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methods, makefile and iscience style

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This commit is contained in:
Jan Grewe 2024-02-23 15:00:26 +01:00
parent 2fa9d860b0
commit 08b23490dd
9 changed files with 2375 additions and 360 deletions
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1
.gitignore vendored
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@ -4,4 +4,5 @@ __pychache__
*.bbl
*.spl
*.out
*.log
*synctex*

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Makefile Normal file
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TEXBASE=susceptibility1
BIBFILE=references.bib
REBUTTALBASE=
TEXFILE=$(TEXBASE).tex
PDFFILE=$(TEXBASE).pdf
TXTFILE=$(TEXBASE).txt
REVISION=
ifdef REBUTTALBASE
REBUTTALTEXFILE=$(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
# rescue_local_eod 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"\

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%% Driver file to produce iscience.bst from merlin.mbs
%% Generated with makebst, version 4.1 (2003/09/08)
%% Produced on 2023/04/21 at 8:05
%%
\input docstrip
\preamble
----------------------------------------
*** bibliography style matching iscience ***
\endpreamble
\postamble
End of customized bst file
\endpostamble
\keepsilent
\askforoverwritefalse
\def\MBopts{\from{merlin.mbs}{%
%EXTERNAL FILES:
%Name of language file: \cfile=.
%No included files.
%INTERNAL LANGUAGE SUPPORT (if no external language file)
%: (def) English
% babel,%: Babel
%--------------------
%STYLE OF CITATIONS:
%: (def) Numerical
% ay,%: Author-year
% alph,%: Alpha style, Jon90 or JWB90
% alph,alf-1,%: Alpha style, Jon90
% alph,alf-f,%: Alpha style, Jones90
% cite,%: Cite key
%--------------------
%HTML OUTPUT (if non author-year citations)
%: (def) Normal LaTeX
% html,%: Hypertext
% html,htlist,%: Hypertext list
% html,htdes,%: Hypertext with keys
%--------------------
%AUTHOR--YEAR SUPPORT SYSTEM (if author-year citations)
% nat,%: Natbib
% %: (def) Older Natbib
% alk,%: Apalike
% har,%: Harvard
% ast,%: Astronomy
% cay,%: Chicago
% nmd,%: Named
% cn,%: Author-date
%--------------------
%HARVARD EXTENSIONS INCLUDED (if Harvard support selected)
% harnm,%: With Harvard extensions
% %: (def) Older Harvard
%--------------------
%LANGUAGE FIELD
%: (def) No language field
% lang,%: Add language field
%--------------------
%ANNOTATIONS:
%: (def) No annotations
% annote,%: Annotations
%--------------------
%PRESENTATIONS:
%: (def) Do not add presentation type
% pres,%: Add presentation, speaker not highlighted
% pres,pres-bf,%: Presentation, speaker bold face
% pres,pres-it,%: Presentaion, speaker italic
% pres,pres-sc,%: Presentaion, speaker in small caps
%--------------------
%ORDERING OF REFERENCES (if non-author/year and non-alph)
% %: (def) Alphabetical
seq-no,%: Citation order
% seq-yr,%: Year ordered
% seq-yrr,%: Reverse year ordered
%--------------------
%ORDERING OF REFERENCES (if author-year citations)
% %: (def) Alphabetical
% seq-lab,%: By label
% seq-labc,%: By label and cite order
% seq-key,%: By label and cite key
% seq-yr,%: Year ordered
% seq-yrr,%: Reverse year ordered
% seq-no,%: Citation order
%--------------------
%ORDER ON VON PART (if not citation order)
%: (def) Sort on von part
% vonx,%: Sort without von part
%--------------------
%IGNORE FIRST NAMES (if author-year citations)
% %: (def) Respect first names
% xintls,%: Sort on surname only
%--------------------
%AUTHOR NAMES:
% ed-au,%: Full, surname last
% nm-revf,%: Full, surname first
% nm-init,ed-au,%: Initials + surname
nm-rev,%: Surname + initials
