apteronotus leptorhynchus}. In our combined experimental and modeling approach we identify the predicted nonlinear responses in low-noise P-units and much stronger in all ampullary cells. Our results provide experimental evidence for nonlinear responses of spike generators in the weakly nonlinear regime. We conclude that such nonlinear responses occur in any sensory neuron that operates in similar regimes particularly at near-threshold stimulus conditions. + +% Such nonlinear responses boost responses to weak sinusoidal stimuli and are therefore of immediate relevance for wave-type electric fish that are exposed to superpositions of many frequencies in social contexts. + +% Please keep the Author Summary between 150 and 200 words +% Use the first person. PLOS ONE authors please skip this step. +% Author Summary not valid for PLOS ONE submissions. +%\section{Author summary} +%Weakly electric fish use their self-generated electric field to detect a wide range of behaviorally relevant stimuli. Intriguingly, they show detection performances of stimuli that are (i) extremely weak and (ii) occur in the background of strong foreground signals, reminiscent of what is often described as the cocktail party problem. Such performances are achieved by boosting the signal detection through nonlinear mechanisms. We here analyze nonlinear encoding in two different populations of primary electrosensory afferents of the weakly electric fish. We derive the rules under which nonlinear effects can be observed in both electrosensory subsystems. In a combined experimental and modeling approach we generalize the approach of nonlinear susceptibility to systems that respond to amplitude modulations of a carrier signal. + +\note{Ad Aertsen paper suggestions:} +\url{https://brainworks.biologie.uni-freiburg.de/1981/journal%20papers/Aertsen-BiolCyb-1981b.pdf} \url{https://brainworks.biologie.uni-freiburg.de/1983/journal%20papers/eggermont-quartrevbiophys-1983.pdf} \url{https://brainworks.biologie.uni-freiburg.de/1981/journal%20papers/The%20Phonocrome%20(1981).pdf} + + +\section{Introduction} + +\begin{figure*}[t] + \includegraphics[width=\columnwidth]{plot_chi2.pdf} + \caption{\label{fig:lifresponse} First- (linear) and second-order response functions of the leaky integrate-and-fire model. \figitem{A} Magnitude of the first-order response function $|\chi_1(f)|$, also known as the ``gain'' function, quantifies the response amplitude relative to the stimulus amplitude, both measured at the stimulus frequency. \figitem{B} Magnitude of the second-order response function $|\chi_2(f_1, f_2)|$ quantifies the response at the sum of two stimulus frequencies. For linear systems, the second-order response function is zero, because linear systems do not create new frequencies and thus there is no response at the sum of the two frequencies. The plots show the analytical solutions from \citep{Lindner2001} and \citep{Voronenko2017} with $\mu = 1.1$ and $D = 0.001$. Note that the leaky integrate-and-fire model is formulated without dimensions, frequencies are given in multiples of the inverse membrane time constant.} +\end{figure*} +We like to think about signal encoding in terms of linear relations with unique mapping of a given input value to a certain output of the system under consideration. Indeed, such linear methods, for example the transfer function or first-oder susceptibility shown in figure~\ref{fig:lifresponse}, have been widely and successfully applied to describe and predict neuronal responses and are an invaluable tool to characterize neural systems \citep{Borst1999}. Nonlinear mechanisms, on the other hand, are key on different levels of neural processing. Deciding for one action over another is a nonlinear process on the systemic level. On the cellular level, spiking neurons are inherently nonlinear. Whether an action potential is elicited depends on the membrane potential to exceed a threshold \citep{Hodgkin1952, Koch1995}. Because of such nonlinearities, understanding and predicting neuronal responses to sensory stimuli is in general a difficult task. + +The transfer function that describes the linear properties of a system, is the first-order term of a Volterra series. Higher-order terms successively approximate nonlinear features of a system \citep{Rieke1999}. Second-order kernels have been used in the time domain to predict visual responses in catfish \citep{Marmarelis1972}. In the frequency domain, second-order kernels are known as second-order response functions or susceptibilities. Nonlinear interactions of two stimulus frequencies generate peaks in the response spectrum at the sum and the difference of the two. Including higher-order terms of the Volterra series, the nonlinear nature of spider mechanoreceptors \citep{French2001}, mammalian visual systems \citep{Victor1977, Schanze1997}, locking in chinchilla auditory nerve fibers \citep{Temchin2005}, and bursting responses in paddlefish \citep{Neiman2011} have been demonstrated. + +Noise in nonlinear systems, however, linearizes the system's response properties \citep{Yu1989, Chialvo1997}. \notejg{kann den Gegensatz nicht erkennen..., kann der noise Einschub vielleicht woanders hin oder ist das eine Weiterfuehrung des noise Gedankens? Dann kann das vice versa weg.} Vice versa, in the limit to small stimuli, nonlinear systems can be well described by linear response theory \citep{Roddey2000, Doiron2004, Rocha2007, Sharafi2013}. With increasing stimulus amplitude, the contribution of the second-order kernel of the Volterra series becomes more relevant. For these weakly nonlinear responses analytical expressions for the second-order susceptibility have been derived for leaky-integrate-and-fire (LIF) \citep{Voronenko2017} and theta model neurons \citep{Franzen2023}. In the suprathreshold regime, in which the LIF generates a baseline firing rate in the absence of an external stimulus, the linear response function has a peak at the baseline firing rate and its harmonics (\subfigrefb{fig:lifresponse}{A}) and the second-order susceptibility shows very distinct ridges of elevated nonlinear responses, exactly where one of two stimulus frequencies equals or both frequencies add up to the neuron's baseline firing rate (\subfigrefb{fig:lifresponse}{B}). In experimental data, such structures in the second-order susceptibility have not been reported yet. \notejg{... one of two stimulus frequencies... includes the case that one equals but the other is something completely different} + +Here we search for such weakly nonlinear responses in electroreceptors of the two electrosensory systems of the wave-type electric fish \textit{Apteronotus leptorhynchus}, i.e. the tuberous (active) and the ampullary (passive) electrosensory system. The p-type electroreceptor afferents of the active system (P-units) are driven by the fish's high-frequency, quasi-sinusoidal electric organ discharges (EOD) and encode disturbances of it \citep{Bastian1981a}. The electroreceptors of the passive system are tuned to lower-frequency exogeneous electric fields such as caused by muscle activity of prey \citep{Kalmijn1974}. As different animals have different EOD-frequencies, being exposed to stimuli of multiple distinct frequencies is part of the animal's everyday life \citep{Benda2020,Henninger2020} and weakly nonlinear interactions may occur in the electrosensory periphery. In communication contexts \citep{Walz2014, Henninger2018} the EODs of interacting fish superimpose and lead to periodic amplitude modulations (AMs or beats) of the receiver's EOD. Nonlinear mechanisms in P-units, enable encoding of AMs in their time-dependent firing rates \citep{Bastian1981a, Walz2014, Middleton2006, Barayeu2023}. When multiple animals interact, the EOD interferences induce second-order amplitude modulations referred to as envelopes \citep{Yu2005, Fotowat2013, Stamper2012Envelope} and saturation nonlinearities allow also for the encoding of these in the electrosensory periphery \citep{Savard2011}. Field observations have shown that courting males were able to react to the extremely weak signals of distant intruding males despite the strong foreground EOD of the nearby female \citep{Henninger2018}. Weakly nonlinear interactions at particular combinations of signals can be of immediate relevance in such settings as they could boost detectability of the faint signals \citep{Schlungbaum2023}. + +\section{Results} + +\begin{figure*}[t] + \includegraphics[width=\columnwidth]{motivation.pdf} + \caption{\label{fig:motivation} Nonlinearity in an electrophysiologically recorded P-unit of \lepto{} in a three-fish setting (cell identifier ``2021-08-03-ac"). Receiver with EOD frequency $\feod{} =664$\,Hz encounters fish with EOD frequencies $f_{1}=631$\,Hz and $f_{2}=797$\,Hz. Both foreign signals have the same strength relative to the own field amplitude (10\,\% contrast). Top row: Sketch of signal processing in the nonlinear system (black box). Second row: Interference of the receiver EOD with the EODs of other fish, bold line highlights the amplitude modulation. Third row: Respective spike trains of the recorded P-unit. Fourth row: Firing rate, estimated by convolution of the spike trains with a Gaussian kernel ($\sigma = 1$\,ms). Bottom row: Power spectrum of the firing rate. \figitem{A} Baseline condition: The cell is driven by the self-generated field alone. The baseline firing rate \fbase{} dominates the power spectrum of the firing rate ($f_{base} = 139$\,Hz). \figitem{B} The receiver's EOD and a foreign fish with an EOD frequency $f_{1}=631$\,Hz are present. EOD interference induces an amplitude modulation, referred to as beat. \figitem{C} The receiver and a fish with an EOD frequency $f_{2}=797$\,Hz are present. The resulting beat is faster as the difference between the individual frequencies is larger. \figitem{D} All three fish with the EOD frequencies \feod{}, $f_{1}$ and $f_{2}$ are present, a second-order amplitude modulation occurs, commonly referred to as envelope. Nonlinear peaks occur at the sum and difference of the two beat frequencies in the power spectrum of the firing rate. + } +\end{figure*} + +Theoretical work on leaky integrate-and-fire and conductance-based models suggests a distinct structure of the second-order response function for neurons with low levels of intrinsic noise driven in the supra-threshold regime with low stimulus amplitudes (\figrefb{fig:lifresponse}, \citealp{Voronenko2017}). Here, we explored a large set of recordings of P-units and ampullary cells of the active and passive electrosensory systems of the brown ghost knifefish \textit{Apteronotus leptorhynchus} to search for such weakly nonlinear responses in real neurons. Additional simulations of LIF-based models of P-unit spiking put the experimental findings into context. We start with demonstrating the basic concepts using example P-units and models. \notejg{relativ viel Wiederholung des ob gesagten, kuerzen?} + +\subsection{Nonlinear responses in P-units stimulated with two frequencies} +Without external stimulation, a P-unit is driven by the fish's own EOD alone (with a specific EOD frequency \feod{}) and spontaneously fires action potentials at the baseline rate \fbase{}. Accordingly, the power spectrum of the baseline activity has a peak at \fbase{} (\subfigrefb{fig:motivation}{A}). Superposition of the receiver's EOD with an EOD of another fish with frequency $f_1$ results in a beat, a periodic amplitude modulation of the receiver's EOD. The frequency of the beat is given by the difference frequency $\Delta f_1 = f_1 - \feod$ between the two fish. P-units encode this beat in their firing rate \citep{Bastian1981a, Barayeu2023} and consequently the power spectrum of the response has a peak at the beat frequency (\subfigrefb{fig:motivation}{B}). A second peak at the first harmonic of the beat frequency is indicative of a nonlinear process that here is easily identified by the clipping of the P-unit's firing rate at zero. Pairing the fish with another fish at a higher beat frequency $\Delta f_2 = f_2 - \feod > \Delta f_1$ results in a weaker response with a single peak in the response power spectrum, suggesting a linear response (\subfigrefb{fig:motivation}{C}). The weaker response to this beat can be explained by the beat tuning of the cell \citep{Walz2014}. Note, $\Delta f_2$ has been deliberately chosen to match the recorded P-unit's baseline firing rate. + +When stimulating with both foreign signals simultaneously, additional peaks appear in the response power spectrum at the sum $\Delta f_1 + \Delta f_2$ and the difference frequency $\Delta f_2 - \Delta f_1$ (\subfigrefb{fig:motivation}{D}). Thus, the cellular response is not equal to the sum of the responses to the two beats presented separately. These peaks at the sum and the difference of the two stimulus frequencies are a hallmark of nonlinear interactions that, by definition, are absent in linear systems\notejg{should not occur?}. + + +\subsection{Linear and weakly nonlinear regimes} + +\begin{figure*}[p] + \includegraphics[width=\columnwidth]{nonlin_regime.pdf} + \caption{\label{fig:nonlin_regime} Linear and nonlinear responses of a model P-unit in a three-fish setting in dependence on increasing stimulus amplitudes. The model P-unit was stimulated with two sinewaves of equal amplitude (contrast) at difference frequencies $\bone=30$\,Hz and $\btwo=130$\,Hz relative the receiver's EOD frequency. \btwo{} was set to match the baseline firing rate \fbase{} of the P-unit. The model used has the cell identifier 2013-01-08-aa (table~\ref{modelparams}). \figitem{A--D} Top: the stimulus, an amplitude modulation of the receiver's EOD resulting from the stimulation with the two sine waves. The contrasts of both beats increase from \panel{A} to \panel{D} as indicated. Middle: Spike raster of the model P-unit response. Bottom: power spectrum of the firing rate estimated from the spike raster with a Gaussian kernel ($\sigma=1$\,ms). \figitem{A} At low stimulus contrasts the response is linear. The only peaks in the response spectrum are at the two stimulating beat frequencies (green and purple marker) and their amplitudes increase linearly with stimulus contrast (thin lines). \figitem{B} At intermediate stimulus contrasts, nonlinear responses appear at the sum and the difference of the stimulus frequencies (orange and red marker). Their amplitudes grow quadraticlaly with stimulus constrast (thin lines). \figitem{C} At stronger stimulation the amplitudes of these nonlinear repsonses deviate from the quadratic dependency on stimulus contrast. \figitem{D} At higher stimulus contrasts additional peaks appear in the power spectrum. \figitem{E} Amplitude of the linear (at $\Delta f_1$ and $\Delta f_2$) and nonlinear (at $\Delta f_2 - \Delta f_1$ and $\Delta f_1 + \Delta f_2$) responses of the model P-unit as a function of beat contrast (thick lines). Thin lines indicate the initial linear and quadratic dependence on stimulus amplitude for the linear and nonlinear responses, respectively.} +\end{figure*} + +The stimuli used in \figref{fig:motivation} had the same not-small amplitude. Whether this stimulus condition falls into the weakly nonlinear regime as in \citet{Voronenko2017} is not clear. In order to illustrate how the responses to two beat frequencies develop over a range of amplitudes we use a stochastic leaky-integrate-and-fire (LIF) based P-unit model fitted to a specific electrophysiologically measured cell \citep{Barayeu2023}. + +At very low stimulus contrasts (in the example cell less than approximately 1.5\,\% relative to the receiver's EOD amplitude) the spectrum has small peaks only at the beat frequencies (\subfigref{fig:nonlin_regime}{A}, green and purple). The amplitudes of these peaks initially increase linearly with stimulus amplitude (\subfigref{fig:nonlin_regime}{E}, thin lines), an indication of the linear response at lowest stimulus amplitudes. + +This linear regime is followed by the weakly nonlinear regime (in the example cell between approximately 1.5\,\% and 4\,\% stimulus contrasts). In addition to the peaks at the stimulus frequencies, peaks at the sum and the difference of the stimulus frequencies appear in the response spectrum (\subfigref{fig:nonlin_regime}{B}, orange and red). The amplitudes of these two peaks initially increase quadratically with stimulus amplitude (\subfigref{fig:nonlin_regime}{E}, thin lines). Note, that we have chosen $\Delta f_2$ to match the baseline firing rate $f_{base}$ of the neuron. + +At higher stimulus amplitudes, the linear response and the weakly-nonlinear response begin to deviate from their linear and quadratic dependency on amplitude (\subfigrefb{fig:nonlin_regime}{C \& E}) and additional peaks appear in the response spectrum (\subfigrefb{fig:nonlin_regime}{D}). At high stimulus contrasts, additional nonlinearities in the system, in particular clipping of the firing rate, shape the responses. + +For this example, we chose very specific stimulus (beat) frequencies. %One of these matching the P-unit's baseline firing rate. +In the following, however, we are interested in how the nonlinear responses depend on different combinations of stimulus frequencies in the weakly nonlinear regime. For the sake of simplicity we will drop the $\Delta$ notation even though P-unit stimuli are beats. + + +\subsection{Nonlinear signal transmission in low-CV P-units} +Weakly nonlinear responses are expected in cells with sufficiently low intrinsic noise levels, i.e. low baseline CVs \citep{Voronenko2017}. P-units fire action potentials probabilistically phase-locked to the self-generated EOD \citep{Bastian1981a}. Skipping of EOD cycles leads to the characteristic multimodal ISI distribution with maxima at integer multiples of the EOD period (\subfigrefb{fig:punit}{A}). In this example, the baseline ISI distribution has a CV$_{\text{base}}$ of 0.2, which is at the lower end of the P-unit population \citep{Hladnik2023}. Spectral analysis of the baseline activity shows two major peaks: the first is located at the baseline firing rate \fbase, the second is located at the discharge frequency \feod{} of the electric organ and is flanked by two smaller peaks at $\feod \pm \fbase{}$ (\subfigref{fig:punit}{B}). + + +\begin{figure*}[t] +\includegraphics[width=\columnwidth]{cells_suscept.pdf} +\caption{\label{fig:punit} Linear and nonlinear stimulus encoding in a low-CV P-unit (cell identifier ``2010-06-21-ai"). \figitem{A} Interspike interval (ISI) distribution of the cell's baseline activity, i.e. the cell is driven only by the unperturbed own electric field. The low CV of the ISIs indicates quite regular firing. \figitem{B} Power spectral density of the baseline response with peaks at the cell's baseline firing rate \fbase{} and the fish's EOD frequency \feod{}. \figitem{C} Random amplitude modulation stimulus (top, with cutoff frequency of 300\,Hz) and evoked responses (spike raster, bottom) of the same P-unit. The stimulus contrast (right) measures the strength of the AM. \figitem{D} Gain of the transfer function (first-order susceptibility), \eqnref{linearencoding_methods}, computed from the responses to 10\,\% (light purple) and 20\,\% contrast (dark purple) RAM stimulation of 10\,s duration. \figitem{E, F} Absolute value of the second-order susceptibility, \eqnref{eq:susceptibility}, for both the low and high stimulus contrast. Pink triangles mark vertical, horizontal, and diagonal lines where \fone, \ftwo{} or \fsum{} are equal to \fbase{}. \figitem{G} Second-order susceptibilities projected onto the diagonal (means of all anti-diagonals of the matrices shown in \panel{E, F}). Dots mark \fbase{}, horizontal dashed lines mark medians of the projected susceptibilities.} +\end{figure*} + +Noise stimuli, here random amplitude modulations (RAM) of the EOD (\subfigref{fig:punit}{C}, top trace, red line), are commonly used to characterize stimulus-driven responses of sensory neurons using transfer functions (first-order susceptibility), spike-triggered averages, or stimulus-response coherences. Here, we additionally estimate the second-order susceptibility to quantify nonlinear encoding. P-unit spikes align more or less clearly with fluctuations in the RAM stimulus. A higher stimulus intensity, here a higher contrast of the RAM relative to the EOD amplitude (see methods), entrains the P-unit response more clearly (light and dark purple for low and high contrast stimuli, \subfigrefb{fig:punit}{C}). Linear encoding, quantified by the transfer function, \eqnref{linearencoding_methods}, is similar for the two RAM contrasts in this low-CV P-unit (\subfigrefb{fig:punit}{D}), as expected for a linear system. The first-order susceptibility is low for low frequencies, peaks in the range below 100\,Hz and then falls off again \citep{Benda2005}. + +The second-order susceptibility, \eqnref{eq:susceptibility}, quantifies for each combination of two stimulus frequencies \fone{} and \ftwo{} the amplitude and phase of the stimulus-evoked response at the sum \fsum{} (and also the difference, \subfigrefb{fig:model_full}{A}). Large values of the second-order susceptibility indicate stimulus-evoked peaks in the response spectrum at the summed frequency that cannot be explained by linear response theory. Similar to the first-order susceptibility, the second-order susceptibility can be estimated directly from the response evoked by a RAM stimulus that stimulates the neuron with a whole range of frequencies simultaneously (\subfigsref{fig:punit}{E, F}). For LIF and theta neuron models driven in the supra-threshold regime, theory predicts nonlinear interactions between the two stimulus frequencies, when the two frequencies \fone{} and \ftwo{} or their sum \fsum{} exactly match the neuron's baseline firing rate \fbase{} \citep{Voronenko2017,Franzen2023}. Only then, additional stimulus-evoked peaks appear in the spectrum of the spiking response that would show up in the second-order susceptibility as a horizontal, a vertical, and an anti-diagonal line (\subfigrefb{fig:lifresponse}{B}, pink triangle in \subfigsref{fig:punit}{E, F}). + +For the low-CV P-unit, we observe a band of slightly elevated second-order susceptibility for the low RAM contrast at \fsumb{} (yellowish anti-diagonal between pink edges, \subfigrefb{fig:punit}{E}). This structure vanishes for the stronger stimulus (\subfigref{fig:punit}{F}). Further, the overall level of the second-order susceptibility is reduced with increasing stimulus strength. To quantify the structural changes in the susceptibility matrices we projected the susceptibility values onto the diagonal by averaging over the anti-diagonals (\subfigrefb{fig:punit}{G}). At low RAM contrast this projected second-order susceptibility indeed has a small peak at \fbase{} (\subfigrefb{fig:punit}{G}, dot on top line). For the higher RAM contrast, however, this peak vanishes and the overall level of the second-order susceptibility is reduced (\subfigrefb{fig:punit}{G}). The reason behind this reduction is that a RAM with a higher contrast is not only a stimulus with an increased amplitude, but also increases the total noise in the system. Increased noise is known to linearize signal transmission \citep{Longtin1993, Chialvo1997, Roddey2000, Voronenko2017} and thus the second-order susceptibility is expected to decrease. + +In contrast, a high-CV P-unit (CV$_{\text{base}}=0.4$) does not exhibit pronounced nonlinearities even at low stimulus contrasts (\figrefb{fig:punithighcv}). Irrespective of the CV, neither of the two example P-units shows the complete expected structure of nonlinear interactions. + + +\subsection{Ampullary afferents exhibit strong nonlinear interactions} + +\begin{figure*}[t] +\includegraphics[width=\columnwidth]{ampullary.pdf} + \caption{\label{fig:ampullary} Linear and nonlinear stimulus encoding in an ampullary afferent (cell identifier ``2012-04-26-ae"). \figitem{A} Interspike interval (ISI) distribution of the cell's baseline activity. The very low CV of the ISIs indicates almost perfect periodic spiking. \figitem{B} Power spectral density of baseline activity with peaks at the cell's baseline firing rate and its harmonics. \figitem{C} Bad-limited white noise stimulus (top, with a cutoff frequency of 150\,Hz) added to the fish's self-generated electric field and spike raster of the evoked responses (bottom) for two stimulus contrasts as indicated (right). \figitem{D} Gain of the transfer function, \eqnref{linearencoding_methods}, of the responses to stimulation with 2\,\% (light green) and 20\,\% contrast (dark green) of 10\,s duration. \figitem{E, F} Absolute value of the second-order susceptibility, \eqnref{eq:susceptibility}, for both stimulus contrasts as indicated. Pink triangles indicate the baseline firing rate. \figitem{G} Projections of the second-order susceptibilities in \panel{E, F} onto the diagonal. } +\end{figure*} + +Electric fish possess an additional electrosensory system, the passive or ampullary electrosensory system, that responds to low-frequency exogenous electric stimuli. The population of ampullary afferents is much less heterogeneous, and known for the much lower CVs of their baseline ISIs (CV$_{\text{base}}=0.06$ to $0.22$, \citealp{Grewe2017}). Ampullary cells do not phase-lock to the EOD and the ISIs are unimodally distributed (\subfigrefb{fig:ampullary}{A}). As a consequence of the high regularity of their baseline spiking activity, the corresponding power spectrum shows distinct peaks at the baseline firing rate \fbase{} and its harmonics. Since the cells do not respond to the self-generated EOD, there is no peak at \feod{} (\subfigrefb{fig:ampullary}{B}). When driven by a low-contrast noise stimulus (note: this is no longer an AM stimulus, \subfigref{fig:ampullary}{C}), ampullary cells exhibit very pronounced bands in the second-order susceptibility, where \fsum{} is equal to \fbase{} or its harmonic (yellow diagonals in \subfigrefb{fig:ampullary}{E}), implying strong nonlinear response components at these frequency combinations (\subfigrefb{fig:ampullary}{G}, top). With higher stimulus contrasts these bands disappear (\subfigrefb{fig:ampullary}{F}), the projection onto the diagonal loses its distinct peak at \fsum{} and its overall level is reduced (\subfigrefb{fig:ampullary}{G}, bottom). + + +\subsection{Model-based estimation of the second-order susceptibility} +In the example recordings shown above (\figsrefb{fig:punit} and \fref{fig:ampullary}), we only observe nonlinear responses on the anti-diagonal of the second-order susceptibility, where the sum of the two stimulus frequencies matches the neuron's baseline firing rate, which is in line with theoretical expectations \citep{Voronenko2017,Franzen2023}. However, a pronounced nonlinear response at frequencies \foneb{} or \ftwob{}, although predicted by theory, cannot be observed. In the following, we investigate how these discrepancies can be understood. + +\begin{figure*}[t] + \includegraphics[width=\columnwidth]{model_and_data.pdf} + \notejb{This model in the next figure shows a triangle for 3\% contrast ...} + \notejb{We cannot really make up this twist with the 3\% contrast not converging into a triangle.} + \caption{\label{fig:noisesplit} Estimation of second-order susceptibilities in the limit of weak stimuli. \figitem{A} \suscept{} estimated from $N=11$ 0.5\,s long segments of an electrophysiological recording of another low-CV P-unit (cell 2012-07-03-ak, $\fbase=120$\,Hz, CV=0.20) driven with a weak RAM stimulus with contrast 2.5\,\%. Pink edges mark the baseline firing rate where enhanced nonlinear responses are expected. \figitem[i]{B} \textit{Standard condition} of model simulations with intrinsic noise (bottom) and a RAM stimulus (top). \figitem[ii]{B} \suscept{} estimated from simulations of the cell's LIF model counterpart (cell 2012-07-03-ak, table~\ref{modelparams}) based on the same number of FFT segments $N=11$ as in the electrophysiological recording. \figitem[iii]{B} Same as \panel[ii]{B} but using $10^6$ segments. \figitem[i-iii]{C} Same as in \panel[i-iii]{B} but in the \textit{noise split} condition: there is no external RAM signal driving the model. Instead, a large part (90\,\%) of the total intrinsic noise is treated as a signal and is presented as an equivalent amplitude modulation (\signalnoise, center), while the intrinsic noise is reduced to 10\,\% of its original strength (see methods for details). Simulating one million segments, this reveals the full expected trangular structure of the second-order susceptibility.} +\end{figure*} + +%\notejb{Since the model overestimated the sensitivity of the real P-unit, we adjusted the RAM contrast to 0.9\,\%, such that the resulting spike trains had the same CV as the electrophysiological recorded P-unit during the 2.5\,\% contrast stimulation (see table~\ref{modelparams} for model parameters).} \notejb{chi2 scale is higher than in real cell} + +One simple reason could be the lack of data, i.e. the estimation of the second-order susceptibility is not good enough. Electrophysiological recordings are limited in time, and therefore only a limited number of trials, i.e. repetitions of the same RAM stimulus, are available. As a consequence, the cross-spectra, \eqnref{eq:crosshigh}, are insufficiently averaged and the full structure of the second-order susceptibility might be hidden in finite-data noise. This experimental limitation can be overcome by using a computational model for the P-unit, a stochastic leaky integrate-and-fire model with adaptation current, dendritic preprocessing, and parameters fitted to the experimentally recorded P-unit (\figrefb{flowchart}) \citep{Barayeu2023}. The model faithfully reproduces the second-order susceptibility of a low-CV cell estimated from the same low number of FFT (fast fourier transform) segments as in the experiment ($\n{}=11$, compare \panel{A} and \panel[ii]{B} in \figrefb{fig:noisesplit}). + +In model simulations we can increase the number of FFT segments beyond what would be experimentally possible, here to one million (\subfigrefb{fig:noisesplit}\,\panel[iii]{B}). In this example, the estimate of the second-order susceptibility indeed improves. It gets less noisy and the diagonal at \fsum{} is emphasized. However, the expected vertical and horizontal lines at \foneb{} and \ftwob{} are still mainly missing. + +Using a broadband stimulus increases the effective input-noise level. This may linearize signal transmission and suppress potential nonlinear responses \citep{Longtin1993, Chialvo1997, Roddey2000, Voronenko2017}. Assuming that the intrinsic noise level in this P-unit is small enough, the full expected structure of the second-order susceptibility should appear in the limit of weak AMs. Again, this cannot be done experimentally, because the problem of insufficient averaging becomes even more severe for weak AMs (low contrast). In the model, however, we know the time course of the intrinsic noise and can use this knowledge to determine the susceptibilities by input-output correlations via the Furutsu-Novikov theorem \citep{Furutsu1963, Novikov1965}. This theorem, in its simplest form, states that the cross-spectrum $S_{x\eta}(\omega)$ of a Gaussian noise $\eta(t)$ driving a nonlinear system and the system's output $x(t)$ is proportional to the linear susceptibility according to $S_{x\eta}(\omega)=\chi(\omega)S_{\eta\eta}(\omega)$. Here $\chi(\omega)$ characterizes the linear response to an infinitely weak signal $s(t)$ in the presence of the background noise $\eta(t)$. Likewise, the nonlinear susceptibility can be determined in an analogous fashion from higher-order input-output cross-spectra (see methods, equations \eqref{eq:crosshigh} and \eqref{eq:susceptibility}) \citep{Egerland2020}. In line with an alternative derivation of the Furutsu-Novikov theorem \citep{Lindner2022}, we can split the total noise and consider a fraction of it as a stimulus. This allows us to calculate the susceptibility from the cross-spectrum between the output and this stimulus fraction of the noise. Adapting this approach to our P-unit model (see methods), we replace the intrinsic noise by an approximately equivalent RAM stimulus $s_{\xi}(t)$ and a weak remaining intrinsic noise $\sqrt{2D \, c_{\rm{noise}}}\;\xi(t)$ with $c_\text{noise} = 0.1$ (see methods, equations \eqref{eq:ram_split}, \eqref{eq:Noise_split_intrinsic}, \eqref{eq:Noise_split_intrinsic_dendrite}, \subfigrefb{fig:noisesplit}\,\panel[i]{C}). We tune the amplitude of the RAM stimulus $s_{\xi}(t)$ such that the output firing rate and variability (CV) are the same as in the baseline activity (i.e. full intrinsic noise $\sqrt{2D}\;\xi(t)$ in the voltage equation but no RAM) and compute the cross-spectra between the RAM part of the noise $s_{\xi}(t)$ and the output spike train. This procedure has two consequences: (i) by means of the cross-spectrum between the output and \signalnoise, which is a large fraction of the noise, the signal-to-noise ratio of the measured susceptibilities is drastically improved; (ii) the total noise in the system has been reduced (by what was before the external RAM stimulus $s(t)$), which makes the system more nonlinear. For both reasons we now see the expected nonlinear features in the second-order susceptibility for a sufficient number of segments (\subfigrefb{fig:noisesplit}\,\panel[iii]{C}), but not for a number of segments comparable to the experiment (\subfigrefb{fig:noisesplit}\,\panel[ii]{C}). In addition to the strong response for \fsumb{}, we now also observe pronounced nonlinear responses at \foneb{} and \ftwob{} (vertical and horizontal lines, \subfigrefb{fig:noisesplit}\,\panel[iii]{C}). + +Note, that the increased number of segments goes along with a substantial reduction of second-order susceptibility values (\subfigrefb{fig:noisesplit}\,\panel[iii]{C}). Only for more than about $10^5$ segments does the estimate of the second-order susceptibility converge for most of the model cells (\subfigrefb{fig:trialnr}{A--D}). + + +\begin{figure}[p] + \includegraphics[width=\columnwidth]{modelsusceptcontrasts} + \caption{\label{fig:modelsusceptcontrasts}Dependence of second order susceptibility on stimulus contrast. \figitem{A} Second-order susceptibilities estimated for increasing stimulus contrasts $c=0, 1, 3$ and $10$\,\% as indicated ($N=10^7$ FFT segments for $c=1$\,\%, $N=10^6$ segments for all other contrasts, see \subfigrefb{fig:trialnr}{E}). $c=0$\,\% refers to the noise-split configuration (limit to vanishing external RAM signal, see \figrefb{fig:noisesplit}). Shown are simulations of the P-unit model cell ``2017-07-18-ai'' (table~\ref{modelparams}) with a baseline firing rate of $82$\,Hz and CV$=0.23$. The cell shows a clear triangular pattern in its second-order susceptibility even up to a contrast of $10$\,\%. Note, that for $c=1$\,\% (\panel[ii]{D}), the estimate did not converge yet. \figitem{B} Cell ``2012-12-13-ao'' (baseline firing rate of $146$\,Hz, CV$=0.23$) also has strong interactions at its baseline firing rate that survive up to a stimulus contrast of $3$\,\%. \figitem{C} Model cell ``2012-12-20-ac'' (baseline firing rate of $212$\,Hz, CV$=0.26$) shows a weak triangular structure in the second-order susceptibility that vanishes for stimulus contrasts greater than $1$\,\%. \figitem{D} Cell ``2013-01-08-ab'' (baseline firing rate of $218$\,Hz, CV$=0.55$) does not show any triangular pattern in its second-order susceptibility. Nevertheless, interactions between low stimulus frequencies become substantial at higher contrasts. \figitem{E} The presence of an elevated second-order susceptibility where the stimulus frequency add up to the neuron's baseline frequency, can be identified by values of the peakedness of the projected nonlinearity (\nli{}, \eqnref{eq:nli_equation2}) greater than one (horizontal black line). The \nli{} (density to the right) is plotted as a function of the model neuron's baseline CV for all $39$ model cells (table~\ref{modelparams}). Model cells have been visually categorized based on the presence of a triangular pattern in their second-order susceptibility estimated in the noise-split configuration (legend). The cells from \panel{A--D} are marked by a black circle. Pearson's correlation coefficients $r$, the corresponding significance level $p$ and regression line (dashed gray line) are indicated. The higher the stimulus contrast, the less cells show weakly nonlinear interactions as expressed by the triangular structure in the second-order susceptibility.} +\end{figure} + +\subsection{Weakly nonlinear interactions in many model cells} +In the previous section we have shown one example cell for which we find in the corresponding model strong ridges in the second-order susceptibility where one \notejg{same here...} or the sum of two stimulus frequencies match the neuron's baseline firing rate (\figrefb{fig:noisesplit}\,\panel[iii]{C}). Using our 39 P-unit models, we now can explore how many P-unit model neurons show such a triangular structure. + +By just looking at the second-order susceptibilities estimated using the noise-split method (first column of \figrefb{fig:modelsusceptcontrasts}) we can readily identify strong triangular patterns in 11 of the 39 model cells (28\,\%, see \figrefb{fig:modelsusceptcontrasts}\,\panel[i]{A}\&\panel[i]{B} for two examples). In another 5 cells (13\,\%) the triangle is much weaker and sits on top of a smooth bump of elevated second-order susceptibility (\figrefb{fig:modelsusceptcontrasts}\,\panel[i]{C} shows an example). The remaining 23 model cells (59\,\%) show no triangle (see \figrefb{fig:modelsusceptcontrasts}\,\panel[i]{D} for an example). This categorization is supported by the peakedness of the nonlinearity, \nli{} \eqnref{eq:nli_equation2}, which quantifies the height of the ridge where the stimulus frequencies add up to the neuron's baseline firing rate. Values above one indicate an elevated ridge. The absence of such a ridge results in values close to one. Indeed, the cells showing only a weak triangle (orange) arise out of values around one and the cells showing strong triangles (red) have consistently \nli{} values exceeding 1.9 (\figrefb{fig:modelsusceptcontrasts}\,\panel[i]{E}). + +The \nli{} correlates with the cell's CV of its baseline interspike intervals ($r=-0.59$, $p<0.001$). The lower the cell's CV, the higher the \nli{} value and thus the stronger the triangular structure of its second-order susceptibility. The model cells with the most distinct triangular pattern in their second-order susceptibility are the ones with the lowest CVs, hinting at low intrinsic noise levels. + + +\subsection{Weakly nonlinear interactions vanish for higher stimulus contrasts} +As pointed out in the context of stimulation with sine waves (\figrefb{fig:nonlin_regime}), the weakly nonlinear regime can only be observed for sufficiently weak stimulus amplitudes. In the model cells we estimated second-order susceptibilities for RAM stimuli with a contrast of 1, 3, and 10\,\%. For the 10\,\% contrast, $10^5$ FFT segments were sufficient for estimating the susceptibility (\figrefb{fig:trialnr}\,\panel[iv]{E}). The estimate converged similarly as in the noise-split configuration (\figrefb{fig:trialnr}\,\panel[i]{E}). For 3\,\% contrast, one million segments were just sufficient (\figrefb{fig:trialnr}\,\panel[iii]{E}) and for 1\,\% contrast even $10^7$ segments were sometimes not enough for a good estimate (\figrefb{fig:trialnr}\,\panel[ii]{E}). This again demonstrates the detrimental effect of smaller signal-to-noise ratios on the estimate of the second-order susceptibility and the advantage of the noise-split method. + +The estimates for 1\,\% contrast (\figrefb{fig:modelsusceptcontrasts}\,\panel[ii]{E}), however, were quite similar to the estimates from the noise-split method, corresponding to a stimulus contrast of 0\,\% ($r=0.92$, $p\ll 0.001$). Thus, RAM stimuli with 1\,\% contrast are sufficiently small to not destroy weakly nonlinear interactions by their linearizing effect. 48\,\% of the model cells have a \nli{} value greater than 1.2. + +At a RAM contrast of 3\,\% the \nli{} values become smaller (\figrefb{fig:modelsusceptcontrasts}\,\panel[iii]{E}). Only 9 cells (23\,\%) have \nli{} values exceeding 1.2. Finally, at 10\,\% the \nli{} values of all cells drop below 1.2, except for two cells (5\,\%, \figrefb{fig:modelsusceptcontrasts}\,\panel[iv]{E}). The cell shown in \subfigrefb{fig:modelsusceptcontrasts}{A} is one of them. Interestingly, the baseline CVs of these two cells (0.16 and 0.23) are not the lowest one (0.11) of the model cells, but their sensitivities are quite low (small response modulations and thus small output noise). At 10\,\% contrast the \nli{} values are no longer correlated with the ones in the noise-split configuration ($r=0.23$, $p=0.15$). To summarize, the regime of distinct nonlinear interactions at frequencies matching the baseline firing rate extends in this set of P-unit model cells to stimulus contrasts ranging from a few percents to about 10\,\%. + +\begin{figure}[tp] + \includegraphics[width=\columnwidth]{modelsusceptlown} + \notejb{We could remove D?} + \notejb{Replace D by C for 100 or 1000 trials?} + \caption{\label{fig:modelsusceptlown}Inferring the triangular structure of the second-order susceptibility from limited data. \figitem{A} Reliably estimating the structure of the second-order susceptibility requires a high number of FFT segements $N$ in the order of one or even ten millions (\figrefb{fig:trialnr}). As an example, susceptibilities of the model cell ``2012-12-21-ak-invivo-1'' (baseline firing rate of 157\,Hz, CV=0.15) are shown for the noise-split configuration ($c=0$\,\%) and RAM stimulus contrasts of $c=1$, $3$, and $10$\,\% as indicated. For contrasts below $10$\,\% this cell shows a nice triangular pattern in its susceptibilities, quite similar to the introductory example of a LIF in \figrefb{fig:lifresponse}. \figitem{B} However, with limited data of $N=10$ trials the susceptibility estimates are noisy and show almost no structure, except for a faint diagonal at the cell's baseline firing rate. \figitem{C} Correlating the estimates of \nli{}, that quantify the height of the ridge where the two stimulus frequencies add up to the neuron's baseline firing rate, based on ten segments (density to the right) with the converged ones based on one or ten million segments at a given stimulus contrast. The black diagonal line is the identity line and the dashed line is a linear regression. The correlation coefficient and corresponding significance level are indicated in the top left corner. The thin vertical line is a threshold at 1.2, the thin horizontal line a threshold at 1.6. The number of cells within each of the resulting four quadrants denote the false positives (top left), true positives (top right), true negatives (bottom left), and false negatives (bottom right). \figitem{D} Relation between the estimates based on ten trials with the one in the noise-split configuration based on one million trials. Cells are categorized as in \subfigref{fig:modelsusceptcontrasts}{E}.