% nm-rv,%: Surname + dotless initials
% nm-rvvc,%: Surname + comma + spaceless initials
% nm-rvx,%: Surname + pure initials
% nm-rvcx,%: Surname + comma + pure initials
% nm-rvv,%: Surname + spaceless initials
% nm-rev1,%: Only first name reversed, initials
% nm-revv1,%: First name reversed, with full names
%--------------------
%EDITOR NAMES IN COLLECTIONS (if author names reversed)
% %: (def) Editor names NOT reversed
ed-rev,%: Editor names reversed
%--------------------
%POSITION OF JUNIOR (if author names reversed)
jnrlst,%: Junior comes last
% %: (def) Junior between
%--------------------
%JUNIOR PART IN THE CITATION (if author-year citations)
% %: (def) No `junior' part in the citations
% jnrlab,%: `Junior' in citations
%--------------------
%PUNCTUATION BETWEEN AUTHOR NAMES:
%: (def) Author names separated by commas
% aunm-semi,%: Names separated by semi-colon
% aunm-sl,%: Names separated by slash
%--------------------
%ADJACENT REFERENCES WITH REPEATED NAMES:
%: (def) Author/editor names always present
% nmdash,%: Repeated author/editor names replaced by dash
% nmdash,nmd-2,%: Repeated author/editor names replaced by 2 dashes
% nmdash,nmd-3,%: Repeated author/editor names replaced by 3 dashes
%--------------------
%NUMBER OF AUTHORS IN BIBLIOGRAPHY:
% %: (def) All authors
nmlm,%: Limited authors
%--------------------
x10,x0,%: Maximum of 10 authors
m1,%: Minimum of 1 authors
%AUTHORS IN CITATIONS:
%: (def) One author et al
% mcite,%: Some other truncation scheme
%--------------------
%MAX AUTHORS BEFORE ET AL: (if regular cite not selected)
% mct-1,%: One et al
% mct-2,%: One, Two et al
% mct-3,%: One, Two, Three et al
% mct-4,%: One, Two, Three, Four et al
% mct-5,%: One, Two, Three, Four, Five et al
% mct-6,%: One, Two, Three, Four, Five, Six et al
%--------------------
%MAX AUTHORS WITHOUT ET AL: (if regular cite not selected)
% mct-x2,%: Two authors without truncating
% mct-x3,%: Three authors
% mct-x4,%: Four authors
% mct-x5,%: Five authors
% mct-x6,%: Six authors
%--------------------
%TYPEFACE FOR AUTHORS IN LIST OF REFERENCES:
%: (def) Normal font for author names
% nmft,nmft-sc,%: Small caps authors
% nmft,nmft-it,%: Italic authors
% nmft,nmft-bf,%: Bold authors
% nmft,nmft-def,%: User defined author font
%--------------------
%FONT FOR FIRST NAMES (if non-default font for authors)
% %: (def) First names same font as surnames
% fnm-rm,%: First names in normal font
% fnm-def,%: First names in user defined font
%--------------------
%EDITOR NAMES IN INCOLLECTION ETC:
% %: (def) Editors incollection normal font
% nmfted,%: Editors incollection like authors
%--------------------
%FONT FOR `AND' IN LIST:
% %: (def) `And' in author font
% nmand-rm,%: `And' in normal font
%--------------------
%FONT OF CITATION LABELS IN TEXT (if author-year citations)
% %: (def) Cited authors plain
% lab,lab-it,%: Cited authors italic
% lab,lab-sc,%: Cited authors small caps
% lab,lab-bf,%: Cited authors bold
% lab,lab-def,%: User defined citation font
%--------------------
%FONT FOR `AND' IN CITATIONS (if non-default font for citation lables)
% %: (def) Cited `and' in author font
% and-rm,%: Cited `and' in normal font
%--------------------
%FONT OF EXTRA LABEL (The extra letter on the year)
% %: (def) Extra label plain
% xlab-it,%: Extra label italic
%--------------------
%LABEL WHEN AUTHORS MISSING (if author-year citations)
% keyxyr,%: Year blank when KEY replaces missing author
% %: (def) Year included when KEY replaces missing author
%--------------------
%MISSING DATE (if author-year citations)
% %: (def) Missing date set to ????