} +\end{figure} + +\subsection{Weakly nonlinear interactions can be deduced from limited data} +Estimating second-order susceptibilities reliably requires large numbers (millions) of FFT segments (\figrefb{fig:trialnr}). Electrophysiological measurements, however, suffer from limited recording durations and hence limited numbers of available FFT segments and estimating weakly nonlinear interactions from just ten segments appears futile. The question arises, to what extend such limited-data estimates are still informative? + +The second-order susceptibility matrices that are based on only 10 segements look flat and noisy, lacking the triangular structure \subfigref{fig:modelsusceptcontrasts}{B}. The anti-diagonal ridge, however, when the sum of the stimulus frequencies matches the neuron's baseline firing rate seems to be present whenever the converged estimate shows a clear triangular structure (compare \subfigref{fig:modelsusceptcontrasts}{B} and \subfigref{fig:modelsusceptcontrasts}{a}). + +%A comparison of well converged estimates based on millions of segments with estimates based on just ten segments as a worst-case scenario (\subfigrefb{fig:modelsusceptlown}{A\&B}) seems hopeless on a first glance. These estimates using just ten segments look flat and noisy, no triangular structure is visible. However, the anti-diagonal ridge where the stimulus frequencies add up to the neuron's baseline firing rate seems to be present when the converged estimate shows a clear triangular structure. + +The \nli{} characterizes the ridgeness of the second-oder susceptibility plane. Comparing it when based on 10 versus one or ten million segments for all 39 model cells (\subfigrefb{fig:modelsusceptlown}{C}) supports this impression. As we have seen in the context of \subfigref{fig:modelsusceptcontrasts}{E} for converged estimates, values greater than one indicate triangular structures in the second-order susceptibility. The \nli{} values based on just ten segments correlate quite well with the ones from the converged estimates for contrasts 1\,\% and 3\,\% ($r=0.9$, $p<0.001$). At a contrast of 10\,\% this correlation is weaker ($r=0.53$, $p<0.001$), because there are only two cells left with \nli{} values greater than one. Despite the good correlations, care has to be taken to set a threshold on the \nli{} values for deciding whether a triangular structure would emerge for a much higher number of segments. Because the estimates are noisier, there could be false positives for a too low threshold. Setting the threshold to 1.6 avoids false positives for the price of a few false negatives. + +Trying to predict whether there is a triangular structure in the noise-split configuration is more difficult (\subfigrefb{fig:modelsusceptlown}{D}). The correlations are weaker and at a stimulus contrast of 10\,\% the correlation is no longer significant. One false positive arises at a contrast of 1\,\%, and false positives are absent for higher contrasts. False negatives increase with increasing contrast and at a contrast of 10\,\% all \nli{} values based on 10 segments are so low that just one triangular pattern can be predicted. This makes sense given the absent correlation between \nli{} values estimated at 10\,\% stimulus contrast and the noise-split configuration described above. + +Overall, observing \nli{} values greater than at least 1.6, even for a number of FFT segments as low as ten, seems to be a reliable indication for a triangular structure in the second-order susceptibility at the corresponding stimulus contrast. Small stimulus contrasts of 1\,\% are less informative, because of the bad signal-to-noise ratio. Intermediate stimulus contrasts around 3\,\% seem to be optimal, because there, most cells still have a triangular structure in their susceptibility and the signal-to-noise ratio is better. At RAM stimulus contrasts of 10\,\% or higher the signal-to-noise ratio is even better, but only few cells remain with weak triangularly shaped susceptibilities that might be missed as a false positives. Note that increasing the number of segements used for estimating the susceptibilities to 100 or 1000 improves the situation only marginally (not shown). + + +\begin{figure*}[tp] + \includegraphics[width=\columnwidth]{data_overview_mod.pdf} + \caption{\label{fig:dataoverview} Nonlinear responses in P-units and ampullary cells. The second-order susceptibility is condensed into the peakedness of the nonlinearity, \nli{} \eqnref{eq:nli_equation}, that relates the amplitude of the projected susceptibility at a cell's baseline firing rate to its median (see \subfigrefb{fig:punit}{G}). Each of the recorded neurons contributes at maximum with two stimulus contrasts. Black squares and circles highlight recordings conducted in a single cell. Squares in \panel{A, C, E} correspond to the cell in \figrefb{fig:punit} and circles to the cell in \figrefb{fig:punithighcv}. Squares in \panel{B, D, F} correspond to the cell in \figrefb{fig:ampullary}. \figitem{A, B} There is a negative correlation between the CV during baseline and \nli. \figitem{C, D} There is a negative correlation between the CV during stimulation and \nli. \figitem{E, F} \nli{} is plotted against the response modulation, (see methods), an indicator of the subjective stimulus strength for a cell. There is a negative correlation between response modulation and \nli. Restricting the analysis to the weakest stimulus that was presented to each unique neuron, does not change the results. The number of unique neurons is 221 for P-units and 45 for ampullary cells. + % The two example P-units shown before are highlighted with dark markers in \subfigrefb{fig:dataoverview}{A, C, E} (squares -- \figrefb{fig:punit}, circles -- \figrefb{fig:punithighcv}). + % Several of the recorded neurons contribute with two samples to the population analysis as their responses have been recorded to two different contrasts of the same RAM stimulus. Higher stimulus contrasts lead to a stronger drive and thus stronger response modulations (see color code bar in \subfigref{fig:dataoverview}{A}, see methods). + % The example cell shown above (\figref{fig:ampullary}) was recorded at two different stimulus intensities and the \nli{} values are highlighted with black squares. + } +\end{figure*} + +\begin{figure*}[tp] + \includegraphics[width=\columnwidth]{dataoverview} + \caption{\label{fig:dataoverview} Nonlinear responses in P-units and ampullary cells. + } +\end{figure*} + +\subsection{Low CVs and weak stimuli are associated with distinct nonlinearity in recorded electroreceptive neurons} +Now we are prepared to evaluate our pool of 221 P-units and 47 ampullary afferents recorded in 71 specimen. +\notejb{We need to state the number of trials} +\notejb{We need to know which contrasts} +% All the statements about nonlinear encoding in p-type and ampullary electroreceptor afferents based on single-cell examples shown above are supported by the analysis of our pool of 221 P-units and 47 ampullary afferents recorded in 71 specimen. +\notejb{\nli{} explanation is needed earlier} +For comparison across cells we summarize the structure of the second-order susceptibilities in a single number, the peakedness of the projected nonlinearity at \fbase{} (\nli{}) \eqnref{eq:nli_equation}, that characterizes the size of the expected peak of the projections of a \suscept{} matrix onto its diagonal at the baseline firing rate (e.g. \subfigref{fig:punit}{G}). \nli{} assumes high values when the peak at \fbase{} is pronounced relative to the median of projections onto the diagonal and is small when there is no distinct peak. + +Three P-units stand out with \nli{} values exceeding two, but additional \notejb{XXX} cells have \nli{} values greater than 1.8. Based on our insights from the P-unit models these would have the expected triangular structure in their susceptibilities when estimated with a sufficiently high number of segments. However, we can only speculate how many of the cells with lower \nli{} values are false negatives. \notejb{because also many have been measured at too strong contrasts}. +The \nli{} values of the P-unit population correlate weakly with the CV of the baseline ISIs. Cells with lower baseline CVs tend to have more pronounced peaks in their projections than those that have high baseline CVs (\subfigrefb{fig:dataoverview}{A}). This negative correlation is more pronounced against the CV measured during stimulation (\subfigrefb{fig:dataoverview}{C}). + +The effective stimulus strength also plays an important role. We quantify the effect of stimulus strength on a cell's response by the response modulation --- the standard deviation of a cell's firing rate in response to a RAM stimulus. P-units are heterogeneous in their sensitivity, their response modulations to the same stimulus contrast vary a lot \citep{Grewe2017}. Cells with weak responses to a stimulus, be it an insensitive cell or a weak stimulus, have higher \nli{} values and thus a more pronounced ridge in the second-order susceptibility at \fsumb{} in comparison to strongly responding cells that basically have flat second-order susceptibilities (\subfigrefb{fig:dataoverview}{E}). How pronounced nonlinear response components are in P-units thus depends on the baseline CV (a proxy for the internal noise level), and both the CV and response strength during stimulation (effective output noise). +%(Pearson's $r=-0.35$, $p<0.001$)221 P-units and 47 (Pearson's $r=-0.16$, $p<0.01$) +%In a P-unit population where each cell is represented not by several contrasts but by the lowest recorded contrast, \nli{} significantly correlates with the CV during baseline ($r=-0.17$, $p=0.01$), the response modulation ($r=-0.35$, $p<0.001$) and \fbase{} ($r=-0.32$, $p<0.001$).%, $\n{}=221$*, $\n{}=221$******, $\n{}=221$ + +The population of ampullary cells is generally more homogeneous, with lower baseline CVs than P-units. Accordingly, \nli{} values of ampullary cells are indeed much higher than in P-units by about a factor of ten. \notejb{XXX (percent)} ampullary cells with values greater than 1.8 would have a triangular structure in their second-order susceptibilities. Ampullary cells also show a negative correlation with baseline CV. Again, sensitive cells with strong response modulations are at the bottom of the distribution and have \nli{} values close to one (\subfigrefb{fig:dataoverview}{B, D}). The weaker the response modulation, because of less sensitive cells or weaker stimulus amplitudes, the stronger the nonlinear component of a cell's response (\subfigrefb{fig:dataoverview}{F}). +%(Pearson's $r=-0.35$, $p < 0.01$) (Pearson's $r=-0.59$, $p < 0.0001$) + + +\begin{figure*}[t] + \includegraphics[width=\columnwidth]{model_full.pdf} + \caption{\label{fig:model_full} Using second-order susceptibility to predict responses to sine-wave stimuli. \figitem[]{A} Absolute value of the second-order susceptibility, \eqnref{eq:susceptibility}, for both positive and negative frequencies. \susceptf{} was estimated from $N=10^6$ segments of model simulations in the noise-split condition (cell 2013-01-08-aa, see table~\ref{modelparams} for model parameters). White lines indicate zero frequencies. Nonlinear responses at \fsum{} are quantified in the upper right and lower left quadrants. Nonlinear responses at \fdiff{} are quantified in the upper left and lower right quadrants. The baseline firing rate of this cell was at $\fbase=120$\,Hz. The position of the orange/red letters corresponds to the beat frequencies used for the stimulation with pure sine waves in the subsequent panels and indicates the sum/difference of those beat frequencies. \figitem{B--E} Black line -- power spectral density of model simulations in response to stimulation with two pure sine waves, \fone{} and \ftwo, in addition to the receiving fish's own EOD (three-fish scenario). The contrast of beat beats is 0.02. Colored circles highlight the height of selected peaks in the power spectrum. Grey line -- power spectral density of model in the baseline condition. \figitem{B} The sum of the two beat frequencies match \fbase{}. \figitem{C} The difference of \fone{} and \ftwo{} match \fbase{}. \figitem{D} Only the first beat frequency matches \fbase{}. \figitem{E} None of the two beat frequencies matches \fbase{}.} +\end{figure*} + +\subsection{Second-order susceptibility can explain nonlinear peaks in pure sinewave stimulation} +Using the RAM stimulation we found pronounced nonlinear responses in the limit to weak stimulus amplitudes. How do these findings relate to the situation of pure sinewave stimuli with finite amplitudes that approximate the interference of EODs of real animals? For the P-units, the relevant signals are the beat frequencies \fone{} and \ftwo{} that arise from the interference of either of the two foreign EODs with the receiving fish's own EOD (\figref{fig:motivation}). In the introductory example, the response power spectrum showed peaks from nonlinear interactions at the sum of the two beat frequencies (orange marker, \subfigrefb{fig:motivation}{D}) and at the difference between the two beat frequencies (red marker, \subfigrefb{fig:motivation}{D}). In this example, \ftwo{} was similar to \fbase{}, corresponding to the horizontal line of the second-order susceptibility estimated for a vanishing external RAM stimulus (\subfigrefb{fig:noisesplit}\,\panel[iii]{C}). In the three-fish example, there was a second nonlinearity at the difference between the two beat frequencies (red dot, \subfigrefb{fig:motivation}{D}), that is not covered by the so-far shown part of the second-order susceptibility (\subfigrefb{fig:noisesplit}\,\panel[iii]{C}), in which only the response at the sum of the two stimulus frequencies is addressed. % less prominent, + +However, the second-order susceptibility \eqnref{eq:susceptibility} is a spectral measure that is based on Fourier transforms and thus is also defined for negative stimulus frequencies. The full \susceptf{} matrix is symmetric with respect to the origin. In the upper-right and lower-left quadrants of \susceptf{}, stimulus-evoked responses at \fsum{} are shown, whereas in the lower-right and upper-left quadrants nonlinear responses at the difference \fdiff{} are shown (\figref{fig:model_full}). The vertical and horizontal lines at \foneb{} and \ftwob{} are very pronounced in the upper-right quadrant of \subfigrefb{fig:model_full}{A} for nonlinear responses at \fsum{} and extend into the upper-left quadrant (representing \fdiff), where they fade out towards more negative $f_1$ frequencies. The peak in the response power-spectrum at \fdiff{} evoked by pure sine-wave stimulation (\subfigrefb{fig:motivation}{D}) is predicted by the horizontal line in the upper-left quadrant (\subfigrefb{fig:model_full}{A}, \citealp{Schlungbaum2023}). + +Is it possible to predict nonlinear responses in a three-fish setting based on second-order susceptibility matrices estimated from RAM stimulation (\subfigrefb{fig:model_full}{A})? We test this by stimulating the same model with two weak beats (\subfigrefb{fig:model_full}{B--E}). If we choose a frequency combination in which the sum of the two beat frequencies is equal to the model's baseline firing rate \fbase{}, a peak at the sum of the two beat frequencies appears in the power spectrum of the response (\subfigrefb{fig:model_full}{B}), as expected from \suscept. If instead we choose two beat frequencies that differ from \fbase{}, a peak is present at the difference frequency (\subfigrefb{fig:model_full}{C}). If only one of the beat frequency matches \fbase{}, both, a peak at the sum and at the difference frequency are present in the P-unit response (\subfigrefb{fig:model_full}{D}). And if none of these conditions are met, neither a peak at the sum nor at the difference of the two beat frequencies appears (\subfigrefb{fig:model_full}{E}). +\notejb{This works only qualitatively. In fact, the beat matrix looks quite a bit different and also heavily depends on contrast. This will be addressed in a future paper.} + + +\section{Discussion} + +Theoretical work \citep{Voronenko2017,Franzen2023} derived analytical expressions for weakly-nonlinear responses in LIF and theta model neurons driven by two sine waves with distinct frequencies. We here investigated such nonlinear responses in two types of electroreceptor afferents that differ in their intrinsic noise levels \citep{Grewe2017} using white-noise stimuli to estimate second-order susceptibilities. Following \citet{Voronenko2017} we expected to observe increased levels of second-order susceptibility where either of the stimulus frequencies alone or the sum of the stimulus frequencies matches the baseline firing rate ($f_1=\fbase{}$, $f_2=\fbase{}$ or \fsumb{}). We find traces of these nonlinear responses in most of the low-noise ampullary afferents and only those P-units with very low intrinsic noise levels. Complementary model simulations demonstrate, in the limit to vanishing stimulus amplitudes and extremely high number of repetitions, that the second order susceptibilities estimated from the electrophysiological data are indeed indicative of the theoretically expected weakly nonlinear responses. With this, we provide experimental evidence for nonlinear responses of a spike generator at low stimulus amplitudes. + +% EOD locking: +% Phase-locking to the own field also leads to a representation of \feod{} in the P-unit firing rate (see \figref{fig:punit}\panel{B}) \citep{Sinz2020}. + +% Weakly nonlinear responses versus saturation regime + +\subsection{Intrinsic noise limits nonlinear responses} +The weakly nonlinear regime with its triangular pattern of elevated second-order susceptibility resides between the linear and a stochastic mode-locking regime. Too strong intrinsic noise linearizes the system and wipes out the triangular structure of the second-order susceptibility \citep{Voronenko2017}. Our electrophysiological recordings match this theoretical expectation. Only P-units with low coefficients of variation (CV $<$ 0.25) of the interspike-interval distribution in their baseline response show the expected nonlinearities (\figref{fig:punit}, \figref{fig:model_full}, \subfigref{fig:dataoverview}{A}). Such low-CV cells are rare among the 221 P-units used in this study. On the other hand, the majority of the ampullary cells have generally lower CVs (median of 0.12) and have an approximately ten-fold higher level of second-order susceptibilities where \fsumb{} (\figref{fig:ampullary}, \subfigrefb{fig:dataoverview}{B}). + +The CV is a proxy for the intrinsic noise in the cells (\citealp{Vilela2009}, note however the effect of coherence resonance for excitable systems close to a bifurcation, \citealp{Pikovsky1997, Lindner2004}). In both cell types, we observe a negative correlation between the second-order susceptibility at \fsumb{} and the CV (\figrefb{fig:dataoverview}), indicating that it is the level of intrinsic noise that shapes nonlinear responses. These findings are in line with previous theoretical and experimental studies showing the linearizing effects of noise in nonlinear systems \citep{Roddey2000, Chialvo1997, Voronenko2017}. Increased intrinsic noise has been demonstrated to increase the CV and to reduce nonlinear phase-locking in vestibular afferents \citep{Schneider2011}. Reduced noise, on the other hand, has been associated with stronger nonlinearity in pyramidal cells of the ELL \citep{Chacron2006}. Only in cells with sufficiently low levels of intrinsic noise, weakly nonlinear responses can be observed. + +\subsection{Linearization by white-noise stimulation} +Not only the intrinsic noise but also the stimulation with external white-noise linearizes the cells. This applies to both, the stimulation with AMs in P-units (\subfigrefb{fig:dataoverview}{E}) and direct stimulation in ampullary cells (\subfigrefb{fig:dataoverview}{F}). The stronger the effective stimulus, the less pronounced are the peaks in second-order susceptibility (see \subfigref{fig:punit}{E\&F} for a P-unit example and \subfigref{fig:ampullary}{E\&F} for an ampullary cell). This linearizing effect of noise stimuli limits the weakly nonlinear regime to small stimulus amplitudes. At higher stimulus amplitudes, however, other nonlinearities of the system eventually show up in the second-order susceptibility. + +In order to characterize weakly nonlinear responses of the cells in the limit to vanishing stimulus amplitudes we utilized the Furutsu-Novikov theorem \citep{Novikov1965, Furutsu1963}. Following \citet{Lindner2022}, a substantial part of the intrinsic noise of a P-unit model \citep{Barayeu2023} is treated as signal. Performing this noise-split trick we can estimate the weakly nonlinear response without the linearizing effect of an additional external white noise stimulus. The model of a low-CV P-unit then shows the full nonlinear structure (\figref{fig:noisesplit}) known from analytical derivations and simulations of basic LIF and theta models driven with pairs of sine-wave stimuli \citep{Voronenko2017,Franzen2023}. Previous studies on second-order nonlinearities have not observed the weakly nonlinear regime, probably because of the linearizing effects of strong noise stimuli \citep{Victor1977, Schanze1997, Neiman2011}. + +\subsection{Characterizing nonlinear coding from limited experimental data} +Estimating the Volterra series from limited experimental data is usually restricted to the first two or three orders, which might not be sufficient for a proper prediction of the neuronal response \citep{French2001}. A proper estimation of just the second-order susceptibility in the weakly nonlinear regime is challenging in electrophysiological experiments. Making assumptions about the nonlinearities in a system reduces the amount of data needed for parameter estimation. In particular, models combining linear filtering with static nonlinearities \citep{Chichilnisky2001} have been successful in capturing functionally relevant neuronal computations in visual \citep{Gollisch2009} as well as auditory systems \citep{Clemens2013}. Linear methods based on backward models for estimating the stimulus from neuronal responses, have been extensively used to quantify information transmission in neural systems \citep{Theunissen1996, Borst1999, Wessel1996, Machens2001}, because backward models do not need to generate action potentials that involve strong nonlinearities \citep{Rieke1999}. + +\subsection{Nonlinear encoding in ampullary cells} +The afferents of the passive electrosensory system, the ampullary cells, exhibit strong second-order susceptibilities (\figref{fig:dataoverview}). Ampullary cells more or less directly translate external low-frequency electric fields into afferent spikes, much like in the standard LIF and theta models used by Lindner and colleagues \citep{Voronenko2017,Franzen2023}. Indeed, we observe in the ampullary cells similar second-order nonlinearities as in LIF models. + +Ampullary stimuli originate from the muscle potentials induced by prey movement \citep{Kalmijn1974, Engelmann2010, Neiman2011fish}. For a single prey items such as \textit{Daphnia}, these potentials are often periodic but the simultaneous activity of a swarm of prey resembles Gaussian white noise \citep{Neiman2011fish}. Linear and nonlinear encoding in ampullary cells has been studied in great detail in the paddlefish \citep{Neiman2011fish}. The power spectrum of the baseline response shows two main peaks: One peak at the baseline firing frequency, a second one at the oscillation frequency of primary receptor cells in the epithelium, and interactions of both. Linear encoding in the paddlefish shows a gap at the epithelial oscillation frequency, instead, nonlinear responses are very pronounced there. + +Ampullary stimulus encoding is somewhat different in \lepto{}. The power spectrum of the spontaneous response is dominated by only the baseline firing rate and its harmonics, a second oscillator is not visible. The baseline firing frequency, however, is outside the linear coding range \citep{Grewe2017} while it is within the linear coding range in paddlefish \citep{Neiman2011fish}. Interestingly, the nonlinear response in the paddlefish ampullaries increases with stimulus intensity while it disappears in our case (\subfigrefb{fig:dataoverview}{F}) indicating that paddlefish data have been recorded above the weakly-nonlinear regime. + +The population of ampullary cells is very homogeneous with respect to the baseline rate (131$\pm$29\,Hz) and stimulus encoding properties \citep{Grewe2017}. This implies that, if the stimulus contains the appropriate frequency components that sum up to the baseline rate, there should be a nonlinear response at a frequency that is similar in the full population of ampullary cells (at the baseline firing frequency) that is outside the linear coding range. Postsynaptic cells integrating ampullary input might be able to extract such nonlinear responses. How such nonlinear effects might influence prey detection should be addressed in future studies. + +\subsection{Nonlinear encoding in P-units} +Noise stimuli have the advantage that a range of frequencies can be measured with a single stimulus presentation and they have been successfully applied to characterize sensory coding in many systems \citep{French1973, Marmarelis1999, Borst1999, Chacron2005, Grewe2017}. In the real-world situation of wave-type electric fish, however, the natural stimuli encoded by P-units are periodic amplitude modulations of the self-generated electric field which arise from the superposition of the own and foreign EODs. Natural interactions usually occur between low numbers of close-by fish and thus the AMs are a mixture of a few distinct frequencies with substantial amplitudes \citep{Stamper2010,Fotowat2013, Henninger2020}. How informative are the second-order susceptibilities observed under noise stimulation for the encoding of distinct frequencies? + +We here applied broad-band noise amplitude-modulation stimuli to estimate the second-order susceptibility. +%The total signal power in noise stimuli is uniformly distributed over a wide frequency band while the power is spectrally focused in pure sinewave stimuli. +Broadband noise stimuli introduce additional noise that linearizes the dynamics of the system. In contrast, pure sinewave stimulation is spectrally focussed and drives the system on the background of the intrinsic noise. This explains why we can observe nonlinear interactions between sinewave stimuli with distinct frequencies (\figrefb{fig:motivation}) although they are barely visible when stimulating with strong broad-band noise (\figrefb{fig:noisesplit}). As discussed above in the context of broad-band noise stimulation, we expect interactions with a cell's baseline frequency only for the very few P-units with low enough CVs of the baseline interspike intervals. +%We thus conclude that the presence of the anti-diagonal pattern in the \suscept{} matrix is sufficient to infer that the same nonlinear interactions happen here, in accordance with the the second-order susceptibilities found in LIF models without a carrier \citep{Voronenko2017, Schlungbaum2023}. This also validates the application of the white noise approach to characterize the full \suscept{} matrix instead of using all combinations of frequencies. + +Extracting the AM from the stimulus already requires a (threshold) nonlinearity \citep{Middleton2006, Stamper2012Envelope, Savard2011, Barayeu2023}. This nonlinearity, however, does not show up in our estimates of the susceptibilities, because in our analysis we directly relate the AM waveform to the recorded cellular responses. Encoding the time-course of the AM, however, has been shown to be linear over a wide range of AM amplitudes and frequencies \citep{Xu1996, Benda2005, Gussin2007, Grewe2017, Savard2011}. In contrast, we here have demonstrated nonlinear interactions originating from the spike generator for broad-band noise stimuli in the limit of vanishing amplitudes and for stimulation with two distinct frequencies. Both settings have not been studied yet. + +The encoding of secondary or social envelopes that arise from relative movement or the interaction of more than two animals \citep{Stamper2012Envelope} requires an additional nonlinearity in the system that was initially attributed to downstream processing \citep{Middleton2006, Middleton2007}. Later studies showed that already the electroreceptors can encode such information whenever the firing rate saturates at zero or the maximum rate at the EOD frequency \citep{Savard2011}. Based on our work, we predict that P-units with low CVs encode the social envelopes even under weak stimulation, whenever the resulting beat frequencies match or add up to the baseline firing rate. Then difference frequencies show up in the response spectrum that characterize the slow envelope. + +The weakly nonlinear interactions in low-CV P-units could facilitate the detectability of faint signals during three-animal interactions as found in courtship contexts in the wild \citep{Henninger2018}, the electrosensory cocktail party. The detection of a faint, distant intruder male could be improved by the presence of a nearby strong female stimulus, because of the nonlinear interaction terms \citep{Schlungbaum2023}. This boosting effect is, however, very specific with respect to the stimulus frequencies and a given P-unit's baseline frequency. The population of P-units is very heterogeneous in their baseline firing rates and CVs (50--450\,Hz and 0.1--1.4, respectively, \figref{fig:dataoverview}\panel{A}, \citealp{Grewe2017, Hladnik2023}). The range of baseline firing rates thus covers substantial parts of the beat frequencies that may occur during animal interactions \citep{Henninger2018, Henninger2020}, while the number of low-CV P-units is small. Whether and how this information is specifically maintained and read out by pyramidal cells in the electrosensory lateral line lobe (ELL) in the hindbrain onto which P-units converge \citep{Krahe2014, Maler2009a} is an open question. + +\subsection{Conclusions} + +We have demonstrated pronounced nonlinear responses in primary electrosensory afferents at weak stimulus amplitudes and sufficiently low intrinsic noise levels. The observed nonlinearities match the expectations from previous theoretical studies \citep{Voronenko2017,Franzen2023}. The resulting nonlinear components introduce spectral components not present in the original stimulus, but may provide an edge in the context of signal detection problems at stimulus amplitudes close to threshold \citep{Schlungbaum2023}. Electrosenory afferents share an evolutionary history with hair cells \citep{Baker2019} and share many response properties with mammalian auditory nerve fibers \citep{Barayeu2023, Joris2004}. Thus, we expect weakly nonlinear responses for near-threshold stimulation in auditory nerve fibers. + + +\section{Methods} + +\subsection{Experimental subjects and procedures} + +Within this project, we re-evaluated datasets that were recorded between 2010 and 2023 at the Ludwig Maximilian University (LMU) M\"unchen and the Eberhard-Karls University T\"ubingen. All experimental protocols complied with national and European law and were approved by the respective Ethics Committees of the Ludwig-Maximilians Universität München (permit no. 55.2-1-54-2531-135-09) and the Eberhard-Karls Unversität Tübingen (permit no. ZP 1/13 and ZP 1/16). +The final sample consisted of 221 P-units and 47 ampullary electroreceptor afferents recorded in 71 weakly electric fish of the species \lepto{}. Electrophysiological recordings were performed on male and female weakly electric fish of the species \lepto{}. Fish were obtained from a commercial supplier for tropical fish (Aquarium Glaser GmbH, Rodgau, Germany) and kept in tanks with a water temperature of $25\pm1\,^\circ$C and a conductivity of around $270\,\micro\siemens\per\centi\meter$ under a 12\,h:12\,h light-dark cycle. + +Before surgery, the animals were deeply anesthetized via bath application of a solution of MS222 (120\,mg/l, PharmaQ, Fordingbridge, UK) buffered with Sodium Bicarbonate (120\,mg/l). The posterior anterior lateral line nerve (pALLN) was exposed by making a small cut into the skin covering the nerve. The cut was placed dorsal of the operculum just before the nerve descends towards the anterior lateral line ganglion (ALLNG). Those parts of the skin that were to be cut were locally anesthetized by cutaneous application of liquid lidocaine hydrochloride (20\,mg/ml, bela-pharm GmbH). During the surgery, water supply was ensured by a mouthpiece to maintain anesthesia with a solution of MS222 (100\,mg/l) buffered with Sodium Bicarbonate (100\,mg/l). After surgery, fish were immobilized by intramuscular injection of from 25\,$\micro$l to 50\,$\micro$l of tubocurarine (5\,mg/ml dissolved in fish saline; Sigma-Aldrich). +Respiration was then switched to normal tank water and the fish was transferred to the experimental tank. + +\subsection{Experimental setup} +For the recordings fish were positioned centrally in the experimental tank, with the major parts of their body submerged into the water. Those body parts that were above the water surface were covered with paper tissue to avoid drying of the skin. Local analgesia was refreshed in intervals of two hours by cutaneous application of Lidocaine (2\,\%; bela-pharm, Vechta, Germany) around the surgical wounds. Electrodes (borosilicate; 1.5\,mm outer diameter; GB150F-8P; Science Products, Hofheim, Germany) were pulled to a resistance of 50--100\,\mega\ohm{} (model P-97; Sutter Instrument, Novato, CA) and filled with 1\,M KCl solution. Electrodes were fixed in a microdrive (Luigs-Neumann, Ratingen, Germany) and lowered into the nerve. Recordings of electroreceptor afferents were amplified and lowpass filtered at 10\,kHz (SEC-05, npi-electronics, Tamm, Germany, operated in bridge mode). All signals, neuronal recordings, recorded EOD, and the generated stimulus, were digitized with sampling rates of 20 or 40\,kHz (PCI-6229, National Instruments, Austin, TX). RELACS (\url{www.relacs.net}) running on a Linux computer was used for online spike and EOD detection, stimulus generation, and calibration. Recorded data was then stored on the hard drive for offline analysis. + +\subsection{Identification of P-units and ampullary cells} +The neurons were classified into cell types during the recording by the experimenter. P-units were classified based on baseline firing rates of 50--450\,Hz, a clear phase-locking to the EOD, and by their responses to amplitude modulations of their own EOD \citep{Grewe2017, Hladnik2023}. Ampullary cells were classified based on firing rates of 80--200\,Hz, absent phase-locking to the EOD, and responses to low-frequency sinusoidal stimuli \citep{Grewe2017}. We here selected only those cells of which the neuron's baseline activity as well as the responses to frozen noise stimuli were recorded. + +\subsection{Electric field recordings} +For monitoring the EOD without the stimulus, two vertical carbon rods ($11\,\centi\meter$ long, 8\,mm diameter) in a head-tail configuration were placed isopotential to the stimulus. Their signal was differentially amplified with a gain factor between 100 and 500 (depending on the recorded animal) and band-pass filtered (3 to 1500\,Hz pass-band, DPA2-FX; npi electronics, Tamm, Germany). For an estimate of the transdermal potential that drives the electroreceptors, two silver wires spaced by 1\,cm were located next to the left gill of the fish and orthogonal to the fish's longitudinal body axis (amplification 100 to 500 times, band-pass filtered with 3 to 1\,500\,Hz pass-band, DPA2-FX; npi-electronics, Tamm, Germany). This local EOD measurement recorded the combination of the fish's own EOD and the applied stimulus. + + +\subsection{Stimulation}\label{rammethods} +Electric stimuli were attenuated (ATN-01M, npi-electronics, Tamm, Germany), isolated from ground (ISO-02V, npi-electronics, Tamm, Germany) and delivered via two horizontal carbon rods (30 cm length, 8 mm diameter) located $15\,\centi\meter$ laterally to the fish. + +The fish were stimulated with band-limited white noise stimuli with a cut-off frequency of 150, 300 or 400\,Hz. The stimulus intensity is given as the contrast, i.e. the standard deviation of the white noise stimulus in relation to the fish's EOD amplitude. The contrast varied between 1 and 20\,\%. Only cells with at least 10\,s of white noise stimulation were included for the analysis. When ampullary cells were recorded, the white noise was directly applied as the stimulus. To create random amplitude modulations (RAM) for P-unit recordings, the EOD of the fish was multiplied with the desired random amplitude modulation profile (MXS-01M; npi electronics). + +% and between 2.5 and 40\,\% for \eigen + +\subsection{Data analysis} Data analysis was done in Python 3 using the packages matplotlib \citep{Hunter2007}, numpy \citep{Walt2011}, scipy \citep{scipy2020}, pandas \citep{Mckinney2010}, nixio \citep{Stoewer2014}, and thunderlab (\url{https://github.com/bendalab/thunderlab}). + +%sklearn \citep{scikitlearn2011}, + +\paragraph{Baseline analysis}\label{baselinemethods} +The baseline firing rate \fbase{} was calculated as the number of spikes divided by the duration of the baseline recording (on average 18\,s). The coefficient of variation (CV) of the interspike intervals (ISI) is their standard deviation relative to the average ISI: $\rm{CV} = \sqrt{\langle (ISI- \langle ISI \rangle) ^2 \rangle} / \langle ISI \rangle$. If the baseline was recorded several times in a recording, the average \fbase{} and CV were calculated. + +\paragraph{White noise analysis} \label{response_modulation} +In the stimulus-driven case, the neuronal activity of the recorded cell is modulated around the average firing rate that is similar to \fbase{} and in that way encodes the time-course of the stimulus. Spiking activity +\begin{equation} + \label{eq:spikes} + x_k(t) = \sum_i\delta(t-t_{k,i}) +\end{equation} +is recorded for each stimulus presentation $k$, as a train of times $t_{k,i}$ where action potentials occured. If only a single trial was recorded or is used for the analysis, we drop the trial index $k$. + +The single-trial firing rate +\begin{equation} + r_k(t) = x_k(t) * K(t) = \int_{-\infty}^{+\infty} x_k(t') K(t-t') \, \mathrm{d}t' +\end{equation} +was estimated by convolving the spike train with a kernel. We used a Gaussian kernel +\begin{equation} +K(t) = {\scriptstyle \frac{1}{\sigma\sqrt{2\pi}}} e^{-\frac{t^2}{2\sigma^2}} +\end{equation} +with standard deviation $\sigma$ set to 2.5\,ms if not stated otherwise. Averaging over $n$ repeated stimulus presentations results in the trial averaged firing rate +\begin{equation} + \label{eq:rate} + r(t) = \left\langle r_k(t) \right\rangle _k = \frac{1}{n} \sum_{k=1}^n r_k(t) +\end{equation} + +The average firing rate during stimulation, $r_s = \langle r(t) \rangle_t$, is given by the temporal average $\langle \cdot \rangle_t$ over the duration of the stimulus of the trial-averaged firing rate. To quantify how strongly a neuron was driven by the stimulus, we computed the response modulation as the standard deviation $\sigma_{s} = \sqrt{\langle (r(t)-r_s)^2\rangle_t}$ of the trial-averaged firing rate. + +\paragraph{Spectral analysis}\label{susceptibility_methods} +The neuron is driven by the stimulus and thus its spiking response depends on the time course of the stimulus. To characterize the relation between stimulus $s(t)$ and response $x(t)$, we calculated the first- and second-order susceptibilities in the frequency domain. + +Fast fourier transforms (FFT) $\tilde s_T(\omega)$ and $\tilde x_T(\omega)$ of $s(t)$ and $x(t)$, respectively, were computed according to $\tilde x_T(\omega) = \int_{0}^{T} \, x(t) e^{- i \omega t}\,dt$ for $T=0.5$\,s long segments with no overlap, resulting in a spectral resolution of 2\,Hz for the experimental data. For simplicity we use angular frequencies $\omega=2\pi f$ instead of frequencies $f$. In the experimental data, most stimuli had a duration of 10\,s and were chopped into 20 segments. Spectral measures were computed for single trials of neural responses, series of spike times, \eqnref{eq:spikes}. For spectral parameters used in simulations, see below. + +The power spectrum of the stimulus $s(t)$ was estimated as +\begin{equation} + \label{powereq} + S_{ss}(\omega) = \frac{\langle \tilde s_T(\omega) \tilde s_T^*(\omega)\rangle}{T} +\end{equation} +with $\tilde s^*$ being the complex conjugate of $\tilde s$ and $\langle \cdot \rangle$ denoting the average over the segments. The power spectrum of the spike trains $S_{xx}(\omega)$ was estimated accordingly. The cross-spectrum $S_{xs}(\omega)$ between stimulus and evoked spike trains was estimated according to +\begin{equation} + \label{cross} + S_{xs}(\omega) = \frac{\langle \tilde x_T(\omega) \tilde s_T^*(\omega)\rangle}{T} +\end{equation} + +The first-order susceptibility (transfer function) +\begin{equation} + \label{linearencoding_methods} + \chi_{1}(\omega) = \frac{S_{xs}(\omega) }{S_{ss}(\omega) } +\end{equation} +was then computed from $S_{xs}(\omega)$ and $ S_{ss}(\omega)$. + +The second-order cross-spectrum +\begin{equation} + \label{eq:crosshigh} + S_{xss} (\omega_{1},\omega_{2}) = \frac{\langle \tilde x_T(\omega_{1} + \omega_{2}) \tilde s_T^*(\omega_{1}) \tilde s_T^*(\omega_{2}) \rangle}{T} +\end{equation} +describes nonlinear interactions that generate responses at the sum and difference (at negative $\omega_2$) of two stimulus frequencies $\omega_1$ and $\omega_2$. +The second-order susceptibility +\begin{equation} + \label{eq:susceptibility} + \chi_{2}(\omega_{1}, \omega_{2}) = \frac{S_{xss} (\omega_{1},\omega_{2})}{2\sqrt{S_{ss} (\omega_{1}) S_{ss} (\omega_{2})}} +\end{equation} +normalizes the second-order cross-spectrum by the spectral power at the two stimulus frequencies. +% Applying the Fourier transform this can be rewritten resulting in: +% \begin{equation} +% \label{susceptibility} +% \chi_{2}(\omega_{1}, \omega_{2}) = \frac{TN \sum_{n=1}^N \int_{0}^{T} dt\,r_{n}(t) e^{-i(\omega_{1}+\omega_{2})t} \int_{0}^{T}dt'\,s_{n}(t')e^{i \omega_{1}t'} \int_{0}^{T} dt''\,s_{n}(t'')e^{i \omega_{2}t''}}{2 \sum_{n=1}^N \int_{0}^{T} dt\, s_{n}(t)e^{-i \omega_{1}t} \int_{0}^{T} dt'\,s_{n}(t')e^{i \omega_{1}t'} \sum_{n=1}^N \int_{0}^{T} dt\,s_{n}(t)e^{-i \omega_{2}t} \int_{0}^{T} dt'\,s_{n}(t')e^{i \omega_{2}t'}} +% \end{equation} +Throughout the manuscript we only show the absolute values of the complex-valued second-order susceptibility matrix and ignore the corresponding phases. + +\paragraph{Nonlinearity index}\label{projected_method} +We expected to see elevated values in the second-order susceptibility at $\omega_1 + \omega_2 = \fbase$ \citep{Voronenko2017,Franzen2023}. To characterize this in a single number we computed the peakedness of the nonlinearity via +\begin{equation} + \label{eq:nli_equation} + \nli{} = \frac{\max D(\fbase{}-5\,\rm{Hz} \leq f \leq \fbase{}+5\,\rm{Hz})}{\mathrm{median}(D(f))} +\end{equation} +from the second-order susceptibilities estimated from experimental data. $D(f)$ is the projection of the absolute values of the second-order susceptibility matrix onto the diagonal, calculated by taking the mean of the anti-diagonal elements. The peak of $D(f)$ at the neuron's baseline firing rate $\fbase$ was found by finding the maximum of $D(f)$ in the range $\fbase \pm 5$\,Hz. This peak was then normalized by the median of $D(f)$ (\subfigrefb{fig:punit}{G}). Since in most experimentally measured cells the second-order susceptibilities was more or less flat, normalizing by the median is working well. If the same RAM was recorded several times in a cell, each trial resulted in a separate second-order susceptibility matrix. For the population statistics in \figref{fig:dataoverview} the mean of the resulting \nli{} values is used. + +For the model simulations, the second-order susceptibilities where not flat but often showed a broader bump on which the peak at the neuron's baseline firing rate occured (see, for example, \figrefb{fig:modelsusceptcontrasts}, panels \panel[i]{B}, \panel[iii]{C}, and \panel[iv]{D}). Instead of normalizing by the median, we normalized the model simulations by the mean values of the projection $D(f)$ in small ranges close to the left and right of the neuron's baseline firing rate: +\begin{equation} + \label{eq:nli_equation2} + \nli{} = \frac{\max D(\fbase{}-5\,\rm{Hz} \leq f \leq \fbase{}+5\,\rm{Hz})}{\frac{1}{2}\left[\mathrm{mean}(D(\fbase{}-20\,\rm{Hz} \leq f \leq \fbase{}-10\,\rm{Hz})) + \mathrm{mean}(D(\fbase{}+10\,\rm{Hz} \leq f \leq \fbase{}+20\,\rm{Hz}))\right]} +\end{equation} +Using \eqnref{eq:nli_equation} instead of \eqnref{eq:nli_equation2} for the estimates of the second-order susceptibility based on $N=10$ segments does not change the results in \subfigref{fig:modelsusceptlown}{C \& D}. That is, experimental data based on low numbers of segments can be safely analyzed using the more robust \eqnref{eq:nli_equation}. + + +\begin{figure*}[t] + \includegraphics[width=\columnwidth]{flowchart.pdf} + \caption{\label{flowchart} + Architecture of the P-unit model. Each row illustrates subsequent processing steps for three different stimulation regimes: (i) baseline activity without external stimulus, only the fish's self-generated EOD (the carrier, \eqnref{eq:eod}) is present. (ii) RAM stimulation, \eqnref{eq:ram_equation}. The amplitude of the EOD carrier is modulated with a weak (2\,\% contrast) band-limited white-noise stimulus. (iii) Noise split, \eqnsref{eq:ram_split}--\eqref{eq:Noise_split_intrinsic}, where 90\,\% of the intrinsic noise is replaced by a RAM stimulus, whose amplitude is scaled to maintain the mean firing rate and the CV of the ISIs of the model's baseline activity. As an example, simulations of the model for cell ``2012-07-03-ak'' are shown (table~\ref{modelparams}). \figitem{A} The stimuli are thresholded, \eqnref{eq:threshold2}, by setting all negative values to zero. \figitem{B} Subsequent low-pass filtering, \eqnref{eq:dendrite}, attenuates the carrier and carves out the AM signal. \figitem{C} Intrinsic Gaussian white-noise is added to the signals shown in \panel{B}. Note the reduced internal noise amplitude in the noise split (iii) condition. \figitem{D} Spiking output of the LIF model, \eqnsref{eq:LIF}--\eqref{spikethresh}, in response to the sum of \panel{B} and \panel{C}. \figitem{E} Power spectra of the LIF neuron's spiking activity. Both, baseline activity (\panel[i]{E}) and noise split (\panel[iii]{E}), have the same peaks in the response spectrum at $\fbase$, $f_{EOD} - \fbase$, $f_{EOD}$, and $f_{EOD} + \fbase$. With RAM stimulation (\panel[ii]{E}), the peak at the baseline firing rate, $\fbase$, is washed out.} +\end{figure*} + +\subsection{Leaky integrate-and-fire models for P-units}\label{lifmethods} + +Modified leaky integrate-and-fire (LIF) models were constructed to reproduce the specific firing properties of P-units \citep{Chacron2001, Sinz2020}. The sole driving input into the P-unit model during baseline, i.e. when no external stimulus was given, is the fish's own EOD, modeled as a cosine wave +\begin{equation} + \label{eq:eod} + \carrierinput = y_{EOD}(t) = \cos(2\pi f_{EOD} t) + \end{equation} +with EOD frequency $f_{EOD}$ and an amplitude normalized to one. + +To mimic the interaction with other fish, the EODs of a second or third fish with EOD frequencies $f_1$ and $f_2$, respectively, were added to the normalized EOD, \eqnref{eq:eod}, of the receiving fish according to their contrasts, $c_1$ and $c_2$ at the position of the receiving fish: +\begin{equation} + \label{eq:modelbeats} + \carrierinput = \cos(2\pi f_{EOD} t) + c_1 \cos(2\pi f_1 t) + c_2\cos(2\pi f_2 t) +\end{equation} +For two fish, $c_2 = 0$. + +Random amplitude modulations (RAMs) were simulated by first generating the AM as a band-limited white noise stimulus $s(t)$. For this, random real and imaginary numbers were drawn from Gaussian distributions for each frequency component in the range from 0 to 300\,Hz in the Fourier domain \citep{Billah1990,Skorjanc2023}. By means of the inverse Fourier transform, the time course of the RAM stimulus, $s(t)$, was generated. The input to the model was then +\begin{equation} + \label{eq:ram_equation} + y(t) = (1+ s(t)) \cos(2\pi f_{EOD} t) +\end{equation} +The contrast $c$ of the RAM is the standard deviation of the RAM relative to the amplitude of the receiving fish. + +First, the input \carrierinput{} is thresholded by setting negative values to zero: +\begin{equation} + \label{eq:threshold2} + \lfloor \carrierinput \rfloor_0 = \left\{ \begin{array}{rcl} \carrierinput & ; & \carrierinput \ge 0 \\ 0 & ; & \carrierinput < 0 \end{array} \right. +\end{equation} +(\subfigrefb{flowchart}{A}). This thresholds models the transfer function of the synapses between the primary receptor cells and the afferent. Together with a low-pass filter +\begin{equation} + \label{eq:dendrite} + \tau_{d} \frac{d V_{d}}{d t} = -V_{d}+ \lfloor \carrierinput \rfloor_{0} +\end{equation} +the threshold operation is required for extracting the amplitude modulation from the input \citep{Barayeu2024}. The low-pass filter models passive signal conduction in the afferent's dendrite (\subfigrefb{flowchart}{B}) and $\tau_{d}$ is the membrane time constant of the dendrite. Dendritic low-pass filtering was also necessary to reproduce the loose coupling of P-unit spikes to the EOD while maintaining high sensitivity at small amplitude modulations. + +The dendritic voltage $V_d(t)$ is then fed into a stochastic leaky integrate-and-fire (LIF) model with adaptation, +\begin{equation} + \label{eq:LIF} + \tau_{m} \frac{d V_{m}}{d t} = - V_{m} + \mu + \alpha V_{d} - A + \sqrt{2D}\;\xi(t) +\end{equation} +where $\tau_{m}$ is the membrane time-constant, $\mu$ is a fixed bias current, $\alpha$ is a scaling factor for $V_{d}$, $A$ is an inhibiting adaptation current, and $\sqrt{2D}\;\xi(t)$ is a white noise with strength $D$. Note, that all state variables, membrane voltages $V_d$ and $V_m$ as well as the adaptation current, are dimensionless. + +The adaptation current $A$ follows +\begin{equation} + \label{eq:adaptation} + \tau_{A} \frac{d A}{d t} = - A +\end{equation} +with adaptation time constant $\tau_A$ \citep{Benda2003,Benda2005,Benda2010}. + +Whenever the membrane voltage $V_m(t)$ crosses the spiking threshold $\theta=1$, a spike was generated, $V_{m}(t)$ was reset to $0$, the adaptation current was incremented by $\Delta A$, and integration of $V_m(t)$ was paused for the duration of a refractory period $t_{ref}$ (\subfigrefb{flowchart}{D}): +\begin{equation} + \label{spikethresh} + V_m(t) \ge \theta \; : \left\{ \begin{array}{rcl} V_m & \mapsto & 0 \\ A & \mapsto & A + \Delta A/\tau_A \end{array} \right. +\end{equation} + +The P-unit models were integrated by the Euler forward method with a time-step of $\Delta t = 0.05$\,ms. The intrinsic noise $\xi(t)$ (\eqnref{eq:LIF}, \subfigrefb{flowchart}{C}) was added by drawing a random number from a normal distribution $\mathcal{N}(0,\,1)$ with zero mean and standard deviation of one in each time step $i$. This number was multiplied with $\sqrt{2D}$ and divided by $\sqrt{\Delta t}$. For each trial of a simulation, the variables $A$, $V_{d}$ and $V_{m}$ were drawn from a distribution of initial values, estimated from a 100\,s long simulation of baseline activity after an initial 100\,s long integration that was discarded as a transient. +%\begin{equation} +% \label{eq:LIFintegration} +% V_{m_{i+1}} = V_{m_i} + \left(-V_{m_i} + \mu + \alpha V_{d_i} - A_i + \sqrt{\frac{2D}{\Delta t}}\mathcal{N}(0,\,1)_i\right) \frac{\Delta t}{\tau_m} +%\end{equation} + +%\paragraph{Fitting the model to recorded P-units} +The eight free parameters of the P-unit model $\beta$, $\tau_m$, $\mu$, $D$, $\tau_A$, $\Delta_A$, $\tau_d$, and $t_{ref}$, were fitted to both the baseline activity (baseline firing rate, CV of ISIs, serial correlation of ISIs at lag one, and vector strength of spike coupling to EOD) and the responses to step increases and decreases in EOD amplitude (onset and steady-state responses, effective adaptation time constant, \citealp{Benda2005}) of recorded P-units (table~\ref{modelparams}). + +\begin{table*}[tp] + \caption{\label{modelparams} Model parameters of LIF models, fitted to 3 electrophysiologically recorded P-units \citep{Ott2020}.} + \begin{tabular}{lrrrrrrrr} + \hline + \bfseries cell & \bfseries $\mu$ & \bfseries $\beta$ & \bfseries $\tau_{m}$/ms & \bfseries $D$/$\mathbf{ms}$ & \bfseries $\tau_{A}$/ms & \bfseries $\Delta_A$ & \bfseries $\tau_{d}$/ms & \bfseries $t_{ref}$/ms \\\hline + 2012-07-03-ak& $-1.32$& $10.6$& $1.38$& $0.001$& $96.05$& $0.01$& $1.18$& $0.12$ \\ + 2013-01-08-aa& $0.59$& $4.5$& $1.20$& $0.001$& $37.52$& $0.01$& $1.18$& $0.38$ \\ + 2018-05-08-ae& $-21.09$& $139.6$& $1.49$& $0.214$& $123.69$& $0.16$& $3.93$& $1.31$ \\ + \hline + \end{tabular} +\end{table*} + +In \figrefb{fig:noisesplit} and \figrefb{fig:model_full}, for each of the stimulus and response segments needed for the spectral analysis, \eqnsref{powereq}--\eqref{eq:susceptibility}, a simulation was run. The first second was discarded and the analysis was based on the last second of the data. The resulting spectra thus have a spectral resolution of 1\,Hz. To speed up model simulations for \figrefb{fig:modelsusceptcontrasts} and \figrefb{fig:trialnr} we simulated up to $10^6$ trials of 3\,s duration. In each trial the first 0.5\,s were skipped, yielding 10 FFT segments of $T=0.25$\,s (4\,Hz resolution). + + +\subsection{Noise split} +\label{intrinsicsplit_methods} +Based on the Furutsu-Novikov theorem \citep{Furutsu1963,Novikov1965,Lindner2022,Egerland2020}, we split the total noise, $\sqrt{2D}\;\xi(t)$, of a LIF model, \eqnref{eq:LIF}, into two parts. The first part is the intrinsic noise term, $\sqrt{2D \, c_{\rm{noise}}}\;\xi(t)$, whose strength is reduced by a factor $c_{\rm{noise}}=0.1$ (\subfigrefb{flowchart}\,\panel[iii]{C}). The second part replaces the now missing intrinsic noise by a driving input signal $s_{\xi}(t)$, a RAM stimulus with frequencies up to 300\,Hz (\subfigrefb{flowchart}\,\panel[iii]{A}). The LIF model with splitted noise then reads +\begin{eqnarray} + \label{eq:ram_split} + y(t) & = & (1+ s_\xi(t)) \cos(2\pi f_{EOD} t) \\ + \label{eq:Noise_split_intrinsic_dendrite} + \tau_{d} \frac{d V_{d}}{d t} & = & -V_{d}+ \lfloor y(t) \rfloor_{0} \\ + \label{eq:Noise_split_intrinsic} + \tau_{m} \frac{d V_{m}}{d t} & = & - V_{m} + \mu + \alpha V_{d} - A + \sqrt{2D \, c_{\rm{noise}}}\;\xi(t) +\end{eqnarray} +Both, the reduced intrinsic noise and the RAM stimulus, need to replace the original intrinsic noise. Because the RAM stimulus is band-limited and undergoes some transformations before it is added to the reduced intrinsic noise, it is not \textit{a priori} clear, what the amplitude of the RAM should be. We bisected the amplitude of $s_\xi(t)$, until the CV of the resulting interspike intervals matched the one of the original model's baseline activity. The second-order cross-spectra, \eqnref{eq:crosshigh}, were computed between the RAM stimulus $s_{\xi}(t)$ and the spike train $x(t)$ it evoked. In this way, the effective signal-to-noise ratio can be increased while maintaining the total noise in the system. + +%\bibliographystyle{apalike}%alpha}%}%alpha}%apalike} +\bibliography{journalsabbrv,references} +% \bibliographystyle{apalike} %or any other style you like +%\bibliography{references} +%\bibliography{journalsabbrv,references} + + +\setcounter{figure}{0} +\renewcommand{\thefigure}{S\arabic{figure}} + +\newpage + +\section{Supporting information} + +\subsection{S1 Second-order susceptibility of high-CV P-unit} +CVs in P-units can range up to 1.5 \citep{Grewe2017, Hladnik2023}. We show the same analysis as in \figrefb{fig:punit} for an example higher-CV P-unit. Similar to the low-CV cell, high-CV P-units fire at multiples of the EOD period (\subfigrefb{fig:punithighcv}{A}). In contrast to low-CV P-units, however, the higher CV characterizes the noisier baseline firing pattern and the peak at \fbase{} is less pronounced in the power spectrum of the baseline activity (\subfigrefb{fig:punithighcv}{B}). High-CV P-units do not exhibit a clear nonlinear structure related to \fbase{} neither in the second-order susceptibility matrices (\subfigrefb{fig:punithighcv}{E--F}), nor in the projected diagonals (\subfigrefb{fig:punithighcv}{G}). The overall level of nonlinearity, however, shows the same dependence on the stimulus contrast. It is much reduced for high-contrast stimuli that drive the neuron much stronger (\subfigrefb{fig:punithighcv}{F}). + +\label{S1:highcvpunit} +\begin{figure*}[!ht] +\includegraphics[width=\columnwidth]{cells_suscept_high_CV.pdf} + \caption{\label{fig:punithighcv} Response of a noisy P-units (cell ``2018-08-24-af") with a relatively high baseline CV of 0.34 to RAM stimuli with two different contrasts. \figitem{A} Interspike intervals (ISI) distribution during baseline. \figitem{B} Baseline power spectrum. \figitem{C} Top: EOD carrier (gray) with RAM (red). Center: Spike trains in response to the 5\,\% RAM contrast. Bottom: Spike trains in response to the 10\,\% RAM contrast. \figitem{D} First-order susceptibility (\eqnref{linearencoding_methods}). \figitem{E} Absolute value $|\chi_2(f_1, f_2)|$ of the second-order susceptibility, \eqnref{eq:susceptibility}, for the 5\,\% RAM contrast. Pink lines -- edges of the structure when \fone, \ftwo{} or \fsum{} are equal to \fbase{}. \figitem{F} $|\chi_2(f_1, f_2)|$ for the 10\,\% RAM contrast. \figitem{G} Projected diagonals, calculated as the mean of the anti-diagonals of the matrices in \panel{E--F}. Gray dots: \fbase{}. Dashed lines: Medians of the projected diagonals.} +\end{figure*} + + +\begin{figure*}[t] + \includegraphics[width=\columnwidth]{modelsusceptovern.pdf} + \caption{\label{fig:trialnr} Dependence of the estimate of the second-order susceptibility on the number of FFT segments $\n$. \figitem[i]{A} -- \figitem[iv]{A} Second-order susceptibilities estimated from an increasing number of segments $N=10, 100, 1000$ and $10^6$ as indicated. Shown are simulations of the P-unit model cell ``2017-07-18-ai'' (table~\ref{modelparams}) in the noise-split configuration (limit to vanishing external RAM signal, see \figrefb{fig:noisesplit}). \figitem[v]{A} Distribution of second-order susceptibility values as a function of simulated segments. See \panel[iv]{E} for a legend of the percentiles. Here, the estimates converge from about $N=10^4$ segments on. \figitem{B--D} Same for model cells ``2012-12-13-ao'', ``2012-12-20-ac'', and ``2013-01-08-ab'', respectively, same models as in \figrefb{fig:modelsusceptcontrasts}. \figitem{E} Dependence of the estimate of the second-order susceptibility on the number segments for four different contrasts of external RAM stimuli as indicated. Same model cell as in \panel{A}. \figitem[i]{E} Noise-split configuration without additional external RAM stimulus ($c=0$\,\%). Here, the RAM stimulus that was used to estimate the second-order susceptibility replaced $90$\,\% of the intrinsic noise and had a contrast of $10.6$\,\%. Same as \panel[v]{A}, but with a different range of the $y$-axis. \figitem[ii]{E} For a low stimulus contrast of $c=1\,\%$, the estimate does not converge yet even for $N=10^7$ segments. \figitem[iii]{E} For $c=3$\,\% the estimate just starts to converge at $N=10^6$ segments. \figitem[iv]{E} At $c=10$\,\% the situation is similar to the noise split, because similarly strong RAM stimuli were used for estimating the second-order susceptibility.} +\end{figure*} + +\end{document} diff --git a/references.bib b/references.bib new file mode 100644 index 0000000..f52f017 --- /dev/null +++ b/references.bib @@ -0,0 +1,7087 @@ +% Encoding: UTF-8 + +@article{Abel2009, + title={{Sensitive response to low-frequency cochlear distortion products in the auditory midbrain}}, + author={Abel, Cornelius and K\"ossl, Manfred}, + journal={J Neurophysiol}, + volume={101}, + number={3}, + pages={1560--1574}, + year={2009}, + publisher={American Physiological Society} +} + +@article{Adelson1985, + title={{Spatiotemporal energy models for the perception of motion}}, + author={Adelson, Edward H and Bergen, James R}, + journal={Journal of the Optical Society of America}, + volume={2}, + number={2}, + pages={284--299}, + year={1985}, + publisher={Optical Society of America} +} + +@article{Aertsen1981, + title={{The spectro-temporal receptive field: a functional characteristic of auditory neurons}}, + author={Aertsen, Ad M H J and Johannesma, P I M}, + journal={Biological Cybernetics}, + volume={42}, + number={2}, + pages={133--143}, + year={1981}, + publisher={Springer} +} + +@incollection{Baker2019, +author="Baker, Clare V. 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Taken together, these support the hypothesis that electroreceptors evolved in the vertebrate ancestor via the diversification of lateral line hair cells.", +isbn="978-3-030-29105-1", +doi="10.1007/978-3-030-29105-1_2", +url="https://doi.org/10.1007/978-3-030-29105-1_2" +} + +@article{Barnett1971, + title={Bispectrum analysis of electroencephalogram signals during waking and sleeping}, + author={Barnett, TP and Johnson, LC and Naitoh, P and Hicks, N and Nute, C}, + journal={Science}, + volume={172}, + number={3981}, + pages={401--402}, + year={1971}, + publisher={American Association for the Advancement of Science} +} + +@article{Bullock1997, + title={Bicoherence of intracranial {EEG} in sleep, wakefulness and seizures}, + author={Bullock, TH and Achimowicz, JZ and Duckrow, RB and Spencer, SS and Iragui-Madoz, VJ}, + journal={Electroencephalography and clinical Neurophysiology}, + volume={103}, + number={6}, + pages={661--678}, + year={1997}, + publisher={Elsevier} +} + +@ARTICLE{Aguilera2003, + AUTHOR = {Pedro A. Aguilera and Angel A. Caputi}, + TITLE = {{Electroreception in \textit{G. carapo}: detection of changes in waveform of the electrosensory signals.}}, + JOURNAL = {J Exp Biol}, + YEAR = {2003}, + VOLUME = {206}, + PAGES = {989--998} +} + + +@Article{Akre2010, + Title = {{Complexity Increases Working Memory for Mating Signals.}}, + Author = {Karin L. Akre and Michael J. Ryan}, + Journal = CurrBiol, + Year = {2010}, + Pages = {502-505}, + Volume = {20} +} + + +@Article{Albert2001, +author = {Albert, James}, +year = {2001}, +month = {01}, +pages = {}, +title = {{Species diversity and phylogenetic systematics of American knifefishes (Gymnotiformes, Teleostei)}}, +volume = {190}, +pages = {1-127}, +journal = {Miscellaneous Publications Museum of Zoology University of Michigan}, +} + + + + +@ARTICLE{Alda2013, + AUTHOR = { Fernando Alda and Sophie Picq and Luis Fernando De Le\'on and Rigoberto Gonz\'alez and Henriette Walz and Eldredge Bermingham and R\"udiger Krahe}, + TITLE = {{First record of \textit{Gymnotus henni} ({Albert}, {Crampton} and {Maldonado}, 2003) in Panama: Phylogenetic position and electric signal characterization.}}, + JOURNAL = {Check List}, + YEAR = {2013}, + VOLUME = {9}, + PAGES = {655--659} +} + + +@techreport{Amidror2015Consonance, + title={{Analytic derivation of the (k/j)-order modulation envelopes in the sum of two mistuned (co) sine waves}}, + author={Amidror, Isaac}, + year={2015} +} + +@ARTICLE{Ammari2014, + AUTHOR = {Habib Ammari and Thomas Boulier and Josselin Garnier and Han Wang}, + TITLE = {{Shape recognition and classification in electro-sensing.}}, + JOURNAL = {Proceedings of the National Academy of Sciences}, + YEAR = {2014}, + VOLUME = {111}, + PAGES = {11652--11657} +} + +@ARTICLE{Ammari2017, + AUTHOR = {Habib Ammari and Thomas Boulier and Josselin Garnier and Han Wang}, + TITLE = {{Mathematical modelling of the electric sense of fish: the role of multi-frequency measurements and movement.}}, + JOURNAL = {Bioinspir Biomim}, + YEAR = {2017}, + VOLUME = {12}, + PAGES = {025002} +} + +@Article{Amoore1986, + title={{Effects of chemical exposure on olfaction in humans}}, + author={Amoore, JE}, + journal={Toxicology of the Nasal Passages}, + pages={155--190}, + year={1986}, + publisher={Hemisphere Publishing Corporation, Washington, DC} +} + +@Article{Anderson2014, + Title = {{Toward a Science of Computational Ethology}}, + Author = {Anderson, DJ and Perona, P}, + Journal = Neuron, + Year = {2014}, + Number = {1}, + Pages = {18--31}, + Volume = {84} +} + +@article{Arendt2008, + title={{Convergence and parallelism reconsidered: what have we learned about the genetics of adaptation?}}, + author={Arendt, Jeff and Reznick, David}, + journal={Trends in Ecology \& Evolution}, + volume={23}, + number={1}, + pages={26--32}, + year={2008}, + publisher={Elsevier} +} + +@ARTICLE{Arnegard2005, + AUTHOR = {Matthew E. Arnegard and Bruce A. Carlson}, + TITLE = {{Electric organ discharge patterns during group hunting by a mormyrid fish.}}, + JOURNAL = ProcRSocLondBBiolSci, + YEAR = {2005}, + VOLUME = {272}, + PAGES = {1305--1314} +} + +@ARTICLE{Arnegard2006, + AUTHOR = {Matthew E. Arnegard and B. Scott Jackson and Carl D. Hopkins}, + TITLE = {{Time-domain signal divergence and discrimination without receptor modification in sympatric morphs of electric fishes.}}, + JOURNAL = {J Exp Biol}, + YEAR = {2006}, + VOLUME = {209}, + PAGES = {2182--2198} +} + +@ARTICLE{Arnegard2010, + AUTHOR = {Matthew E. Arnegard and Peter B. McIntyre and Luke J. Harmon and Miriam L. Zelditch and William G. R. Crampton and Justin K. Davis and John P. Sullivan and S\'ébastien Lavou\'é and +Carl D. Hopkins}, + TITLE = {{Sexual signal evolution outpaces ecological divergence during electric fish species radiation.}}, + JOURNAL = {American Naturalist}, + YEAR = {2010}, + VOLUME = {176}, + PAGES = {335--356} +} + +@Article{Arnold1994, + Title = {{Is there a Unifying Concept of Sexual Selection that Applies to Both Plants and Animals?}}, + Author = {Stevan J. Arnold}, + Journal = {The American Naturalist}, + Year = {1994}, + Pages = {S1-S12}, + Volume = {144}, + + Doi = {10.2307/2462726}, + Owner = {raab}, + Timestamp = {2020.01.30} +} + +@article{Arthur1971, + title={{Properties of ``two-tone inhibition" in primary auditory neurones}}, + author={Arthur, RM and Pfeiffer, RR and Suga, N}, + journal={J Physiol}, + volume={212}, + number={3}, + pages={593--609}, + year={1971}, + publisher={Wiley Online Library} +} + +@Article{Ashida2011, + Title = {{Sound localization: Jeffress and beyond.}}, + Author = {Go Ashida and Katherine E Carr}, + Journal = CurrOpinNeurobiol, + Year = {2011}, + Pages = {745-751}, + Volume = {21} +} + +@ARTICLE{Assad1999, + AUTHOR = {Christopher Assad and Brian Rasnow and Philip K. Stoddard}, + TITLE = {{Electric organ discharges and electric images during electrolocation.}}, + JOURNAL = {J Exp Biol}, + YEAR = {1999}, + VOLUME = {202}, + PAGES = {1185--1193} +} + +@InProceedings{Attias1997, + Title = {{Temporal Low-Order Statistics of Natural Sounds}}, + Author = {H. Attias and C. E. Schreiner}, + Booktitle = {Advances in Neural Information Processing Systems}, + Year = {1997}, + Editor = {Michael C. Mozer and Michael {I}. Jordan and Thomas Petsche}, + Pages = {27}, + Publisher = {The {MIT} Press}, + Volume = {9} +} + +@Article{Attick1991, + Title = {{Could information theory provide an ecological theory of sensory processing?}}, + Author = {Joseph J. Attick}, + Journal = Network, + Year = {1991}, + Pages = {213-251}, + Volume = {3} +} + +@article{Audouze2014, + title={{Identification of odorant-receptor interactions by global mapping of the human odorome}}, + author={Audouze, Karine and Tromelin, Anne and Le Bon, Anne Marie and Belloir, Christine and Petersen, Rasmus Koefoed and Kristiansen, Karsten and Brunak, S{\o}ren and Taboureau, Olivier}, + journal={PLoS One}, + volume={9}, + number={4}, + pages={e93037}, + year={2014}, + publisher={Public Library of Science San Francisco, USA} +} + +@Article{Averbeck2006, + title={{Neural correlations, population coding and computation}}, + author={Averbeck, Bruno B and Latham, Peter E and Pouget, Alexandre}, + journal={Nature Reviews Neuroscience}, + volume={7}, + number={5}, + pages={358--366}, + year={2006}, + publisher={Nature Publishing Group UK London} +} + +@article{Avoli1989, + title={{Electrophysiological properties and synaptic responses in the deep layers of the human epileptogenic neocortex in vitro}}, + author={Avoli, M and Olivier, A}, + journal={J Neurophysiol}, + volume={61}, + number={3}, + pages={589--606}, + year={1989} +} + +@ARTICLE{Babineau2006, + AUTHOR = {David Babineau and Andr\'e Longtin and John E. Lewis}, + TITLE = {{Modeling the electric field of weakly electric fish.}}, + JOURNAL = {J Exp Biol}, + YEAR = {2006}, + VOLUME = {209}, + PAGES = {3636--3651} +} + +@ARTICLE{Babineau2007, + AUTHOR = {David Babineau and Andr\'e Longtin and John E. Lewis}, + TITLE = {{Spatial acuity and prey detection in weakly electric fish.}}, + JOURNAL = {PLoS Comput Biol}, + YEAR = {2007}, + VOLUME = {3}, + PAGES = {e38} +} + +@article{Bach2008, + title={{Rising sound intensity: an intrinsic warning cue activating the amygdala}}, + author={Bach, Dominik R and Sch{\"a}chinger, Hartmut and Neuhoff, John G and Esposito, Fabrizio and Salle, Francesco Di and Lehmann, Christoph and Herdener, Marcus and Scheffler, Klaus and Seifritz, Erich}, + journal={Cerebral Cortex}, + volume={18}, + number={1}, + pages={145--150}, + year={2008}, + publisher={Oxford University Press} +} + + +@ARTICLE{Bacher1983, + AUTHOR = {M. Bacher}, + TITLE = {{A new method for the simulation of electric fields, generated by electric fish, and their distorsions by objects}}, + JOURNAL = BiolCybern, + YEAR = {1983}, + VOLUME = {47}, + PAGES = {51--58} +} + +@Article{Baktoft2015, + Title = {{Performance Assessment of Two Whole-Lake Acoustic Positional Telemetry Systems - Is Reality Mining of Free-Ranging Aquatic Animals Technologically Possible?}}, + Author = {Baktoft, Henrik and Zajicek, Petr and Klefoth, Thomas and Svendsen, Jon C. and Jacobsen, Lene and Pedersen, Martin W{\ae}ver and March Morla, David and Skov, Christian and Nakayama, Shinnosuke and Arlinghaus, Robert}, + Journal = PLOSOne, + Year = {2015}, + Number = {5}, + Pages = {1-20}, + Volume = {10}, + Doi = {10.1371/journal.pone.0126534}, + Publisher = {Public Library of Science}, + Timestamp = {2020.02.11} +} + +@article{Ball1971, + title={{Infant responses to impending collision: optical and real}}, + author={Ball, William and Tronick, Edward}, + journal={Science}, + volume={171}, + number={3973}, + pages={818--820}, + year={1971}, + publisher={American Association for the Advancement of Science} +} + +@Article{Baluch2011, + Title = {{Mechanisms of top-down attention.}}, + Author = {Farhan Baluch and Laurent Itti}, + Journal = TINS, + Year = {2011}, + Number = {4}, + Pages = {210-224}, + Volume = {34} +} + +@article{Barayeu2023, +title = {Beat encoding at mistuned octaves within single electrosensory neurons}, +journal = {iScience}, +volume = {26}, +number = {7}, +pages = {106840}, +year = {2023}, +issn = {2589-0042}, +doi = {https://doi.org/10.1016/j.isci.2023.106840}, +url = {https://www.sciencedirect.com/science/article/pii/S2589004223009173}, +author = {Alexandra Barayeu and Ramona Schäfer and Jan Grewe and Jan Benda}, +keywords = {Behavioral neuroscience, Animal science, Modeling signal processing system}, +abstract = {Summary +Beats are slow periodic amplitude modulations resulting from the superposition of two spectrally close periodic signals. The difference frequency between the signals sets the frequency of the beat. A field study in the electric fish Apteronotus rostratus showed the behavioral relevance of very high difference frequencies. Contrary to expectations from previous studies, our electrophysiological data show strong responses of p-type electroreceptor afferents whenever the difference frequency approaches integer multiples (mistuned octaves) of the fish’s own electric field frequency (carrier). Mathematical reasoning and simulations show that common approaches to extract amplitude modulations, such as Hilbert transform or half-wave rectification, are not sufficient to explain the responses at carrier octaves. Instead, half-wave rectification needs to be smoothed out, for example by a cubic function. Because electroreceptive afferents share many properties with auditory nerve fibers, these mechanisms may underly the human perception of beats at mistuned octaves as described by Ohm and Helmholtz.} +} + +@article{Barayeu2024, + title={Bursts boost nonlinear encoding in electroreceptor afferents}, + author={Barayeu, Alexandra and Schlungbaum, Maria and Lindner, Benjamin and Grewe, Jan and Benda, Jan}, + journal={bioRxiv}, + pages={2024--06}, + year={2024}, + publisher={Cold Spring Harbor Laboratory} +} + +@Article{Barber2000, + Title = {{The importance of stable schooling: do familiar sticklebacks stick together?}}, + Author = {Barber, Iain and Ruxton, Graeme D}, + Journal = ProcRSocLondBBiolSci, + Year = {2000}, + Number = {1439}, + Pages = {151-155}, + Volume = {267}, + + Doi = {10.1098/rspb.2000.0980}, + Owner = {raab}, + Timestamp = {2020.01.27} +} + +@article{Barlow1957, + title={{Change of organization in the receptive fields of the cat's retina during dark adaptation}}, + author={Barlow, HB and Fitzhugh, Roo and Kuffler, SW}, + journal={J Physiol}, + volume={137}, + number={3}, + pages={338}, + year={1957}, + publisher={Wiley-Blackwell} +} + +@InCollection{Barlow1961, + Title = {{Possible principles underlying the transformation of sensory messages.}}, + Author = {H. B. Barlow}, + Booktitle = {Sensory Communication}, + Publisher = {MIT Press}, + Year = {1961}, + + Address = {Cambridge}, + Editor = {W. Rosenblith}, + Pages = {217--234} +} + +@article{Barlow1972, + title={{Single units and sensation: a neuron doctrine for perceptual psychology?}}, + author={Barlow, Horace B}, + journal={Perception}, + volume={1}, + number={4}, + pages={371--394}, + year={1972}, + publisher={SAGE Publications Sage UK: London, England} +} + +@Article{Barlow2001a, + Title = {Redundancy reduction revisited.}, + Author = {Horace Barlow}, + Journal = Network, + Year = {2001}, + Pages = {241--253}, + Volume = {12} +} + + +@Article{Bastian1980, + Title = {{Neural Correlates of the Jamming Avoidance Response of \textit{{E}genmannia}.}}, + Author = {Joseph Bastian and Walter Heiligenberg}, + Journal = JCompPhysiolA, + Year = {1980}, + Pages = {135--152}, + Volume = {136} +} + +@article{Bastian1981, + title={Electrolocation}, + author={Bastian, Joseph}, + journal={J Comp Physiol}, + volume={144}, + number={4}, + pages={465--479}, + year={1981}, + publisher={Springer} +} + +@Article{Bastian1981a, + Title = {Electrolocation {I}. {H}ow Electroreceptors of \textit{{A}pteronotus albifrons} Code for Moving Objects and Other Electrical Stimuli.}, + Author = {Joseph Bastian}, + Journal = {J Comp Physiol}, + Year = {1981}, + Pages = {465--479}, + Volume = {144}, +} + +@Article{Bastian1981b, + Title = {Electrolocation {II}. {The} Effects of Moving Objects and Other Electrical Stimuli on the Activities of Two Categories of Posterior Lateral Line Lobe Cells in \textit{Apteronotus albifrons}.}, + Author = {Joseph Bastian}, + Journal = {Journal of Comparative Physiology}, + Year = {1981}, + Pages = {481--494}, + Volume = {144} +} + + +@Article{Bastian1985, + Title = {Gain Control in the Electrosensory System Mediated by Descending Inputs to the Electrosensory Lateral Line Lobe.}, + Author = {Joseph Bastian}, + Journal = JNeurosci, + Year = {1986}, + Number = {2}, + Pages = {553--562}, + Volume = {6} +} + +@article{Bastian1987, +author = {Joseph Bastian}, +title = {Electrolocation in the presence of jamming signals: behavior}, +journal = JCompPhysiolA, +year = {1987}, +volume = {161}, +pages = {811--824} +} + +@Article{Bastian1990, + Title = {{Descending Control of Electroreception. I. Properties of Nucleus Praeeminentialis Neurons Projecting Indirectly to the Electrosensory Lateral Line Lobe.}}, + Author = {Joseph Bastian and Bradford Bratton}, + Journal = JNeurosci, + Year = {1990}, + Number = {4}, + Pages = {1226-1240}, + Volume = {10} +} + +@Article{Bastian1991, + title={Morphological correlates of pyramidal cell adaptation rate in the electrosensory lateral line lobe of weakly electric fish}, + author={Bastian, Joseph and Courtright, Jay}, + journal={Journal of Comparative Physiology A}, + volume={168}, + pages={393--407}, + year={1991}, + publisher={Springer} +} + +@Article{Bastian1993a, + Title = {The role of amino acid neurotransmitters in the descending control of electroreception.}, + Author = {J. Bastian}, + Journal = JCompPhysiolA, + Year = {1993}, + Pages = {409-423}, + Volume = {172} +} + + +@Article{Bastian1993b, + Title = {Commisural neurons of the electrosensory lateral line lob of \textit{Apteronotus leptorhynchus}: morphological and physiological characteristics.}, + Author = {J. Bastian and J. Courtright and J. Crawford}, + Journal = JCompPhysiolA, + Year = {1993}, + Pages = {257-274}, + Volume = {173} +} + +@Article{Bastian1995, + Title = {Pyramidal-cell plasticity in weakly electric fish: a mechanism for attenuating responses to reafferent electrosensory inputs.}, + Author = {J. Bastian}, + Journal = JCompPhysiolA, + Year = {1995}, + Pages = {63-78}, + Volume = {176} +} + + + +@Article{Bastian1996a, + Title = {{Plasticity in an Electrosensory System. I. General Features of a Dynamic Sensory Filter.}}, + Author = {Joseph Bastian}, + Journal = {Journal of Neurophysiology}, + Year = {1996}, + Number = {4}, + Pages = {2483-2496}, + Volume = {76} +} + +@Article{Bastian1996b, + Title = {{Plasticity in an Electrosensory System. II. Postsynaptic Events Associated With a Dynamic Sensory Filter.}}, + Author = {Joseph Bastian}, + Journal = {Journal of Neurophysiology}, + Year = {1996}, + Number = {4}, + Pages = {2497-2507}, + Volume = {76} +} + +@Article{Bastian1998, + Title = {{Modulation of Calcium-Dependent Postsynaptic Depression Contributes to an Adaptive Sensory Filter.}}, + Author = {Joseph Bastian}, + Journal = {Journal of Neurophysiology}, + Year = {1998}, + Pages = {3352-3355}, + Volume = {80} +} + +@Article{Bastian2001, + Title = {Dentritic Modulation of Burst-Like Firing in Sensory Neurons.}, + Author = {Joseph Bastian and Jerry Nguyenkim}, + Journal = {Journal of Neurophysiology}, + Year = {2001}, + Number = {1}, + Pages = {10-22}, + Volume = {85} +} +@article{Bastian2002, + title={Receptive field organization determines pyramidal cell stimulus-encoding capability and spatial stimulus selectivity}, + author={Bastian, Joseph and Chacron, Maurice J and Maler, Leonard}, + journal={Journal of Neuroscience}, + volume={22}, + number={11}, + pages={4577--4590}, + year={2002}, + publisher={Soc Neuroscience} +} + +@Article{Bastian2004, + title={Plastic and nonplastic pyramidal cells perform unique roles in a network capable of adaptive redundancy reduction}, + author={Bastian, Joseph and Chacron, Maurice J and Maler, Leonard}, + journal={Neuron}, + volume={41}, + number={5}, + pages={767--779}, + year={2004}, + publisher={Elsevier} +} + +@article{Batra1989, + title={Temporal coding of envelopes and their interaural delays in the inferior colliculus of the unanesthetized rabbit}, + author={Batra, R and Kuwada, S and Stanford, TR}, + journal={Journal of Neurophysiology}, + volume={61}, + number={2}, + pages={257--268}, + year={1989} +} + +@Article{Behrend1977, + Title = {Processing information carried in a high frequency wave: properties of cerebellar units in a high frequency electric fish.}, + Author = {Konstantin Behrend}, + Journal = JCompPhysiol, + Year = {1977}, + Pages = {357-371}, + Volume = {118} +} + +@article{Beiran2018, + title={Coding of time-dependent stimuli in homogeneous and heterogeneous neural populations}, + author={Beiran, Manuel and Kruscha, Alexandra and Benda, Jan and Lindner, Benjamin}, + journal={Journal of Computational Neuroscience}, + volume={44}, + pages={189--202}, + year={2018}, + publisher={Springer} +} + +@article{Beiran2018coding, + title={Coding of time-dependent stimuli in homogeneous and heterogeneous neural populations}, + author={Beiran, Manuel and Kruscha, Alexandra and Benda, Jan and Lindner, Benjamin}, + journal={Journal of Computational Neuroscience}, + volume={44}, + pages={189--202}, + year={2018}, + publisher={Springer} +} + +@ARTICLE{Belbenoit1970, + AUTHOR = {Pierre Belbenoit}, + TITLE = {Conditionnement instrumental de l'\'electroperception des objets chez \textit{Gnathonemus petersii} ({Mormyridae}, {Teleostei}, {Pisces}).}, + JOURNAL = {Z vergl Physiol}, + YEAR = {1970}, + VOLUME = {67}, + PAGES = {192--204} +} + +@ARTICLE{Bell1976, + AUTHOR = {C. C. Bell and J. Bradbury and C. J. Russell}, + TITLE = {The electric organ of a mormyrid as a current and voltage source.}, + JOURNAL = JCompPhysiol, + YEAR = {1976}, + VOLUME = {110}, + PAGES = {65--88} +} + + +@ARTICLE{Benda2003, + AUTHOR = {Jan Benda and Andreas V. M. Herz}, + TITLE = {A universal model for spike-frequency adaptation.}, + YEAR = {2003}, + JOURNAL = NeuralComput, + VOLUME = {15}, + NUMBER = {11}, + PAGES = {2523--2564}, + PDF = {Benda2003a.pdf}, + URL = {http://neco.mitpress.org/cgi/content/abstract/15/11/2523} +} + +@ARTICLE{Benda2005, + AUTHOR = {Jan Benda and Andr\'e Longtin and Leonard Maler}, + TITLE = {Spike-frequency adaptation separates transient communication signals from background oscillations.}, + YEAR = {2005}, + JOURNAL = {J Neurosci}, + VOLUME = {25}, + NUMBER = {9}, + PAGES = {2312--2321} } + + +@ARTICLE{Benda2006, + AUTHOR = {Jan Benda and Andr\'e Longtin and Leonard Maler}, + TITLE = {A synchronization-desynchronization code for natural communication signals.}, + YEAR = {2006}, + JOURNAL = Neuron, + VOLUME = {52}, + PAGES = {347--358} } + +@ARTICLE{Benda2010, + AUTHOR = {Jan Benda and Leonard Maler and Andr\'e Longtin}, + TITLE = {Linear versus Nonlinear Signal Transmission in Neuron Models + with Adaptation-Currents or Dynamic Thresholds.}, + YEAR = {2010}, + JOURNAL = {J Neurophysiol}, + VOLUME = {104}, + PAGES = {2806-2820} } + +@incollection{Benda2013, + author = {Benda, Jan and Grewe, Jan and Krahe, R{\~A}ƒ{\^A}ƒ{\~A}‚{\^A}ƒ{\~A}ƒ{\^A}‚{\~A}‚{\^A}¼diger}, + booktitle = {Animal Communication and Noise}, + doi = {10.1007/978-3-642-41494-7_12}, + editor = {Brumm, Henrik}, + isbn = {978-3-642-41493-0}, + language = {English}, + pages = {331-372}, + publisher = {Springer Berlin Heidelberg}, + refid = {876}, + series = {Animal Signals and Communication}, + timestamp = {2014.02.03}, + title = {Neural Noise in Electrocommunication: From Burden to Benefits}, + url = {http://dx.doi.org/10.1007/978-3-642-41494-7_12}, + volume = {2}, + year = {2013}, + bdsk-url-1 = {http://dx.doi.org/10.1007/978-3-642-41494-7_12}} + +@incollection{Benda2020, + title={The physics of electrosensory worlds.}, + author={Benda, Jan}, + editor={Fritsch, B. and Bleckmann, H}, + volume={7}, + pages={228--254}, + year={2020}, + publisher={Elsevier, Academic Press}, + booktitle={The Senses: a Comprehensive Reference} +} + +@article{Benda2021, + title={Neural adaptation}, + author={Benda, Jan}, + journal={Current Biology}, + volume={31}, + number={3}, + pages={R110--R116}, + year={2021}, + publisher={Elsevier} +} + +@ARTICLE{Bennett1970, + AUTHOR = {Michael V. L. Bennett}, + TITLE = {Comparative physiology: electric organs.}, + JOURNAL = AnnuRevPhysiol, + YEAR = {1970}, + VOLUME = {32}, + PAGES = {471--528} +} + +@ARTICLE{Bennett1971, + AUTHOR = {Michael V. L. Bennett}, + TITLE = {Electroreception.}, + JOURNAL = {Fish Physiology}, + YEAR = {1971}, + VOLUME = {5}, + PAGES = {493--574} +} + +@Article{Berdahl2018, + author = {Berdahl, Andrew M. and Kao, Albert B. and Flack, Andrea and Westley, Peter A. H. and Codling, Edward A. and Couzin, Iain D. and Dell, Anthony I. and Biro, Dora}, + title = {Collective animal navigation and migratory culture: from theoretical models to empirical evidence}, + journal = PhilTransRSocLondBBiolSci, + year = {2018}, + volume = {373}, + pages = {20170009}, + doi = {10.1098/rstb.2017.0009} +} + +@Article{Berman1995, + title={Inositol 1, 4, 5-trisphosphate receptor localization in the brain of a weakly electric fish (\textit{Apteronotus leptorhynchus}) with emphasis on the electrosensory system}, + author={Berman, Neil J and Hincke, Maxwell T and Maler, Leonard}, + journal={Journal of comparative neurology}, + volume={361}, + number={3}, + pages={512--524}, + year={1995}, + publisher={Wiley Online Library} +} + +@article{Berman1998inhibition, + title={Inhibition evoked from primary afferents in the electrosensory lateral line lobe of the weakly electric fish \textit{(Apteronotus leptorhynchus)}.}, + author={Berman, Neil J and Maler, Leonard}, + journal={Journal of Neurophysiology}, + volume={80}, + number={6}, + pages={3173--3196}, + year={1998} +} + +@article{Berman1999, + title={Neural architecture of the electrosensory lateral line lobe: adaptations for coincidence detection, a sensory searchlight and frequency-dependent adaptive filtering}, + author={Berman, Neil J and Maler, Leonard}, + journal={Journal of Experimental Biology}, + volume={202}, + number={10}, + pages={1243--1253}, + year={1999}, + publisher={The Company of Biologists Ltd} +} + +@Article{Betsch2004, + Title = {The world from a cat{'}s perspective --- statistics of natural videos.}, + Author = {Belinda Y. Betsch and Wolfgang Einh\"auser and Konrad P. K\"ording and Peter K\"onig}, + Journal = BiolCybern, + Year = {2004}, + Pages = {41-50}, + Volume = {90} +} + +@Article{Bilde2007, + Title = {Survival benefits select for group living in a social spider despite reproductive costs}, + Author = {Bilde, T. and Coates, K. S. and Birkhofer, K. and Bird, T. and Maklakov, A. A. and Lubin, Y. and Avil\'es, L.