% blkyear,%: Missing date left blank
%--------------------
%DATE POSITION:
% %: (def) Date at end
dt-beg,%: Date after authors
% dt-jnl,%: Date part of journal spec.
% dt-end,%: Date at very end
%--------------------
%DATE FORMAT (if non author-year citations)
% %: (def) Plain month and year
yr-par,%: Date in parentheses
% yr-brk,%: Date in brackets
% yr-col,%: Date preceded by colon
% yr-per,%: Date preceded by period
% yr-com,%: Date preceded by comma
% yr-blk,%: Date preceded by space
%--------------------
%SUPPRESS MONTH:
% %: (def) Date is month and year
xmth,%: Date is year only
%--------------------
%REVERSED DATE (if including month)
% %: (def) Date as month year
% dtrev,%: Date as year month
%--------------------
%DATE FORMAT (if author-year citations)
% %: (def) Year plain
% yr-par,%: Year in parentheses
% yr-brk,%: Year in brackets
% yr-col,%: Year preceded by colon
% yr-per,%: Year preceded by period
% yr-com,%: Date preceded by comma
% yr-blk,%: Year preceded by space
%--------------------
%INCLUDE MONTHS:
% %: (def) Date is year only
% aymth,%: Include month in date
%--------------------
%REVERSED DATE (if including month)
% %: (def) Date as month year
% dtrev,%: Date as year month
%--------------------
%DATE PUNCTUATION (if date not at end)
% %: (def) Date with standard block punctuation
% yrp-col,%: Colon after date
% yrp-semi,%: Semi-colon after date
yrp-per,%: Period after date
% yrp-x,%: No punct. after date
%--------------------
%BLANK AFTER DATE:
% %: (def) Space after date
yrpp-xsp,%: No space after date
%--------------------
%DATE FONT:
%: (def) Date in normal font
% dtbf,%: Date in bold face
%--------------------
%TRUNCATE YEAR (if author-year citations)
% note-yr,%: Year text full
% %: (def) Year truncated
%--------------------
%TITLE OF ARTICLE:
%: (def) Title plain
% tit-it,%: Title italic
% tit-qq,qt-s,%: Title and punctuation in single quotes
% tit-qq,%: Title and punctuation in double quotes
% tit-qq,qt-g,%: Title and punctuation in guillemets
% tit-qq,qt-s,qx,%: Title in single quotes
% tit-qq,qx,%: Title in double quotes
% tit-qq,qt-g,qx,%: Title in guillemets
%--------------------
%COLLECTION/PROCEEDINGS TITLES (if quoted title)
% bt-qq,%: Quote collection and proceedings titles
% %: (def) Collection and proceedings titles not in quotes
%--------------------
%CAPITALIZATION OF ARTICLE TITLE:
% %: (def) Sentence style
atit-u,%: Title style
%--------------------
%ARTICLE TITLE PRESENT:
%: (def) Article title present
% jtit-x,%: No article title
%--------------------
%JOURNAL NAMES:
%: (def) Periods in journal names
% jxper,%: Dotless journal names
%--------------------
%JOURNAL NAME FONT:
%: (def) Journal name italics
% jttl-rm,%: Journal name normal
%--------------------
%THESIS TITLE:
%: (def) Thesis titles like books
% thtit-a,%: Thesis title like article
% thtit-x,%: No thesis title
%--------------------
%TECHNICAL REPORT TITLE:
%: (def) Tech. report title like articles
% trtit-b,%: Tech. report title like books
%--------------------
%TECHNICAL REPORT NUMBER:
%: (def) Tech. report and number plain
% trnum-it,%: Tech. report and number italic
%--------------------
%JOURNAL VOLUME:
% %: (def) Volume plain
% vol-it,%: Volume italic
vol-bf,%: Volume bold
% vol-2bf,%: Volume and number bold
%--------------------
%JOURNAL VOL AND NUMBER:
% %: (def) Journal vol(num)
% vnum-sp,%: Journal vol (num)
% vnum-cm,%: Journal vol, num
% vnum-nr,%: Journal vol, no. num
% vnum-h,%: Journal vol, \# number
% vnum-b,%: Journal vol number