}, + Journal = JEvolBiol, + Year = {2007}, + Number = {6}, + Pages = {2412-2426}, + Volume = {20}, + + Abstract = {Abstract The evolution of cooperation requires benefits of group living to exceed costs. Hence, some components of fitness are expected to increase with increasing group size, whereas others may decrease because of competition among group members. The social spiders provide an excellent system to investigate the costs and benefits of group living: they occur in groups of various sizes and individuals are relatively short-lived, therefore life history traits and Lifetime Reproductive Success (LRS) can be estimated as a function of group size. Sociality in spiders has originated repeatedly in phylogenetically distant families and appears to be accompanied by a transition to a system of continuous intra-colony mating and extreme inbreeding. The benefits of group living in such systems should therefore be substantial. We investigated the effect of group size on fitness components of reproduction and survival in the social spider Stegodyphus dumicola in two populations in Namibia. In both populations, the major benefit of group living was improved survival of colonies and late-instar juveniles with increasing colony size. By contrast, female fecundity, female body size and early juvenile survival decreased with increasing group size. Mean individual fitness, estimated as LRS and calculated from five components of reproduction and survival, was maximized for intermediate- to large-sized colonies. Group living in these spiders thus entails a net reproductive cost, presumably because of an increase in intra-colony competition with group size. This cost is traded off against survival benefits at the colony level, which appear to be the major factor favouring group living. In the field, many colonies occur at smaller size than expected from the fitness curve, suggesting ecological or life history constraints on colony persistence which results in a transient population of relatively small colonies.}, + Doi = {10.1111/j.1420-9101.2007.01407.x}, + Keywords = {cooperation, fitness components, lifetime reproductive success, multilevel selection, social spiders, Stegodyphus dumicola}, + Owner = {raab}, + Timestamp = {2020.01.21} +} + +@article{Birmingham1999, + title={Encoding of muscle movement on two time scales by a sensory neuron that switches between spiking and bursting modes}, + author={Birmingham, JT and Szuts, ZB and Abbott, LF and Marder, Eve}, + journal={Journal of Neurophysiology}, + volume={82}, + number={5}, + pages={2786--2797}, + year={1999}, + publisher={American Physiological Society Bethesda, MD} +} + +@ARTICLE{Black1970, + AUTHOR = {Patricia Black-Cleworth}, + TITLE = {The Role of electrical discharges in the non-reproductive social behaviour of \textit{Gymnotus carapo} ({Gymnotidae}, {Pisces}).}, + JOURNAL = {Animal Behaviour Monographs}, + YEAR = {1970}, + VOLUME = {3}, + PAGES = {1--78} +} + +@Article{Bleckmann1993, + Title = {The responses of peripheral and central mechanosensory lateral line units of weakly electric fish to moving objects.}, + Author = {H. Bleckmann and R. Zelick}, + Journal = JCompPhysiolA, + Year = {1993}, + Pages = {115-128}, + Volume = {172} +} + +@ARTICLE{Bleckmann2009, + AUTHOR = {Horst Bleckmann and Randy Zelick}, + TITLE = {Lateral line system of fish.}, + YEAR = {2009}, + JOURNAL = {Integrative Zoology}, + VOLUME = {4}, + PAGES = {13--25} } + +@Article{Blumstein2001, + Title = {Yellow-Footed Rock-Wallaby Group Size Effects Reflect A Trade-Off}, + Author = {Blumstein, Daniel T. and Daniel, Janice C. and Evans, Christopher S.}, + Journal = {Ethology}, + Year = {2001}, + Number = {7}, + Pages = {655-664}, + Volume = {107}, + Owner = {raab}, + Timestamp = {2020.01.21} +} + +@Article{Boerlin2013, + Title = {Predictive Coding of Dynamical Variables in Balanced Spiking Networks.}, + Author = {Martin Boerlin and Christian K. Machens and Sophie Den\`eve}, + Journal = {PLoS Computational Biology}, + Year = {2013}, + Number = {11}, + Pages = {e1003258}, + Volume = {9} +} + +@Article{Bol2011, + Title = {Frequency-Tuned Cerebellar Channels and Burst Induced {LTD} Lead to the Cancellation of Redundant Sensory Inputs.}, + Author = {Kieran Bol and Gary Marsat and Eric Harvey-Girard and Andr\'e Longtin and Leonard Maler}, + Journal = JNeurosci, + Year = {2011}, + Number = {30}, + Pages = {11028-11038}, + Volume = {31} +} + +@Article{Bol2013, + Title = {Modeling cancellation of periodic inputs with burst-{STDP} and feedback.}, + Author = {K. Bol and G. Marsat and J.F. Mejias and L. Maler and A. Longtin}, + Journal = NeuralNetw, + Year = {2013}, + Pages = {120-133}, + Volume = {47} +} + +@Article{Borst1999, + author = {Borst, A. and Theunissen, F.E.}, + journal = {Nature Neurosci.}, + keywords = {Information, Information Theory, neural code, review, theory}, + number = {11}, + owner = {grewe}, + pages = {947--957}, + refid = {216}, + timestamp = {2008.09.26}, + title = {Information theory and neural coding}, + volume = {2}, + year = {1999}} + +@Book{Bradbury2011, + Title = {Principles of animal communication}, + Author = {Bradbury, JW and Vehrencamp, SL}, + Publisher = {Sinauer}, + Year = {2011}, + + Address = {Sunderland}, + Edition = {2nd} +} + +@Article{Bratton1990, + Title = {Descending Control of Electroreception. {II.} Properties of Nucleus Praeeminentialis Neurons Projecting Directly to the Electrosensory Lateral Line Lobe.}, + Author = {Bradford Bratton and Joseph Bastian}, + Journal = JNeurosci, + Year = {1990}, + Number = {4}, + Pages = {1241-1253}, + Volume = {10} +} + + +@Article{Bretschneider1985, + Title = {Functioning of catfish electroreceptors: fractional order filtering and non-linearity.}, + Author = {F. Bretschneider and J.R. De Weille and J.F.L. Klis}, + Journal = CompBiochemPhysiol, + Year = {1985}, + Number = {2}, + Pages = {191-198}, + Volume = {80A} +} + +@incollection{Briand2016, + title={Taste perception and integration}, + author={Briand, Lo{\"\i}c and Salles, Christian}, + booktitle={Flavor}, + pages={101--119}, + year={2016}, + publisher={Elsevier} +} + +@Article{Brincat2004, + title={Underlying principles of visual shape selectivity in posterior inferotemporal cortex}, + author={Brincat, Scott L and Connor, Charles E}, + journal={Nature Neuroscience}, + volume={7}, + number={8}, + pages={880--886}, + year={2004}, + publisher={Nature Publishing Group US New York} +} + +@article{Brownell1990, + title={Outer hair cell electromotility and otoacoustic emissions}, + author={Brownell, William E}, + journal={Ear Hearing}, + volume={11}, + number={2}, + pages={82}, + year={1990}, + publisher={NIH Public Access} + } + +@ARTICLE{Budelli2000, + AUTHOR = {Ruben Budelli and Angel A. Caputi}, + TITLE = {The electric image in weakly electric fish: perception of objects of complex impedance.}, + JOURNAL = {Journal of Experimental Biology}, + YEAR = {2000}, + VOLUME = {203}, + PAGES = {481--492} +} + +@ARTICLE{Budelli2002, + AUTHOR = {R. Budelli and A. Caputi and L. Gomez and D. Rother and K. Grant}, + TITLE = {The electric image of \textit{Gnathonemus petersii}.}, + JOURNAL = {Journal of Physiology-Paris}, + YEAR = {2002}, + VOLUME = {96}, + PAGES = {421--429} +} + +@ARTICLE{Bullock1969, + AUTHOR = {Theodore H. Bullock}, + TITLE = {Species differences in effect of electroreceptor input on electric organ pacemakers and other aspects of behavior i +n electric fish.}, + JOURNAL = BrainBehavEvol, + YEAR = {1969}, + VOLUME = {2}, + PAGES = {85--118} +} + +@article{Bullock1970, + author = {Bullock, TH}, + journal = JGenPhysiol, + number = {5}, + pages = {565--584}, + title = {The reliability of neurons.}, + volume = {55}, + year = {1970} +} + +@Article{Bullock1972a, + Title = {The jamming avoidance response of high frequency electric fish. {I.} General Features.}, + Author = {Bullock, Th H and Hamstra, RH and Scheich, H}, + Journal = JCompPhysiol, + Year = {1972}, + Number = {1}, + Pages = {1--22}, + Volume = {77} +} + +@Article{Bullock1972b, + Title = {The jamming avoidance response of high frequency electric fish. {II.} {Quantitative} aspects.}, + Author = {Bullock, TH and H, RH and Scheich, H}, + Journal = JCompPhysiol, + Year = {1972}, + Number = {1}, + Pages = {23--48}, + Volume = {77} +} + +@ARTICLE{Bullock1972General, + AUTHOR = {Theodore H. Bullock and Robert H. Hamstra, Jr. and Henning Scheich}, + TITLE = {The jamming avoidance response of high frequency electric fish {I.} General features.}, + JOURNAL = JCompPhysiol, + YEAR = {1972}, + VOLUME = {77}, + PAGES = {1--22} +} + +@Article{Bullock1982, + Title = {Evolution of electroreception.}, + Author = {T.H. Bullock and R.G. Northcutt and D.A. Bodznick}, + Journal = TINS, + Year = {1982}, + Pages = {50-53}, + Volume = {5} +} + +@ARTICLE{Bullock1983, + AUTHOR = {T. H. Bullock and D. A. Bodznick and R. G. Northcutt}, + TITLE = {The phylogenetic distribution of electroreception: evidence for convergent evolution of a primitive vertebrate sense modality.}, + YEAR = {1983}, + JOURNAL = BrainResRev, + VOLUME = {6}, + PAGES = {25--46} } + +@book{Bullock2006, + title={Electroreception}, + author={Bullock, Theodore Holmes and Hopkins, Carl D and Fay, Richard R}, + volume={21}, + year={2006}, + publisher={Springer Science \& Business Media} +} + +@ARTICLE{Burham1969, + AUTHOR = {E. G. Burham and W. B. Huckaby and R. Gowdy and B. Burns}, + TITLE = {Microvolt electric signals from fishes and the environment.}, + JOURNAL = Science, + YEAR = {1969}, + VOLUME = {164}, + PAGES = {965--968} +} + +@article{Bushdid2014, + title={Humans can discriminate more than 1 trillion olfactory stimuli}, + author={Bushdid, Caroline and Magnasco, Marcelo O and Vosshall, Leslie B and Keller, Andreas}, + journal={Science}, + volume={343}, + number={6177}, + pages={1370--1372}, + year={2014}, + publisher={American Association for the Advancement of Science} +} + +@article{Cai1996, + title={Temporal patterns of the responses of auditory-nerve fibers to low-frequency tones}, + author={Cai, Yidao and Geisler, C Daniel}, + journal={Hearing Research}, + volume={96}, + number={1-2}, + pages={83--93}, + year={1996}, + publisher={Elsevier} +} + +@article{Caldwell1978, + title={New properties of rabbit retinal ganglion cells.}, + author={Caldwell, JH and Daw, NW}, + journal={The Journal of Physiology}, + volume={276}, + number={1}, + pages={257--276}, + year={1978}, + publisher={Wiley Online Library} +} + +@ARTICLE{Capurro1997, + AUTHOR = {A. Capurro and M. Reyes-Parada and D. Olazabal and R. Perrone and R. Silveira and O. Macadar}, + TITLE = {Aggressive behavior and jamming avoidance response in the weakly electric fish \textit{Gymnotus carapo}: effects of {3,4-Methylenedioxymethamphetamine} ({MDMA}).}, + JOURNAL = {Comp Biochem Physiol}, + YEAR = {1997}, + VOLUME = {188A}, + PAGES = {831--840} +} + +@ARTICLE{Caputi1998, + AUTHOR = {Angel A. Caputi and R. Budelli and K. Grant and C. C. Bell}, + TITLE = {The electric image in weakly electric fish: physical images of resistive objects in \textit{Gnathonemus petersii}.}, + JOURNAL = {Journal of Experimental Biology}, + YEAR = {2000}, + VOLUME = {203}, + PAGES = {481--492} +} + + +@ARTICLE{Caputi1998Brachy, + AUTHOR = {A. A. Caputi and A. C. Silva and O. Macadar}, + TITLE = {The electric organ discharge of \textit{Brachyhypopomus pinnicaudatus}. The effects of environmental variables on waveform generation.}, + JOURNAL = BrainBehavEvol, + YEAR = {1998}, + VOLUME = {52}, + PAGES = {148--158} +} + + +@ARTICLE{Caputi1999, + AUTHOR = {A. A. Caputi}, + TITLE = {The electric organ discharge of pulse gymnotiforms: the transformation of a simple +impulse into a complex spatiotemporal electromotor pattern.}, + JOURNAL = {Journal of Experimental Biology}, + YEAR = {1999}, + VOLUME = {202}, + PAGES = {1229--1241} +} + +@ARTICLE{Caputi2006, + AUTHOR = {A. A. Caputi and R. Budelli}, + TITLE = {Peripheral electrosensory imaging by weakly electric fish.}, + JOURNAL = JCompPhysiolA, + YEAR = {2006}, + VOLUME = {192}, + PAGES = {587--600} +} + +@ARTICLE{Caputi2008, + AUTHOR = {\'Angel A. Caputi and Mar\'ia E. Castell\'o and Pedro A. Aguilera and Carolina Pereira and Javier Nogueira and Alejo Rodr\'iguez-Cattaneo and Carolina Lezcano}, + TITLE = {Active electroreception in \textit{Gymnotus omari}: imaging, object discrimination, and early processing of actively generated signals.}, + JOURNAL = {Journal of Physiology-Paris}, + YEAR = {2008}, + VOLUME = {102}, + PAGES = {256--271} +} + +@article{Cariani2001, + title={Temporal coding of sensory information in the brain}, + author={Cariani, Peter A}, + journal={Acoustical Science and Technology}, + volume={22}, + number={2}, + pages={77--84}, + year={2001}, + publisher={ACOUSTICAL SOCIETY OF JAPAN} +} + +@ARTICLE{Carlson2000, + AUTHOR = {Bruce A. Carlson and Carls D. Hopkins and Peter Thomas}, + TITLE = {Androgen correlates of socially induced changes in the electric organ discharge waveform of a mormyrid fish.}, + JOURNAL = HormBehav, + YEAR = {2000}, + VOLUME = {38}, + PAGES = {177--186} +} + + + + + +@ARTICLE{Carlson2002, + AUTHOR = {Bruce A. Carlson}, + TITLE = {Electric signaling behavior and the mechanisms of electric organ discharge production in mormyrid fish.}, + JOURNAL = {Journal of Physiology-Paris}, + YEAR = {2002}, + VOLUME = {96}, + PAGES = {405--419} +} + +@ARTICLE{Carlson2011, + AUTHOR = {Bruce A. Carlson and Saad M. Hasan and Michael Hollmann and Derek B. Miller and Luke J. Harmon and Matthew E. Arnegard}, + TITLE = {Brain evolution triggers increased diversification of electric fishes.}, + JOURNAL = Science, + YEAR = {2011}, + VOLUME = {332}, + PAGES = {583--586} +} + + +@Article{Carlson2013, + Title = {From Sequence to Spike to Spark: Evo-devo-neuroethology of Electric Communication Mormyrid Fishes.}, + Author = {Bruce A Carlson and Jason R. Gallant}, + Journal = JNeuroGenetics, + Year = {2013}, + Number = {3}, + Pages = {106-129}, + Volume = {27} +} + +@Article{Carr1982, + Title = {Peripheral organization and central projections of the electrosensory nerves in gymnotiform fish.}, + Author = {C. E. Carr and L. Maler and E. Sas}, + Journal = {Journal of Comparative Neurology}, + Year = {1982}, + Pages = {139--153}, + Volume = {211} +} + +@Article{Carr1986, + title={Electroreception in gymnotiform fish: central anatomy and physiology}, + author={Carr, CE}, + journal={Electroreception}, + pages={319--373}, + year={1986}, + publisher={John Wiley} +} + +@article{Carriot2017, + title={Envelope statistics of self-motion signals experienced by human subjects during everyday activities: Implications for vestibular processing}, + author={Carriot, J{\'e}rome and Jamali, Mohsen and Cullen, Kathleen E and Chacron, Maurice J}, + journal={PLoS One}, + volume={12}, + number={6}, + pages={e0178664}, + year={2017}, + publisher={Public Library of Science San Francisco, CA USA} +} + +@ARTICLE{Castello2000, + AUTHOR = {Mar\'ia E. Castell\'o and Pedro A. Aguilera and Omar Trujillo-Cen\'oz and Angel A. Caputi}, + TITLE = {Electroreception in \textit{Gymnotus carapo}: pre-receptor processing and the distribution of electroreceptor types.}, + JOURNAL = {Journal of Experimental Biology}, + YEAR = {2000}, + VOLUME = {203}, + PAGES = {3279--3287} +} + +@Article{Catania2014, + Title = {The shocking predatory strike of the electric eel}, + Author = {Catania, KC}, + Journal = Science, + Year = {2014}, + Number = {6214}, + Pages = {1231--1234}, + Volume = {346} +} + +@Article{Catania2015a, + Title = {Electric eels use high-voltage to track fast-moving prey}, + Author = {Catania, KC}, + Journal = NatCommun, + Year = {2015}, + Pages = {8638}, + Volume = {6} +} + +@Article{Cattaneo1981, + title={Patterns in the discharge of simple and complex visual cortical cells}, + author={Cattaneo, A and Maffei, L and Morrone, Concetta}, + journal={Proceedings of the Royal Society of London. Series B. Biological sciences}, + volume={212}, + number={1188}, + pages={279--297}, + year={1981}, + publisher={The Royal Society London} +} + +@Article{Cavigelli1999, + Title = {Behavioural patterns associated with faecal cortisol levels in free-ranging female ring-tailed lemurs, {Lemur catta}}, + Author = {Sonia A. Cavigelli}, + Journal = AnimBehav, + Year = {1999}, + Number = {4}, + Pages = {935 - 944}, + Volume = {57}, + + Abstract = {The study of physiological stress and its context in free-ranging animals provides a means for understanding the challenges found in the natural habitat. Patterns of physiological stress in free-ranging animals have yet to be well characterized. Methodological difficulties in measuring physiological responses in the natural habitat have limited this area of research. In this research, physiological stress in free-ranging ring-tailed lemurs,Lemur catta, was estimated using a steroid-extraction method to measure cortisol levels from female faeces. Ten females were observed across two social groups in southwestern Madagascar during a 5-month period including portions of the annual wet and dry seasons. I used behavioural measures to estimate predation threat, food accessibility and individual dominance status, to determine whether these variables predict faecal cortisol levels. Faecal cortisol levels were relatively high during two distinct periods: one period coincided with late gestation and the other period corresponded with the end of the dry season, when high-intensity antipredatory behaviour and estimates of feeding effort were elevated. In addition, faecal cortisol measures were significantly correlated with dominance indices: high-index individuals had high cortisol values, and low-index individuals had low cortisol values. These results suggest that faecal cortisol measures can be used to assess seasonal and individual differences in adrenal activity in this lemurid primate, and that this measure could provide a means for quantifying physiological stress in free-ranging animals.}, + Owner = {raab}, + Timestamp = {2020.01.27} +} + +@article{Chacron2000, + title={Suprathreshold stochastic firing dynamics with memory in {P-type} electroreceptors}, + author={Chacron, Maurice J and Longtin, Andr{\'e} and St-Hilaire, Martin and Maler, Len}, + journal={Physical Review Letters}, + volume={85}, + number={7}, + pages={1576}, + year={2000}, + publisher={APS} +} + +@article{Chacron2001, + title={Negative interspike interval correlations increase the neuronal capacity for encoding time-dependent stimuli}, + author={Chacron, Maurice J and Longtin, Andre and Maler, Leonard}, + journal={J Neurosci}, + volume={21}, + number={14}, + pages={5328--5343}, + year={2001}, + publisher={Soc Neuroscience} +} + +@Article{Chacron2004, + title={To burst or not to burst?}, + author={Chacron, Maurice J and Longtin, Andr{\'e} and Maler, Leonard}, + journal={Journal of Computational Neuroscience}, + volume={17}, + pages={127--136}, + year={2004}, + publisher={Springer} +} + +@Article{Chacron2005, + title={Electroreceptor neuron dynamics shape information transmission}, + author={Chacron, Maurice J and Maler, Leonard and Bastian, Joseph}, + journal={Nature Neurosci}, + volume={8}, + number={5}, + pages={673--678}, + year={2005}, + publisher={Nature Publishing Group US New York} +} + +@Article{Chacron2006, + title={Nonlinear information processing in a model sensory system}, + author={Chacron, Maurice J}, + journal={J Neurophysiol}, + volume={95}, + number={5}, + pages={2933--2946}, + year={2006}, + publisher={American Physiological Society} +} + +@Article{Chagnaud2008, + Title = {Receptive field organization of electrosensory neurons in the paddlefish (\textit{Polyodon spathula}.}, + Author = {B.P. Chagnaud and L.A. Wilkens and M.H. Hofmann}, + Journal = JPhysiol, + Year = {2008}, + Pages = {246-255}, + Volume = {102} +} + +@article{Chakravarthy2018, + title={Burst spinal cord stimulation: review of preclinical studies and comments on clinical outcomes}, + author={Chakravarthy, Krishnan and Kent, Alexander R and Raza, Adil and Xing, Fang and Kinfe, Thomas M}, + journal={Neuromodulation: Technology at the Neural Interface}, + volume={21}, + number={5}, + pages={431--439}, + year={2018}, + publisher={Elsevier} +} + +@Article{Chan2005, + title={{Ca2+} current--driven nonlinear amplification by the mammalian cochlea in vitro}, + author={Chan, Dylan K and Hudspeth, AJ}, + journal={Nature Neuroscience}, + volume={8}, + number={2}, + pages={149--155}, + year={2005}, + publisher={Nature Publishing Group US New York} +} + +@Article{Chapman1995, + Title = {Ecological constraints on group size: an analysis of spider monkey and chimpanzee subgroups}, + Author = {Chapman, C. and Chapman, L. and Wrangham, R.}, + Journal = BehavEcolSociobiol, + Year = {1995}, + Number = {59}, + Volume = {36}, + Owner = {raab}, + Timestamp = {2020.01.30} +} + +@Article{Charpentier2005, + Title = {Constraints on control: factors influencing reproductive success in male mandrills ({Mandrillus sphinx})}, + Author = {Charpentier, Marie and Peignot, Patricia and Hossaert-McKey, Martine and Gimenez, Olivier and Setchell, Joanna M. and Wickings, E. Jean}, + Journal = BehavEcol, + Year = {2005}, + Number = {3}, + Pages = {614-623}, + Volume = {16}, + + Owner = {raab}, + Timestamp = {2020.01.23} +} + +@ARTICLE{Chen2005, + AUTHOR = {Ling Chen and Jonathan L. House and R\"udiger Krahe and Mark E. Nelson}, + TITLE = {Modeling signal and background components of electrosensory scenes.}, + JOURNAL = JCompPhysiolA, + YEAR = {2005}, + VOLUME = {191}, + PAGES = {331--345} +} + +@article{Cherry1953, + title={Some experiments on the recognition of speech, with one and with two ears}, + author={Cherry, E Colin}, + journal={The Journal of the Acoustical Society of America}, + volume={25}, + number={5}, + pages={975--979}, + year={1953}, + publisher={acoustical society of America} +} + +@Article{Chikkerur2010, + Title = {What and where: {A Bayesian} inference theory of attention.}, + Author = {Sharat Chikkerur and Thomas Serre and Cheston Tan and Tomaso Poggio}, + Journal = VisionRes, + Year = {2010}, + Pages = {2233-2247}, + Volume = {50} +} + +@Article{Chivers1995, + Title = {Familiarity and shoal cohesion in fathead minnows ({Pimephales promelas}): implications for antipredator behaviour}, + Author = {Douglas P. Chivers and Grant E. Brown and R. Jan F. Smith}, + Journal = {Can J Zool}, + Year = {1995}, + Pages = {955-960}, + Volume = {73}, + + Doi = {https://doi.org/10.1139/z95-111}, + Owner = {raab}, + Timestamp = {2020.01.27} +} + +@article{Chocholle1957, + title={About the sensation of beats between two tones whose frequencies are nearly in a simple ratio}, + author={Chocholle, R and Legouix, JP}, + journal={The Journal of the Acoustical Society of America}, + volume={29}, + number={6}, + pages={750--750}, + year={1957}, + publisher={Acoustical Society of America} +} + +@ARTICLE{Clarke2020, + AUTHOR = {Shelby B. Clarke and Lauren J. Chapman and R\"udiger Krahe}, + TITLE = {The effect of normoxia exposure on hypoxia tolerance and sensory sampling in a swamp-dwelling mormyrid fish.}, + JOURNAL = {Comp Biochem Physiol A}, + YEAR = {2020}, + VOLUME = {240}, + PAGES = {110586} +} + +@article{Clevert2015, + title={{Fast and accurate deep network learning by exponential linear units (ELUs)}}, + author={Clevert, DjorkArn{\'e} and Unterthiner, Thomas and Hochreiter, Sepp}, + journal={arXiv preprint arXiv:1511.07289}, + year={2015} +} + +@Article{Clutton-Brock1999, + Title = {Predation, group size and mortality in a cooperative mongoose, {Suricata suricatta}}, + Author = {Clutton-Brock, T. H. and Gaynor, D. and McIlrath, G. M. and Maccoll, A. D. C. and Kansky, R. and Chadwick, P. and Manser, M. and Skinner, J. D. and Brotherton, P. N. M.}, + Journal = {J Anim Ecol}, + Year = {1999}, + Number = {4}, + Pages = {672-683}, + Volume = {68}, + Keywords = {cooperative breeding, demography, mammals, mortality}, + Owner = {raab}, + Timestamp = {2020.01.21} +} + +@ARTICLE{Coates1954, + AUTHOR = {C. W. Coates}, + TITLE = {Activity in electrogenic organs of knifefishes}, + JOURNAL = Science, + YEAR = {1954}, + VOLUME = {120}, + PAGES = {845--846} +} + +@Article{Collin2012, + Title = {The Neuroecology of Cartilaginous Fishes: Sensory Strategies for Survival.}, + Author = {Shaun P. Collin}, + Journal = BrainBehavEvol, + Year = {2012}, + Pages = {80-96}, + Volume = {80} +} + + +@Article{Cote1995, + Title = {Parasitism and group size in social animals: a meta-analysis}, + Author = {Isabelle M. C\^ot\'e and Robert Poulinb}, + Journal = BehavEcol, + Year = {1995}, + Pages = {159-165}, + Volume = {6}, + + Doi = {https://doi.org/10.1093/beheco/6.2.159}, + Owner = {raab}, + Timestamp = {2020.01.30} +} + +@ARTICLE{Cox2004, + AUTHOR = {C. Cox-Fernandes and J. Podos and J. G. Lundberg}, + TITLE = {Amazonian ecology: tributaries enhance the diversity of electric fishes.}, + JOURNAL = Science, + YEAR = {2004}, + VOLUME = {305}, + PAGES = {1960--1962} +} + +@INCOLLECTION{Crampton2006, + TITLE = {Evolution of electric signal diversity in gymnotiform fishes. {I. Phylogenetic} systematics, ecology and biogeography.}, + AUTHOR = {W. G. R. Crampton and J. S. Albert}, + Year = {2006}, + Pages = {647--696}, + BOOKTITLE = {Communication in fishes}, + EDITOR = {F. Ladich and S. P. Collin and P. Moller and B. G. Kapoor}, + PUBLISHER = {Science Publishers}, + ADDRESS = {Enfield, N.H.} +} + +@INCOLLECTION{Crampton2011, + TITLE = {An ecological perspective on diversity and distributions.}, + AUTHOR = {W. G. R. Crampton}, + BOOKTITLE = {Historical biogeography of neotropical freshwater fishes.}, + PUBLISHER = {University of California Press}, + YEAR = {2011}, + ADDRESS = {California}, + EDITOR = {J. S. Albert and R. Reis}, + PAGES = {165--189} +} + +@Article{Crampton2013, + Title = {Proximate and ultimate causes of signal diversity in the electric fish {Gymnotus}.}, + Author = {W.G.R. Crampton and A. Rodriguez-Catt\'aneo and N.R. Lovejoy and A.A. Caputi}, + Journal = {Journal of Experimental Biology}, + Year = {2013}, + Pages = {2523-2541}, + Volume = {216} +} + +@Article{Creel1996, + Title = {Social stress and dominance}, + Author = {S. Creel and N. Marusha Creel and S. Monfort}, + Journal = {Nature}, + Year = {1996}, + Pages = {212}, + Volume = {379}, + + Doi = {https://doi.org/10.1038/379212a0}, + Owner = {raab}, + Timestamp = {2020.01.27} +} + + +@Article{Crick1984, + Title = {Function of the thalamic reticular complex: the searchlight hypothesis.}, + Author = {Francis Crick}, + Journal = {Proceedings of the National Academy of Sciences}, + Year = {1984}, + Pages = {4586--4590}, + Volume = {81} +} + +@ARTICLE{Crook2004, + AUTHOR = {David A. Crook}, + TITLE = {Is the home range concept compatible with the movements of two species of lowland river fish?}, + JOURNAL = JAnimEcol, + YEAR = {2004}, + VOLUME = {73}, + PAGES = {353--366} +} + +@article{Csicsvari1998, + title={Reliability and state dependence of pyramidal cell--interneuron synapses in the hippocampus: an ensemble approach in the behaving rat}, + author={Csicsvari, Jozsef and Hirase, Hajime and Czurko, Andras and Buzs{\'a}ki, Gy{\"o}rgy}, + journal={Neuron}, + volume={21}, + number={1}, + pages={179--189}, + year={1998}, + publisher={Elsevier} +} + +@Article{Cuadrado1987, + Title = {The Cytoarchitecture of the {Torus Semicircularis} in the Teleost \textit{Barbus meridionalis}.}, + Author = {M.I. Cuadrado}, + Journal = {Journal of Morphology}, + Year = {1987}, + Pages = {233-245}, + Volume = {191} +} + +@Article{Cuadrado1992, + Title = {Neuropeptides and Monoamines in the {Torus Semicircularis} of the Carp ({Cyprinus carpio}).}, + Author = {M. Isabel Cuadrado and Rafael Cove{\~n}as and G\'erard Tramu}, + Journal = BrainResBull, + Year = {1992} +} + +@Article{Cunningham2004, + title={A role for fast rhythmic bursting neurons in cortical gamma oscillations in vitro}, + author={Cunningham, Mark O and Whittington, Miles A and Bibbig, Andrea and Roopun, Anita and LeBeau, Fiona EN and Vogt, Angelika and Monyer, Hannah and Buhl, Eberhard H and Traub, Roger D}, + journal={Proceedings of the National Academy of Sciences}, + volume={101}, + number={18}, + pages={7152--7157}, + year={2004}, + publisher={National Acad Sciences} +} + + +@Article{Cunningham2017, + title={{Measuring nonlinear signal combination using EEG}}, + author={Cunningham, Darren GM and Baker, Daniel H and Peirce, Jonathan W}, + journal={Journal of Vision}, + volume={17}, + number={5}, + pages={10--10}, + year={2017}, + publisher={The Association for Research in Vision and Ophthalmology} +} + +@Article{Cvikel2015, + Title = {On-board recordings reveal no jamming avoidance in wild bats}, + Author = {Cvikel, Noam and Levin, Eran and Hurme, Edward and Borissov, Ivailo and Boonman, Arjan and Amichai, Eran and Yovel, Yossi}, + Journal = {Proc. R. Soc. B}, + Year = {2015}, + Number = {1798}, + Volume = {282}, + + Doi = {10.1098/rspb.2014.2274}, + Owner = {raab}, + Timestamp = {2020.02.11} +} + +@Article{Dalton2000, + title={The merging of the senses: integration of subthreshold taste and smell}, + author={Dalton, P and Doolittle, N and Nagata, H and Breslin, PAS}, + journal={Nature Neuroscience}, + volume={3}, + number={5}, + pages={431--432}, + year={2000}, + publisher={Nature Publishing Group} +} + +@article{Dau1997, + title={{Modeling auditory processing of amplitude modulation. I. Detection and masking with narrow-band carriers}}, + author={Dau, Torsten and Kollmeier, Birger and Kohlrausch, Armin}, + journal={The Journal of the Acoustical Society of America}, + volume={102}, + number={5}, + pages={2892--2905}, + year={1997}, + publisher={Acoustical Society of America} +} + +@ARTICLE{Dawson2018, + AUTHOR = {D. R. Dawson and W. M. Koster}, + TITLE = {Habitat use and movements of Australian grayling (\textit{Prototroctes maraena}) in a Victorian coastal stream.}, + JOURNAL = {Marine and Freshwater Research}, + YEAR = {2018}, + VOLUME = {69}, + PAGES = {1259--1267} +} + +@Article{Deemyad2013, + Title = {Serotonin selectively enhances perception and sensory neural response to stimuli generated by same sex conspecifics.}, + Author = {Tara Deemyad and Michael G. Metzen and Yingzhou Pan and Maurice J. Chacron}, + Journal = {Proceedings of the National Academy of Sciences}, + Year = {2013}, + Number = {48}, + Pages = {19609-19614}, + Volume = {110} +} + +@article{Delgutte1990, + title={Two-tone rate suppression in auditory-nerve fibers: Dependence on suppressor frequency and level}, + author={Delgutte, Bertrand}, + journal={Hearing Research}, + volume={49}, + number={1-3}, + pages={225--246}, + year={1990}, + publisher={Elsevier} +} + +@Article{Dell2014, + Title = {Automated image-based tracking and its application in ecology}, + Author = {Anthony I. Dell and John A. Bender and Kristin Branson and Iain D. Couzin and Gonzalo G. de Polavieja and Lucas P.J.J. Noldus and Alfonso P\'erez-Escudero and Pietro Perona and Andrew D. Straw and Martin Wikelski and Ulrich Brose}, + Journal = TIEE, + Year = {2014}, + Number = {7}, + Pages = {417 - 428}, + Volume = {29}, + Keywords = {behavior, bio-logging, ecological interactions, tracking, automated image-based tracking}, + Owner = {raab}, + Timestamp = {2020.02.11} +} + +@article{DeMorgan1864, + title={On the beats of imperfect consonances}, + author={De Morgan, Augustus}, + journal={Transactions of the Cambridge Philosophical Society}, + volume={10}, + pages={129}, + year={1864} +} + +@article{DeSantana2013, +author = {de Santana, Carlos David and Vari, Richard P.}, +doi = {10.1111/zoj.12022}, +journal = {Zoological Journal of the Linnean Society}, +number = {3}, +pages = {564--596}, +title = {{Brown ghost electric fishes of the \textit{Apteronotus leptorhynchus} species-group (Ostariophysi, Gymnotiformes); monophyly, major clades, and revision}}, +volume = {168}, +year = {2013} +} + +@ARTICLE{DeSantana2019, + AUTHOR = {C. David de Santana and W. G. R. Crampton and Casey B. Dillman and Renata G. Frederico and Mark H. Sabaj and Rapha\"el Covain and Jonathan Ready and Jansen Zuanon and Renildo R. de Oliveira and Raimundo N. Mendes-J\'unior and Douglas A. Bastos and Tulio F. Teixeira and Jan Mol and Willian Ohara and Nat\'alia Castro e Castro and Luiz A. Peixoto and Cleusa Nagamachi and Leandro Sousa and Luciano F. A. Montag and Frank Ribeiro and Joseph C. Waddell and Nivaldo M. Piorsky and Richard P. Vari and Wolmar B. Wosiacki}, + TITLE = {Unexpected species diversity in electric eels with a description of the strongest living bioelectricity generator.}, + JOURNAL = NatCommun, + YEAR = {2019}, + VOLUME = {10}, + PAGES = {4000} +} + +@Article{Destexhe1993, + title={Ionic mechanisms for intrinsic slow oscillations in thalamic relay neurons}, + author={Destexhe, Alain and Babloyantz, Agnessa and Sejnowski, Terrence J}, + journal={Biophysical Journal}, + volume={65}, + number={4}, + pages={1538--1552}, + year={1993}, + publisher={Elsevier} +} + +@article{DeValois1982, + title={Spatial frequency selectivity of cells in macaque visual cortex}, + author={De Valois, Russell L and Albrecht, Duane G and Thorell, Lisa G}, + journal={Vision Research}, + volume={22}, + number={5}, + pages={545--559}, + year={1982}, + publisher={Pergamon} +} + +@Article{DeWeille1983, + Title = {Electrosensory information processing by lateral-line lobe neurons of catfish investigated by means of white noise cross-correlation.}, + Author = {J.R. De Weille}, + Journal = CompBiochemPhysiol, + Year = {1983}, + Number = {3}, + Pages = {677-680}, + Volume = {74A} +} + +@Article{DeWoody2000, + Title = {Genetic monogamy and biparental care in an externally fertilizing fish, the largemouth bass ({Micropterus salmoides})}, + Author = {J. Andrew DeWoody and Dean E. Fletcher and S. David Wilkins and William S. Nelson and John C. Avise}, + Journal = ProcRSocLondBBiolSci, + Year = {2000}, + Pages = {2431 - 2437}, + Volume = {267}, + + Doi = {10.1098/rspb.2000.1302}, + Owner = {raab}, + Timestamp = {2020.01.30} +} + +@article{Doiron2002, + title={Ghostbursting: a novel neuronal burst mechanism}, + author={Doiron, Brent and Laing, Carlo and Longtin, Andr{\'e} and Maler, Leonard}, + journal={Journal of Computational Neuroscience}, + volume={12}, + pages={5--25}, + year={2002}, + publisher={Springer} +} + +@Article{Dong1995, + Title = {Statistics of natural time varying-images.}, + Author = {Dawei W Dong and Joseph J Atick}, + Journal = Network, + Year = {1995}, + Pages = {345-358}, + Volume = {6} +} + +@article{Dunlap1998, + author = {Dunlap, KD and Thomas, P and Zakon, HH}, + journal = JCompPhysiolA, + number = {1}, + pages = {77--86}, + title = {{Diversity of sexual dimorphism in + electrocommunication signals and its androgen + regulation in a genus of electric fish, + \textit{Apteronotus}.}}, + volume = {183}, + year = {1998} +} + +@ARTICLE{Dunlap2000, + AUTHOR = {Kent D. Dunlap and G. T. Smith and A. Yekta}, + TITLE = {Temperature Dependence of Electrocommunication Signals and Their Underlying Neural Rhythms in the Weakly Electric Fish, \textit{Apteronotus leptorhynchus}.}, + JOURNAL = BrainBehavEvol, + YEAR = {2000}, + VOLUME = {55}, + PAGES = {152--162} +} + +@Article{Dunlap2002, + AUTHOR = {K. D. Dunlap and L. M. Oliveri}, + TITLE = {Retreat site selection and social organization in captive electric fish, \textit{Apteronotus leptorhynchus}.}, + JOURNAL = {Journal of Comparative Physiology A}, + YEAR = {2002}, + VOLUME = {188}, + PAGES = {469--477} +} + +@ARTICLE{Dunlap2003a, + AUTHOR = {K. D. Dunlap and J. Larkins-Ford}, + TITLE = {Production of aggressive electrocommunication signals to progressively realistic social stimuli in male \textit{Apteronotus leptorhynchus}.}, + YEAR = {2003}, + JOURNAL = {Ethology}, + VOLUME = {109}, + PAGES = {243--258} } + +@ARTICLE{Dunlap2003b, + AUTHOR = {K. D. Dunlap and J. Larkins-Ford}, + TITLE = {Diversity in the structure of electrocommunication signals within a genus of electric fish, \textit{Apteronotus}.}, + YEAR = {2003}, + JOURNAL = JCompPhysiolA, + VOLUME = {189}, + PAGES = {153--161} } + +@article{Dux2006, + title={Isolation of a central bottleneck of information processing with time-resolved {fMRI}}, + author={Dux, Paul E and Ivanoff, Jason and Asplund, Christopher L and Marois, Ren{\'e}}, + journal={Neuron}, + volume={52}, + number={6}, + pages={1109--1120}, + year={2006}, + publisher={Elsevier} +} + +@ARTICLE{Dye1987, + AUTHOR = {John Dye}, + TITLE = {Dynamics and stimulus-dependence of pacemaker control during behavioral modulations in the weakly electric fish, \textit{Apteronotus}.}, + JOURNAL = JCompPhysiolA, + YEAR = {1987}, + VOLUME = {161}, + PAGES = {175--185} +} + +@article{Edwards2010, + title={{Association of the \textit{OCA2} polymorphism His615Arg with melanin content in east Asian populations: further evidence of convergent evolution of skin pigmentation}}, + author={Edwards, Melissa and Bigham, Abigail and Tan, Jinze and Li, Shilin and Gozdzik, Agnes and Ross, Kendra and Jin, Li and Parra, Esteban J}, + journal={PLoS Genetics}, + volume={6}, + number={3}, + pages={e1000867}, + year={2010}, + publisher={Public Library of Science San Francisco, USA} +} + + +@Article{Eeuwes2008, + Title = {{Behavioural relevance of AC and DC in prey detection by the brown bullhead, Ameiurus nebulosus.}}, + Author = {Lonneke B.M. Eeuwes and Robert C. Peters and Franklin Bretschneider}, + Journal = AnimBiol, + Year = {2008}, + Pages = {321-336}, + Volume = {58} +} + +@article{Ott2020, + title={Modeling the Heterogeneity of Electrosensory Afferents in Electric Fish}, + author={Ott, Alexander}, + year={2020}, + journal = {Unpublished master thesis}, + volume = {Eberhard Karls Universit\"at T\"ubingen} +} + +@article{Egerland2020, + title={Estimation and approximation of the nonlinear response of stochastic neuron models with adaptation}, + author={Egerland, Christoph H}, + year={2021}, + journal = {Unpublished master thesis}, + volume = {Humboldt-Universität zu Berlin} +} + +phdthesis{Egerland2020, + author={Egerland, Christoph H}, + title={Estimation and approximation of the nonlinear response of stochastic neuron models with adaptation}, + school = {Humboldt-Universität zu Berlin},% + year = {2021}, + note = {unpublished master thesis} +} + +article{Egerland2020, + author={Egerland, Christoph H}, + year = {2021}, + title={Estimation and approximation of the nonlinear response of stochastic neuron models with adaptation}, +} + +@article{Eggermont1993, + title={Wiener and Volterra analyses applied to the auditory system}, + author={Eggermont, Jos J}, + journal={Hearing Research}, + volume={66}, + number={2}, + pages={177--201}, + year={1993}, + publisher={Elsevier} +} + +@article{Eggermont1996, + title={Burst-firing sharpens frequency-tuning in primary auditory cortex.}, + author={Eggermont, Jos J and Smith, Geoff M}, + journal={Neuroreport}, + volume={7}, + number={3}, + pages={753--757}, + year={1996} +} + +@Article{Egner2010, + Title = {Expectation and Surprise Determine Neural Population Responses int the Ventral Visual Stream.}, + Author = {Tobias Egner and Jim M. Monti and Christopher Summerfield}, + Journal = JNeurosci, + Year = {2010}, + Number = {49}, + Pages = {16601-16608}, + Volume = {30} +} + +@Article{Egnor2016, + Title = {Computational Analysis of Behavior.}, + Author = {S. E. Roian Egnor and Kristin Branson}, + Journal = AnnuRevNeurosci, + Year = {2016}, + Pages = {217-36}, + Volume = {39}, + + Doi = {10.1146/annurev-neuro-070815-013845}, + Owner = {raab}, + Timestamp = {2020.02.11} +} + +@article{Elfwing2018, + title={Sigmoid-weighted linear units for neural network function approximation in reinforcement learning}, + author={Elfwing, Stefan and Uchibe, Eiji and Doya, Kenji}, + journal={Neural Networks}, + volume={107}, + pages={3--11}, + year={2018}, + publisher={Elsevier} +} + +@ARTICLE{Emde1990, + AUTHOR = {Gerhard von der Emde}, + TITLE = {Discrimination of objects through electrolocation in the weakly electric fish, \textit{Gnathonemus petersii}.}, + JOURNAL = JCompPhysiolA, + YEAR = {1990}, + VOLUME = {167}, + PAGES = {413--421} +} + +@ARTICLE{Emde1992, + AUTHOR = {Gerhard von der Emde and Thomas Ringer}, + TITLE = {Electrolocation of capacitive objects in four species of pulse-type weakly electric fish.}, + JOURNAL = {Ethology}, + YEAR = {1992}, + VOLUME = {91}, + PAGES = {326--338} +} + +@ARTICLE{Emde1993, + AUTHOR = {Gerhard von der Emde}, + TITLE = {The sensing of electrical capacitances by weakly electric mormyrid fish: effects of water conductivity.}, + JOURNAL = {Journal of Experimental Biology}, + YEAR = {1993}, + VOLUME = {181}, + PAGES = {157--173} +} + +@ARTICLE{Emde1994, + AUTHOR = {G. von der Emde and B. Ronacher}, + TITLE = {Perception of electric properties of objects in electrolocating weakly electric fish: two-dimensional similarity scaling reveals a {City-Block} metric.}, + JOURNAL = JCompPhysiolA, + YEAR = {1994}, + VOLUME = {175}, + PAGES = {801--812} +} + +@ARTICLE{Emde1998, + AUTHOR = {Gerhard von der Emde}, + TITLE = {Capacitance detection in the wave-type electric fish \textit{Eigenmannia} during active electrolocation.}, + JOURNAL = JCompPhysiolA, + YEAR = {1998}, + VOLUME = {182}, + PAGES = {217--224} +} + +@ARTICLE{Emde1998Distance, + AUTHOR = {Gerhard von der Emde and Stephan Schwarz and Leonel Gomez and Ruben Budelli and Kirsty Grant}, + TITLE = {Electric fish measure distance in the dark.}, + JOURNAL = Nature, + YEAR = {1998}, + VOLUME = {395}, + PAGES = {890--894} +} + +@INCOLLECTION{Emde2001, + TITLE = {Electric fields and electroreception: how electrosensory fish perceive their environment.}, + AUTHOR = {Gerhard von der Emde}, + PAGES = {313--329}, + BOOKTITLE = {Ecology of sensing}, + PUBLISHER = {Springer}, + ADDRESS = {Berlin, Heidelberg}, + YEAR = {2001}, + EDITOR = {Friedrich G. Barth and Axel Schmid} +} + + +@ARTICLE{Emde2006, + AUTHOR = {Gerhard von der Emde}, + TITLE = {Non-visual environmental imaging and object detection through active electrolocation in weakly electric fish.}, + JOURNAL = JCompPhysiolA, + YEAR = {2006}, + VOLUME = {192}, + PAGES = {601--612} +} + +@ARTICLE{Emde2010Signalling, + AUTHOR = {Gerhard von der Emde}, + TITLE = {Electrolocation of capacitive objects in four species of pulse-type weakly electric fish {II}. electric signalling behaviour.}, + JOURNAL = Ethology, + YEAR = {1992}, + VOLUME = {92}, + PAGES = {177--192} +} + +@Article{Engelmann2010, + Title = {Coding of stimuli by ampullary afferents in \textit{Gnathonemus petersii}.