vnum-x,%: Journal vol, without number
%--------------------
%VOLUME PUNCTUATION:
% %: (def) Volume with colon
% volp-sp,%: Volume with colon and space
% volp-semi,%: Volume with semi-colon
volp-com,%: Volume with comma
% volp-blk,%: Volume with blank
%--------------------
%YEAR IN JOURNAL SPECIFICATION:
%: (def) Journal year like others
% jdt-v,%: Journal vol(year)
% jdt-vs,%: Journal vol (year)
% jdt-p,%: Year with pages
% jdt-pc,%: Year, comma, pages
%--------------------
%PAGE NUMBERS:
%: (def) Start and stop page numbers
% jpg-1,%: Only start page number
%--------------------
%LARGE PAGE NUMBERS:
%: (def) No separators for large page numbers
% pgsep-c,%: Comma inserted over 9999
% pgsep-s,%: Thin space inserted over 9999
% pgsep-p,%: Period inserted over 9999
%--------------------
%WORD `PAGE' IN ARTICLES:
%: (def) Article pages numbers only
% jwdpg,%: Include `page' in articles
%--------------------
%POSITION OF PAGES:
%: (def) Pages given mid text
% pp-last,%: Pages at end
%--------------------
%WORD `VOLUME' IN ARTICLES:
%: (def) Article volume as number only
% jwdvol,%: Include `volume' in articles
%--------------------
%NUMBER AND SERIES FOR COLLECTIONS:
num-xser,%: Allows number without series
% %: (def) Standard BibTeX
%--------------------
%POSITION OF NUMBER AND SERIES:
%: (def) After chapter and pages
% numser,%: Just before publisher
%--------------------
%VOLUME AND SERIES FOR BOOKS/COLLECTIONS:
%: (def) Vol. 23 of Series
% ser-vol,%: Series, vol. 23
%--------------------
%POSITION OF VOLUME AND SERIES FOR INCOLLECTIONS:
%: (def) Series and volume after the editors
% ser-ed,%: Series and volume after booktitle
%--------------------
%JOURNAL NAME PUNCTUATION:
% %: (def) Comma after journal
jnm-x,%: Space after journal
%--------------------
%BOOK TITLE:
%: (def) Book title italic
% btit-rm,bt-rm,%: Book title plain
%--------------------
%PAGES IN BOOKS:
%: (def) Pages in book plain
% bkpg-par,%: Pages in book in parentheses
% bkpg-x,%: Pages in book bare
%--------------------
%TOTAL PAGES OF A BOOK:
%: (def) Total book pages not printed
% pg-bk,%: For book: 345 pages
% pg-bk,pg-pre,%: Total book pages before publisher
%--------------------
%PUBLISHER ADDRESS:
% %: (def) Publisher, address
% add-pub,%: Address: Publisher
%--------------------
%PUBLISHER IN PARENTHESES:
% %: (def) Publisher as normal block
pub-par,%: Publisher in parentheses
% pub-date,%: Publisher and date in parentheses
% pub-date,pub-xc,%: Publisher and date in parentheses, no comma
% pub-date,pub-xpar,%: Publisher and date without parentheses
% pub-date,pub-xpar,pub-xc,%: Publisher and date, no parentheses, no comma
%--------------------
%PUBLISHER POSITION:
% %: (def) Publisher after chapter, pages
% pre-pub,%: Publisher before chapter, pages
pre-edn,%: Publisher after edition
%--------------------
%ISBN NUMBER:
% isbn,%: Include ISBN
%: (def) No ISBN
%--------------------
%ISSN NUMBER:
% issn,%: Include ISSN
%: (def) No ISSN
%--------------------
%DOI NUMBER:
% doi,%: Include DOI
% url-doi,%: Format DOI as URL //dx.doi.org/doi
agu-doi,doi,%: Insert DOI AGU style
% %: (def) No DOI
%--------------------
%`EDITOR' AFTER NAMES (EDITED BOOKS WITHOUT AUTHORS):
%: (def) Word `editor' after name
% edpar,%: `Name (editor),'
% edpar,bkedcap,%: `Name (Editor),'
% edparc,%: `Name, (editor)'
% edparc,bkedcap,%: `Name, (Editor)'
% edparxc,%: `Name (editor)'
% edparxc,bkedcap,%: `Name (Editor)'
%--------------------
%EDITOR IN COLLECTIONS:
% %: (def) Same as for edited book
% edby,%: In booktitle, edited by ..