}, + Author = {J. Engelmann and S. Gertz and J. Goulet and A. Schuh and G. von der Emde}, + Journal = {J Neurophysiol}, + Year = {2010}, + + Month = {Oct}, + Number = {4}, + Pages = {1955--1968}, + Volume = {104}, + + Abstract = {Weakly electric fish use electroreception for both active and passive electrolocation and for electrocommunication. While both active and passive electrolocation systems are prominent in weakly electric Mormyriform fishes, knowledge of their passive electrolocation ability is still scarce. To better estimate the contribution of passive electric sensing to the orientation toward electric stimuli in weakly electric fishes, we investigated frequency tuning applying classical input-output characterization and stimulus reconstruction methods to reveal the encoding capabilities of ampullary receptor afferents. Ampullary receptor afferents were most sensitive (threshold: 40 μV/cm) at low frequencies (<10 Hz) and appear to be tuned to a mix of amplitude and slope of the input signals. The low-frequency tuning was corroborated by behavioral experiments, but behavioral thresholds were one order of magnitude higher. The integration of simultaneously recorded afferents of similar frequency-tuning resulted in strongly enhanced signal-to-noise ratios and increased mutual information rates but did not increase the range of frequencies detectable by the system. Theoretically the neuronal integration of input from receptors experiencing opposite polarities of a stimulus (left and right side of the fish) was shown to enhance encoding of such stimuli, including an increase of bandwidth. Covariance and coherence analysis showed that spiking of ampullary afferents is sufficiently explained by the spike-triggered average, i.e., receptors respond to a single linear feature of the stimulus. Our data support the notion of a division of labor of the active and passive electrosensory systems in weakly electric fishes based on frequency tuning. Future experiments will address the role of central convergence of ampullary input that we expect to lead to higher sensitivity and encoding power of the system.}, + Institution = {University of Bonn, Institute for Zoology, Neuroethology-Sensory Ecology, Bonn, Germany. Jacob.Engelmann@uni-bielefeld.de}, + Keywords = {Action Potentials; Animals; Electric Fish; Electric Stimulation; Female; Hair Cells, Ampulla; Male; Neurons, Afferent; Random Allocation}, + Timestamp = {2011.10.12} +} + +@ARTICLE{Enger1968, + AUTHOR = {Per S. Enger and Thomas Szabo}, + TITLE = {Effect of temperature on the discharge rates of the electric organ of some gymnotids.}, + JOURNAL = CompBiochemPhysiol, + YEAR = {1968}, + VOLUME = {27}, + PAGES = {625--627} +} + +@Article{Engh2002, + Title = {Reproductive skew among males in a female-dominated mammalian society}, + Author = {Engh, Anne L. and Funk, Stephan M. and Horn, Russell C. Van and Scribner, Kim T. and Bruford, Michael W. and Libants, Scot and Szykman, Micaela and Smale, Laura and Holekamp, Kay E.}, + Journal = BehavEcol, + Year = {2002}, + Number = {2}, + Pages = {193-200}, + Volume = {13}, + + Owner = {raab}, + Timestamp = {2020.01.23} +} + +@Article{Engler2000, + Title = {Spontaneous modulations of the electric organ discharge in the weakly electric fish, \textit{Apteronotus leptorhynchus}: a biophysical and behavioral analysis}, + Author = {Engler, G. and Fogarty, C.M. and Banks, J.R. and Zupanc, G.K.H.}, + Journal = {Journal of Comparative Physiology}, + Year = {2000}, + Number = {7}, + Pages = {645--660}, + Volume = {186}, + Owner = {raab}, + Timestamp = {2017.05.04} +} + +@Article{Engler2001, + Title = {Differential production of chirping behavior evoked by electrical stimulation of the weakly electric fish, \textit{Apteronotus leptorhynchus}.}, + Author = {Engler, G and Zupanc, G K}, + Journal = {Journal of Comparative Physiology A}, + Year = {2001}, + Number = {9}, + Pages = {747--756}, + Volume = {187} +} + +@ARTICLE{Escamilla2019, + AUTHOR = {Carolina Escamilla-Pinilla and Jos\'e Iv\'an Mojica and Jorge Molina}, + TITLE = {Spatial and temporal distribution of \textit{Gymnorhamphichthys rondoni} ({Gymnotiformes}: {Rhamphichthyidae}) in a long-term study of an Amazonian terra firme stream, {Leticia} - {Colombia}.}, + JOURNAL = {Neotropical Ichtyology}, + YEAR = {2019}, + VOLUME = {17}, + PAGES = {e190006} +} + +@article{Evans1972, + title={The frequency response and other properties of single fibres in the guinea-pig cochlear nerve}, + author={Evans, EF1331164}, + journal={The Journal of Physiology}, + volume={226}, + number={1}, + pages={263--287}, + year={1972}, + publisher={Wiley Online Library} +} + +@incollection{Evans1981, + title={The dynamic range problem: place and time coding at the level of cochlear nerve and nucleus}, + author={Evans, EF}, + booktitle={Neuronal Mechanisms of Hearing}, + pages={69--85}, + year={1981}, + publisher={Springer} +} + +@article{Ewert2000, + title={Characterizing frequency selectivity for envelope fluctuations}, + author={Ewert, Stephan D and Dau, Torsten}, + journal={The Journal of the Acoustical Society of America}, + volume={108}, + number={3}, + pages={1181--1196}, + year={2000}, + publisher={Acoustical Society of America} +} + +@ARTICLE{Fechler2013, + AUTHOR = {Katharina Fechler and Gerhard von der Emde}, + TITLE = {Figure–ground separation during active electrolocation in the weakly electric fish, \textit{Gnathonemus petersii}.}, + JOURNAL = {Journal of Physiology-Paris}, + YEAR = {2013}, + VOLUME = {107}, + PAGES = {72--83} +} + +@Article{Fenske2006, + Title = {Top-down facilitation of visual object recognition: object-based and context-based contributions.}, + Author = {Mark J. Fenske and Elissa Aminoff and Nurit Gronau and Moshe Bar}, + Journal = ProgBrainRes, + Year = {2006}, + Pages = {3-21}, + Volume = {155} +} + +@Article{Fernald2014, + Title = {Communication about social status}, + Author = {Russell D Fernald}, + Journal = CurrOpinNeurobiol, + Year = {2014}, + Note = {SI: Communication and language}, + Pages = {1 - 4}, + Volume = {28}, + + Abstract = {Dominance hierarchies are ubiquitous in social species and serve to organize social systems. Social and sexual status is communicated directly among animals via sensory systems evolved in the particular species. Such signals may be chemical, visual, auditory, postural or a combination of signals. In most species, status is initially established through physical conflict between individuals that leads to ritualized conflict or threats, reducing possibly dangerous results of fighting. Many of the status signals contain other information, as in some bird species that communicate both the size of their group and their individual rank vocally. Recent studies have shown that scent signaling among hyenas of east Africa is unique, being produced by fermentative, odor producing bacteria residing in the scent glands.}, + Owner = {raab}, + Timestamp = {2020.01.23}, +} + +@ARTICLE{Ferraris2017, + AUTHOR = {Ferraris, Jr., C. J. and C. D. de Santana and R. P. Vari}, + TITLE = {Checklist of Gymnotiformes ({Osteichthyes: Ostariophysi}) and catalogue of primary types.}, + JOURNAL = {Neotropical Ichthyology}, + YEAR = {2017}, + VOLUME = {15}, + PAGES = {1--44} +} + +@inproceedings{Ferwerda1996, + title={A model of visual adaptation for realistic image synthesis}, + author={Ferwerda, James A and Pattanaik, Sumanta N and Shirley, Peter and Greenberg, Donald P}, + booktitle={Proceedings of the 23rd annual conference on computer graphics and interactive techniques}, + pages={249--258}, + year={1996} +} + +@ARTICLE{Feulner2009, + AUTHOR = {Philine G. D. Feulner and Martin Plath and Jacob Engelmann and Frank Kirschbaum and Ralph Tiedemann}, + TITLE = {Electrifying love: electricfish use species-specificdischarge formate recognition.}, + JOURNAL = BiolLett, + YEAR = {2009}, + VOLUME = {5}, + PAGES = {225--228} +} + +@Article{Field1994, + Title = {What Is the Goal of Sensory Coding?}, + Author = {David J. Field}, + Journal = NeuralComput, + Year = {1994}, + Pages = {559-601}, + Volume = {6} +} + +@Article{Fischer2011, + Title = {Owl's behavior and neural representation predicted by Bayesian inference.}, + Author = {Brain Fischer and Jos\'e Luis Pena}, + Journal = {Nature Neuroscience}, + Year = {2011}, + Pages = {1061--1067}, + Volume = {14} +} + +@article{Fleischer2010, + title={Compliance profiles derived from a three-dimensional finite-element model of the basilar membrane}, + author={Fleischer, Mario and Schmidt, Rolf and Gummer, Anthony W}, + journal={The Journal of the Acoustical Society of America}, + volume={127}, + number={5}, + pages={2973--2991}, + year={2010}, + publisher={Acoustical Society of America} +} + + +@article{Ford1973, + title={Divergence and evolution in {Darwin's} finches}, + author={Ford, Hugh A and Parkin, David T and Ewing, Alastair W}, + journal={Biological Journal of the Linnean Society}, + volume={5}, + number={3}, + pages={289--295}, + year={1973}, + publisher={Oxford University Press} +} + +@Article{Foster1985, + title={{Spatial and temporal frequency selectivity of neurones in visual cortical areas V1 and V2 of the macaque monkey.}}, + author={Foster, KH and Gaska, James P and Nagler, M and Pollen, DA}, + journal={The Journal of Physiology}, + volume={365}, + number={1}, + pages={331--363}, + year={1985}, + publisher={Wiley Online Library} +} + +@Article{Fotowat2013, + author = {Fotowat, H and Harrison, RR. and Krahe, R}, + journal = {J Neurosci}, + number = {34}, + pages = {13758--13772}, + title = {Statistics of the electrosensory input in the freely swimming weakly electric fish \textit{Apteronotus leptorhynchus}.}, + volume = {33}, + year = {2013} +} + +@article {Fourcaud-Trocme2003, + author = {Fourcaud-Trocm{\'e}, Nicolas and Hansel, David and van Vreeswijk, Carl and Brunel, Nicolas}, + title = {How Spike Generation Mechanisms Determine the Neuronal Response to Fluctuating Inputs}, + volume = {23}, + number = {37}, + pages = {11628--11640}, + year = {2003}, + publisher = {Society for Neuroscience}, + abstract = {This study examines the ability of neurons to track temporally varying inputs, namely by investigating how the instantaneous firing rate of a neuron is modulated by a noisy input with a small sinusoidal component with frequency (f). Using numerical simulations of conductance-based neurons and analytical calculations of one-variable nonlinear integrate-and-fire neurons, we characterized the dependence of this modulation on f. For sufficiently high noise, the neuron acts as a low-pass filter. The modulation amplitude is approximately constant for frequencies up to a cutoff frequency, fc, after which it decays. The cutoff frequency increases almost linearly with the firing rate. For higher frequencies, the modulation amplitude decays as C/fα, where the power α depends on the spike initiation mechanism. For conductance-based models, α = 1, and the prefactor C depends solely on the average firing rate and a spike {\textquotedblleft}slope factor,{\textquotedblright} which determines the sharpness of the spike initiation. These results are attributable to the fact that near threshold, the sodium activation variable can be approximated by an exponential function. Using this feature, we propose a simplified one-variable model, the {\textquotedblleft}exponential integrate-and-fire neuron,{\textquotedblright} as an approximation of a conductance-based model. We show that this model reproduces the dynamics of a simple conductance-based model extremely well. Our study shows how an intrinsic neuronal property (the characteristics of fast sodium channels) determines the speed with which neurons can track changes in input.}, + issn = {0270-6474}, + journal = {Journal of Neuroscience} +} + +@ARTICLE{Franchina1998, + AUTHOR = {C. R. Franchina and P. K. Stoddard}, + TITLE = {Plasticity of the electric organ discharge waveform of the electric fish \textit{Brachyhypopomus pinnicaudatus} {I.} Quantification of day-night changes.}, + JOURNAL = JCompPhysiolA, + YEAR = {1998}, + VOLUME = {183}, + PAGES = {759--768} +} + +@Article{Freeman2013, + Title = {A functional and perceptual signature of the second visual area in primates.}, + Author = {Jeremy Freeman and Corey M. Ziemba and David H. Heeger and Eero P. Simoncelli and J. Anthony Movshon}, + Journal = {Nature Neuroscience}, + Year = {2013}, + Number = {7}, + Pages = {doi:10.1038/nn.3402.}, + Volume = {16} +} + +@article{French1973, + title={Measuring the Wiener kernels of a non-linear system using the fast {Fourier} transform algorithm}, + author={French, AS and Butz, EG}, + journal={International Journal of Control}, + volume={17}, + number={3}, + pages={529--539}, + year={1973}, + publisher={Taylor \& Francis} +} + +@article{French1976, + title={Practical nonlinear system analysis by {Wiener} kernel estimation in the frequency domain}, + author={French, AS}, + journal={Biological Cybernetics}, + volume={24}, + number={2}, + pages={111--119}, + year={1976}, + publisher={Springer} +} + +@article{Marmarelis1999, + title={Principal dynamic mode analysis of nonlinear transduction in a spider mechanoreceptor}, + author={Marmarelis, Vasilis Z and Juusola, Mikko and French, Andrew S}, + journal={Annals of Biomedical Engineering}, + volume={27}, + pages={391--402}, + year={1999}, + publisher={Springer} +} + +@Article{Freund2002, + Title = {Behavioral Stochastic Resonance: How the Noise from a Daphnia Swarm Enhances Individual Prey Capture by Juvenile Paddlefish.}, + Author = {Jan A. Freund and Lutz Schimanski-Geier and Beatrix Beisner and Alexander Neiman and David F. Russell and Tatyana Yakusheva and Frank Moss}, + Journal = JTheorBiol, + Year = {2002} +} + +@Article{Friard2016, + Title = {{BORIS}: a free, versatile open-source event-logging software for video/audio coding and live observations}, + Author = {Friard, Olivier and Gamba, Marco}, + Journal = {Methods in Ecology and Evolution}, + Year = {2016}, + Number = {11}, + Pages = {1325-1330}, + Volume = {7} +} + +@ARTICLE{Friedman1996, + AUTHOR = {M. A. Friedman and C. D. Hopkins}, + TITLE = {Tracking individual mormyrid electric fish in the field using electric organ discharge waveforms.}, + JOURNAL = AnimBehav, + YEAR = {1996}, + VOLUME = {51}, + PAGES = {391--407} +} + +@Article{Froudarakis2014, + Title = {Population code in mouse {V1} facilitates readout of natural scenes through increased sparseness.}, + Author = {Emmanouil Froudarakis and Philipp Berens and Alexander S Ecker and R James Cotton and Fabian H Sinz and Dimitri Yatsenko and Peter Saggau and Matthias Bethge and Andreas S Tolias}, + Journal = {Nature Neuroscience}, + Year = {2014}, + Pages = {doi:10.1038/nn.3707}, + Volume = {Advance online publication} +} + +@ARTICLE{Fugere2010, + AUTHOR = {Vincent Fug\`ere and R\"udiger Krahe}, + TITLE = {Electric signals and species recognition in the wave-type gymnotiform fish \textit{Apteronotus leptorhynchus}.}, + JOURNAL = {Journal of Experimental Biology}, + YEAR = {2010}, + VOLUME = {213}, + PAGES = {225--236} +} + +@ARTICLE{Fugere2011, + AUTHOR = {Vincent Fug\`ere and Hernan Ortega and R\"udiger Krahe}, + TITLE = {Electrical signalling of dominance in a wild population of electric fish.}, + JOURNAL = BiolLett, + YEAR = {2011}, + VOLUME = {7}, + PAGES = {197--200} +} + +@ARTICLE{Fujita2010, + AUTHOR = {Kazuhisa Fujita and Yoshiki Kashimori}, + TITLE = {Modeling the electric image produced by objects with complex impedance in weakly electric fish.}, + JOURNAL = BiolCybern, + YEAR = {2010}, + VOLUME = {103}, + PAGES = {105--118} +} + +@ARTICLE{Fujita2019, + AUTHOR = {Kazuhisa Fujita and Yoshiki Kashimori}, + TITLE = {Representation of object’s shape by multiple electric images in electrolocation.}, + JOURNAL = BiolCybern, + YEAR = {2019}, + VOLUME = {113}, + PAGES = {239--255} +} + +@article{Fukutomi2020, + title={A history of corollary discharge: contributions of mormyrid weakly electric fish}, + author={Fukutomi, Matasaburo and Carlson, Bruce A}, + journal={Frontiers in Integrative Neuroscience}, + volume={14}, + pages={42}, + year={2020}, + publisher={Frontiers Media SA} +} + +@Article{Furutsu1963, + title={On the statistical theory of electromagnetic waves in a fluctuating medium}, + author={Furutsu, Koichi}, + journal={Journal of Research of the National Bureau of Standards}, + volume={67}, + pages={303--323}, + year={1963} +} + +@Article{Gabbiani1996, + title={From stimulus encoding to feature extraction in weakly electric fish}, + author={Gabbiani, Fabrizio and Metzner, Walter and Wessel, Ralf and Koch, Christof}, + journal={Nature}, + volume={384}, + number={6609}, + pages={564--567}, + year={1996}, + publisher={Nature Publishing Group UK London} +} + +@Article{Gabbiani1999, + title={Encoding and processing of sensory information in neuronal spike trains}, + author={Gabbiani, Fabrizio and Metzner, W}, + journal={Journal of Experimental Biology}, + volume={202}, + number={10}, + pages={1267--1279}, + year={1999}, + publisher={The Company of Biologists Ltd} +} + +@ARTICLE{Gavassa2012, + AUTHOR = {Sat Gavassa and Ana C. Silva and Emmanuel Gonzalez and Philip K. Stoddard}, + TITLE = {Signal modulation as a mechanism for handicap disposal.}, + JOURNAL = AnimBehav, + YEAR = {2012}, + VOLUME = {83}, + PAGES = {935--944} +} + +@Article{Geffen1996, + Title = {Size, Life-History Traits, and Social Organization in the {Canidae}: A Reevaluation}, + Author = {Geffen, Eli and Gompper, Matthew E. and Gittleman, John L. and Luh, Hang-Kwang and MacDonald, David W. and Wayne, Robert K.}, + Journal = {The American Naturalist}, + Year = {1996}, + Number = {1}, + Pages = {140-160}, + Volume = {147}, + Owner = {raab}, + Timestamp = {2020.01.30}, +} + +@Article{Geisler2008, + Title = {Visual perception and the statistical properties of natural scenes.}, + Author = {Wilson S. Geisler}, + Journal = AnnuRevPsychol, + Year = {2008} +} + +@Article{Gershman2012, + Title = {Multistability and Perceptual Inference.}, + Author = {Samuel J. Gersham and Edward Vul and Joshua B. Tenenbaum}, + Journal = NeuralComput, + Year = {2012}, + Pages = {1-24}, + Volume = {24} +} + +@Article{Gilbert2007, + Title = {Brain States: Top-down Influences in Sensory Processing.}, + Author = {Charles D. Gilbert and Mariano Sigman}, + Journal = Neuron, + Year = {2007}, + Pages = {677-696}, + Volume = {54} +} + +@inproceedings{Glorot2011, + title={Deep sparse rectifier neural networks}, + author={Glorot, Xavier and Bordes, Antoine and Bengio, Yoshua}, + booktitle={Proceedings of the fourteenth international conference on artificial intelligence and statistics}, + pages={315--323}, + year={2011} +} + +@phdthesis{Goldstein1966, + title={An investigation of monaural phase perception.}, + author={Goldstein, Julius L}, + year={1966} +} + +@ARTICLE{Gomez2014, + AUTHOR = {Alex Gomez-Marin and Joseph J. Paton and Adam R. Kampff and Rui M. Costa and Zachary F. Mainen}, + TITLE = {Big behavioral data: psychology, ethology and the foundations of neuroscience.}, + JOURNAL = {Nature Neuroscience}, + YEAR = {2014}, + VOLUME = {17}, + PAGES = {1455--1462} +} + +@Article{Goris2014, + Title = {Partitioning neuronal variability.}, + Author = {Robbe L T Goris and J Anthony Movshon and Eero P Simoncelli}, + Journal = {Nature Neuroscience}, + Year = {2014}, + Pages = {doi:10.1038/nn.3711}, + Volume = {Advanced online publication} +} + +@ARTICLE{Gottwald2017, + AUTHOR = {Martin Gottwald and Raya A. Bott and Gerhard von der Emde}, + TITLE = {Estimation of distance and electric impedance of capacitive objects in the weakly electric fish \textit{Gnathonemus petersii}.}, + JOURNAL = {Journal of Experimental Biology}, + YEAR = {2017}, + VOLUME = {220}, + PAGES = {3142--3153} +} + +@ARTICLE{Gottwald2018, + AUTHOR = {Martin Gottwald and Neha Singh and Andr\'e Haubrich and Sophia Regett and Gerhard von der Emde}, + TITLE = {Electric-color sensing in weakly electric fish suggests color perception as a sensory concept beyond vision.}, + JOURNAL = CurrBiol, + YEAR = {2018}, + VOLUME = {220}, + PAGES = {3142--3153} +} + +@article{Gollisch2010, + title={Eye smarter than scientists believed: neural computations in circuits of the retina}, + author={Gollisch, Tim and Meister, Markus}, + journal={Neuron}, + volume={65}, + number={2}, + pages={150--164}, + year={2010}, + publisher={Elsevier} +} + +@ARTICLE{Graff1992, + AUTHOR = {Christian Graff and Bernd Kramer}, + TITLE = {Trained weakly-electric fishes \textit{Pollimyrus isidori} and \textit{Gnathonemus petersii} {(Mormyridae, Teleostei)} discriminate between waveforms of electric pulse discharges.}, + JOURNAL = {Ethology}, + YEAR = {1992}, + VOLUME = {90}, + PAGES = {279--292} +} + +@article{Grahn2012, + title={Neural mechanisms of rhythm perception: current findings and future perspectives}, + author={Grahn, Jessica A}, + journal={Topics in Cognitive Science}, + volume={4}, + number={4}, + pages={585--606}, + year={2012}, + publisher={Wiley Online Library} +} + +@Article{Grewe2017, + Title = {Synchronous spikes are necessary but not sufficient for a synchrony code in populations of spiking neurons}, + Author = {Grewe, Jan and Kruscha, Alexandra and Lindner, Benjamin and Benda, Jan}, + Journal = {Proc Natl Acad Sci}, + Year = {2017}, + Number = {10}, + Pages = {E1977-E1985}, + Volume = {114} +} + +@Article{Gross2002, + title={Genealogy of the “grandmother cell”}, + author={Gross, Charles G}, + journal={The Neuroscientist}, + volume={8}, + number={5}, + pages={512--518}, + year={2002}, + publisher={Sage Publications Sage CA: Thousand Oaks, CA} +} + +@article{Gussin2007, + title={Limits of linear rate coding of dynamic stimuli by electroreceptor afferents}, + author={Gussin, Daniel and Benda, Jan and Maler, Leonard}, + journal={J Neurophysiol}, + volume={97}, + number={4}, + pages={2917--2929}, + year={2007} +} + +@Article{Hagedorn1985, + Title = {Court and spark: electric signals in the courtship and mating of gymnotoid fish}, + Author = {Hagedorn, Mary and Walter Heiligenberg}, + Journal = AnimBehav, + Year = {1985}, + Number = {1}, + Pages = {254 - 265}, + Volume = {33}, + + Doi = {http://doi.org/10.1016/S0003-3472(85)80139-1}, + Owner = {raab}, + Timestamp = {2017.04.27}, + Url = {http://www.sciencedirect.com/science/article/pii/S0003347285801391} +} + +@ARTICLE{Hagedorn1985Hypopomus, + AUTHOR = {Mary Hagedorn and Catherine Carr}, + TITLE = {Single electrocytes produce a sexually dimorphic signal in {South American} electric fish, \textit{Hypopomus occidentalis} {(Gymnotiformes, Hypopomidae)}.}, + JOURNAL = JCompPhysiolA, + YEAR = {1985}, + VOLUME = {156}, + PAGES = {511--523} +} + + +@Article{Hagedorn1988, + Title = {Ecology and behavior of a pulse-type electric fish, \textit{Hypopomus occidentalis} {(Gymnotiformes, Hypopomidae)}, in a fresh-water stream in {Panama}.}, + Author = {Mary Hagedorn}, + Journal = {Copeia}, + Year = {1988}, + Number = {2}, + Pages = {324-335}, + Volume = {1988} +} + +@Article{Hager1991, + Title = {Safety in numbers: shoal size choice by minnows under predatory threat}, + Author = {Hager, M.C. and Helfman, G.S.}, + Journal = BehavEcolSociobiol, + Year = {1991}, + Number = {4}, + Pages = {271-276}, + Volume = {29}, + + Doi = {https://doi.org/10.1007/BF00163984}, + Owner = {raab}, + Timestamp = {2020.01.27} +} + +@article{Haggard2023, + title={Coding of object location by heterogeneous neural populations with spatially dependent correlations in weakly electric fish}, + author={Haggard, Myriah and Chacron, Maurice J}, + journal={PLOS Computational Biology}, + volume={19}, + number={3}, + pages={e1010938}, + year={2023}, + publisher={Public Library of Science San Francisco, CA USA} +} + +@ARTICLE{Hagiwara1963, + AUTHOR = {S. Hagiwara and H. Morita}, + TITLE = {Coding mechanisms of electroreceptor fibers in some electric fish.}, + JOURNAL = {Journal of Neurophysiology}, + YEAR = {1963}, + VOLUME = {26}, + PAGES = {551--567} +} + +@ARTICLE{Harder1964, + AUTHOR = {Wilhelm Harder and Alfred Schief and Hartmut Uhlemann}, + TITLE = {{Zur Funktion des Elektrischen Organs von \textit{Gnathonemus petersii} (Gthr. 1862) (Mormyriformes, Teleostei)}.}, + JOURNAL = {Zeitschrift f\'ur vergleichende Physiologie}, + YEAR = {1964}, + VOLUME = {48}, + PAGES = {302--331} +} + +@article{Hartmann1979, + title={Detection of amplitude modulation}, + author={Hartmann, WM}, + journal={The Journal of the Acoustical Society of America}, + volume={65}, + number={S1}, + pages={S59--S59}, + year={1979}, + publisher={Acoustical Society of America} +} + +@Article{Harvey-Girard2013, + Title = {Expression of the Cannabinoid {CB1} Receptor in the Gymnotiform Fish Brain and Its Implications for the Organization of the Telleost Pallium.}, + Author = {Erik Harvey-Girard and Ana C.C. Giassi and William Ellis and Leonard Maler}, + Journal = {Journal of Comparative Neurology}, + Year = {2013}, + Pages = {949-975}, + Volume = {521} +} + +@ARTICLE{Harvey2010, + AUTHOR = {Erik Harvey-Girard and Jessica Tweedle and Joel Ironstone and Martin Cuddy and William Ellis and Leonard Maler}, + TITLE = {Long-Term recognition memory of individual conspecifics is associated with telencephalic expression of {Egr-1} in the electric fish \textit{Apteronotus leptorhynchus}.}, + JOURNAL = {Journal of Comparative Neurology}, + YEAR = {2010}, + VOLUME = {518}, + PAGES = {2666--2692} +} + +@Article{Harvey2013, + Title = {Dendritic {SK.} Channels convert {NMDA-R-dependent LTD} to burst timing-dependent plasticity}, + Author = {Eric Harvey-Girard and Leonard Maler}, + Journal = {Journal of Neurophysiology}, + Year = {2013}, + Pages = {2689-2703}, + Volume = {110} +} + +@Article{Hass2002, + Title = {Anti-predator benefits of group living in white-nosed coatis {(Nasua narica)}}, + Author = {Hass, Christine C. +and Valenzuela, David}, + Journal = BehavEcolSociobiol, + Year = {2002}, + Number = {6}, + Pages = {570--578}, + Volume = {51}, + Day = {01}, + Doi = {10.1007/s00265-002-0463-5}, + Owner = {raab}, + Timestamp = {2020.01.21}, + Url = {https://doi.org/10.1007/s00265-002-0463-5} +} + +@Article{Hawken1996, + title={Temporal-frequency selectivity in monkey visual cortex}, + author={Hawken, MJ and Shapley, Robert M and Grosof, DH}, + journal={Visual neuroscience}, + volume={13}, + number={3}, + pages={477--492}, + year={1996}, + publisher={Cambridge University Press} +} + + +@article{Haykin2005, + title={The cocktail party problem}, + author={Haykin, Simon and Chen, Zhe}, + journal={Neural Computation}, + volume={17}, + number={9}, + pages={1875--1902}, + year={2005}, + publisher={MIT Press One Rogers Street, Cambridge, MA 02142-1209, USA journals-info~…} +} + +@article{Heil2015, + title={Basic response properties of auditory nerve fibers: a review}, + author={Heil, Peter and Peterson, Adam J}, + journal={Cell and tissue research}, + volume={361}, + pages={129--158}, + year={2015}, + publisher={Springer} +} + + +@article{Heil2016, + title={Spike timing in auditory-nerve fibers during spontaneous activity and phase locking}, + author={Heil, Peter and Peterson, Adam J}, + journal={Synapse}, + volume={71}, + number={1}, + pages={5--36}, + year={2017}, + publisher={Wiley Online Library} +} + +@ARTICLE{Heiligenberg1973, + AUTHOR = {Walter Heiligenberg}, + TITLE = {Electrolocation of objects in the electric fish \textit{Eigenmannia} ({Rhamphichthyidae}, {Gymnotoidei}).}, + JOURNAL = JCompPhysiol, + YEAR = {1973}, + VOLUME = {87}, + PAGES = {137--164} +} + +@ARTICLE{Heiligenberg1975, + AUTHOR = {Walter Heiligenberg}, + TITLE = {Theoretical and experimental approaches to spatial aspects of electrolocation.}, + JOURNAL = JCompPhysiol, + YEAR = {1975}, + VOLUME = {103}, + PAGES = {247--272} +} + +@ARTICLE{Heiligenberg1976, + AUTHOR = {Walter Heiligenberg}, + TITLE = {Electrolocation and jamming avoidance in the mormyrid fish \textit{Brienomyrus}.}, + JOURNAL = JCompPhysiol, + YEAR = {1976}, + VOLUME = {109}, + PAGES = {357--372} +} + +@ARTICLE{Heiligenberg1978, + AUTHOR = {Walter Heiligenberg and Richard A. Altes}, + TITLE = {Phase sensitivity in electrorecption}, + JOURNAL = Science, + YEAR = {1978}, + VOLUME = {199}, + PAGES = {1001--1003} +} + + +@article{Heiligenberg1981, + title={How electroreceptors encode {JAR}-eliciting stimulus regimes: reading trajectories in a phase-amplitude plane}, + author={Heiligenberg, Walter and Partridge, Brian L}, + journal={Journal of Comparative Physiology}, + volume={142}, + pages={295--308}, + year={1981}, + publisher={Springer} +} + + +@Article{Heiligenberg1982, + title={Labelling of electroreceptive afferents in a gymnotoid fish by intracellular injection of {HRP}: the mystery of multiple maps}, + author={Heiligenberg, Walter and Dye, John}, + journal={Journal of Comparative Physiology}, + volume={148}, + pages={287--296}, + year={1982}, + publisher={Springer} +} + + +@book{Heiligenberg1991, + title={Neural nets in electric fish}, + author={Heiligenberg, Walter}, + year={1991}, + publisher={MIT press Cambridge, MA} +} + +@ARTICLE{Heiligenberg1996, + AUTHOR = {W. Heiligenberg and W. Metzner and C. J. H. Wong and C. H. Keller}, + TITLE = {Motor control of the jamming avoidance response of \textit{Apteronotus leptorhynchus}: evolutionary changes of a behavior and its neuronal substrates.}, + JOURNAL = JCompPhysiolA, + YEAR = {1996}, + VOLUME = {179}, + PAGES = {653--674} +} + + +@book{Helmholtz2009, + title={On the sensations of tone as a physiological basis for the theory of music}, + author={Helmholtz, Hermann LF}, + year={1875}, + publisher={Cambridge University Press} +} + + +@article{Hendrycks2016, + title={Gaussian error linear units {(gelus)}}, + author={Hendrycks, Dan and Gimpel, Kevin}, + journal={arXiv preprint arXiv:1606.08415}, + year={2016} +} + + +@Article{Hennig2004, + Title = {Processing of auditory information in insects.}, + Author = {R. M. Hennig and A. Franz and A. Stumpner}, + Journal = MicroscResTech, + Year = {2004}, + Pages = {351--374}, + Volume = {63} +} + +@Article{Henninger2018, + Title = {Statistics of natural communication signals observed in the wild identify important yet neglected stimulus regimes in weakly electric fish.}, + Author = {J\"org Henninger and R\"udiger Krahe and Frank Kirschbaum and Jan Grewe and Jan Benda}, + Journal = {J Neurosci}, + Year = {2018}, + Pages = {5456--5465}, + Volume = {38} +} + +@Article{Henninger2020, + Title = {Tracking activity patterns of a multispecies community of gymnotiform weakly electric fish in their neotropical habitat without tagging}, + Author = {Henninger, J{\"o}rg and Krahe, R{\"u}diger and Sinz, Fabian and Benda, Jan}, + Journal = {J Exp Biol}, + Year = {2020}, + Volume = {223}, + + Abstract = {Field studies on freely behaving animals commonly require tagging and often are focused on single species. Weakly electric fish generate a species- and individual-specific electric organ discharge (EOD) and therefore provide a unique opportunity for individual tracking without tagging. Here, we present and test tracking algorithms based on recordings with submerged electrode arrays. Harmonic structures extracted from power spectra provide fish identity. Localization of fish based on weighted averages of their EOD amplitudes is found to be more robust than fitting a dipole model. We apply these techniques to monitor a community of three species, \textit{Apteronotus rostratus}, Eigenmannia humboldtii and Sternopygus dariensis, in their natural habitat in Dari{\'e}n, Panama. We found consistent upstream movements after sunset followed by downstream movements in the second half of the night. Extrapolations of these movements and estimates of fish density obtained from additional transect data suggest that some fish cover at least several hundreds of meters of the stream per night. Most fish, including E. humboldtii, were traversing the electrode array solitarily. From in situ measurements of the decay of the EOD amplitude with distance of individual animals, we estimated that fish can detect conspecifics at distances of up to 2 m. Our recordings also emphasize the complexity of natural electrosensory scenes resulting from the interactions of the EODs of different species. Electrode arrays thus provide an unprecedented window into the so-far hidden nocturnal activities of multispecies communities of weakly electric fish at an unmatched level of detail.}, + Pages = {jeb206342}, + Owner = {raab}, + Publisher = {The Company of Biologists Ltd}, + Timestamp = {2020.02.11} +} + +@article{Henry2017, + title={What can we learn about beat perception by comparing brain signals and stimulus envelopes?}, + author={Henry, Molly J and Herrmann, Bj{\"o}rn and Grahn, Jessica A}, + journal={PLoS One}, + volume={12}, + number={2}, + pages={e0172454}, + year={2017}, + publisher={Public Library of Science San Francisco, CA USA} +} + +@article{Hind1967, + title={Coding of information pertaining to paired low-frequency tones in single auditory nerve fibers of the squirrel monkey.}, + author={Hind, JOSEPH E and Anderson, DAVID J and Brugge, JOHN F and Rose, JERZY E}, + journal={Journal of Neurophysiology}, + volume={30}, + number={4}, + pages={794--816}, + year={1967} +} + + +@Article{Hirabayashi2014, + Title = {Computational principles of microcircuits for visual object processing in the macaque temporal cortex.}, + Author = {Toshiyuki Hirabayashi and Yasushi Miyashita}, + Journal = TINS, + Year = {2014}, + Number = {3}, + Pages = {178-187}, + Volume = {37} +} + +@Article{Hladnik2023, + AUTHOR = {T. C. Hladnik and J. Grewe}, + TITLE = {Receptive field sizes and neuronal encoding bandwidth are constrained by axonal conduction delays}, + JOURNAL = {PLoS Comput Biol}, + YEAR = {2023}, + NUMBER = {19}, + VOLUME = {8}, + Doi = {https://doi.org/ +10.1371/journal.pcbi.1010871} +} + +@Article{Hodgkin1952, + Title = {A Quantitative Description of Membrane Current and its Application to Conduction and Excitation in Nerve.}, + Author = {A. L. Hodgkin and A. F. Huxley}, + Journal = JPhysiol, + Year = {1952}, + Pages = {500--544}, + Volume = {117} +} + +@Article{Hofmann2008, + Title = {Response properties of electrosensory units in the midbrain tectum of the paddlefish {(Polyodon spathula Walbaum)}.}, + Author = {M.H. Hofmann and S.N. Jung and U. Siebenaller and M. Prei{\ss}ner and B.P. Chagnaud and L.A. Wilkens}, + Journal = {Journal of Experimental Biology}, + Year = {2008}, + Pages = {773-779}, + Volume = {211} +} + +@ARTICLE{Hofmann2013, + AUTHOR = {Volker Hofmann and Juan I. Sanguinetti-Scheck and Leonel G\'omez-Sena and Jacob Engelmann}, + TITLE = {From static electric images to electric flow: Towards dynamic perceptual cues +in active electroreception.}, + JOURNAL = {Journal of Physiology-Paris}, + YEAR = {2013}, + VOLUME = {107}, + PAGES = {95--106} +} + +@ARTICLE{Hofmann2017, + AUTHOR = {Volker Hofmann and Juan I. Sanguinetti-Scheck and Leonel G\'omez-Sena and Jacob Engelmann}, + TITLE = {Flow as a basis for a novel distance cue in freely behaving electric fish.}, + JOURNAL = JNeurosci, + YEAR = {2017}, + VOLUME = {37}, + PAGES = {302--312} +} + +@Article{Hojesjo1998, + Title = {The importance of being familiar: individual recognition and social behavior in sea trout {(Salmo trutta)}}, + Author = {H\"ojesj\"o, Johan and Johnsson, J\"orgen I. and Petersson, Erik and J\"arvi, Torbj\"orn}, + Journal = BehavEcol, + Year = {1998}, + Number = {5}, + Pages = {445-451}, + Volume = {9}, + + Doi = {https://doi.org/10.1093/beheco/9.5.445}, + Owner = {raab}, + Timestamp = {2020.01.27} +} + + +@ARTICLE{Hopkins1972, + AUTHOR = {Carl D. Hopkins}, + TITLE = {Sex differences in electric signaling in an electric fish.}, + JOURNAL = Science, + YEAR = {1972}, + VOLUME = {176}, + PAGES = {1035--1037} +} + +@ARTICLE{Hopkins1974Eigen, + AUTHOR = {Carl D. Hopkins}, + TITLE = {Electric communication: functions in the social behavior of \textit{Eigenmannia virescens}.}, + JOURNAL = {Behavior}, + YEAR = {1974}, + VOLUME = {50}, + PAGES = {270--304} +} + +@ARTICLE{Hopkins1974Sterno, + AUTHOR = {Carl D. Hopkins}, + TITLE = {Electric communication in the reproductive behavior of \textit{Sternopygus macrurus} {(Gymnotoidei)}.}, + JOURNAL = {Zeitschrift für Tierpsychologie}, + YEAR = {1974}, + VOLUME = {35}, + PAGES = {518--535} +} + +@ARTICLE{Hopkins1976, + AUTHOR = {Carl D. Hopkins}, + TITLE = {Stimulus filtering and electroreception: tuberous electroreceptors in three species of gymnotoid fish.}, + JOURNAL = {Journal of Comparative Physiology}, + YEAR = {1976}, + VOLUME = {111}, + PAGES = {171--207} +} + +@ARTICLE{Hopkins1978, + AUTHOR = {Carl D. Hopkins and Walter F. Heiligenberg}, + TITLE = {Evolutionary designs for electric signals and electroreceptors in gymnotoid fishes of {Surinam}.}, + JOURNAL = BehavEcolSociobiol, + YEAR = {1978}, + VOLUME = {3}, + PAGES = {113--134} +} + +@ARTICLE{Hopkins1980, + AUTHOR = {Carl D. Hopkins}, + TITLE = {Evolution of electric communication channels of mormyrids.}, + JOURNAL = BehavEcolSociobiol, + YEAR = {1980}, + VOLUME = {7}, + PAGES = {1--13} +} + +@ARTICLE{Hopkins1981, + AUTHOR = {Carl D. Hopkins and Andrew H. Bass}, + TITLE = {Temporal coding of species recognition signals in an electric fish.}, + JOURNAL = Science, + YEAR = {1981}, + VOLUME = {212}, + PAGES = {85--87} +} + +@ARTICLE{Hopkins1986Temporal, + AUTHOR = {Carl D. Hopkins}, + TITLE = {Temporal strucuture of non-propagated electric communication signals.}, + JOURNAL = BrainBehavEvol, + YEAR = {1986}, + VOLUME = {28}, + PAGES = {43--59} +} + +@ARTICLE{Hopkins1986Time, + AUTHOR = {Carl D. Hopkins and G. W. Max Westby}, + TITLE = {Time domain processing of electric organ discharge waveforms by pulse-type electric fish.}, + JOURNAL = BrainBehavEvol, + YEAR = {1986}, + VOLUME = {29}, + PAGES = {77--104} +} + +@ARTICLE{Hopkins1990, + AUTHOR = {Carl D. Hopkins and Nathaniel C. Comfort and Joseph Bastian and Andreas H. Bass}, + TITLE = {Functional analysis of sexual dimorphism in an electric fish, \textit{Hypopomus pinnicaudatus}, order {Gymnotiformes}.}, + JOURNAL = BrainBehavEvol, + YEAR = {1990}, + VOLUME = {35}, + PAGES = {350--367} +} + +@ARTICLE{Hopkins1999, + AUTHOR = {Carl D. Hopkins}, + TITLE = {Design features for electric communication.}, + JOURNAL = {Journal of Experimental Biology}, + YEAR = {1999}, + VOLUME = {202}, + PAGES = {1217--128} +} + +@ARTICLE{Hoshimiya1980, + AUTHOR = {N. Hoshimiya and K. Shogen and T. Matsuo and S. Chichibu}, + TITLE = {The \textit{Apteronotus} {EOD} field: waveform and {EOD} field simulation}, + JOURNAL = JCompPhysiol, + YEAR = {1980}, + VOLUME = {135}, + PAGES = {283--290} +} + +@Article{Hosoya2005, + Title = {Dynamic predictive coding by the retina.}, + Author = {Toshihiko Hosoya and Stephen A. Baccus and Markus Meister}, + Journal = Nature, + Year = {2005}, + Pages = {71-77}, + Volume = {436} +} + +@ARTICLE{Howard1988, + AUTHOR = {J. Howard and A. J. Hudspeth}, + TITLE = {Compliance of the hair bundle associated with gating of mechanoelectrical transduction channels in the bullfrog's saccular hair cell.}, + YEAR = {1988}, + JOURNAL = {Neuron}, + VOLUME = {1}, + PAGES = {189--199} } + +@Article{Hubel1959, + title={Receptive fields of single neurones in the cat's striate cortex}, + author={Hubel, David H and Wiesel, Torsten N}, + journal={The Journal of Physiology}, + volume={148}, + number={3}, + pages={574}, + year={1959}, + publisher={Wiley-Blackwell} +} + +@article{Hubel1962, + title={Receptive fields, binocular interaction and functional architecture in the cat's visual cortex}, + author={Hubel, David H and Wiesel, Torsten N}, + journal={The Journal of Physiology}, + volume={160}, + number={1}, + pages={106}, + year={1962}, + publisher={Wiley-Blackwell} +} + +@article{Hubel1965, + title={Receptive fields and functional architecture in two nonstriate visual areas (18 and 19) of the cat}, + author={Hubel, David H and Wiesel, Torsten N}, + journal={Journal of Neurophysiology}, + volume={28}, + number={2}, + pages={229--289}, + year={1965} +} + +@article{Hudspeth1988kinetic, + title={{Kinetic analysis of voltage-and ion-dependent conductances in saccular hair cells of the bull-frog, Rana catesbeiana.}}, + author={Hudspeth, AJ and Lewis, RS}, + journal={The Journal of Physiology}, + volume={400}, + number={1}, + pages={237--274}, + year={1988}, + publisher={Wiley Online Library} +} + +@article{Hudspeth1988model, + title={A model for electrical resonance and frequency tuning in saccular hair cells of the bull-frog, {Rana catesbeiana}.}, + author={Hudspeth, AJ and Lewis, RS}, + journal={J Physiol}, + volume={400}, + number={1}, + pages={275--297}, + year={1988}, + publisher={Wiley Online Library} +} + +@Article{Huetz2011, + Title = {Neural codes in the thalamocortical auditory system: from artificial stimuli to communication sounds.}, + Author = {Chlo\'e Huetz and Boris Gour\'evitch and Jean-Marc Edeline}, + Journal = HearRes, + Year = {2011}, + Pages = {147-158}, + Volume = {271} +} + +@Article{Hughey2018, + Title = {Challenges and solutions for studying collective animal behaviour in the wild}, + Author = {Hughey, Lacey F. and Hein, Andrew M. and Strandburg-Peshkin, Ariana and Jensen, Frants H.}, + Journal = PhilTransRSocLondBBiolSci, + Year = {2018}, + Number = {1746}, + Volume = {373}, + + Doi = {10.1098/rstb.2017.0005}, + Owner = {raab}, + Timestamp = {2020.02.11} +} + +@article{Hunter2007, + title={Matplotlib: A {2D} graphics environment}, + author={Hunter, John D}, + journal={Computing in Science \& Engineering}, + volume={9}, + number={3}, + pages={90--95}, + year={2007}, + publisher={IEEE Computer Society} +} + +@Article{Hupe2008, + Title = {Electrocommunication signals in free swimming brown ghost knifefish, \textit{Apteronotus leptorhynchus}}, + Author = {Ginette Hup\'e and John Lewis}, + Journal = {Journal of Experimental Biology}, + Year = {2008}, + Pages = {1657-67}, + Volume = {211}, + + Doi = {10.1242/jeb.013516}, + Owner = {raab}, + Timestamp = {2020.02.11} +} + +@ARTICLE{Hupe2008DF, + AUTHOR = {Ginette J. Hup\'e and John E. Lewis and Jan Benda}, + TITLE = {The effect of difference frequency on electrocommunication: chirp production and encoding in a species of weakly electric fish, \textit{Apteronotus leptorhynchus}.}, + YEAR = {2008}, + JOURNAL = {Journal of Physiology-Paris}, + VOLUME = {102}, + NUMBER = {4--6}, + PAGES = {164--172} } + +@Article{Izhikevich2000, + title={Neural excitability, spiking and bursting}, + author={Izhikevich, Eugene M}, + journal={International Journal of Bifurcation and Chaos}, + volume={10}, + number={06}, + pages={1171--1266}, + year={2000}, + publisher={World Scientific} +} + +@book{Izhikevich2007, + title={Dynamical systems in neuroscience}, + author={Izhikevich, Eugene M}, + year={2007}, + publisher={MIT press} +} + +@Article{Janson1985, + Title = {Aggresive competition and individual food consumption in wild brown capuchin monkeys ({Cebus apella})}, + Author = {Janson, Charles}, + Journal = BehavEcolSociobiol, + Year = {1985}, + Number = {2}, + Pages = {125--138}, + Volume = {18}, + + Abstract = {The impact of aggresive competition on food intake at all the resources used is analysed for every member of a group of brown capuchin monkeys (Cebus apella) in the Manu National Park, Peru, where they live in groups of 8--14 animals. An individual's food intake at a given tree was affected independently both by its domirance rank (Fig. 1) and by how much aggression it received (Table 5). Food intake was not strongly affected by body size when dominance rank was held constant by partial correlation. At food sources where high rates of fighting occurred, an individual's food intake depended more on its domirance status than on the rate of aggression it received (Fig. 2). However, food intake at resources where rates of fighting were low depended mostly on the rate of aggression received. When aggression over food was absent, the food intakes of dominants and subordinates were equal. Dominants had significantly greater total energy intake (20.5{\%} more) than did subordinates, even though more than one third of their diet came from food sources where little or no fighting occurred (Fig. 3). Energy intake was also significantly greater for individuals that received little aggression. The only adult that emigrated from the rescue_local_eod study group was the individua with the lowest energy intake. Competition for food within groups was more than ten times as intense as competition between brown capuchin groups.