% edby-par,%: In booktitle (edited by ..)
% edby-parc,%: In booktitle, (edited by ..)
edby,edbyx,%: In booktitle, editor ..
% edby,edbyw,%: In booktitle, (editor) ..
% edby-par,edbyx,%: In booktitle (editor..)
% edby-parc,edbyx,%: In booktitle, (editor..)
% edby,edbyy,%: In booktitle, .., editor
% edby-par,edbyy,%: In booktitle (.., editor)
%--------------------
%CAPITALIZE `EDITOR' OR `EDITED BY' (if editor capitalizable)
% %: (def) `(editor,..)' or `(edited by..)'
% edcap,%: `(Editor,..)' or `(Edited by..)'
%--------------------
%PUNCTUATION BETWEEN SECTIONS (BLOCKS):
%: (def) \newblock after blocks
% blk-com,%: Comma between blocks
% blk-com,com-semi,%: Semi-colon between blocks
% blk-com,com-blank,%: Blanks between blocks
% blk-tit,%: Period after titles of articles, books, etc
% blk-tit,tit-col,%: Colon after titles of articles, books, etc
% blk-tita,%: Period after titles of articles
% blk-tita,tit-col,%: Colon after titles of articles
%--------------------
%PUNCTUATION BEFORE NOTES (if not using \newblock)
% %: (def) Notes have regular punctuation
% blknt,%: Notes preceded by period
%--------------------
%PUNCTUATION AFTER AUTHORS:
%: (def) Author block normal
% au-col,%: Author block with colon
%--------------------
%PUNCTUATION AFTER `IN':
%: (def) Space after `in'
% in-col,%: Colon after `in'
% in-it,%: Italic `in'
% in-col,in-it,%: Italic `in' and colon
% in-x,%: No word `in'
%--------------------
%`IN' WITH JOURNAL NAMES (if using 'in' with collections)
%: (def) No `in' before journal name
% injnl,%: Add `in' before journal name
%--------------------
%FINAL PUNCTUATION:
%: (def) Period at very end
% fin-bare,%: No period at end
%--------------------
%ABBREVIATE WORD `PAGES' (if not using external language file)
% %: (def) `Page(s)'
% pp,%: `Page' abbreviated
ppx,%: `Page' omitted
%--------------------
%ABBREVIATE WORD `EDITORS':
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@ -60,7 +60,7 @@ month = {01},
pages = {},
title = {{Species diversity and phylogenetic systematics of American knifefishes (Gymnotiformes, Teleostei)}},
volume = {190},
pages = {1-127}
pages = {1-127},
journal = {Miscellaneous Publications Museum of Zoology University of Michigan},
}
@ -1846,19 +1846,19 @@ year = {2013}
volume = {Humboldt-Universität zu Berlin}
}
%@phdthesis{Egerland2020,
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% 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},
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},%
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note = {unpublished master thesis}
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%}
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},
@ -4927,7 +4927,7 @@ and Keller, Clifford H.},
@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,
Journal = {Nature Neuroscience},
Year = {2013},
Pages = {1170--1178},
Volume = {16}
@ -5001,7 +5001,7 @@ and Keller, Clifford H.},
@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,
Journal = {Nature Neuroscience},
Year = {1999},
Number = {1},
Pages = {79-87},
@ -5529,7 +5529,7 @@ groups and electrogenic mechanisms.},
@Article{Schwartz2001,
Title = {Natural Signal statistics and sensory gain control.},
Author = {Odelia Schwartz and Eero P. Simoncelli},
Journal = Nature Neuroscience,
Journal = {Nature Neuroscience},
Year = {2001},
Number = {8},
Pages = {819-825},
@ -5554,6 +5554,18 @@ groups and electrogenic mechanisms.},
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}
}
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@ -648,263 +648,149 @@ When using noise stimulation strong nonlinearity was demonstrated to appear for
\section{Methods}
\subsection{Experimental subject details}
Experiments were performed on male and female weakly electric fish
of the species \lepto{} obtained from a
commercial tropical fish supplier (Aquarium Glaser GmbH, Rodgau,
Germany). The fish were kept in tanks with a water temperature
of $25\,^\circ$C and a conductivity of around
$270\,\micro\siemens\per\centi\meter$ under a 12\,h:12\,h light-dark
cycle. All experimental
protocols complied with national and European law and were approved by
the Ethics Committee of the Regierungspräsidium T\"ubingen (permit no: ZP1-16).
\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 222 P-units and 45 ampullary electroreceptor afferents recorded in 71 weakly electric fish of the species \lepto{}. The original electrophysiological recordings were performed on male and female weakly electric fish of the species \lepto{} that were obtained from a commercial supplier for tropical fish (Aquarium Glaser GmbH, Rodgau,
Germany). The fish were 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 with 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 $\mu$L to 50 $\mu$L of tubocurarine (5 mg\,$\cdot$\,mL−1 dissolved in fish saline; Sigma-Aldrich).
Respiration was then switched to normal tank water and the fish was transferred to the experimental tank.
No experiments were performed. Instead, cells recorded in \lepto{} and \eigen{} at the Ludwig Maximilian University (LMU) M\"unchen and at the Eberhard-Karls University T\"ubingen between 2010 and 2023 were used. The final sample consisted of 222 P-units and 45 ampullary cells from 71 weakly electric fish of the species \lepto{} and 60 P-units and 18 ampullary cells from 17 weakly
electric fish of the species \eigen.
%\subsection{Experimental model and subject details In chapter \ref{chapter4} }
% glued to the skull
\subsection{Surgery} Before surgery, anesthesia was provided via bath application with a solution of MS222 (120\,mg/l, PharmaQ, Fordingbridge, UK) buffered with Sodium Bicarbonate (120\,mg/l). The posterior anterior lateral line nerve (pALLN) above the gills before its descent towards the anterior lateral line ganglion (ALLNG) was disclosed for subsequent P-unit recordings. During the surgery water supply was ensured by a mouthpiece, sustaining
anesthesia with a solution of MS222 (100\,mg/l) buffered with Sodium Bicarbonate (100\,mg/l).
%For the surgery the fish was fixed on a stage via a metallic rod.
\subsection{Experimental setup} During the experiments fish were immobilized by a single
intramuscular injection of Tubocurarine (Sigma-Aldrich, Steinheim,
Germany; 25--50\,\micro\litre{} of 5\,mg/ml solution). For the
recordings fish were positioned on a stage in a tank, with a major part
of their body in the water. Analgesia was refreshed in intervals of two hours by cutaneous Lidocaine application (2\,\%; bela-pharm, Vechta, Germany) around the nerve. 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 (\figrefb{Settup}, blue triangle). Recordings of electroreceptor afferents were amplified (SEC-05, npi-electronics, Tamm, Germany, operated in bridge mode). All signals, P-unit recording, recorded EOD and the generated
stimulus, were digitized with sampling rates of 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.