}, + Day = {01}, + Doi = {10.1007/BF00299041}, + Owner = {raab}, + Timestamp = {2020.01.21}, + Url = {https://doi.org/10.1007/BF00299041} +} + +@article{Janson2022, + title={Motive-modulated attentional orienting: Implicit power motive predicts attentional avoidance of signals of interpersonal dominance.}, + author={Janson, Kevin T and K{\"o}llner, Martin G and Khalaidovski, Ksenia and P{\"u}lschen, Lea-Sarah and Rudnaya, Alexandra and Stamm, Laura and Schultheiss, Oliver C}, + journal={Motivation Science}, + volume={8}, + number={1}, + pages={56}, + year={2022}, + publisher={Educational Publishing Foundation} +} + +@Article{Jason1990, + Title = {Ecological consequences of individual spatial choice in foraging groups of brown capuchin monkeys, {Cebus apella}}, + Author = {Charles H. Janson}, + Journal = AnimBehav, + Year = {1990}, + Number = {5}, + Pages = {922 - 934}, + Volume = {40}, + + Abstract = {Individuals in a foraging group of brown capuchin monkeys choose different spatial positions relative to the rest of the group. An individual's choice of spatial positiion affects its foraging success and perceived predation risk (as measured by vigilance behaviour). The two most dominant group members preferred to forage where their expected forwaging success was greatest. Juveniles chose to forage where their perceived predation risk was least, not where they would achieve the highest foraging success. The positions used by non-dominant adults neither maximized foraging success nor minimized predation risk. It is likely that subordinate adults accept spatial positions with suboptimal ecological consequences to avoid the costs of frequent confrontations with the dominant members of the group over foraging sites in poreferred positions.}, + Doi = {https://doi.org/10.1016/S0003-3472(05)80994-7}, + Owner = {raab}, + Timestamp = {2020.01.21}, + Url = {http://www.sciencedirect.com/science/article/pii/S0003347205809947} +} + +@Article{Jazayeri2006, + Title = {Optimal representation of sensory information by neural populations.}, + Author = {Mehrdad Jazayeri and J Anthony Movshon}, + Journal = {Nature Neuroscience}, + Year = {2006}, + Number = {5}, + Pages = {690-696}, + Volume = {9} +} + +@article{Joris1992, + title={Responses to amplitude-modulated tones in the auditory nerve of the cat}, + author={Joris, Philip X and Yin, Tom CT}, + journal={The Journal of the Acoustical Society of America}, + volume={91}, + number={1}, + pages={215--232}, + year={1992}, + publisher={Acoustical Society of America} +} + +@article{Joris2004, + title={Neural processing of amplitude-modulated sounds}, + author={Joris, PX and Schreiner, CE and Rees, A}, + journal={Physiological Reviews}, + volume={84}, + number={2}, + pages={541--577}, + year={2004} +} + +@article{Juergens1999, + title={{Visual stimulation elicits locked and induced gamma oscillations in monkey intracortical-and {EEG-potentials}, but not in human {EEG}}}, + author={Juergens, Egbert and Guettler, Andreas and Eckhorn, Reinhard}, + journal={Experimental Brain Research}, + volume={129}, + pages={247--259}, + year={1999}, + publisher={Springer} +} + +@article{Julicher2001, + title={Physical basis of two-tone interference in hearing}, + author={J{\"u}licher, Frank and Andor, Daniel and Duke, Thomas}, + journal={Proceedings of the National Academy of Sciences}, + volume={98}, + number={16}, + pages={9080--9085}, + year={2001}, + publisher={National Acad Sciences} +} + +@Article{Jun2013, + Title = {Real-Time Localization of Moving Dipole Sources for Tracking Multiple Free-Swimming Weakly Electric Fish}, + Author = {Jun, James Jaeyoon and Longtin, Andr\'e and Maler, Leonard}, + Journal = PLOSOne, + Year = {2013}, + Number = {6}, + Pages = {1-14}, + Volume = {8}, + Doi = {10.1371/journal.pone.0066596}, + Owner = {raab}, + Publisher = {Public Library of Science}, + Timestamp = {2020.02.11}, + Url = {https://doi.org/10.1371/journal.pone.0066596} +} + +@ARTICLE{Jun2014, + AUTHOR = {James J. Jun and Andr\'e Longtin and Leonard Maler}, + TITLE = {Enhanced sensory sampling precedes spef-initiated locomotion in an electric fish.}, + JOURNAL = {Journal of Experimental Biology}, + YEAR = {2014}, + VOLUME = {217}, + PAGES = {3615--3628} +} + +@INCOLLECTION{Kalmijn1974, + TITLE = {The detection of electric fields from inanimate and animate sources other than electric organs.}, + AUTHOR = {A. J. Kalmijn}, + Year = {1974}, + Pages = {148--194}, + BOOKTITLE = {Electroreceptors and other specialized receptors in lower vertrebrates}, + EDITOR = {A. Fessard}, + PUBLISHER = {Springer}, + ADDRESS = {Heidelberg} +} + +@book{Kandel2000, + title={Principles of neural science}, + author={Kandel, Eric R and Schwartz, James H and Jessell, Thomas M and Siegelbaum, Steven and Hudspeth, A James and Mack, Sarah and others}, + volume={4}, + year={2000}, + publisher={McGraw-hill New York} +} + +@Article{Kappeler2008, + Title = {The lemur syndrome unresolved: extreme male reproductive skew in sifakas ({Propithecus verreauxi}), a sexually monomorphic primate with female dominance}, + Author = {Kappeler, Peter M. +and Sch{\"a}ffler, Livia}, + Journal = BehavEcolSociobiol, + Year = {2008}, + Number = {6}, + Pages = {1007--1015}, + Volume = {62}, + Day = {01}, + Doi = {10.1007/s00265-007-0528-6}, + Owner = {raab}, + Timestamp = {2020.01.23}, + Url = {https://doi.org/10.1007/s00265-007-0528-6} +} + +@Article{Karri2020, + title={Spinal cord stimulation for chronic pain syndromes: a review of considerations in practice management}, + author={Karri, Jay and Joshi, Mihir and Polson, George and Tang, Tuan and Maxwell, Lee and Orhurhu, Vwaire and Deer, Timothy and Abd-Elsayed, Alaa}, + journal={Pain Physician}, + volume={23}, + number={6}, + pages={599}, + year={2020}, + publisher={American Society of Interventional Pain Physician} +} + +@article{Kashimori1996, + title={Model of P-and {T-electroreceptors} of weakly electric fish}, + author={Kashimori, Yoshiki and Goto, Mituyuki and Kambara, Takeshi}, + journal={Biophysical Journal}, + volume={70}, + number={6}, + pages={2513--2526}, + year={1996}, + publisher={Elsevier} +} + +@ARTICLE{Kelly2008, + AUTHOR = {Marc Kelly and David Babineau and Andr\'e Longtin and John E. Lewis}, + TITLE = {Electric field interactions in pairs of electric fish: modeling and mimicking naturalistic inputs.}, + JOURNAL = BiolCybern, + YEAR = {2008}, + VOLUME = {98}, + PAGES = {479--490} +} + +@Article{Kemp1978, + title={Stimulated acoustic emissions from within the human auditory system}, + author={Kemp, David T}, + journal={The Journal of the Acoustical Society of America}, + volume={64}, + number={5}, + pages={1386--1391}, + year={1978}, + publisher={Acoustical Society of America} +} + +@Article{Kern2005, + Title = {Function of a Fly Motion-Sensitive Neuron Matches Eye Movements during Free Flight.}, + Author = {Roland Kern and J. H. van Hateren and Christian Michaelis and Jens Peter Lindemann and Martin Egelhaaf}, + Journal = PLoSBiol, + Year = {2005}, + Pages = {e171}, + Volume = {3} +} + +@Article{Kerth2003, + Title = {Information Transfer about Roosts in Female Bechstein's Bats: An Experimental Field Study}, + Author = {Gerald Kerth and Karsten Reckardt}, + Journal = {Proceedings: Biological Sciences}, + Year = {2003}, + Number = {1514}, + Pages = {511-515}, + Volume = {270}, + + Doi = {10.2307/3558892}, + Owner = {raab}, + Timestamp = {2020.01.30} +} + +@Article{Khanbabaie2010, + title={Kinetics of fast short-term depression are matched to spike train statistics to reduce noise}, + author={Khanbabaie, Reza and Nesse, William H and Longtin, Andre and Maler, Leonard}, + journal={Journal of Neurophysiology}, + volume={103}, + number={6}, + pages={3337--3348}, + year={2010}, + publisher={American Physiological Society Bethesda, MD} +} + +@article{Khanna1989, + title={Spectral characteristics of the responses of primary auditory-nerve fibers to amplitude-modulated signals}, + author={Khanna, SM and Teich, MC}, + journal={Hearing Research}, + volume={39}, + number={1-2}, + pages={143--157}, + year={1989}, + publisher={Elsevier} +} + +@Article{Khosravi-Hashemi2014, + Title = {Motion processing across multiple topographic maps in the electrosensory system.}, + Author = {Navid Khosravi-Hashemi and Maurice J. Chacron}, + Journal = PhysiolRep, + Year = {2014}, + Number = {3}, + Pages = {e00253}, + Volume = {2} +} + +@article{King2019, + title={Accounting for masking of frequency modulation by amplitude modulation with the modulation filter-bank concept}, + author={King, Andrew and Varnet, L{\'e}o and Lorenzi, Christian}, + journal={The Journal of the Acoustical Society of America}, + volume={145}, + number={4}, + pages={2277--2293}, + year={2019}, + publisher={AIP Publishing} +} + +@ARTICLE{Kirschbaum1983, + AUTHOR = {F. Kirschbaum}, + TITLE = {Myogenic electric organ precedes the neurogenic organ in apteronotid fish.}, + JOURNAL = {Naturwissenschaften}, + YEAR = {1983}, + VOLUME = {70}, + PAGES = {205--207} +} + +@Article{Kirschbaum2002, + Title = {Reproductive strategies and developmental aspects in mormyrid and gymnotiform fishes}, + Author = {Frank Kirschbaum and Christian Schugardt}, + Journal = {Journal of Physiology-Paris}, + Year = {2002}, + Number = {5}, + Pages = {557 - 566}, + Volume = {96}, + Doi = {https://doi.org/10.1016/S0928-4257(03)00011-1}, + Keywords = {Reproductive strategies, Mormyrids, Gymnotiforms, Fecundity, Cyclical reproduction}, + Owner = {raab}, + Timestamp = {2020.02.11}, + Url = {http://www.sciencedirect.com/science/article/pii/S0928425703000111} +} + +@article{Kiskinis2018, + title={{All-optical electrophysiology for high-throughput functional characterization of a human iPSC-derived motor neuron model of ALS}}, + author={Kiskinis, Evangelos and Kralj, Joel M and Zou, Peng and Weinstein, Eli N and Zhang, Hongkang and Tsioras, Konstantinos and Wiskow, Ole and Ortega, J Alberto and Eggan, Kevin and Cohen, Adam E}, + journal={Stem Cell Reports}, + volume={10}, + number={6}, + pages={1991--2004}, + year={2018}, + publisher={Elsevier} +} + +@ARTICLE{Knight1972a, + AUTHOR = {Bruce W. Knight}, + TITLE = {Dynamics of Encoding in a Population of Neurons.}, + YEAR = {1972}, + JOURNAL = {The Journal of General Physiology}, + VOLUME = {59}, + PAGES = {734--766} } + +@article{Knudsen1974, + author = {Knudsen, EI}, + journal = {Journal of Comparative Physiology}, + number = {4}, + pages = {333--353}, + publisher = {Springer}, + title = {Behavioral thresholds to electric signals in high + frequency electric fish}, + volume = {91}, + year = {1974} +} + +@article{Knudsen1975, + author = {Knudsen, EI}, + journal = {Journal of Comparative Physiology}, + number = {2}, + pages = {103--118}, + publisher = {Springer}, + title = {Spatial aspects of the electric fields generated by + weakly electric fish}, + volume = {99}, + year = {1975} +} + +@Article{Knudsen1976a, + Title = {Midbrain Responses to Electroreceptive Input in Catfish - Evidence of Orientation Preferences and Somatotopic Organization.}, + Author = {Eric I. Knudsen}, + Journal = JCompPhysiol, + Year = {1976}, + Pages = {51-67}, + Volume = {106} +} + +@Article{Knudsen1976b, + Title = {Midbrain Units in Catfish: Response Properties to Electroreceptive Input.}, + Author = {Eric I. Knudsen}, + Journal = JCompPhysiol, + Year = {1976}, + Pages = {315-335}, + Volume = {109} +} + +@Article{Knudsen1978, + Title = {Funcitonal Organization in Electroreceptive Midbrain of the Catfish.}, + Author = {Eric I. Knudsen}, + Journal = {Journal of Neurophysiology}, + Year = {1978}, + Number = {2}, + Pages = {350-364}, + Volume = {41} +} + +@article{Knudsen2007, + title={Fundamental components of attention}, + author={Knudsen, Eric I}, + journal={Annual Review of Neuroscience}, + volume={30}, + pages={57--78}, + year={2007}, + publisher={Annual Reviews} +} + +@Article{Koelsch2005, + title={Towards a neural basis of music perception}, + author={Koelsch, Stefan and Siebel, Walter A}, + journal={Trends in Cognitive Sciences}, + volume={9}, + number={12}, + pages={578--584}, + year={2005}, + publisher={Elsevier} +} + + + +@article{Koenig1876, + title={{LI. On the simultaneous sounding of two notes}}, + author={K{\"o}nig, Rudolph}, + journal={The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science}, + volume={1}, + number={6}, + pages={417--446}, + year={1876}, + publisher={Taylor \& Francis} +} + +@article{Koenig1881, + title={Ueber den Ursprung der St{\"o}sse und Stosst{\"o}ne bei harmonischen Intervallen}, + author={Koenig, Rudolph}, + journal={Annalen der Physik}, + volume={248}, + number={3}, + pages={335--349}, + year={1881}, + publisher={Wiley Online Library} +} + +@Article{Koerding2004, + Title = {How Are Complex Cell Properties Adapted to the Statistics of Natural Stimuli?}, + Author = {Konrad P. K\"ording and Christoph Kayser and Wolfgang Einh\"auser and Peter K\"onig}, + Journal = {Journal of Neurophysiology}, + Year = {2004}, + Pages = {206-212}, + Volume = {91} +} + +@article{Koch1995, + title={Do neurons have a voltage or a current threshold for action potential initiation?}, + author={Koch, Christof and Bernander, {\"O}jvind and Douglas, Rodney J}, + journal={J Comput Neurosci}, + volume={2}, + pages={63--82}, + year={1995}, + publisher={Springer} +} + +@ARTICLE{Kolodziejski2005, + AUTHOR = {Johanna A. Kolodziejski and Brian S. Nelson and G. Troy Smith}, + TITLE = {Sex and species differences in neuromodulatory input to a premotor nucleus: a comparative study of substance {P} and communication behavior in weakly electric fish.}, + JOURNAL = {J Neuro Biol}, + YEAR = {2005}, + VOLUME = {62}, + PAGES = {299--315} +} + +@article{Koppl1997, + title={Phase locking to high frequencies in the auditory nerve and cochlear nucleus magnocellularis of the barn owl, {Tyto alba}}, + author={K{\"o}ppl, Christine}, + journal={Journal of Neuroscience}, + volume={17}, + number={9}, + pages={3312--3321}, + year={1997} +} + +@Article{Korstjens2006, + Title = {Time as a constraint on group size in spider monkeys}, + Author = {Korstjens, Amanda H. +and Verhoeckx, Ingrid Lugo +and Dunbar, Robin I. M.}, + Journal = BehavEcolSociobiol, + Year = {2006}, + Number = {5}, + Pages = {683}, + Volume = {60}, + + Abstract = {An animal can only survive in a given habitat if it has enough time to find, process and digest food whilst avoiding predation. The time it has for food acquisition is affected by the vegetation and competition with conspecifics, which depends on aggregation tendencies. We used the relationships between time allocations, on the one hand, and climatic variables (as a proxy for habitat quality) and group size, on the other, to develop a model that predicts maximum ecologically tolerable group size at different locations for spider monkeys. Spider monkeys are particularly interesting because the social communities often split up into small units. Temperature variation and rainfall variation were the rescue_local_eod determinants of time budgets. Community size and average annual rainfall determined party size. The model correctly predicted presence or absence of spider monkeys at 78--83{\%} of 217 New World forest sites. Within the geographical range of the species, this time budget model predicted the presence of spider monkeys better than a model based directly on climate variables. Predicted community and party sizes were significantly larger at sites where spider monkeys are present than at sites where they are absent. As required by the model, predicted maximum community sizes were significantly larger than observed community sizes. Moving time showed a U-shaped relationship with party size, which suggests that moving time is the factor that keeps spider monkey communities from travelling together in a tight group.}, + Day = {20}, + Doi = {10.1007/s00265-006-0212-2}, + Owner = {raab}, + Timestamp = {2020.01.21}, + Url = {https://doi.org/10.1007/s00265-006-0212-2} +} + +@article{Kozmik2008, + title={Assembly of the cnidarian camera-type eye from vertebrate-like components}, + author={Kozmik, Zbynek and Ruzickova, Jana and Jonasova, Kristyna and Matsumoto, Yoshifumi and Vopalensky, Pavel and Kozmikova, Iryna and Strnad, Hynek and Kawamura, Shoji and Piatigorsky, Joram and Paces, Vaclav and others}, + journal={Proceedings of the National Academy of Sciences}, + volume={105}, + number={26}, + pages={8989--8993}, + year={2008}, + publisher={National Acad Sciences} +} + + + +@Article{Krahe2004, + Title = {Burst firing in sensory systems.}, + Author = {R\"udiger Krahe and Fabrizio Gabbiani}, + Journal = {Nature Reviews Neuroscience}, + Year = {2004}, + Month = {Jan}, + Number = {1}, + Pages = {13--23}, + Volume = {5}, + DOI = {10.1038/nrn1296}, + File = {:Krahe_Gabbiani_{Nature Neuroscience}Rev_.pdf:PDF}, + Institution = {Beckman Institute for Advanced Science and Technology and Department of Molecular and Integrative Physiology, University of Illinois at Urbana/Champaign, 405 North Mathews Avenue, Urbana, Illinois 61801, USA.}, + Keywords = {Action Potentials; Animals; Brain; Humans; Nerve Net; Neurons; Neurons, Afferent}, + Pii = {nrn1296}, + Pmid = {14661065}, + Refid = {731}, + Timestamp = {2011.06.14}, + URL = {http://dx.doi.org/10.1038/nrn1296} +} + +@Article{Krahe2008, + title={Temporal processing across multiple topographic maps in the electrosensory system}, + author={Krahe, Rudiger and Bastian, Joseph and Chacron, Maurice J}, + journal={Journal of Neurophysiology}, + volume={100}, + number={2}, + pages={852--867}, + year={2008}, + publisher={American Physiological Society} +} + +@Article{Krahe2014, + Title = {Neural maps in the electrosensory system of weakly elcectric fish.}, + Author = {R\"udiger Krahe and Leonard Maler}, + Journal = {Current Opinion in Neurobiology}, + Year = {2014}, + Pages = {13-21}, + Volume = {24} +} + + + +@incollection{Kramer1981, +title = {Species specificity of electric organ discharges in a sympatric group of gymnotoid fish from {Manaus} ({Amazonas}).}, +editor = {T. Szabó and G. Czéh}, +booktitle = {Sensory physiology of aquatic lower vertebrates}, +publisher = {Pergamon}, +pages = {195-219}, +year = {1981}, +isbn = {978-0-08-027352-5}, +doi = {https://doi.org/10.1016/B978-0-08-027352-5.50018-5}, +url = {https://www.sciencedirect.com/science/article/pii/B9780080273525500185}, +author = {Bernd Kramer and Frank Kirschbaum and Hubert Markl}, +abstract = {SUMMARY +We collected weakly electric gymnotoid fish in the vicinity of Manaus, Amazonas, in the Solimoes river (white water). We tried to find out whether Electric Organ Discharges (EODs) are species specific which is essential for their presumed role in recognition of conspecifics and reproductive isolation. We considered at least 43 valid sympatric species, some of them unnamed. All of these displayed stable EOD waveform patterns, most of them clearly distinct from the other species' EODs. Eleven species are of the pulse EOD type, 32 of the wave EOD type (one of the latter is intermediate). The EODs of pulse species were analysed (1) by EOD repetition rate at rest (variation from 1 Hz to 60 Hz), (2) by Fourier amplitude spectrum analysis of single EODs (Fig. 1; in these spectra, frequencies of peak amplitude ranged up to 2300 Hz). There was a significant, positive correlation between both parameters (Fig. 2). Identification of pairs of species with similar EODs by these parameters does not appear to be possible because of inter-individual EOD variations. In wave species there is conclusive evidence that EOD fundamental frequencies (= repetition rate of a complete EOD period) do not allow species identification: twenty-eight wave species displayed EOD fundamental frequencies from 300 to 1800 Hz (Fig. 3). This yields a hypothetical frequency band of 0.09 octave to signal species identity; the actual value of EOD frequency variations in Eigenmannia is much greater (1.2 octaves). Seven species of the family Apteronotidae displayed a new signal type: the main energy of the signal was contained in higher harmonics, and not at the fundamental frequencies (Figs. 6 and 7). For all wave species there was a significant, positive correlation between their dominant frequency (= the strongest signal component) and harmonic content of their EOD although individual species deviated considerably from what was predicted by the regression line (Fig. 8). Thus separation of species was greatly improved compared to the criterion of fundamental frequency (Fig. 3) but still appeared insufficient in a number of cases. Therefore, in both wave and pulse species still other parameters must be involved in recognition of conspecifics.} +} + +@ARTICLE{Kramer1988, + AUTHOR = {Bernd Kramer and B. Otto}, + TITLE = {Female discharges are more electrifying: spontaneous preference in the electric fish, \textit{Eigenmannia} ({Gymnotiformes}, {Teleostei}).}, + JOURNAL = BehavEcolSociobiol, + YEAR = {1988}, + VOLUME = {23}, + PAGES = {55--60} +} + +@ARTICLE{Kramer1999, + AUTHOR = {Bernd Kramer}, + TITLE = {Waveform discrimination, phase sensitivity and jamming avoidance in a wave-type electric fish.}, + JOURNAL = {Journal of Experimental Biology}, + YEAR = {1999}, + VOLUME = {202}, + PAGES = {1387--1398} +} + +@article{Krishna2000, + title={Auditory temporal processing: responses to sinusoidally amplitude-modulated tones in the inferior colliculus}, + author={Krishna, B Suresh and Semple, Malcolm N}, + journal={Journal of Neurophysiology}, + volume={84}, + number={1}, + pages={255--273}, + year={2000} +} + +@article{Kubo1957, + title={Statistical-mechanical theory of irreversible processes. {I}. General theory and simple applications to magnetic and conduction problems}, + author={Kubo, Ryogo}, + journal={Journal of the physical society of Japan}, + volume={12}, + number={6}, + pages={570--586}, + year={1957}, + publisher={The Physical Society of Japan} +} + +@article{Kujawa1995, + title={{Time-varying alterations in the {f2- f1 DPOAE} response to continuous primary stimulation {I}: Response characterization and contribution of the olivocochlear efferents}}, + author={Kujawa, SG and Fallon, M and Bobbin, RP}, + journal={Hearing Research}, + volume={85}, + number={1-2}, + pages={142--154}, + year={1995}, + publisher={Elsevier} +} + +@inproceedings{Kunkel2010, + title={A reassessment of the simultaneous dynamic range of the human visual system}, + author={Kunkel, Timo and Reinhard, Erik}, + booktitle={Proceedings of the 7th symposium on applied perception in graphics and visualization}, + pages={17--24}, + year={2010} +} + +@article{Lamore1986, + title={Envelope detection of amplitude-modulated high-frequency sinusoidal signals by skin mechanoreceptors}, + author={Lamore, PJJ and Muijser, H and Keemink, CJ}, + journal={The Journal of the Acoustical Society of America}, + volume={79}, + number={4}, + pages={1082--1085}, + year={1986}, + publisher={Acoustical Society of America} +} + +@Article{Land1977, + title={The retinex theory of color vision}, + author={Land, Edwin H}, + journal={Scientific american}, + volume={237}, + number={6}, + pages={108--129}, + year={1977}, + publisher={JSTOR} +} + +@article{Langley1996, + title={Linear filtering precedes nonlinear processing in early vision}, + author={Langley, K and Fleet, DJ and Hibbard, PB}, + journal={Current Biology}, + volume={6}, + number={7}, + pages={891--896}, + year={1996}, + publisher={Elsevier} +} + +@Article{Larson2014, + Title = {Serotonin modulates electrosensory processing and behavior via {5-HT2-like} receptors.}, + Author = {E.A. Larson and M.G. Metzen and M.J. Chacron}, + Journal = Neuroscience, + Year = {2014}, + Volume = {in press} +} + +@Article{Laughlin1981, + Title = {A simple coding procedure enhances a neuron's information capacity.}, + Author = {S. B. Laughlin}, + Journal = {Zeitschrift für Naturforschung}, + Year = {1981}, + Pages = {910--912}, + Volume = {36C} +} + +@Article{Lavoue2000, + Title = {Phylogenetic Relationships of Mormyrid Electric Fishes ({Mormyridae; Teleostei}) Inferred from Cytochrome b Sequences}, + Author = {S\'ebastien Lavou\'e and R\'emy Bigorne and Guillaume Lecointre and Jean-Fran{\c c}ois Agn\`ese}, + Journal = {Molecular Phylogenetics and Evolution}, + Year = {2000}, + Number = {1}, + Pages = {1 - 10}, + Volume = {14}, + Doi = {https://doi.org/10.1006/mpev.1999.0687}, + Keywords = {Mormyridae, electric fish, phylogeny, cytochrome , electric organ.}, + Owner = {raab}, + Timestamp = {2020.02.11}, + Url = {http://www.sciencedirect.com/science/article/pii/S1055790399906875} +} + +@article{Lavoue2012, + title={Comparable ages for the independent origins of electrogenesis in {African and South American} weakly electric fishes}, + author={Lavou{\'e}, S{\'e}bastien and Miya, Masaki and Arnegard, Matthew E and Sullivan, John P and Hopkins, Carl D and Nishida, Mutsumi}, + journal={PLoS One}, + volume={7}, + number={5}, + pages={e36287}, + year={2012}, + publisher={Public Library of Science San Francisco, USA} +} + +@Article{Lee2003, + Title = {Hierarchical {Bayesian} inference in the visual cortex.}, + Author = {Tai Sing Lee and David Mumford}, + Journal = JOSA, + Year = {2003}, + Number = {7}, + Pages = {1434-1448}, + Volume = {20} +} + +@article{Leek2001, + title={Adaptive procedures in psychophysical research}, + author={Leek, Marjorie R}, + journal={Perception \rm{\&} \textit{Psychophysics}}, + volume={63}, + number={8}, + pages={1279--1292}, + year={2001}, + publisher={Springer} +} + +@Article{Lewicki2002, + Title = {Efficient coding of natural sounds.}, + Author = {Michael S. Lewicki}, + Journal = {Nature Neuroscience}, + Year = {2002}, + Number = {4}, + Pages = {356-363}, + Volume = {5} +} + +@Article{Lewicki2014, + Title = {Scene analysis in the natural environment.}, + Author = {Michael S. Lewicki and Bruno A. Olshausen and Annemarie Surlykke and Cynthia F. Moss}, + Journal = FrontPsychol, + Year = {2014}, + Pages = {1--21}, + Volume = {5} +} + +@Article{Liberman1982, + title={Single-neuron labeling in the cat auditory nerve}, + author={Liberman, MC}, + journal={Science}, + volume={216}, + number={4551}, + pages={1239--1241}, + year={1982}, + publisher={American Association for the Advancement of Science} +} + + +@Article{Lindner2022, + title={Fluctuation-dissipation relations for spiking neurons}, + author={Lindner, Benjamin}, + journal={Physical Review Letters}, + volume={129}, + number={19}, + pages={198101}, + year={2022}, + publisher={APS} +} + + + + +@article{Lisman1997, + title={Bursts as a unit of neural information: making unreliable synapses reliable}, + author={Lisman, John E}, + journal={Trends in Neurosciences}, + volume={20}, + number={1}, + pages={38--43}, + year={1997}, + publisher={Elsevier} +} + +@ARTICLE{Lissmann1951, + AUTHOR = {H. W. Lissmann}, + TITLE = {Continous electrical signals from the tail of a fish, \textit{Gymnarchus niloticus} Cuv.}, + YEAR = {1951}, + JOURNAL = Nature, + VOLUME = {167}, + PAGES = {201--202} } + +@ARTICLE{Lissmann1958Function, + AUTHOR = {H. W. Lissmann}, + TITLE = {On the function and evolution of electric organs in fish.}, + JOURNAL = {Journal of Experimental Biology}, + YEAR = {1958}, + VOLUME = {35}, + PAGES = {156--191} +} + +@ARTICLE{Lissmann1958Mechanism, + AUTHOR = {H. W. Lissmann and K. E. Machin}, + TITLE = {The mechanism of object location in \textit{Gymnarchus niloticus} and similar fish.}, + JOURNAL = {Journal of Experimental Biology}, + YEAR = {1958}, + VOLUME = {35}, + PAGES = {451--486} +} + +@ARTICLE{Lissmann1965, + AUTHOR = {Hans W. Lissmann and Hosrt O. Schwassmann}, + TITLE = {Activity rhythm of an electric fish, \textit{Gymnorhamphichtys hypostomus}, Ellis.}, + JOURNAL = {Z vergl Physiol}, + YEAR = {1965}, + VOLUME = {51}, + PAGES = {153--171} +} + +@Article{Litwin-Kumar2012, + Title = {The Spatial Structure of Stimuli Shapes the Timescale of Correlations in Population Spiking Activity.}, + Author = {Ashok Litwin-Kumar and Maurice J. Chacron and Brent Doiron}, + Journal = {PLoS Computational Biology}, + Year = {2012}, + Number = {9}, + Pages = {e1002667}, + Volume = {8} +} + +@Article{Lochmann2011, + Title = {Neural processing as causal inference.}, + Author = {Timm Lochmann and Sophie Deneve}, + Journal = CurrOpinNeurobiol, + Year = {2011}, + Pages = {774-781}, + Volume = {21} +} + +@article{Longtin1993, + title={Stochastic resonance in neuron models}, + author={Longtin, Andr{\'e}}, + journal={J Statistical Physics}, + volume={70}, + pages={309--327}, + year={1993}, + publisher={Springer} +} + +@Article{Longtin1996, + title={Encoding with bursting, subthreshold oscillations, and noise in mammalian cold receptors}, + author={Longtin, Andre and Hinzer, Karin}, + journal={Neural Computation}, + volume={8}, + number={2}, + pages={215--255}, + year={1996}, + publisher={MIT Press} +} + +@article{Longtin2008, + title={Neural dynamics of envelope coding}, + author={Longtin, Andr{\'e} and Middleton, Jason W and Cieniak, Jakub and Maler, Leonard}, + journal={Mathematical Biosciences}, + volume={214}, + number={1-2}, + pages={87--99}, + year={2008}, + publisher={Elsevier} +} + +@article{Lonsbury1990, + title={The clinical utility of distortion-product otoacoustic emissions.}, + author={Lonsbury-Martin, Brenda L and Martin, Glen K}, + journal={Ear Hearing}, + volume={11}, + number={2}, + pages={144--154}, + year={1990} +} + +@article{Machens2001, + Title = {Representation of acoustic communication signals by insect auditory receptor neurons}, + Abstract = {Despite their simple auditory systems, some insect species recognize certain temporal aspects of acoustic stimuli with an acuity equal to that of vertebrates; however, the underlying neural mechanisms and coding schemes are only partially understood. In this study, we analyze the response characteristics of the peripheral auditory system of grasshoppers with special emphasis on the representation of species- specific communication signals. We use both natural calling songs and artificial random stimuli designed to focus on two low-order statistical properties of the songs: their typical time scales and the distribution of their modulation amplitudes. Based on stimulus reconstruction techniques and quantified within an information- theoretic framework, our data show that artificial stimuli with typical time scales of >40 msec can be read from single spike trains with high accuracy. Faster stimulus variations can be reconstructed only for behaviorally relevant amplitude distributions. The highest rates of information transmission (180 bits/sec) and the highest coding efficiencies (40%) are obtained for stimuli that capture both the time scales and amplitude distributions of natural songs. Use of multiple spike trains significantly improves the reconstruction of stimuli that vary on time scales <40 msec or feature amplitude distributions as occur when several grasshopper songs overlap. Signal-to-noise ratios obtained from the reconstructions of natural songs do not exceed those obtained from artificial stimuli with the same low-order statistical properties. We conclude that auditory receptor neurons are optimized to extract both the time scales and the amplitude distribution of natural songs. They are not optimized, however, to extract higher-order statistical properties of the song-specific rhythmic patterns}, + Address = {Innovationskolleg Theoretische Biologie, Institut fur Biologie, Humboldt-Universitat zu Berlin, 10099 Berlin, Germany}, + Author = {Machens, C.K. and Stemmler, M.B. and Prinz, P. and Krahe, R. and Ronacher, B. and Herz, A.V.}, + Comment = {Machens_etal_2001.pdf}, + ISSN = {1529-2401}, + Journal = {J Neurosci}, + Keywords = {*Animal Communication, Acoustic Stimulation/*methods, Action Potentials/physiology, Animal, Auditory Pathways/*physiology, Female, Grasshoppers, Insect, Male, Models,Neurological, Neurons, Neurons,Afferent/*physiology, Periodicity, Reaction Time/physiology, Receptors,Sensory/*physiology, Sensory Thresholds/physiology, Signal Processing,Computer-Assisted, Species Specificity, Support,Non-U.S.Gov't}, + Month = may, + Number = {9}, + Owner = {grewe}, + Pages = {3215--3227}, + Refid = {28}, + Timestamp = {2008.09.26}, + Url = {PM:11312306}, + Volume = {21}, + Year = {2001} +} + +@ARTICLE{Machnik2008, + AUTHOR = {Peter Machnik and Bernd Kramer}, + TITLE = {Female choice by electric pulse duration: attractiveness of the males' communication signal assessed by female bulldog fish, \textit{Marcusenius pongolensis} {(Mormyridae, Teleostei)}.}, + JOURNAL = {Journal of Experimental Biology}, + YEAR = {2008}, + VOLUME = {211}, + PAGES = {1969--1977} +} + +@ARTICLE{MacIver2010, + AUTHOR = {Malcolm A. MacIver and Neelesh A. Patankar and Anup A. Shirgaonkar}, + TITLE = {Energy-information trade-offs between movement and sensing.}, + JOURNAL = {PLoS Computational Biology}, + YEAR = {2010}, + VOLUME = {6}, + PAGES = {e1000769} +} + +@Article{Madhav2018, + Title = {High-resolution behavioral mapping of electric fishes in Amazonian habitats}, + Author = {Manu S. Madhav and Ravikrishnan P. Jayakumar and Alican Demir and Sarah A. Stamper and Eric S. Fortune and Noah J. Cowan}, + Journal = {Scientific Reports}, + Year = {2018}, + Number = {5830}, + Volume = {8}, + + Doi = {https://doi.org/10.1038/s41598-018-24035-5}, + Owner = {raab}, + Timestamp = {2020.02.11} +} + +@article{Maier2008, + title={Integration of bimodal looming signals through neuronal coherence in the temporal lobe}, + author={Maier, Joost X and Chandrasekaran, Chandramouli and Ghazanfar, Asif A}, + journal={Current Biology}, + volume={18}, + number={13}, + pages={963--968}, + year={2008}, + publisher={Elsevier} +} + + +@Article{Maler1974, + Title = {Differential projections of Ordinary Lateral Line Receptors and Electroreceptors in the Gymnotic Fish, {\textit{Apteronotus (Sternarchus) albifrons}}.}, + Author = {L. Maler and T. Finger and H.J. Karten}, + Journal = {Journal of Comparative Neurology}, + Year = {1974}, + Pages = {363-382}, + Volume = {158} +} + +@Article{Maler1979, + Title = {The Posterior Lateral Line Lobe of Certain Gymnotoid Fish: Quantitative Light Microscopy.}, + Author = {Leonard Maler}, + Journal = {Journal of Comparative Neurology}, + Year = {1979}, + Pages = {323-364}, + Volume = {183} +} + +@ARTICLE{Maler2009a, + AUTHOR = {Leonard Maler}, + TITLE = {Receptive field organization across multiple electrosensory maps. {I}. Columnar organization and estimation of receptive field size.}, + YEAR = {2009}, + JOURNAL = {J Comp Neurol}, + VOLUME = {516}, + PAGES = {376--393} } + +@article{Malone2010, + title={Temporal codes for amplitude contrast in auditory cortex}, + author={Malone, Brian J and Scott, Brian H and Semple, Malcolm N}, + journal={Journal of Neuroscience}, + volume={30}, + number={2}, + pages={767--784}, + year={2010}, + publisher={Soc Neuroscience} +} + + +@Article{Manley1990, + title={Peripheral auditory processing in the bobtail lizard {Tiliqua rugosa}: {I}. Frequency tuning of auditory-nerve fibres}, + author={Manley, Geoffrey A and K{\"o}ppl, Christine and Johnstone, Brian M}, + journal={Journal of Comparative Physiology A}, + volume={167}, + pages={89--99}, + year={1990}, + publisher={Springer} +} + +@article{Margolskee2002, + title={Molecular mechanisms of bitter and sweet taste transduction}, + author={Margolskee, Robert F}, + journal={Journal of Biological Chemistry}, + volume={277}, + number={1}, + pages={1--4}, + year={2002}, + publisher={ASBMB} +} + +@Article{Markham2015, + Title = {Optimal group size in a highly social mammal}, + Author = {Markham, A. Catherine and Gesquiere, Laurence R. and Alberts, Susan C. and Altmann, Jeanne}, + Journal = {{Proceedings of the National Academy of Sciences}}, + Year = {2015}, + Number = {48}, + Pages = {14882--14887}, + Volume = {112}, + + Abstract = {What are the costs and benefits for animals living in groups of different sizes? Balancing the trade-offs between within-group competition (which favors smaller groups) and between-group competition (which favors larger groups) suggests that intermediate-sized groups may be best, yet empirical support for this prediction has largely been lacking. Using long-term data on wild baboons, we provide novel evidence that individuals living in intermediate-sized groups have energetically optimal space-use strategies and lower glucocorticoid (stress hormone) concentrations than individuals in either large or small groups. Our results offer new insight into the costs and benefits of group living.Group size is an important trait of social animals, affecting how individuals allocate time and use space, and influencing both an individual{\textquoteright}s fitness and the collective, cooperative behaviors of the group as a whole. Here we tested predictions motivated by the ecological constraints model of group size, examining the effects of group size on ranging patterns and adult female glucocorticoid (stress hormone) concentrations in five social groups of wild baboons (Papio cynocephalus) over an 11-y period. Strikingly, we found evidence that intermediate-sized groups have energetically optimal space-use strategies; both large and small groups experience ranging disadvantages, in contrast to the commonly reported positive linear relationship between group size and home range area and daily travel distance, which depict a disadvantage only in large groups. Specifically, we observed a U-shaped relationship between group size and home range area, average daily distance traveled, evenness of space use within the home range, and glucocorticoid concentrations. We propose that a likely explanation for these U-shaped patterns is that large, socially dominant groups are constrained by within-group competition, whereas small, socially subordinate groups are constrained by between-group competition and predation pressures. Overall, our results provide testable hypotheses for evaluating group-size constraints in other group-living species, in which the costs of intra- and intergroup competition vary as a function of group size.}, + Doi = {10.1073/{Proceedings of the National Academy of Sciences}.1517794112}, + Owner = {raab}, + Publisher = {National Academy of Sciences}, + Timestamp = {2020.01.21}, + Url = {https://www.{Proceedings of the National Academy of Sciences}.org/content/112/48/14882} +} + +@Article{Markham2016, + Title = {Energetics of Sensing and Communication in Electric Fish: A Blessing and a Curse in the {Anthropocene}?}, + Author = {Michael R. Markham and Yue Ban and Austin G. McCauley and Rosalie Maltby}, + Journal = IntegrCompBiol, + Year = {2016}, + Number = {5}, + Pages = {889-900}, + Volume = {56} +} + +@Article{Markham2017, + Title = {Costs and benefits of group living in primates: an energetic perspective}, + Author = {A. Catherine Markham and Laurence R. Gesquiere}, + Journal = PhilTransRSocLondBBiolSci, + Year = {2017}, + Volume = {372}, + + Doi = {http://doi.org/10.1098/rstb.2016.0239}, + Owner = {raab}, + Timestamp = {2020.01.21} +} + +@Article{Marquez2013a, + Title = {Distribution of Muscarinic Acetylcholine Receptor {mRNA} in the Brain of the Weakly Electric Fish \textit{Apteronotus leptorhynchus}.}, + Author = {Brenda Toscano-M\'arquez and Robert J. Dunn and R\"udiger Krahe}, + Journal = {Journal of Comparative Neurology}, + Year = {2013}, + Pages = {1054-1072}, + Volume = {521} +} + +@Article{Marquez2013b, + Title = {Neuromodulation of early electrosensory processing in gymnotiform weakly electric fish.}, + Author = {Brenda Toscano-M\'arquez and R\"udiger Krahe and Maurice J. Chacron}, + Journal = {Journal of Experimental Biology}, + Year = {2013}, + Pages = {2442-2450}, + Volume = {216} +} + +@ARTICLE{Marrero1991, + AUTHOR = {C. Marrero and D. C. Taphorn}, + TITLE = {Notas sobre la historia natural y la distribuicion de los peces {Gymnotiformes} em la cuenca del {Rio Apure} y otros rios de la {Orinoquia}.}, + JOURNAL = {Biollania}, + YEAR = {1991}, + VOLUME = {8}, + PAGES = {123--142} +} + + + +@Article{Marsat2010burst, + title={The structure and size of sensory bursts encode stimulus information but only size affects behavior}, + author={Marsat, Gary and Pollack, Gerald S}, + journal={Journal of Comparative Physiology A}, + volume={196}, + pages={315--320}, + year={2010}, + publisher={Springer} +} + +@Article{Marsat2012a, + Title = {Cellular and circuit properties supporting different sensory coding strategies in electric fish and other systems.}, + Author = {Gary Marsat and Andr\'e Longtin and Leonard Maler}, + Journal = CurrOpinNeurobiol, + Year = {2012}, + Pages = {1-7}, + Volume = {22} +} + +@Article{Marsat2012b, + Title = {Preparing for the unpredictable: adaptive feedback enhances the response to unexpected communication signals.}, + Author = {Gary Marsat and Leonard Maler}, + Journal = {Journal of Neurophysiology}, + Year = {2012}, + Pages = {1241-1246}, + Volume = {107} +} + +@article{Marsat2012bursting, + title={Bursting neurons and ultrasound avoidance in crickets}, + author={Marsat, Gary and Pollack, Gerald S}, + journal={Frontiers in Neuroscience}, + volume={6}, + pages={95}, + year={2012}, + publisher={Frontiers Research Foundation} +} + + +@Article{Mathis2018, + Title = {{DeepLabCut}: markerless pose estimation of user-defined body parts with deep learning}, + Author = {Alexander Mathis and Pranav Mamidanna and Kevin M. Cury and Taiga Abe and Venkatesh N. Murthy and Mackenzie Weygandt Mathis and Matthias Bethge}, + Journal = {Nature Neuroscience}, + Year = {2018}, + Pages = {1281-1289}, + Volume = {21}, + + Doi = {https://doi.org/10.1038/s41593-018-0209-y}, + Owner = {raab}, + Timestamp = {2020.02.11} +} + + +@ARTICLE{Matias2015, + AUTHOR = {Paulo Matias and Jan Frans Willem Slaets and Reynaldo Daniel Pinto}, + TITLE = {Individual discrimination of freely swimming pulse-type electric fish from electrode array recordings.}, + JOURNAL = {Neurocomputing}, + YEAR = {2015}, + VOLUME = {153}, + PAGES = {191--198} +} + +@Article{McAdams1999, + Title = {Effects of attention on orientation-tuning functions of + single neurons in macaque cortical area {V4}.}, + Author = {C. J. McAdams and J. H. Maunsell}, + Journal = JNeurosci, + Year = {1999}, + Pages = {431--441}, + Volume = {19} +} + +@ARTICLE{McAnelly2000, + AUTHOR = {M. Lynne McAnelly and Harold H. Zakon}, + TITLE = {Coregulation of voltage-dependent kinetics of {Na$^+$} and {K$^+$} currents in electric organ.