%For parts of the data %0, 20 or
\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 reapplication 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 (\figrefb{Setup}, blue triangle). 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 mean baseline firing rates of 50--450\,Hz \citep{Grewe2017, Hladnik2023} and phase-locking to the EOD, leading to a multimodal interspike interval (ISI) distribution (as in \subfigrefb{heterogeneity}{B}). Ampullary cells were classified based on mean firing rates of 80--200\,Hz and no phase-locking to the EOD with an unimodal ISI distribution. Only cells with a baseline recording were included in the final sample. Cells that ceased spiking during the baseline recording were excluded.
\subsection{Field recordings} The EOD of fish without the stimulus was termed global EOD and measured with two vertical carbon rods ($11\,\centi\meter$
long, 8\,mm diameter) in a head-tail configuration (\figrefb{Settup}, green bars). This signal was
amplified 200--500 times and band-pass filtered (3 to 1\,500\,Hz
passband, DPA2-FX; npi electronics, Tamm, Germany).
The EOD of the fish with the stimulus was termed local EOD and was measured between two 1\,cm-spaced silver
wires located next to the left gill of the fish and orthogonal to its longitudinal
body axis (amplification 200--500 times, band-pass filtered with 3 to
1\,500\,Hz pass-band, DPA2-FX; npi-electronics, Tamm,
Germany, \figrefb{Settup}, red markers).
The neurons were classified into cell types during the recording by the experimenter. P-units were classified based on mean baseline firing rates of 50--450\,Hz and a clear phase-locking to the EOD and their responses to amplitude modulations of their own EOD\citep{Grewe2017, Hladnik2023}. Ampullary cells were classified based on mean 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}
The electric field of the fish was recorded in two ways: 1. we measured the so-called \textit{global EOD} with two vertical carbon rods ($11\,\centi\meter$ long, 8\,mm diameter) in a head-tail configuration (\figrefb{Setup}, green bars). The electrodes were placed isopotential to the stimulus. This signal was differentially amplified with a 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). 2. The so-called \textit{local EOD} was measured with 1\,cm-spaced silver wires 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, \figrefb{Setup}, red markers). This local measurement recorded the combination of the fish's own field and the applied stimulus and thus serves as a proxy of the transdermal potential that drives the electroreceptors.
\subsection{Stimulation}
The stimulus was isolated from the 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 (\figrefb{Settup}, gray bars).
The stimulus was isolated from the 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 (\figrefb{Setup}, gray bars). The stimulus was calibrated with respect to the local EOD.
\begin{figure*}[h!]%(\subfigrefb{beat_amplitudes}{B}).
\includegraphics[width=\columnwidth]{Settup}
\caption{\label{Settup} Electrophysiolocical recording set-up. The fish, depicted as a black scheme and surrounded by isopotential lines, was positioned in the middle of the tank. Blue triangle -- electrophysiological recordings were conducted at the posterior anterior lateral line nerve (pALLN) above the
gills. Gray horizontal bars -- electrodes for the stimulation. Green vertical bars -- electrodes to measure the global EOD (the EOD of the fish without the stimulus). Red dots -- electrodes to measure the local EOD (the EOD of the fish with the stimulus). The local EOD was measured with a distance of 1 \,cm between the electrodes. All measured signals were amplified, filtered and stored on a local computer.}
\caption{\label{Setup} Electrophysiolocical recording setup. The fish, depicted as a black scheme and surrounded by isopotential lines, was positioned in the center of the tank. Blue triangle -- electrophysiological recordings were conducted in the posterior anterior lateral line nerve (pALLN). Gray horizontal bars -- electrodes for the stimulation. Green vertical bars -- electrodes to measure the \textit{global EOD} placed isopotential to the stimulus, i.e. recording fish's unperturbed EOD. Red dots -- electrodes to measure the \textit{local EOD} picking up the combination of fish's EOD and the stimulus. The local EOD was measured with a distance of 1 \,cm between the electrodes. All measured signals were amplified, filtered, and stored for offline analysis.}
\end{figure*}
%Fish sketch adapted base on \citep{Hagedorn1985} next to the gills,
%Blue circles - P-units.