}, + JOURNAL = JNeurosci, + YEAR = {2000}, + VOLUME = {20}, + PAGES = {3408--3414} +} + +@Article{McCreery1977, + Title = {Two Types of Electroreceptive Lateral Lemniscal Neurons of the Lateral Line Lobe of the Catfish {Ictalurus nebulosus}; Connections from the Lateral Line Nerve and Steady-State Frequency Response Characteristics.}, + Author = {Douglas B. McCreery}, + Journal = JCompPhysiol, + Year = {1977}, + Pages = {317-339}, + Volume = {113} +} + +@article{Mcdermott2009, + title={The cocktail party problem}, + author={McDermott, Josh H}, + journal={Current Biology}, + volume={19}, + number={22}, + pages={R1024--R1027}, + year={2009}, + publisher={Elsevier} +} + +@Article{McGillivray2012, + Title = {Parallel Coding of First- and Second-Order Stimulus Attributes by Midbrain Electrosensory Neurons.}, + Author = {Patrick McGillivray and Katrin Vonderschen and Eric S. Fortune and Maurice J. Chacron}, + Journal = JNeurosci, + Year = {2012}, + Number = {16}, + Pages = {5510-5524}, + Volume = {32} +} + +@ARTICLE{McGregor1992, + AUTHOR = {Peter K. McGregor and G. W. Max Westby}, + TITLE = {Discrimination of individually charactersitic electric organ discharges by a weakly electric fish.}, + JOURNAL = AnimBehav, + YEAR = {1992}, + VOLUME = {43}, + PAGES = {977--986} +} + +@ARTICLE{McKibben1993, + AUTHOR = {J. R. McKibben and C. D. Hopkins and D. D. Yager}, + TITLE = {Directional sensitivity of tuberous electroreceptors: polarity preferences and frequency tuning.}, + JOURNAL = JCompPhysiolA, + YEAR = {1993}, + VOLUME = {173}, + PAGES = {415--424} +} + +@inproceedings{Mckinney2010, + title={Data structures for statistical computing in python}, + author={McKinney, Wes and others}, + booktitle={Proceedings of the 9th Python in Science Conference}, + volume={445}, + pages={51--56}, + year={2010}, + organization={Austin, TX} +} + +@Article{Mejias2013, + Title = {Learning Contrast-Invariant Cancellation of Redundant Signals in Neural Systems.}, + Author = {Jorge F. Mejias and Gary Marsat and Kieran Bol and Leonard Maler and Andr\'e Longtin}, + Journal = {PLoS Computational Biology}, + Year = {2013}, + Number = {9}, + Pages = {e1003180}, + Volume = {9} +} + +@Article{Menzel2005, + Title = {Honey bees navigate according to a map-like spatial memory}, + Author = {Menzel, Randolf and Greggers, Uwe and Smith, Alan and Berger, Sandra and Brandt, Robert and Brunke, Sascha and Bundrock, Gesine and H{\"u}lse, Sandra and Pl{\"u}mpe, Tobias and Schaupp, Frank and Sch{\"u}ttler, Elke and Stach, Silke and Stindt, Jan and Stollhoff, Nicola and Watzl, Sebastian}, + Journal = {{Proceedings of the National Academy of Sciences}}, + Year = {2005}, + Number = {8}, + Pages = {3040--3045}, + Volume = {102}, + + Abstract = {By using harmonic radar, we report the complete flight paths of displaced bees. Test bees forage at a feeder or are recruited by a waggle dance indicating the feeder. The flights are recorded after the bees are captured when leaving the hive or the feeder and are released at an unexpected release site. A sequence of behavioral routines become apparent: (i) initial straight flights in which they fly the course that they were on when captured (foraging bees) or that they learned during dance communication (recruited bees); (ii) slow search flights with frequent changes of direction in which they attempt to {\textquotedblleft}get their bearings{\textquotedblright}; and (iii) straight and rapid flights directed either to the hive or first to the feeding station and then to the hive. These straight homing flights start at locations all around the hive and at distances far out of the visual catchment area around the hive or the feeding station. Two essential criteria of a map-like spatial memory are met by these results: bees can set course at any arbitrary location in their familiar area, and they can choose between at least two goals. This finding suggests a rich, map-like organization of spatial memory in navigating honey bees.}, + Doi = {10.1073/{Proceedings of the National Academy of Sciences}.0408550102}, + Owner = {raab}, + Publisher = {National Academy of Sciences}, + Timestamp = {2020.02.11}, + Url = {https://www.{Proceedings of the National Academy of Sciences}.org/content/102/8/3040} +} + +@Article{Meredith2002, + title={On the neuronal basis for multisensory convergence: a brief overview}, + author={Meredith, M Alex}, + journal={Cognitive brain research}, + volume={14}, + number={1}, + pages={31--40}, + year={2002}, + publisher={Elsevier} +} + +@Article{Merkel1965, + title={Magnetismus und {R}ichtungsfinden zugunruhiger {R}otkehlchen ({E}rithacus rubecula)}, + author={Merkel, FW and Wiltschko, W}, + journal={Vogelwarte}, + volume={23}, + number={1}, + pages={71--77}, + year={1965} +} + +@Article{Metcalfe1995, + Title = {Fish recognize and prefer to shoal with poor competitors}, + Author = {Metcalfe, Neil B. and Thomson, Bruce C.}, + Journal = ProcRSocLondBBiolSci, + Year = {1995}, + Number = {1355}, + Pages = {207-210}, + Volume = {259}, + + Doi = {10.1098/rspb.1995.0030}, + Owner = {raab}, + Timestamp = {2020.01.27} +} + +@Article{Metzen2016, + title={Burst firing in the electrosensory system of gymnotiform weakly electric fish: mechanisms and functional roles}, + author={Metzen, Michael G and Krahe, R{\"u}diger and Chacron, Maurice J}, + journal={Frontiers in Computational Neuroscience}, + volume={10}, + pages={81}, + year={2016}, + publisher={Frontiers Media SA} +} + +@ARTICLE{Metzen2017, + AUTHOR = {M. G. Metzen and Maurice J. Chacron}, + TITLE = {Stimulus background influences phase invariant coding by correlated neural activity.}, + YEAR = {2017}, + JOURNAL = {eLife}, + VOLUME = {6}, + PAGES = {e24482} } + +@article{Metzen2018descending, + title={Descending pathways generate perception of and neural responses to weak sensory input}, + author={Metzen, Michael G and Huang, Chengjie G and Chacron, Maurice J}, + journal={PLoS Biology}, + volume={16}, + number={6}, + pages={e2005239}, + year={2018}, + publisher={Public Library of Science San Francisco, CA USA} +} + +@Article{Meyer1982, + Title = {Androgens alter the tuning of electroreceptors.}, + Author = {Meyer, J H and Zakon, H H}, + Journal = {Science}, + Year = {1982}, + Pages = {635--637}, + Volume = {217} +} + +@ARTICLE{Meyer1982Impedances, + AUTHOR = {J. Harlan Meyer}, + TITLE = {Behavioral responses of weakly electric fish to complex impedances.}, + JOURNAL = {JCompPhysiol}, + YEAR = {1982}, + VOLUME = {145}, + PAGES = {459--470} +} + +@Article{Meyer1987, + Title = {Hormone-induced and maturational changes in electric organ discharges and electroreceptor tuning in the weakly electric fishApteronotus}, + Author = {Meyer, J. Harlan +and Leong, Margaret +and Keller, Clifford H.}, + Journal = {JCompPhysiolA}, + Year = {1987}, + Number = {3}, + Pages = {385--394}, + Volume = {160}, + + Abstract = {Plasticity in the frequency of the electric organ discharge (EOD) and electroreceptor tuning of weakly electric fish was studied in the genusApteronotus. Both hormone-induced and maturational changes in EOD frequency and electroreceptor tuning were examined.Apteronotus is different from all other steroid-responsive weakly electric fish in that estradiol-17$\beta$, rather than androgens, induces discharge frequency decreases. This result can account for the `reversed' discharge frequency dimorphism found inApteronotus in which, counter to all other known sexually dimorphic electric fish, females have lower discharge frequencies than males. Studies of electroreceptor tuning inApteronotus indicate that electroreceptors are closely tuned to the frequency of the EOD. This finding was noted not only in adult animals, but also in juvenile animals shortly after the onset of their EODs. Tuning plasticity inApteronotus, as in other species studied, is associated with altered EOD frequencies and was noted in both maturational EOD changes and in estrogen-induced changes. Thus, tuning plasticity appears to be a general phenomenon which occurs concurrent with a variety of EOD changes.}, + Day = {01}, + Doi = {10.1007/BF00613028}, + Owner = {raab}, + Timestamp = {2020.02.11}, + Url = {https://doi.org/10.1007/BF00613028} +} + +@article{Michalski2017, + title={Otoferlin acts as a {Ca$^{2+}$} sensor for vesicle fusion and vesicle pool replenishment at auditory hair cell ribbon synapses}, + author={Michalski, Nicolas and Goutman, Juan D and Auclair, Sarah Marie and de Monvel, Jacques Boutet and Tertrais, Margot and Emptoz, Alice and Parrin, Alexandre and Nouaille, Sylvie and Guillon, Marc and Sachse, Martin and Ciric, Danica and Bahloul, Amel and Hardelin, Jean-Pierre and Sutton, Rodger Bryan and Avan, Paul and Krishnakumar, Shyam S. and Rothman, James E. and Dulon, Didier andSafieddine, Saaid and Petit, Christine}, + journal={Elife}, + volume={6}, + pages={e31013}, + year={2017}, +} + +@ARTICLE{Middleton2006, + AUTHOR = {Jason W. Middleton and Andr\'e Longtin and Jan Benda and Leonard Maler}, + TITLE = {The cellular basis for parallel neural transmission of a high-frequency stimulus and its low-frequency envelope.}, + JOURNAL = {Proceedings of the National Academy of Sciences}, + YEAR = {2006}, + VOLUME = {103}, + PAGES = {14596--14601} +} + +@ARTICLE{Middleton2007, + AUTHOR = {Jason W. Middleton and E. Harvey-Girard and Leonard Maler and Andr\'e Longtin}, + TITLE = {Envelope gating and noise shaping in populations of noisy neurons.}, + JOURNAL = {Physical Review E}, + YEAR = {2007}, + VOLUME = {75}, + PAGES = {021918} +} + +@ARTICLE{Migliaro2005, + AUTHOR = {Adriana Migliaro and Angel A. Caputi and Ruben Budelli}, + TITLE = {Theoretical analysis of pre-receptor image conditioning in weakly electric fish.}, + JOURNAL = {PLoS Computational Biology}, + YEAR = {2005}, + VOLUME = {1}, + PAGES = {e16} +} + +@article{Millman2002, + title={Effect of duration on amplitude-modulation masking}, + author={Millman, Rebecca E and Lorenzi, Christian and Apoux, Fr{\'e}d{\'e}ric and F{\"u}llgrabe, Christian and Green, Gary GR and Bacon, Sid P}, + journal={The Journal of the Acoustical Society of America}, + volume={111}, + number={6}, + pages={2551--2554}, + year={2002}, + publisher={Acoustical Society of America} +} + +@Article{Miramontes1996, + Title = {The Nonlinear Dynamics of Survival and Social Facilitation in Termites}, + Author = {Octavio Miramontes and Og DeSouza}, + Journal = {J Theoret Biol}, + Year = {1996}, + Number = {4}, + Pages = {373 - 380}, + Volume = {181}, + + Abstract = {This paper describes a study on termites, investigating the relationship between increasing group size and individual worker longevity under resource-deprived conditions. It was found that survival was significantly lower for isolated individuals and higher for individuals in bigger group sizes, suggesting that social interactions play an important role in the mechanisms leading to longer survival. A computer model, incorporating individual interactions among mobile cellular automata is presented along with experiments.}, + Doi = {https://doi.org/10.1006/jtbi.1996.0138}, + Owner = {raab}, + Timestamp = {2020.01.21}, + Url = {http://www.sciencedirect.com/science/article/pii/S0022519396901381} +} + +@article{Moller1972, + title={Coding of amplitude and frequency modulated sounds in the cochlear nucleus of the rat}, + author={M{\o}ller, Aage R}, + journal={Acta Physiologica Scandinavica}, + volume={86}, + number={2}, + pages={223--238}, + year={1972}, + publisher={Wiley Online Library} +} + +@article{Moller1976, + title={Dynamic properties of primary auditory fibers compared with cells in the cochlear nucleus}, + author={M{\o}ller, Aage R}, + journal={Acta Physiologica Scandinavica}, + volume={98}, + number={2}, + pages={157--167}, + year={1976}, + publisher={Wiley Online Library} +} + +@Article{Montgomery1984, + Title = {Frequency Response Characteristics of primary and secondary Neurons in the electrosensory System of the Thornback Ray.}, + Author = {J.C. Montgomery}, + Journal = CompBiochemPhysiol, + Year = {1984}, + Number = {1}, + Pages = {189-195}, + Volume = {79A} +} + +@Article{Moore1999, + title={Modulation masking produced by beating modulators}, + author={Moore, Brian CJ and Sek, Aleksander and Glasberg, Brian R}, + journal={The Journal of the Acoustical Society of America}, + volume={106}, + number={2}, + pages={908--918}, + year={1999}, + publisher={Acoustical Society of America} +} + +@article{Moortgat1998, + author = {Moortgat, KT and Keller, CH and Bullock, TH and Sejnowski, TJ}, + journal = {Proceedings of the National Academy of Sciences}, + number = {8}, + pages = {4684--4689}, + title = {Submicrosecond pacemaker precision is behaviorally modulated: the gymnotiform electromotor pathway.}, + volume = {95}, + year = {1998} +} + +@Article{Moreno2014, + title={Information-limiting correlations}, + author={Moreno-Bote, Rub{\'e}n and Beck, Jeffrey and Kanitscheider, Ingmar and Pitkow, Xaq and Latham, Peter and Pouget, Alexandre}, + journal={Nature Neuroscience}, + volume={17}, + number={10}, + pages={1410--1417}, + year={2014}, + publisher={Nature Publishing Group US New York} +} + +@ARTICLE{Moser2016, + AUTHOR = {Tobias Moser and Arnold Starr}, + TITLE = {Auditory neuropathy --- neural and synaptic mechanisms.}, + YEAR = {2016}, + JOURNAL = {Nature Reviews Neurology}, + VOLUME = {12}, + PAGES = {189--149} } + +@article{Myers2003, + title={Rectification and non-linear pre-processing of {EMG} signals for cortico-muscular analysis}, + author={Myers, LJ and Lowery, M and O'malley, M and Vaughan, CL and Heneghan, C and Gibson, A St Clair and Harley, YXR and Sreenivasan, R}, + journal={Journal of Neuroscience Methods}, + volume={124}, + number={2}, + pages={157--165}, + year={2003}, + publisher={Elsevier} +} + +@article{Nauhaus2012, + title={Orthogonal micro-organization of orientation and spatial frequency in primate primary visual cortex}, + author={Nauhaus, Ian and Nielsen, Kristina J and Disney, Anita A and Callaway, Edward M}, + journal={Nature Neuroscience}, + volume={15}, + number={12}, + pages={1683}, + year={2012}, + publisher={Nature Publishing Group} +} + +@article{Neiman2011fish, + title={Sensory coding in oscillatory electroreceptors of paddlefish}, + author={Neiman, Alexander B and Russell, David F}, + journal={Chaos: An Interdisciplinary Journal of Nonlinear Science}, + volume={21}, + number={4}, + year={2011}, + publisher={AIP Publishing} +} + +@Article{Nelson1997, + Title = {Characterization and modeling of {P-type} electrosensory afferent responses to amplitude modulations in a wave-type electric fish}, + Author = {Nelson, M. E. and Xu, Z. and Payne, J. R.}, + Journal = {Journal of Comparative Physiology A}, + Year = {1997}, + Number = {5}, + Pages = {532-544}, + Volume = {181}, + ISSN = {0340-7594}, + Keywords = {Key words Computer simulation; Electrolocation Electroreception; Neural model; Sensory coding}, + Language = {English}, + Owner = {jan}, + Publisher = {Springer-Verlag}, + Timestamp = {2015.02.02} +} + +@Article{Nelson1999, + AUTHOR = {M. E. Nelson and M. A. MacIver}, + TITLE = {Prey capture in the weakly electric fish \textit{Apteronotus albifrons}: sensory acquisition strategies and electrosensory consequences}, + JOURNAL = {Journal of Experimental Biology}, + YEAR = {1999}, + NUMBER = {10}, + PAGES = {1195--1203}, + VOLUME = {202} +} + +@ARTICLE{Nelson2006, + AUTHOR = {M. E. Nelson and M. A. MacIver}, + TITLE = {Sensory acquisition in active sensing systems.}, + JOURNAL = JCompPhysiolA, + YEAR = {2006}, + VOLUME = {192}, + PAGES = {573--586} +} + +@Article{Neuhofer2011, + Title = {Neuronal precision and the limits for acoustic signal + recognition in a small neuronal network.}, + Author = {D. Neuhofer and M. Stemmler and B. Ronacher}, + Journal = JCompPhysiol, + Year = {2011}, + Pages = {251--265}, + Volume = {197} +} + +@article{Neuweiler1970, + title={{Neurophysiologische Untersuchungen zum Echoortungssystem der Gro{\ss}en Hufeisennase Rhinolophus ferrum equinum Schreber}, 1774}, + author={Neuweiler, Gerhard}, + journal={Zeitschrift f{\"u}r vergleichende Physiologie}, + volume={67}, + number={3}, + pages={273--306}, + year={1970}, + publisher={Springer} +} + +@article{Nikias1993, + title={Higher-order spectra analysis: a nonlinear signal processing framework}, + author={NChrysostomos L. Nikias and Athina P. Petropulu}, + journal={IEEE Signal Processing Magazine}, + volume={10}, + number={3}, + pages={10--37}, + year={1993}, + publisher={IEEE} +} + +@Incollection{Northcutt1986, + author = {Northcutt, R. G.}, + title = {Electroreception in non-teleost bony fishes}, + Booktitle = {Electroreception}, + Editor = {Bullock T.H., Heiligenberg W.}, + Publisher = {Wiley}, + year = {1986}, + pages = {247 - 285} +} + +@Article{Northcutt2000, + Title = {Distribution and Innervation of Lateral Line Organs in the Channel Catfish.}, + Author = {R. Glenn Northcutt and Preston H. Holmes and James S. Albert}, + Journal = {Journal of Comparative Neurology}, + Year = {2000}, + Pages = {570-592}, + Volume = {421} +} + +@Article{Nortmann2013, + Title = {Primary Visual Cortex Represents the Difference Between Past and Present.}, + Author = {Nora Nortmann and Sascha Rekauzke and Selim Onat and Peter K\"onig and Dirk Jancke}, + Journal = CerebCortex, + Year = {2015}, + Number = {6}, + Pages = {1427--1440}, + Volume = {25} +} + +@Article{Novikov1965, + title={Functionals and the random-force method in turbulence theory}, + author={Novikov, Evgenii A}, + journal={Journal of Experimental Theoretical Physics}, + volume={20}, + number={5}, + pages={1290--1294}, + year={1965} +} + +@Article{Nowak2003, + title={Electrophysiological classes of cat primary visual cortical neurons in vivo as revealed by quantitative analyses}, + author={Nowak, Lionel G and Azouz, Rony and Sanchez-Vives, Maria V and Gray, Charles M and McCormick, David A}, + journal={Journal of Neurophysiology}, + volume={89}, + number={3}, + pages={1541--1566}, + year={2003}, + publisher={American Physiological Society Bethesda, MD} +} + +@article{Ohm1839, + title={Bemerkungen {\"u}ber {C}ombinationst{\"o}ne und {S}t{\"o}sse}, + author={Ohm, Georg Simon}, + journal={Annalen der Physik}, + volume={123}, + number={7}, + pages={463--466}, + year={1839}, + publisher={Wiley Online Library} +} + +@Article{Olshausen1996, + Title = {Emergence of simple-cell + receptive-field properties by learning a sparse code for natural + images.}, + Author = {B. A. Olshausen and D. J. Field}, + Journal = Nature, + Year = {1996}, + Pages = {607--609}, + Volume = {381} +} + +@InCollection{Olshausen2013, + Title = {Perception as an Inference Problem.}, + Author = {Bruno A. Olshausen}, + Booktitle = {The Cognitive Neurosciences}, + Publisher = {MIT Press}, + Year = {2013}, + Editor = {V.M. Gazzaniga and R. Mangun} +} + +@Article{Oswald2004, + title={Parallel processing of sensory input by bursts and isolated spikes}, + author={Oswald, AnneMarie M and Chacron, Maurice J and Doiron, Brent and Bastian, Joseph and Maler, Leonard}, + journal={Journal of Neuroscience}, + volume={24}, + number={18}, + pages={4351--4362}, + year={2004}, + publisher={Soc Neuroscience} +} + + +@ARTICLE{Ozcete2020, + AUTHOR = {\"Ozge D. \"Oz\c{c}ete and Tobias Moser}, + TITLE = {A sensory cell diversifies its output by varying {Ca$^{2+}$} influx-release coupling among active zones.}, + YEAR = {2020}, + JOURNAL = {The EMBO Journal}, + VOLUME = {40}, + PAGES = {e106010} } + +@Article{Padmanabhan2010, + Title = {Intrinsic biophysical diversity decorrelates neuronal firing while increasing information content.}, + Author = {Krishnan Padmanabhan and Nathaniel N Urban}, + Journal = {Nat Neurosci}, + Year = {2010}, + Month = {Oct}, + Number = {10}, + Pages = {1276--1282}, + Volume = {13}, + Abstract = {Although examples of variation and diversity exist throughout the nervous system, their importance remains a source of debate. Even neurons of the same molecular type have notable intrinsic differences. Largely unknown, however, is the degree to which these differences impair or assist neural coding. We examined the outputs from a single type of neuron, the mitral cells of the mouse olfactory bulb, to identical stimuli and found that each cell's spiking response was dictated by its unique biophysical fingerprint. Using this intrinsic heterogeneity, diverse populations were able to code for twofold more information than their homogeneous counterparts. In addition, biophysical variability alone reduced pair-wise output spike correlations to low levels. Our results indicate that intrinsic neuronal diversity is important for neural coding and is not simply the result of biological imprecision.}, + Institution = {Department of Biological Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania, USA.}, + Keywords = {Action Potentials; Animals; Animals, Newborn; Biophysical Phenomena; Biophysics; Electric Stimulation; Entropy; Kv1.2 Potassium Channel; Mice; Mice, Inbred C57BL; Models, Neurological; Nerve Net; Neurons; Olfactory Bulb; Patch-Clamp Techniques; Statistics as Topic}, + Pii = {nn.2630}, + Pmid = {20802489}, + Refid = {792}, + Timestamp = {2011.10.20}, +} + +@article{Palmer1982, + title={Encoding of rapid amplitude fluctuations by cochlear-nerve fibres in the guinea-pig}, + author={Palmer, Alan Richard}, + journal={Archives of oto-rhino-laryngology}, + volume={236}, + number={2}, + pages={197--202}, + year={1982}, + publisher={Springer} +} + +@article{Palmer1986, + title={Phase-locking in the cochlear nerve of the guinea-pig and its relation to the receptor potential of inner hair-cells}, + author={Palmer, AR and Russell, IJ}, + journal={Hearing Research}, + volume={24}, + number={1}, + pages={1--15}, + year={1986}, + publisher={Elsevier} +} + +@Article{Parrish1999, + Title = {Complexity, Pattern, and Evolutionary Trade-Offs in Animal Aggregation}, + Author = {Parrish, Julia K. and Edelstein-Keshet, Leah}, + Journal = {Science}, + Year = {1999}, + Number = {5411}, + Pages = {99--101}, + Volume = {284}, + + Abstract = {One of the most striking patterns in biology is the formation of animal aggregations. Classically, aggregation has been viewed as an evolutionarily advantageous state, in which members derive the benefits of protection, mate choice, and centralized information, balanced by the costs of limiting resources. Consisting of individual members, aggregations nevertheless function as an integrated whole, displaying a complex set of behaviors not possible at the level of the individual organism. Complexity theory indicates that large populations of units can self-organize into aggregations that generate pattern, store information, and engage in collective decision-making. This begs the question, are all emergent properties of animal aggregations functional or are some simply pattern? Solutions to this dilemma will necessitate a closer marriage of theoretical and modeling studies linked to empirical work addressing the choices, and trajectories, of individuals constrained by membership in the group.}, + Doi = {10.1126/science.284.5411.99}, + Owner = {raab}, + Publisher = {American Association for the Advancement of Science}, + Timestamp = {2020.01.30}, + Url = {https://science.sciencemag.org/content/284/5411/99} +} + +@ARTICLE{Pedraja2014, + AUTHOR = {Federico Pedraja and Pedro Aguilera and Angel A. Caputi and Ruben Budelli}, + TITLE = {Electric imaging through evolution, a modeling study of commonalities and differences.}, + JOURNAL = {PLoS Computational Biology}, + YEAR = {2014}, + VOLUME = {10}, + PAGES = {e1003722} +} + +@ARTICLE{Pedraja2018, + AUTHOR = {Federico Pedraja and Volker Hofmann and Kathleen M. Lucas and Colleen Young and Jacob Engelmann and John E. Lewis}, + TITLE = {Motion parallax in electric sensing.}, + JOURNAL = {Proceedings of the National Academy of Sciences}, + YEAR = {2018}, + VOLUME = {115}, + PAGES = {573--577} +} + +@article{Pedregosa2011, + title={Scikit-learn: Machine learning in Python}, + author={Pedregosa, Fabian and Varoquaux, Ga{\"e}l and Gramfort, Alexandre and Michel, Vincent and Thirion, Bertrand and Grisel, Olivier and Blondel, Mathieu and Prettenhofer, Peter and Weiss, Ron and Dubourg, Vincent and others}, + journal={the Journal of machine Learning research}, + volume={12}, + pages={2825--2830}, + year={2011}, + publisher={JMLR. org} +} + +@ARTICLE{Pereira2012, + AUTHOR = {Ana Carolina Pereira and Pedro Aguilera and Angel A. Caputi}, + TITLE = {The active electrosensory range of \textit{Gymnotus omarorum}.}, + JOURNAL = {Journal of Experimental Biology}, + YEAR = {2012}, + VOLUME = {215}, + PAGES = {3266--3280} +} + +@ARTICLE{Perrone2009, + AUTHOR = {Rossana Perrone and Omar Macadar and Ana Silva}, + TITLE = {Social electric signals in freely moving dyads of \textit{Brachyhypopomus pinnicaudatus}.}, + JOURNAL = JCompPhysiolA, + YEAR = {2009}, + VOLUME = {195}, + PAGES = {501--514} +} + +@ARTICLE{Peters1972, + AUTHOR = {R. C. Peters and F. Bretschneider}, + TITLE = {Electric phenomena in the habitat of the catfish \textit{Ictalurus nebulosus} {LeS}.}, + YEAR = {1972}, + JOURNAL = JCompPhysiol, + VOLUME = {81}, + PAGES = {345--362} } + +@Article{Peters2007, + Title = {On the electrodetection threshold of aquatic vertrebrates with ampullary or mucous gland electroreceptor organs.}, + Author = {Rob C. Peters and Lonneke B.M. Eeuwes and Franklin Bretschneider}, + Journal = BiolRev, + Year = {2007}, + Pages = {361-373}, + Volume = {82} +} + +@article{Peterson2019, + title={Phase locking of auditory-nerve fibers reveals stereotyped distortions and an exponential transfer function with a level-dependent slope}, + author={Peterson, Adam J and Heil, Peter}, + journal={Journal of Neuroscience}, + volume={39}, + number={21}, + pages={4077--4099}, + year={2019}, + publisher={Soc Neuroscience} +} + +@ARTICLE{Petzold2016, + AUTHOR = {Jacquelyn M. Petzold and Gary Marsat and G. Troy Smith}, + TITLE = {Co-adaptation of electric organ discharges and chirps in {South} {American} ghost knifefishes ({Apteronotidae}).}, + JOURNAL = {Journal of Physiology-Paris}, + YEAR = {2016}, + VOLUME = {110}, + PAGES = {200--215} +} + +@article{Phillips1990, + title={Neural representation of sound amplitude in the auditory cortex: effects of noise masking}, + author={Phillips, Dennis P}, + journal={Behavioural Brain Research}, + volume={37}, + number={3}, + pages={197--214}, + year={1990}, + publisher={Elsevier} +} + +@article{Plomp1967, + title={Beats of mistuned consonances}, + author={Plomp, Reinier}, + journal={The Journal of the Acoustical Society of America}, + volume={42}, + number={2}, + pages={462--474}, + year={1967} +} + +@Article{Poggio1985, + Title = {Ill-posed problems in early vision: from computational + theory to analogue networks.}, + Author = {T. Poggio and C. Koch}, + Journal = ProcRSocLondBBiolSci, + Year = {1985}, + Pages = {303--323}, + Volume = {226} +} + +@ARTICLE{Post1999, + AUTHOR = {Nils Post and Gerhard von der Emde}, + TITLE = {The "novelty response" in an electric fish: response properties and habituation.}, + JOURNAL = {Physiol Behav}, + YEAR = {1999}, + VOLUME = {68}, + PAGES = {115--128} +} + +@Article{Pouget2013, + Title = {Probabilistic brains: knowns and unknowns.}, + Author = {Alexandre Pouget and Jeffrey M. Beck and Wei Ji Ma and Peter E. Latham}, + Journal = {Nature Neuroscience}, + Year = {2013}, + Pages = {1170--1178}, + Volume = {16} +} + +@article{Preyer1996, + title={Nonlinearity of mechanoelectrical transduction of outer hair cells as the source of nonlinear basilar-membrane motion and loudness recruitment}, + author={Preyer, Serena and Gummer, Anthony W}, + journal={Audiology and Neurotology}, + volume={1}, + number={1}, + pages={3--11}, + year={1996}, + publisher={S. Karger AG Basel, Switzerland} +} + +@Article{Pugh1999, + title={Molecular mechanisms of vertebrate photoreceptor light adaptation}, + author={Pugh Jr, EN and Nikonov, S and Lamb, TD}, + journal={Current Opinion in Neurobiology}, + volume={9}, + number={4}, + pages={410--418}, + year={1999}, + publisher={Elsevier} +} + +@ARTICLE{Pusch2008, + AUTHOR = {Roland Pusch and Gerhard von der Emde and Michael Hollmann and Joao Bacelo and Sabine N\"obel and Kirsty Grant and Jacob Engelmann}, + TITLE = {Active sensing in a mormyrid fish: electric images and peripheral modifications of the signal carrier give evidence of dual foveation.}, + JOURNAL = {Journal of Experimental Biology}, + YEAR = {2008}, + VOLUME = {211}, + PAGES = {921--9334} +} + + +@article{Quiroga2005, + title={Invariant visual representation by single neurons in the human brain}, + author={Quiroga, R Quian and Reddy, Leila and Kreiman, Gabriel and Koch, Christof and Fried, Itzhak}, + journal={Nature}, + volume={435}, + number={7045}, + pages={1102--1107}, + year={2005}, + publisher={Nature Publishing Group UK London} +} + +@article{Quiroga2010, + title={Postscript: About grandmother cells and Jennifer Aniston neurons.}, + author={Quian Quiroga, Rodrigo and Kreiman, Gabriel}, + year={2010}, + publisher={American Psychological Association} +} + +@Article{Raab2019, + Title = {Dominance in Habitat Preference and Diurnal Explorative Behavior of the Weakly Electric Fish \textit{Apteronotus leptorhynchus}}, + Author = {Raab, Till and Linhart, Laura and Wurm, Anna and Benda, Jan}, + Journal = {Frontiers in Integrative Neuroscience}, + Year = {2019}, + Pages = {21}, + Volume = {13}, + + Abstract = {Electrocommunication and -localization behaviors of weakly electric fish have been studied extensively in the lab, mostly by means of short-term observations on constrained fish. Far less is known about their behaviors in more natural-like settings, where fish are less constrained in space and time. We tracked individual fish in a population of fourteen brown ghost knifefish (Apteronotus leptorhynchus) housed in a large 2 m3 indoor tank based on their electric organ discharges (EOD). The tank contained four different natural-like microhabitats (gravel, plants, isolated stones, stacked stones). In particular during the day individual fish showed preferences for specific habitats which provided appropriate shelter. Male fish with higher EOD frequencies spent more time in their preferred habitat during the day, moved more often between habitats during the night, and less often during the day in comparison to low-frequency males. Our data thus revealed a link between dominance indicated by higher EOD frequency, territoriality, and a more explorative personality in male A. leptorhynchus. In females, movement activity during both day and night correlated positively with EOD frequency. In the night, fish of either sex moved to another habitat after about 6 s on average. During the day, the average transition time was also very short at about 20 s. However, these activity phases were interrupted by phases of inactivity that lasted on average about 20 min during the day, but only 3 min in the night. The individual preference for daytime retreat sites did not reflect the frequent explorative movements at night.}, + Doi = {10.3389/fnint.2019.00021}, + Owner = {raab}, + Timestamp = {2020.01.10}, + Url = {https://www.frontiersin.org/article/10.3389/fnint.2019.00021} +} + +@Article{Rao1999, + Title = {Predictive coding in the visual cortex: a functional interpretation of some extra-classical receptive-field effects.}, + Author = {Rajesh P.N. Rao and Dana H. Ballard}, + Journal = {Nature Neuroscience}, + Year = {1999}, + Number = {1}, + Pages = {79-87}, + Volume = {2} +} + +@Article{Rao2005, + Title = {Bayesian inference and attentional modulation in the visual cortex.}, + Author = {Rajesh P.N. Rao}, + Journal = Neuroreport, + Year = {2005}, + Number = {16}, + Pages = {1843-1848}, + Volume = {16} +} + +@article{Rasch1984, + title={Theory of Helmholtz-beat frequencies}, + author={Rasch, Rudolf A}, + journal={Music Perception}, + volume={1}, + number={3}, + pages={308--322}, + year={1984}, + publisher={University of California Press} +} + +@ARTICLE{Rasnow1996, + AUTHOR = {B. Rasnow and J. M. Bower}, + TITLE = {The electric organ discharges of the gymnotiform fishes: {I.} \textit{Apteronotus leptorhynchus}.}, + JOURNAL = JCompPhysiolA, + YEAR = {1996}, + VOLUME = {178}, + PAGES = {383--396} +} + +@article{Ratnam2000, + title={Nonrenewal statistics of electrosensory afferent spike trains: implications for the detection of weak sensory signals}, + author={Ratnam, Rama and Nelson, Mark E}, + journal={Journal of Neuroscience}, + volume={20}, + number={17}, + pages={6672--6683}, + year={2000}, + publisher={Soc Neuroscience} +} + +@Article{Reardon2011, + Title = {Energetic constraints on electric signaling in wave-type weakly electric fishes.}, + Author = {Erin E. Reardon and Alana Parisi and R\"udiger Krahe and Lauren J. Chapman}, + Journal = {Journal of Experimental Biology}, + Year = {2011}, + Pages = {4141-4150}, + Volume = {214} +} + +@article{Rhode1977, + title={Some observations on two-tone interaction measured with the Mossbauer effect}, + author={Rhode, WS t}, + journal={Psychophysics and physiology of hearing}, + pages={27--41}, + year={1977}, + publisher={Academic Press London} +} + +@article{Rhode1994, + title={Encoding of amplitude modulation in the cochlear nucleus of the cat}, + author={Rhode, William S and Greenberg, Steven}, + journal={Journal of Neurophysiology}, + volume={71}, + number={5}, + pages={1797--1825}, + year={1994} +} + +@Article{Ridder2010Auditory, + title={Burst stimulation of the auditory cortex: a new form of neurostimulation for noise-like tinnitus suppression}, + author={De Ridder, Dirk and Vanneste, Sven and van der Loo, Elsa and Plazier, Mark and Menovsky, Tomas and Van de Heyning, Paul}, + journal={Journal of Neurosurgery}, + volume={112}, + number={6}, + pages={1289--1294}, + year={2010}, + publisher={American Association of Neurological Surgeons} +} + +@Article{Ridder2010Cord, + title={Burst spinal cord stimulation: toward paresthesia-free pain suppression}, + author={De Ridder, Dirk and Vanneste, Sven and Plazier, Mark and van der Loo, Elsa and Menovsky, Tomas}, + journal={Neurosurgery}, + volume={66}, + number={5}, + pages={986--990}, + year={2010}, + publisher={Oxford University Press} +} + +@book{Rieke1999, + title={Spikes: exploring the neural code}, + author={Rieke, Fred and Warland, David and Van Steveninck, Rob de Ruyter and Bialek, William}, + year={1999}, + publisher={MIT press} +} + +@Article{Rizzo2009, + Title = {A review of humpback whales' migration patterns worldwide and their consequences to gene flow}, + Author = {L.Y. Rizzo and D. Schulte}, + Journal = {Journal of the Marine Biological Association of the United Kingdom}, + Year = {2009}, + Pages = {995-1002}, + Volume = {89}, + + Doi = {https://doi.org/10.1017/S0025315409000332}, + Owner = {raab}, + Timestamp = {2020.02.10} +} + +@Article{Roddey2000, + title={Assessing the performance of neural encoding models in the presence of noise}, + author={Roddey, J Cooper and Girish, B and Miller, John P}, + journal={J Comput Neurosci}, + volume={8}, + pages={95--112}, + year={2000}, + publisher={Springer} +} + +@Article{Rodriguez2010, + Title = {Natural and Sexual Selection in a Wild Insect Population}, + Author = {Rodr\'irguez-Mu{\~n}oz and A. Bretman, J. Slate and C. A. Walling and T. Tregenza}, + Journal = {Science}, + Year = {2010}, + Pages = {1269-1272}, + Volume = {328}, + + Doi = {10.1126/science.1188102}, + Owner = {raab}, + Timestamp = {2020.02.11} +} + +@ARTICLE{Rodriguez2013, + AUTHOR = {A. Rodr\'iguez-Catt\'aneo1 and P. Aguilera and E. Cilleruelo and W. G. R. Crampton and A. A. Caputi1}, + TITLE = {Electric organ discharge diversity in the genus \textit{Gymnotus}: anatomo-functional +groups and electrogenic mechanisms.}, + JOURNAL = {Journal of Experimental Biology}, + YEAR = {2013}, + VOLUME = {216}, + PAGES = {1501--1515} +} + +@article{Roeber1834, + title={{Untersuchungen des {H}rn. Scheibler in Crefeld {\"u}ber die sogenannten Schl{\"a}ge, Schwebungen oder St{\"o}sse}}, + author={Roeber, August}, + journal={Annalen der Physik}, + volume={108}, + number={31-33}, + pages={492--520}, + year={1834}, + publisher={WILEY-VCH Verlag Leipzig} +} + +@article{Romani1982, + title={Tonotopic organization of the human auditory cortex}, + author={Romani, Gian Luca and Williamson, Samuel J and Kaufman, Lloyd}, + journal={Science}, + volume={216}, + number={4552}, + pages={1339--1340}, + year={1982}, + publisher={American Association for the Advancement of Science} +} + +@article{Romei2009, + title={Preperceptual and stimulus-selective enhancement of low-level human visual cortex excitability by sounds}, + author={Romei, Vincenzo and Murray, Micah M and Cappe, C{\'e}line and Thut, Gregor}, + journal={Current Biology}, + volume={19}, + number={21}, + pages={1799--1805}, + year={2009}, + publisher={Elsevier} +} + +@article{Rose1971, + title={Plasma testosterone, dominance rank and aggressive behaviour in male rhesus monkeys.}, + author={Rose, Robert M and Holaday, John W and Bernstein, Irwin S}, + journal={Nature}, + year={1971}, + publisher={Nature Publishing Group} +} + +@ARTICLE{Roth1972, + AUTHOR = {Anton Roth}, + TITLE = {{Wozu dienen die Elektrorezeptoren der Welse?}}, + JOURNAL = JCompPhysiol, + YEAR = {1972}, + VOLUME = {79}, + PAGES = {113--135} +} + +@ARTICLE{Rother2003, + AUTHOR = {Diego Rother and Adriana Migliaro and Rafael Canetti and Leonel G\'omez and Angel Caputi and Ruben Budelli}, + TITLE = {Electric images of two low resistance objects in weakly electric fish.}, + JOURNAL = BioSystems, + YEAR = {2003}, + VOLUME = {71}, + PAGES = {169--177} +} + +@article{Roux2006, + title={Otoferlin, defective in a human deafness form, is essential for exocytosis at the auditory ribbon synapse}, + author={Roux, Isabelle and Safieddine, Saaid and Nouvian, R{\'e}gis and Grati, M'hamed and Simmler, Marie-Christine and Bahloul, Amel and Perfettini, Isabelle and Le Gall, Morgane and Rostaing, Philippe and Hamard, Ghislaine and others}, + journal={Cell}, + volume={127}, + number={2}, + pages={277--289}, + year={2006}, + publisher={Elsevier} +} + +@Article{Ruderman1994, + Title = {Statistics of Natural Images: Scaling in the Woods.}, + Author = {Daniel L. Ruderman and William Bialek}, + Journal = PhysRevLett, + Year = {1994}, + Number = {6}, + Pages = {814-818}, + Volume = {73} +} + +@Article{Ruggero1992, + title={Two-tone suppression in the basilar membrane of the cochlea: Mechanical basis of auditory-nerve rate suppression}, + author={Ruggero, Mario A and Robles, Luis and Rich, Nola C}, + journal={Journal of Neurophysiology}, + volume={68}, + number={4}, + pages={1087--1099}, + year={1992}, + publisher={American Physiological Society Bethesda, MD} +} + +@Article{Ruggero1997, + title={Basilar-membrane responses to tones at the base of the chinchilla cochlea}, + author={Ruggero, Mario A and Rich, Nola C and Recio, Alberto and Narayan, S Shyamla and Robles, Luis}, + journal={The Journal of the Acoustical Society of America}, + volume={101}, + number={4}, + pages={2151--2163}, + year={1997}, + publisher={Acoustical Society of America} +} + +@article{Russell1978, + title={Intracellular studies of hair cells in the mammalian cochlea.}, + author={Russell, IJ and Sellick, PM1282821}, + journal={J Physiol}, + volume={284}, + number={1}, + pages={261--290}, + year={1978}, + publisher={Wiley Online Library} +} + +@Article{Rust2005, + Title = {Spatiotemporal Elements of Macaque {V1} Receptive Fields.}, + Author = {Nicole C. Rust and Odelia Schwartz and J. Anthony Movshon and Eero P. Simoncelli}, + Journal = Neuron, + Year = {2005}, + Pages = {945-956}, + Volume = {46} +} + +@article{Sachs1968, + title={Two-tone inhibition in auditory-nerve fibers}, + author={Sachs, Murray B and Kiang, Nelson YS}, + journal={The Journal of the Acoustical Society of America}, + volume={43}, + number={5}, + pages={1120--1128}, + year={1968}, + publisher={Acoustical Society of America} +} + +@article{Sachs1974, + title={Rate versus level functions for auditory-nerve fibers in cats: tone-burst stimuli}, + author={Sachs, Murray B and Abbas, Paul J}, + journal={The Journal of the Acoustical Society of America}, + volume={56}, + number={6}, + pages={1835--1847}, + year={1974}, + publisher={Acoustical Society of America} +} + +@Article{Sakmann1969, + title={Scotopic and mesopic light adaptation in the cat's retina}, + author={Sakmann, Bert and Creutzfeldt, Otto D}, + journal={Pfl{\"u}gers Archiv}, + volume={313}, + pages={168--185}, + year={1969}, + publisher={Springer} +} + +@article{Salazar2013, + title={The energetics of electric organ discharge generation in gymnotiform weakly electric fish}, + author={Salazar, Vielka L and Krahe, R{\"u}diger and Lewis, John E}, + journal={Journal of Experimental Biology}, + volume={216}, + number={13}, + pages={2459--2468}, + year={2013}, + publisher={Company of Biologists} +} + +@article{Salazar2022, + title={Neural processing: Cracking the code to extract relevant social information}, + author={Salazar, Vielka and Silva, Ana}, + journal={Current Biology}, + volume={32}, + number={1}, + pages={R32--R34}, + year={2022}, + publisher={Elsevier} +} + +@ARTICLE{Salgado2011, + AUTHOR = {Jos\'e Antonio Gama Salgado and G\"unther K.H. Zupanc}, + TITLE = {Echo response to chirping in the weakly electric brown ghost knifefish (\textit{Apteronotus leptorhynchus}): role of frequency and amplitude modulations.}, + JOURNAL = {J Can Zool}, + YEAR = {2011}, + VOLUME = {89}, + PAGES = {498--508} +} + +@article{Salminen2018, + title={A common periodic representation of interaural time differences in mammalian cortex}, + author={Salminen, Nelli H and Jones, Simon J and Christianson, Gestur B and Marquardt, Torsten and McAlpine, David}, + journal={NeuroImage}, + volume={167}, + pages={95--103}, + year={2018}, + publisher={Elsevier} +} + +@ARTICLE{Sanguinetti2011, + AUTHOR = {Juan Ignacio Sanguinetti-Scheck and Eduardo Federico Pedraja and Esteban Cilleruelo and Adriana Migliaro and Pedro Aguilera and Angel Ariel Caputi and Ruben Budelli}, + TITLE = {Fish geometry and electric organ discharge determine functional organization of the electrosensory epithelium.}, + JOURNAL = PLOSOne, + YEAR = {2011}, + VOLUME = {6}, + PAGES = {e27470} +} + +@Article{Sapolsky2005, + Title = {The Influence of Social Hierarchy on Primate Health}, + Author = {Sapolsky, Robert M.}, + Journal = {Science}, + Year = {2005}, + Number = {5722}, + Pages = {648--652}, + Volume = {308}, + + Abstract = {Dominance hierarchies occur in numerous social species, and rank within them can greatly influence the quality of life of an animal. In this review, I consider how rank can also influence physiology and health. I first consider whether it is high- or low-ranking animals that are most stressed in a dominance hierarchy; this turns out to vary as a function of the social organization in different species and populations. I then review how the stressful characteristics of social rank have adverse adrenocortical, cardiovascular, reproductive, immunological, and neurobiological consequences. Finally, I consider how these findings apply to the human realm of health, disease, and socioeconomic status.}, + Doi = {10.1126/science.1106477}, + Owner = {raab}, + Publisher = {American Association for the Advancement of Science}, + Timestamp = {2020.01.27}, + Url = {https://science.sciencemag.org/content/308/5722/648} +} + +@article{Savard2011, + title={Neural heterogeneities influence envelope and temporal coding at the sensory periphery}, + author={Savard, M and Krahe, R and Chacron, MJ}, + journal={Neuroscience}, + volume={172}, + pages={270--284}, + year={2011}, + publisher={Elsevier} +} + +@article{Sayles2013, + title={Neurometric amplitude-modulation detection threshold in the guinea-pig ventral cochlear nucleus}, + author={Sayles, Mark and F{\"u}llgrabe, Christian and Winter, Ian M}, + journal={The Journal of Physiology}, + volume={591}, + number={13}, + pages={3401--3419}, + year={2013}, + publisher={Wiley Online Library} +} + +@INCOLLECTION{Scheffel2006, + TITLE = {Intra- and interspecific electrocommunication among sympatric mormyrids in the upper {Zambezi} river.}, + AUTHOR = {Andreas Scheffel and Bernd Kramer}, + Year = {2006}, + Pages = {733--751}, + BOOKTITLE = {Communication in fishes}, + EDITOR = {F. Ladich and S. P. Collin and P. Moller and B. G. Kapoor}, + PUBLISHER = {Science Publishers}, + ADDRESS = {Enfield, N.H.} +} + +@article{Scheich1973, + title={Coding properties of two classes of afferent nerve fibers: high-frequency electroreceptors in the electric fish, \textit{Eigenmannia}.}, + author={Scheich, H and Bullock, Th H and Hamstra Jr, RH}, + journal={Journal of Neurophysiology}, + volume={36}, + number={1}, + pages={39--60}, + year={1973} +} + +@article{Schiff1962, + title={Persistent fear responses in rhesus monkeys to the optical stimulus of "looming"}, + author={Schiff, William and Caviness, James A and Gibson, James J}, + journal={Science}, + volume={136}, + number={3520}, + pages={982--983}, + year={1962}, + publisher={American Association for the Advancement of Science} +} + +@Article{Schluger1987, + Title = {Electric Fish approach stationary signal sources by following electric current lines.}, + Author = {James H. Schluger and Carl D. Hopkins}, + Journal = {Journal of Experimental Biology}, + Year = {1987}, + Pages = {359-367}, + Volume = {130} +} + +@article{Schlungbaum2023, + title={Detecting a periodic signal by a population of spiking neurons in the weakly nonlinear response regime}, + author={Schlungbaum, Maria and Lindner, Benjamin}, + journal={The European Physical Journal E}, + volume={46}, + number={11}, + pages={108}, + year={2023}, + publisher={Springer} +} + +@article{Schmiedt1982, + title={Boundaries of two-tone rate suppression of cochlear-nerve activity}, + author={Schmiedt, Richard A}, + journal={Hearing Research}, + volume={7}, + number={3}, + pages={335--351}, + year={1982}, + publisher={Elsevier} +} + +@article{Schneider1976, + title={Transfer characteristics of first and second order lateral canal vestibular neurons in gerbil}, + author={Schneider, LW and Anderson, DJ}, + journal={Brain Research}, + volume={112}, + number={1}, + pages={61--76}, + year={1976}, + publisher={Elsevier} +} + +@article{Schneider2011, + title={In vivo conditions induce faithful encoding of stimuli by reducing nonlinear synchronization in vestibular sensory neurons}, + author={Schneider, Adam D and Cullen, Kathleen E and Chacron, Maurice J}, + journal={PLoS Comput Biol}, + volume={7}, + number={7}, + pages={e1002120}, + year={2011}, + publisher={Public Library of Science San Francisco, USA} +} + +@ARTICLE{Schnitzler2001, + AUTHOR = {Hans-Ulrich Schnitzler and Elisabeth K. V. Kalko}, + TITLE = {Echolocation by insect-eating bats.}, + JOURNAL = {BioScience}, + YEAR = {2001}, + VOLUME = {51}, + PAGES = {557--569} +} + +@article{Schreiner1988, + title={Representation of amplitude modulation in the auditory cortex of the cat. {II}. Comparison between cortical fields}, + author={Schreiner, Christoph E and Urbas, John V}, + journal={Hearing Research}, + volume={32}, + number={1}, + pages={49--63}, + year={1988}, + publisher={Elsevier} +} + +@Article{Chialvo1997, + title={Stochastic resonance in models of neuronal ensembles}, + author={Chialvo, Dante R and Longtin, Andr{\'e} and M{\"u}ller-Gerking, Johannes}, + journal={Phys Rev E}, + volume={55}, + number={2}, + pages={1798}, + year={1997}, + publisher={APS} +} + +@article{Schuller1984, + title={Natural ultrasonic echoes from wing beating insects are encoded by collicular neurons in the {CF-FM bat, Rhinolophus ferrumequinum}}, + author={Schuller, Gerd}, + journal={Journal of Comparative Physiology A}, + volume={155}, + number={1}, + pages={121--128}, + year={1984}, + publisher={Springer} +} + +@ARTICLE{Schwan1963, + AUTHOR = {Herman P. Schwan}, + TITLE = {Electric characteristic of tissues.}, + JOURNAL = {Biophysik}, + YEAR = {1963}, + VOLUME = {1}, + PAGES = {198--208} +} + +@Article{Schwartz2001, + Title = {Natural Signal statistics and sensory gain control.}, + Author = {Odelia Schwartz and Eero P. Simoncelli}, + Journal = {Nature Neuroscience}, + Year = {2001}, + Number = {8}, + Pages = {819-825}, + Volume = {4} +} + +@ARTICLE{Schwarz2001, + AUTHOR = {Stephan Schwarz and Gerhard von der Emde}, + TITLE = {Distance discrimination during active electrolocation in the weakly electric fish \textit{Gnathonemus petersii}.}, + JOURNAL = JCompPhysiolA, + YEAR = {2001}, + VOLUME = {186}, + PAGES = {1185--1197} +} + +@Article{Schweitzer1986, + Title = {Functional organization of the electroreceptive midbrain in an elasmobranch ({Platyrhinoidis triseriata} - A single unit study.}, + Author = {Jeff Schweitzer}, + Journal = JCompPhysiolA, + Year = {1986}, + Pages = {43-58}, + Volume = {158} +} + +@article{scikitlearn2011, + title={Scikit-learn: Machine Learning in {P}ython}, + author={Pedregosa, F. and Varoquaux, G. and Gramfort, A. and Michel, V. + and Thirion, B. and Grisel, O. and Blondel, M. and Prettenhofer, P. + and Weiss, R. and Dubourg, V. and Vanderplas, J. and Passos, A. and + Cournapeau, D. and Brucher, M. and Perrot, M. and Duchesnay, E.}, + journal={Journal of Machine Learning Research}, + volume={12}, + pages={2825--2830}, + year={2011} +} + +@ARTICLE{scipy2020, + author = {Virtanen, Pauli and Gommers, Ralf and Oliphant, Travis E. and + Haberland, Matt and Reddy, Tyler and Cournapeau, David and + Burovski, Evgeni and Peterson, Pearu and Weckesser, Warren and + Bright, Jonathan and {van der Walt}, St{\'e}fan J. and + Brett, Matthew and Wilson, Joshua and Millman, K. Jarrod and + Mayorov, Nikolay and Nelson, Andrew R. J. and Jones, Eric and + Kern, Robert and Larson, Eric and Carey, C J and + Polat, {\.I}lhan and Feng, Yu and Moore, Eric W. and + {VanderPlas}, Jake and Laxalde, Denis and Perktold, Josef and + Cimrman, Robert and Henriksen, Ian and Quintero, E. A. and + Harris, Charles R. and Archibald, Anne M. and + Ribeiro, Ant{\^o}nio H. and Pedregosa, Fabian and + {van Mulbregt}, Paul and {SciPy 1.0 Contributors}}, + title = {{{SciPy} 1.0: Fundamental Algorithms for Scientific + Computing in Python}}, + journal = {Nature Methods}, + year = {2020}, + volume = {17}, + pages = {261--272}, + adsurl = {https://rdcu.be/b08Wh}, + doi = {10.1038/s41592-019-0686-2}, +} + +@Article{Sen2006, + title={Functionality of cochlear micromechanics-as elucidated by upward spread of masking and two tone suppression}, + author={Sen, D and Allen, Jont B}, + journal={Acoustics Australia}, + volume={34}, + number={1}, + pages={37}, + year={2006} +} + +@Article{Serrano2003, + Title = {Gradual frequency rises in interacting black ghost knifefish, \textit{Apteronotus albifrons}}, + Author = {Serrano-Fern{\'a}ndez, P.}, + Journal = JCompPhysiolA, + Year = {2003}, + Number = {9}, + Pages = {685--692}, + Volume = {189}, + + Abstract = {The present paper highlights the relationship between social status and production of gradual frequency rises in interacting \textit{Apteronotus albifrons}. The gradual frequency rise production was mathematically inferred and a discrete classification deliberately avoided. The results showed little gradual frequency rise production before the hierarchy settlement. Afterwards, only the dominant fish kept this gradual frequency rise production at low levels, while the subdominant fish drastically increased it in all following interaction contexts. The hypothesis of gradual frequency rises being involved in communication as submissive signals was thus strengthened.}, + Doi = {10.1007/s00359-003-0445-8}, + Owner = {raab}, + Timestamp = {2017.05.04}, + Url = {http://dx.doi.org/10.1007/s00359-003-0445-8} +} + +@Article{Sharpee2011, + Title = {Hierarchical representations in the auditory cortex.}, + Author = {Tatyana O Sharpee and Craig A Atencio and Christoph E Schreiner}, + Journal = CurrOpinNeurobiol, + Year = {2011}, + Pages = {761-767}, + Volume = {21} +} + +@Article{Shieh1996, + Title = {Short-range Orientation in Electric Fish: An Experimental Study of Passive Electrolocation.}, + Author = {Kwang-Tze Shieh and Willard Willson and Michael Winslow and McBride, Jr., Don W. and Carl D. Hopkins}, + Journal = {Journal of Experimental Biology}, + Year = {1996}, + Pages = {2383-2393}, + Volume = {199} +} + +@ARTICLE{Sicardi2000, + AUTHOR = {Estrella A. Sicardi and Angel A. Caputi and Ruben Budelli}, + TITLE = {Physical basis of distance discrimination in weakly electric fish.}, + JOURNAL = {Physica A}, + YEAR = {2000}, + VOLUME = {283}, + PAGES = {86--93} +} + + +@Article{Sillito1994, + Title = {Feature-linked synchronization of thalamic relay cell firing induced by feedback from the visual cortex.}, + Author = {A. M. Sillito and H. E. Jones and G. L. Gerstein and D. C. West}, + Journal = Nature, + Year = {1994}, + Pages = {479--482}, + Volume = {369} +} + +@ARTICLE{Silva1999, + AUTHOR = {A. Silva and L. Quintana and M. Galeano and P. Errandonea and O. Macadar}, + TITLE = {Water temperature sensitivity of {EOD} waveform in \textit{Brachyhypopomus pinnicaudatus}.}, + JOURNAL = JCompPhysiolA, + YEAR = {1999}, + VOLUME = {185}, + PAGES = {187--197} +} + + +@ARTICLE{Silva2007, + AUTHOR = {Ana Silva and Rossana Perrone and Omar Macadar}, + TITLE = {Environmental, seasonal, and social modulations of basal activity in a weakly electric fish.}, + JOURNAL = {Physiol Behav}, + YEAR = {2007}, + VOLUME = {90}, + PAGES = {525--536} +} + +@ARTICLE{Silva2008, + AUTHOR = {Ana Silva and Laura Quintana and Rossana Perrone and Felipe Sierra}, + TITLE = {Sexual and seasonal plasticity in the emission of social electric signals. Behavioral approach and neural bases.}, + JOURNAL = {Journal of Physiology-Paris}, + YEAR = {2008}, + VOLUME = {102}, + PAGES = {272--278} +} + +@Article{Silva2012, + author = {Batista, Gervasio and Zubizarreta, Lucía and Perrone, Rossana and Silva, Ana}, + title = {Non-sex-biased Dominance in a Sexually Monomorphic Electric Fish: Fight Structure and Submissive Electric Signalling}, + journal = {Ethology}, + year = {2012}, + volume = {118}, + number = {4}, + pages = {398-410}, + doi = {10.1111/j.1439-0310.2012.02022.x}, +} + +@ARTICLE{Sim2011, + AUTHOR = {Miyoung Sim and DaeEun Kim}, + TITLE = {Electrolocation based on tail-bending movements in weakly electric fish.}, + JOURNAL = {Journal of Experimental Biology}, + YEAR = {2011}, + VOLUME = {214}, + PAGES = {2443--2450} +} + +@Article{Simmons2013, + Title = {"To Ear is Human, to Frogive is Divine": {Bob Capranica's} legacy to auditory neuroethology.}, + Author = {Andrea Megela Simmons}, + Journal = JCompPhysiolA, + Year = {2013}, + Pages = {169-182}, + Volume = {199} +} + +@Article{Simoncelli2001, + Title = {Natural image statistics and neural representations.}, + Author = {Eero P. Simoncelli and Bruno A. Olshausen}, + Journal = AnnuRevNeurosci, + Year = {2001}, + Pages = {1193--1216}, + Volume = {24} +} + +@Article{Singh2003, + Title = {Modulation spectra of natural sounds and ethological theories of auditory processing.}, + Author = {Nandini C. Singh and Fr\'ed\'ric E. Theunissen}, + Journal = JAcoustSocAm, + Year = {2003}, + Pages = {3394--3411}, + Volume = {114} +} + +@Article{Sinz2020, + Title = {Simultaneous spike-time locking to multiple frequencies}, + Author = {Sinz, Fabian H. and Sachgau, Carolin and Henninger, J\"org and Benda, Jan and Grewe, Jan}, + Journal = {J Neurophysiol}, + Year = {2020}, + Number = {6}, + Pages = {2355-2372}, + Volume = {123} +} + +@article{Smalt2012, + title={Distortion products and their influence on representation of pitch-relevant information in the human brainstem for unresolved harmonic complex tones}, + author={Smalt, Christopher J and Krishnan, Ananthanarayan and Bidelman, Gavin M and Ananthakrishnan, Saradha and Gandour, Jackson T}, + journal={Hearing Research}, + volume={292}, + number={1-2}, + pages={26--34}, + year={2012}, + publisher={Elsevier} +} + +@Article{Smith2006, + Title = {Efficient auditory coding}, + Author = {Smith, E C and Lewicki, M S}, + Journal = Nature, + Year = {2006}, + Number = {7079}, + Pages = {978--982}, + Volume = {439} +} + +@Article{Smith2013, + Title = {Evolution and hormonal regulation of sex differences in the electrocommunication behavior of ghost knifefishes ({Apteronotidae}).}, + Author = {G. Troy Smith}, + Journal = {Journal of Experimental Biology}, + Year = {2013}, + Pages = {2421-2433}, + Volume = {216} +} + +@ARTICLE{Smith2016, + AUTHOR = {Adam R. Smith and Melissa R. Proffitt and Winnie W. Ho and Claire B. Mullaney and Javier A. Maldonado-Ocampo and Nathan R. Lovejoy and Jos\'e A. Alves-Gomes and G. Troy Smith}, + TITLE = {Evolution of electric communication signals in the {South} {American} ghost knifefishes ({Gymnotiformes}: {Apteronotidae}): A phylogenetic comparative study using a sequence-based phylogeny.}, + JOURNAL = {Journal of Physiology-Paris}, + YEAR = {2016}, + VOLUME = {110}, + PAGES = {302--313} +} + +@ARTICLE{Snyder2007, + AUTHOR = {James B. Snyder and Mark E. Nelson and Joel W. Burdick and Malcolm A. MacIver}, + TITLE = {Omnidirectional sensory and motor volumes in electric fish.}, + JOURNAL = PLOSBiol, + YEAR = {2007}, + VOLUME = {5}, + PAGES = {e301} +} + +@Article{Sonerud2001, + Title = {Ignorant Hooded Crows Follow Knowledgeable Roost-Mates to Food: Support for the Information Centre Hypothesis}, + Author = {Geir A. Sonerud and Christian A. Smedshaug and \Oystein Br{\aa}then}, + Journal = {Proceedings: Biological Sciences}, + Year = {2001}, + Number = {1469}, + Pages = {827-831}, + Volume = {268}, + Owner = {raab}, + Timestamp = {2020.01.30} +} + +@ARTICLE{Squire1982, + AUTHOR = {Ann Squire and Peter Moller}, + TITLE = {Effects of water conductivity on electrocommunication in the weak-electric fish \textit{Brienomyrus niger} {(Mormyriformes)}.}, + JOURNAL = AnimBehav, + YEAR = {1982}, + VOLUME = {30}, + PAGES = {375--382} +} + +@Article{Stamper2010, + Title = {Species differences in group size and electrosensory interference in weakly electric fishes: Implications for electrosensory processing}, + Author = {Sarah A. Stamper and Erika Carrera-G and Eric W. Tan and Vincent Fug\`ere and R\"udiger Krahe and Eric S. Fortune}, + Journal = {Behavioural Brain Research}, + Year = {2010}, + Number = {2}, + Pages = {368 - 376}, + Volume = {207}, + Keywords = {Electrotaxis, Gymnotiformes, Electrosensory, Social behavior}, + Owner = {raab}, + Timestamp = {2020.02.11} +} + +@ARTICLE{Stamper2012Envelope, + AUTHOR = {Sarah A. Stamper and Manu S. Madhav and Noah J. Cowan and Eric S. Fortune}, + TITLE = {Beyond the {Jamming Avoidance Response}: weakly electric fish respond to the envelope of social electrosensory signals.}, + JOURNAL = {J Exp Biol}, + YEAR = {2012}, + VOLUME = {215}, + PAGES = {4196--4207} +} + +@article{stamper2012JAR, + title={Beyond the {Jamming Avoidance Response}: weakly electric fish respond to the envelope of social electrosensory signals}, + author={Stamper, Sarah A and Madhav, Manu S and Cowan, Noah J and Fortune, Eric S}, + journal={Journal of Experimental Biology}, + volume={215}, + number={23}, + pages={4196--4207}, + year={2012}, + publisher={Company of Biologists} +} + +@Article{Stamper2012Shuttle, + Title = {Active sensing via movement shapes spatiotemporal patterns of sensory feedback.}, + Author = {Sarah A. Stamper and Eatai Roth and Noah J. Cowan and Eric S. Fortune}, + Journal = {Journal of Experimental Biology}, + Year = {2012}, + Pages = {1567-1574}, + Volume = {215} +} + +@Article{Stamper2013, + Title = {Perception and coding of envelopes in weakly electric fishes.}, + Author = {Sarah A. Stamper and Eric S. Fortune and Maurice J. Chacron}, + Journal = {Journal of Experimental Biology}, + Year = {2013}, + Pages = {2393-2402}, + Volume = {216} +} + +@ARTICLE{Steinbach1970, + AUTHOR = {A. B. Steinbach}, + TITLE = {Diurnal movements and discharge characteristics of electric gymnotid fishes in the {Rio Negro}, {Brazil}}, + JOURNAL = {The Biological Bulletin}, + YEAR = {1970}, + VOLUME = {138}, + PAGES = {200--210} +} + +@Article{Stephens2013, + Title = {Independent Evolution of Visual and Electrosensory Spezializations in Different Lineages of Mormyrid Electric Fishes.}, + Author = {Jennifer A. Stephens and Kimberley V. Sukhum and Bruce A. Carlson}, + Journal = BrainBehavEvol, + Year = {2013}, + Pages = {185-198}, + Volume = {82} +} + +@Article{Stocks2000, + title={Suprathreshold stochastic resonance in multilevel threshold systems}, + author={Stocks, Nigel G}, + journal={Physical Review Letters}, + volume={84}, + number={11}, + pages={2310}, + year={2000}, + publisher={APS} +} + +@ARTICLE{Stoddard1999, + AUTHOR = {Philip K. Stoddard}, + TITLE = {Predation enhances complexity in the evolution of electric fish signals.}, + JOURNAL = {Nature}, + YEAR = {1999}, + VOLUME = {400}, + PAGES = {254--256} +} + +@ARTICLE{Stoddard1999Brachy, + AUTHOR = {P. K. Stoddard and B. Rasnow and C. Assad}, + TITLE = {Electric organ discharges of the gymnotiform fishes: {III.} \textit{Brachyhypopomus}.}, + JOURNAL = JCompPhysiolA, + YEAR = {1999}, + VOLUME = {184}, + PAGES = {609--630} +} + +@Article{Stoddard2007, + Title = {Circadian rhythms in electric waveform structure and rate in the electric fish {Brachyhypopomus} pinnicaudatus}, + Author = {Stoddard, Philip K and Markham, Michael R and Salazar, Vielka L and Allee, Susan}, + Journal = {Physiology \& Behavior}, + Year = {2007}, + Number = {1}, + Pages = {11-20}, + Volume = {90}, + Owner = {raab}, + Timestamp = {2020.02.11} +} + +@ARTICLE{Stoddard2008, + AUTHOR = {Philip K. Stoddard and Michale R. Markham}, + TITLE = {Signal cloaking by electric fish.}, + JOURNAL = {BioScience}, + YEAR = {2008}, + VOLUME = {58}, + PAGES = {415--425} +} + +@ARTICLE{Stoddard2019, + AUTHOR = {Philip K. Stoddard and Alex Tran and R\"udiger Krahe}, + TITLE = {Predation and crypsis in the evolution of electric signaling in weakly electric fishes.}, + JOURNAL = {Front Ecol Evol}, + YEAR = {2019}, + VOLUME = {7}, + PAGES = {264} +} + +@ARTICLE{Stoekl2014, + AUTHOR = {Anna St\"ockl and Fabian Sinz and Jan Benda and Jan Grewe}, + TITLE = {Encoding of social signals in all three electrosensory pathways of \textit{Eigenmannia virescens}.}, + YEAR = {2014}, + JOURNAL = {Journal of Neurophysiology}, + VOLUME = {112}, + PAGES = {2076-2091} } + +@article{Stoewer2014, + title={File format and library for neuroscience data and metadata}, + author={Stoewer, Adrian and Kellner, Christian Johannes and Benda, Jan and Wachtler, Thomas and Grewe, Jan}, + journal={Front Neuroinf}, + volume={8}, + number={27}, + pages={10--3389}, + year={2014} +} + +@Article{Strandburg2015, + Title = {Shared decision-making drives collective movement in wild baboons}, + Author = {Strandburg-Peshkin, Ariana and Farine, Damien R. and Couzin, Iain D. and Crofoot, Margaret C.}, + Journal = {Science}, + Year = {2015}, + Number = {6241}, + Pages = {1358--1361}, + Volume = {348}, + + Abstract = {How do groups of animals, including humans, make decisions that affect the entire group? Evidence collected from schooling animals suggests that the process is somewhat democratic, with nearest neighbors and the majority shaping overall collective behavior. In animals with hierarchical social structures such as primates or wolves, however, such democracy may be complicated by dominance. Strandburg-Peshkin et al. monitored all the individuals within a baboon troop continuously over the course of their daily activities. Even within this highly socially structured species, movement decisions emerged via a shared process. Thus, democracy may be an inherent trait of collective behavior.Science, this issue p. 1358Conflicts of interest about where to go and what to do are a primary challenge of group living. However, it remains unclear how consensus is achieved in stable groups with stratified social relationships. Tracking wild baboons with a high-resolution global positioning system and analyzing their movements relative to one another reveals that a process of shared decision-making governs baboon movement. Rather than preferentially following dominant individuals, baboons are more likely to follow when multiple initiators agree. When conflicts arise over the direction of movement, baboons choose one direction over the other when the angle between them is large, but they compromise if it is not. These results are consistent with models of collective motion, suggesting that democratic collective action emerging from simple rules is widespread, even in complex, socially stratified societies.}, + Doi = {10.1126/science.aaa5099}, + Owner = {raab}, + Publisher = {American Association for the Advancement of Science}, + Timestamp = {2020.02.11}, + Url = {https://science.sciencemag.org/content/348/6241/1358} +}fmidd + + +@Article{StrandburgPeshkin2017, + Title = {Habitat and social factors shape individual decisions and emergent group structure during baboon collective movement}, + Author = {Strandburg-Peshkin, Ariana and Farine, Damien R and Crofoot, Margaret C and Couzin, Iain D}, + Journal = {eLife}, + Year = {2017}, + Pages = {e19505}, + Volume = {6}, + Doi = {10.7554/eLife.19505}, + Keywords = {collective movement, movement Ecology, social behavior, habitat, baboons (Papio anubis)}, + Url = {https://doi.org/10.7554/eLife.19505} +} + +@Article{StrandburgPeshkin2019, + Title = {Burrow usage patterns and decision-making in meerkat groups}, + Author = {Strandburg-Peshkin, Ariana and Clutton-Brock, Tim and Manser, Marta B}, + Journal = BehavEcol, + Year = {2019}, + + Doi = {10.1093/beheco/arz190}, + Owner = {raab}, + Timestamp = {2020.01.27} +} + +@Article{Striedter1991, + Title = {Auditory, Electrosensory, and Mechanosensory Lateral Line Pathways Through the Forebrain in Channel Catfishes.}, + Author = {Georg F. Striedter}, + Journal = {Journal of Comparative Neurology}, + Year = {1991}, + Pages = {311-331}, + Volume = {312} +} + +@article{Su2001, + title={Extracellular calcium modulates persistent sodium current-dependent burst-firing in hippocampal pyramidal neurons}, + author={Su, Hailing and Alroy, Gil and Kirson, Eilon D and Yaari, Yoel}, + journal={Journal of Neuroscience}, + volume={21}, + number={12}, + pages={4173--4182}, + year={2001}, + publisher={Soc Neuroscience} +} + +@article{Sumner2012, + title={Auditory nerve fibre responses in the ferret}, + author={Sumner, Christian J and Palmer, Alan R}, + journal={European Journal of Neuroscience}, + volume={36}, + number={4}, + pages={2428--2439}, + year={2012}, + publisher={Wiley Online Library} +} + +@article{Surlykke1988, + title={Temporal coding in the auditory receptor of the moth ear}, + author={Surlykke, Annemarie and Larsen, Ole N{\ae}sbye and Michelsen, Axel}, + journal={Journal of Comparative Physiology A}, + volume={162}, + number={3}, + pages={367--374}, + year={1988}, + publisher={Springer} +} + +@Article{Sword2005, + Title = {Migratory bands give crickets protection}, + Author = {G. Sword and P. Lorch and D. Gwynne}, + Journal = {Nature}, + Year = {2005}, + Number = {703}, + Volume = {433}, + + Doi = {doi:10.1038/433703a}, + Owner = {raab}, + Timestamp = {2020.01.21} +} + +@article{Szabo1965, + title={Sense organs of the lateral line system in some electric fish of the {Gymnotidae, Mormyridae and Gymnarchidae}}, + author={Szabo, Thomas}, + journal={Journal of Morphology}, + volume={117}, + number={2}, + pages={229--249}, + year={1965}, + publisher={Wiley Online Library} +} + +@Article{Tallarovic2005, + Title = {Electric organ discharge frequency jamming during social interactions in brown ghost knifefish, \textit{Apteronotus leptorhynchus}}, + Author = {Sara K. Tallarovic and Harold H. Zakon}, + Journal = AnimBehav, + Year = {2005}, + Number = {6}, + Pages = {1355 - 1365}, + Volume = {70}, + + Doi = {https://doi.org/10.1016/j.anbehav.2005.03.020}, + Owner = {raab}, + Timestamp = {2017.05.04}, + Url = {http://www.sciencedirect.com/science/article/pii/S0003347205003088} +} + +@ARTICLE{Tan2005, + AUTHOR = {Eric W. Tan and Jonathan M. Nizar and Eric Carrera-G and Eric S. Fortune}, + TITLE = {Electrosensory interference in naturally occurring aggregates of a species of weakly electric fish, \textit{Eigenmannia virescens}.}, + JOURNAL = {Behavioural Brain Research}, + YEAR = {2005}, + VOLUME = {164}, + PAGES = {83--92} +} + +@Article{Todd1999, + Title = {The Identification of Peaks in Physiological Signals}, + Author = {Bryan S. Todd and David C. Andrews}, + Journal = {Computers and Biomedical Research}, + Year = {1999}, + Number = {4}, + Pages = {322 - 335}, + Volume = {32}, + + Doi = {http://dx.doi.org/10.1006/cbmr.1999.1518}, + Keywords = {peak detection}, + Owner = {raab}, + Timestamp = {2017.03.06}, + Url = {http://www.sciencedirect.com/science/article/pii/S0010480999915185} +} + +@Article{Tong1982a, + Title = {The Nucleus Praeeminentialis: An Electro- and Mechanoreceptive Center in the Brainstem of the Catfish.}, + Author = {Shang-Iiang Tong}, + Journal = JCompPhysiol, + Year = {1982}, + Pages = {299-309}, + Volume = {145} +} + +@Article{Tong1982b, + Title = {Electroreceptive Representation and Its Dynamics in the Cerebellum of the Catfish, {Ictalurus nebulosus (Ictaluridae, Siluriformes)}.}, + Author = {Shang-Iiang Tong and Theodore Holmes Bullock}, + Journal = JCompPhysiol, + Year = {1982}, + Pages = {289-298}, + Volume = {145} +} + +@article{Treutwein1999, + title={Fitting the psychometric function}, + author={Treutwein, Bernhard and Strasburger, Hans}, + journal={Perception \rm{\&} \textit{Psychophysics}}, + volume={61}, + number={1}, + pages={87--106}, + year={1999}, + publisher={Springer} +} + + +@Article{Tricas1995, + Title = {Electrosensory Optimization to conspecific phasic signals for mating.}, + Author = {Timothy C. Tricas and Scott W. Michael and Joseph A. Sisneros}, + Journal = NeurosciLett, + Year = {1995}, + Pages = {129-132}, + Volume = {202} +} + +@Article{Triefenbach2003, + Title = {Effects of sex, sensitivity and status on cue recognition in the weakly electric fish \textit{Apteronotus leptorhynchus}}, + Author = {F. Triefenbach and H. Zakon}, + Journal = AnimBehav, + Year = {2003}, + Number = {1}, + Pages = {19 - 28}, + Volume = {65}, + + Doi = {https://doi.org/10.1006/anbe.2002.2019}, + Owner = {raab}, + Timestamp = {2017.05.04}, + Url = {http://www.sciencedirect.com/science/article/pii/S0003347202920191} +} + +@article{Triefenbach2008, + title={Changes in signalling during agonistic interactions between male weakly electric knifefish, \textit{Apteronotus leptorhynchus}}, + author={Triefenbach, Frank A and Zakon, Harold H}, + journal={Animal Behaviour}, + volume={75}, + number={4}, + pages={1263--1272}, + year={2008}, + publisher={Elsevier} +} + +@Article{Triefenbach2008, + Title = {Changes in signalling during agonistic interactions between male weakly electric knifefish, \textit{Apteronotus leptorhynchus}.}, + Author = {F. Triefenbach and H. Zakon}, + Journal = AnimBehav, + Year = {2008}, + Number = {4}, + Pages = {1263--1272}, + Volume = {75}, + Doi = {https://doi.org/10.1016/j.anbehav.2007.09.027}, + Url = {http://www.sciencedirect.com/science/article/pii/S0003347208000110} +} + +@ARTICLE{Turner2007, + AUTHOR = {Cameron R. Turner and Maksymilian Derylo and C. David de Santana and Jos\'s A. Alves-Gomes and G. Troy Smith}, + TITLE = {Phylogenetic comparative analysis of electric communication signals in ghost knifefishes ({Gymnotiformes}: {Apteronotidae}).}, + JOURNAL = {Journal of Experimental Biology}, + YEAR = {2007}, + VOLUME = {210}, + PAGES = {4104--4122} +} + +@article{VanHemmen2011, + author = {van Hemmen, J. L. and Longtin, A. and + Vollmayr, A. N.}, + journal = {Chaos}, + month = {dec}, + number = {4}, + title = {Testing resonating vector strength: auditory system, + electric fish, and noise.}, + volume = {21}, + pages = {047508}, + year = {2011}, + abstract = {Quite often a response to some input with a specific + frequency $\nu$(○) can be described through a + sequence of discrete events. Here, we study the + synchrony vector, whose length stands for the vector + strength, and in doing so focus on neuronal response + in terms of spike times. The latter are supposed to + be given by experiment. Instead of singling out the + stimulus frequency $\nu$(○) we study the synchrony + vector as a function of the real frequency variable + $\nu$. Its length turns out to be a resonating vector + strength in that it shows clear maxima in the + neighborhood of $\nu$(○) and multiples thereof, + hence, allowing an easy way of determining response + frequencies. We study this "resonating" vector + strength for two concrete but rather different cases, + viz., a specific midbrain neuron in the auditory + system of cat and a primary detector neuron belonging + to the electric sense of the wave-type electric fish + \textit{Apteronotus leptorhynchus}. We show that the + resonating vector strength always performs a clear + resonance correlated with the phase locking that it + quantifies. We analyze the influence of noise and + demonstrate how well the resonance associated with + maximal vector strength indicates the dominant + stimulus frequency. Furthermore, we exhibit how one + can obtain a specific phase associated with, for + instance, a delay in auditory analysis.}, + doi = {10.1063/1.3670512}, + issn = {1089-7682}, + url = {http://www.ncbi.nlm.nih.gov/pubmed/22225382}, +} + +@article{Viancour1979, + title={Electroreceptors of a weakly electric fish}, + author={Viancour, Terry A}, + journal={Journal of Comparative Physiology}, + volume={133}, + number={4}, + pages={327--338}, + year={1979}, + publisher={Springer} +} + +@article{Viemeister1988, + title={Intensity coding and the dynamic range problem}, + author={Viemeister, Neal F}, + journal={Hearing Research}, + volume={34}, + number={3}, + pages={267--274}, + year={1988}, + publisher={Elsevier} +} + +@article{Vila1999, + title={Phylogenetic relationships, evolution, and genetic diversity of the domestic dog}, + author={Vil{\`a}, Carles and Maldonado, Jesus E and Wayne, Robert K}, + journal={Journal of Heredity}, + volume={90}, + number={1}, + pages={71--77}, + year={1999}, + publisher={Oxford University Press} +} + +@Article{Vinje2002, + Title = {Natural Stimulation of the Nonclassical Receptive Field Increases Information Transmission Efficiency in {V1}.}, + Author = {William E. Vinje and Jack L. Gallant}, + Journal = JNeurosci, + Year = {2002}, + Number = {7}, + Pages = {2904-2915}, + Volume = {22} +} + +@article{Virtanen2020, + title={{SciPy} 1.0: fundamental algorithms for scientific computing in {Python}}, + author={Virtanen, Pauli and Gommers, Ralf and Oliphant, Travis E and Haberland, Matt and Reddy, Tyler and Cournapeau, David and Burovski, Evgeni and Peterson, Pearu and Weckesser, Warren and Bright, Jonathan and others}, + journal={Nature methods}, + volume={17}, + number={3}, + pages={261--272}, + year={2020}, + publisher={Nature Publishing Group} +} + +@Article{Vonderschen2014, + Title = {Detecting interaural time differences and remodeling their representation.}, + Author = {Katrin Vonderschen and Hermann Wagner}, + Journal = TINS, + Year = {2014}, + Number = {5}, + Pages = {289-300}, + Volume = {37} +} + +@Article{Voronenko2017, + title={Weakly nonlinear response of noisy neurons}, + author={Voronenko, Sergej O and Lindner, Benjamin}, + journal={New Journal of Physics}, + volume={19}, + number={3}, + pages={033038}, + year={2017}, + publisher={IOP Publishing} +} + +@ARTICLE{Wachtel1966, + AUTHOR = {Allen W. Wachtel and R. Bruce Szamier}, + TITLE = {Special cutaneous receptor organs of fish: the tuberous organs of \textit{Eigenmannia}.}, + YEAR = {1966}, + JOURNAL = {Journal of Morphology}, + VOLUME = {119}, + PAGES = {51--80} } + +@ARTICLE{Waddell2020, + AUTHOR = {Joseph C. Waddell and Angel A. Caputi}, + TITLE = {Waveform discrimination in a pair of pulse‐generating electric fishes.}, + JOURNAL = JFishBiol, + YEAR = {2020}, + VOLUME = {}, + PAGES = {accepted} +} + +@ARTICLE{Wallach2022, + AUTHOR = {Avner Wallach and Alexandre Melanson and Andre Longtin and Leonard Maler}, + TITLE = {Mixed selectivity coding of sensory and motor social signals in the thalamus of a weakly electric fish.}, + YEAR = {2022}, + JOURNAL = {Current Biology}, + VOLUME = {32}, + PAGES = {51--63} } + +@article{Walt2011, + title={The {NumPy} array: a structure for efficient numerical computation}, + author={Walt, St{\'e}fan van der and Colbert, S Chris and Varoquaux, Gael}, + journal={Computing in science \& engineering}, + volume={13}, + number={2}, + pages={22--30}, + year={2011}, + publisher={IEEE Computer Society} +} + +@ARTICLE{Walz2013, + AUTHOR = {Henriette Walz and Ginette J. Hup\'e and Jan Benda and John E. Lewis}, + TITLE = {The neuroethology of electrocommunication: How signal background influences sensory encoding and behaviour in \textit{Apteronotus leptorhynchus}.}, + JOURNAL = {Journal of Physiology-Paris}, + YEAR = {2013}, + VOLUME = {107}, + PAGES = {13--25} +} + +@ARTICLE{Walz2014, + AUTHOR = {Henriette Walz and Jan Grewe and Jan Benda}, + TITLE = {Static frequency tuning accounts for changes in neural synchrony evoked by transient communication signals.}, + YEAR = {2014}, + JOURNAL = {J Neurophysiol}, + VOLUME = {112}, + PAGES = {752--765} } + + +@Article{Wang2007, + Title = {Neural coding strategies in auditory cortex.}, + Author = {Xiaoqin Wang}, + Journal = HearRes, + Year = {2007}, + Pages = {81-93}, + Volume = {229} +} + +@ARTICLE{Watanabe1963, + AUTHOR = {Akira Watanabe and Kimihisa Takeda}, + TITLE = {The change of discharge frequency by {A.C.} stimulus in a weak electric fish.}, + JOURNAL = {Journal of Experimental Biology}, + YEAR = {1963}, + VOLUME = {40}, + PAGES = {57--66} +} + +@article{Victor1977, + title={Nonlinear analysis of cat retinal ganglion cells in the frequency domain.}, + author={Victor, Jonathan D and Shapley, Robert M and Knight, Bruce W}, + journal={Proceedings of the National Academy of Sciences}, + volume={74}, + number={7}, + pages={3068--3072}, + year={1977}, + publisher={National Acad Sciences} +} + +@article{Victor1980, + title={A method of nonlinear analysis in the frequency domain}, + author={Victor, J and Shapley, R}, + journal={Biophysical Journal}, + volume={29}, + number={3}, + pages={459--483}, + year={1980}, + publisher={Elsevier} +} + +@article{Victor1979, + title={Nonlinear systems analysis: comparison of white noise and sum of sinusoids in a biological system.}, + author={Victor, Jonathan D}, + journal={Proceedings of the National Academy of Sciences}, + volume={76}, + number={2}, + pages={996--998}, + year={1979}, + publisher={National Acad Sciences} +} + +@article{Shapley1978, + title={The effect of contrast on the transfer properties of cat retinal ganglion cells.}, + author={Shapley, Robert M and Victor, Jonathan D}, + journal={The Journal of physiology}, + volume={285}, + number={1}, + pages={275--298}, + year={1978}, + publisher={Wiley Online Library} +} + +@article{Wen2009, + title={Dynamic range adaptation to sound level statistics in the auditory nerve}, + author={Wen, Bo and Wang, Grace I and Dean, Isabel and Delgutte, Bertrand}, + journal={Journal of Neuroscience}, + volume={29}, + number={44}, + pages={13797--13808}, + year={2009}, + publisher={Soc Neuroscience} +} + +@ARTICLE{Westby1981, + AUTHOR = {G. 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Max}, + Journal = BehavEcolSociobiol, + Year = {1988}, + Number = {5}, + Pages = {341--354}, + Volume = {22} +} + +@ARTICLE{Westby1988, + AUTHOR = {G. W. Max Westby}, + TITLE = {The ecology, discharge diversity and predatory behaviour of gymnotiforme electric fish in the coastal streams of {French Guiana}.}, + JOURNAL = BehavEcolSociobiol, + YEAR = {1988}, + VOLUME = {22}, + PAGES = {341--354} +} + +@article{Wiesenfeld1995, + author = {Wiesenfeld, K. and Moss, F.}, + journal = {Nature}, + keywords = {noise, statistics}, + pages = {33--36}, + refid = {440}, + timestamp = {2008.09.26}, + title = {Stochastic resonance and the benefits of noise: from ice ages to crayfish and squids}, + volume = {373}, + year = {1995} +} + +@Article{Wilkens2002, + Title = {The electric sense of the paddlefish: a passive system for the detection and capture of zooplankton prey.}, + Author = {Lon A. Wilkens and Michael H. 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Hopkins}, + TITLE = {Electrical and behavioral courtship displays in the mormyrid fish \textit{Brienomyrus brachyistius}.}, + JOURNAL = {Journal of Experimental Biology}, + YEAR = {2007}, + VOLUME = {210}, + PAGES = {2244--2525} +} + +@article{Wypych2012, + title={Standardized {F1--A} consistent measure of strength of modulation of visual responses to sine-wave drifting gratings}, + author={Wypych, Marek and Wang, Chun and Nagy, Attila and Benedek, Gy{\"o}rgy and Dreher, Bogdand and Waleszczyk, Wioletta J}, + journal={Vision Research}, + volume={72}, + pages={14--33}, + year={2012}, + publisher={Elsevier} +} + +@article{Xu1996, + title={Logarithmic time course of sensory adaptation in electrosensory afferent nerve fibers in a weakly electric fish}, + author={Xu, Zhian and Payne, Jeremy R and Nelson, Mark E}, + journal={J Neurophysiol}, + volume={76}, + number={3}, + pages={2020--2032}, + year={1996}, + publisher={American Physiological Society Bethesda, MD} +} + +@Article{Yager1993, + Title = {Directional characteristics of tuberous electroreceptors in the weakly electric fish, {Hypopomus (Gymnotiformes)}.}, + Author = {D.D. 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Lewis and Andr\'e Longtin}, + TITLE = {Coding conspecific identity and motion in the electric sense.}, + JOURNAL = {PLoS Comput Biol}, + YEAR = {2005}, + VOLUME = {8}, + PAGES = {e1002564} +} + +@Article{Yuille2006, + Title = {Vision as Bayesian inference: analysis by synthesis?}, + Author = {Alan Yuille and Daniel Kersten}, + Journal = TICS, + Year = {2006}, + Number = {7}, + Pages = {301-308}, + Volume = {10} +} + + +@article{Zakon2002, + author = {H. H. Zakon and Oestreich, J. and Tallarovic, S. and Triefenbach, F.}, + journal = {Journal of Physiology-Paris}, + number = {5--6}, + pages = {451--458}, + title = {{EOD} modulations of brown ghost electric fish: {JAR}s, chirps, rises, and dips}, + volume = {96}, + year = {2002} +} + +@ARTICLE{Zakon2008, + AUTHOR = {Harold H. Zakon and Derrick J. Zwickl and Ying Lu and David M. Hillis}, + TITLE = {Molecular evolution of communication signals in electric fish.}, + JOURNAL = {Journal of Experimental Biology}, + YEAR = {2008}, + VOLUME = {211}, + PAGES = {1814--1818} +} + +@article{Zeldenrust2018, + title={Neural coding with bursts—current state and future perspectives}, + author={Zeldenrust, Fleur and Wadman, Wytse J and Englitz, Bernhard}, + journal={Frontiers in Computational Neuroscience}, + volume={12}, + pages={48}, + year={2018}, + publisher={Frontiers Media SA} +} + +@Article{zuniga2017, + Title = {Migration confers winter survival benefits in a partially migratory songbird}, + Author = {Z\'u{\~n}iga, Daniel and Gager, Yann and Kokko, Hanna and Fudickar, Adam Michael and Schmidt, Andreas and Naef-Daenzer, Beat and Wikelski, Martin and Partecke, Jesko}, + Journal = {eLife}, + Year = {2017}, + Pages = {e28123}, + Volume = {6}, + + Abstract = {To evolve and to be maintained, seasonal migration, despite its risks, has to yield fitness benefits compared with year-round residency. Empirical data supporting this prediction have remained elusive in the bird literature. To test fitness related benefits of migration, we studied a partial migratory population of European blackbirds (\textit{Turdus merula}) over 7 years. Using a combination of capture-mark-recapture and radio telemetry, we compared survival probabilities between migrants and residents estimated by multi-event survival models, showing that migrant blackbirds had 16\% higher probability to survive the winter compared to residents. A subsequent modelling exercise revealed that residents should have 61.25\% higher breeding success than migrants, to outweigh the survival costs of residency. 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Zupanc}, + Journal = AnimBehav, + Year = {2001}, + Number = {6}, + Pages = {1119 - 1128}, + Volume = {62}, + Doi = {https://doi.org/10.1006/anbe.2001.1867}, + Url = {http://www.sciencedirect.com/science/article/pii/S0003347201918676} +} + +@Article{Zupanc2006, + Title = {Electric interactions through chirping behavior in the weakly electric fish, \textit{Apteronotus leptorhynchus}.}, + Author = {Zupanc, G K H and S\^{\i}rbulescu, R F and Nichols, A and Ilies, I}, + Journal = JCompPhysiolA, + Year = {2006}, + Number = {2}, + Pages = {159--173}, + Volume = {192} +} + +@article{Zhang2022, + title={A robust receptive field code for optic flow detection and decomposition during self-motion}, + author={Zhang, Yue and Huang, Ruoyu and N{\"o}renberg, Wiebke and Arrenberg, Aristides B}, + journal={Current Biology}, + volume={32}, + number={11}, + pages={2505--2516}, + year={2022}, + publisher={Elsevier} +} + +@Article{Marmarelis1972, + title={White-noise analysis of a neuron chain: an application of the {Wiener} theory.}, + author={Marmarelis, Panos Z. and Naka, Ken-Ichi}, + journal={Science}, + volume={175}, + pages={1276--1278}, + year={1972} +} + +@Article{French2001, + title={Predicting the responses of mechanoreceptor neurons to physiological inputs by nonlinear system identification.}, + author={Andrew S. 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Ruggero}, + year={2005}, + journal=JNeurophysiol, + volume={93}, + pages={3635--3648} +} + +@Article{Neiman2011, + title={Sensory coding in oscillatory electroreceptors of paddlefish.}, + author={Alexander B. Neiman and David F. Russell}, + year={2011}, + journal={Chaos}, + volume={21}, + pages={047505} +} + +@Article{Doiron2004, + title={Oscillatory activity in electrosensory neurons increases with the spatial correlation of the stochastic input stimulus.}, + author={Brent Doiron and Benjamin Lindner and André Longtin and Leonard Maler and Joseph Bastian}, + year={2004}, + journal={Physical Review Letters}, + volume={93}, + pages={ 048101-1--048101-4}, +} + +@Article{Chichilnisky2001, + title={A simple white noise analysis of neuronal light responses.}, + author={E. J. 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