\subsection{White noise stimuli}\label{rammethods}
The fish were stimulated with band-pass limited white noise stimuli with a cut-off frequency of 150, 300 or 400\,Hz. The standard deviation of the white noise was expressed in relation to the EOD size of the fish in the experimental set-up and termed contrast. The contrast varied between 1 and 20\,$\%$ for \lepto{} and between 2.5 and 40\,$\%$ for \eigen. Only cell recordings 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. For P-unit recordings, the EOD of the fish was multiplied with the desired random amplitude modulation (RAM, MXS-01M; npi electronics).
%A stimulus had a duration of 10\,s and was subdivided into $\n{}=20$ windows with no overlap, each with the duration of $T=0.5$\,s. S
\subsection{White noise stimulation}\label{rammethods}
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\,$\%$ for \lepto{} and between 2.5 and 40\,$\%$ for \eigen. Only cell recordings 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).
\subsection{Data analysis} Data analysis was performed with Python 3 using the packages matplotlib\cite{Hunter2007}, numpy\cite{Walt2011}, scipy\cite{scipy2020}, sklearn\cite{scikitlearn2011}, pandas\cite{Mckinney2010}, nixio\cite{Stoewer2014}, and thunderfish (\url{https://github.com/bendalab/thunderfish}).
\paragraph{Baseline analysis}\label{baselinemethods}
The mean 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) was calculated as the standard deviation of the interspike intervals (ISI) divided by 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.
%The size of the sinewaves was set to a contrast of 10\,$\%$ of the EOD of the receiver.
%If one sine wave was present this resulted in the one-beat condition, if two sine waves were present in the two-beat condition.
\subsection{Data analysis} Data analysis was performed with Python~3
using the packages matplotlib, numpy, scipy, sklearn, pandas, nixio
\citep{Stoewer2014}, and thunderfish
(\url{https://github.com/bendalab/thunderfish}).
\paragraph{Baseline calculation}\label{baselinemethods}
The mean 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) was calculated as the standard deviation of the interspike intervals ISI divided by the mean ISI: $\rm{CV} = \sqrt{\langle (ISI- \langle ISI \rangle) ^2 \rangle}\langle ISI \rangle$. If the baseline was recorded several times in a cell, the mean \fbase{} and mean CV were calculated.
%The serial correlation was calculated with lag 1 ($SC_1$, \eqnref{serial}).
%To get a burst-corrected spike train all spikes in a burst package after the first spike were removed.
%as the mean number of spikes in the burst-corrected spike train. % CV \cvbasecorr{} after burst correction
%\subsubsection{burstfraction} %1.5: 147,2.5: 59,3.0: 1,3.5: 6,4.5: 3,5.5: 1,
%\subsection{Data analysis for chapter 2}
\paragraph{Response modulation} \label{response_modulation}
The firing rate of a cell is modulated around an average firing rate similar to \fbase{} in response to a stimulus. The response modulation was calculated based on the mean firing rate $f(t)$. For $f(t)$ the binary spike trains, with zero everywhere no spike occurred and the sampling rate everywhere a spike occurred, were convolved with a Gaussian with a standard deviation of 2.5\,ms and the mean over the stimulus repeats was calculated. The response modulation $\sigma_{M} = \sqrt{\langle (f(t)-\langle f(t) \rangle)^2\rangle}$ was calculated as the standard deviation of the mean firing rate $f(t)$, where the averages are taken over time. The response modulation was calculated as an estimate of the effective stimulus strength.
% _{t}_{n}
% smoothed = pad_for_mean(smoothed, max_len)
% response_modulation = np.nanstd(np.mean(smoothed, axis=0)) Spectral analysis and linear encoding
%the transfer function
%Applying the Fourier transform to the stimulus $s(t)$ resulted in $\tilde{s}(f)$ and applying the Fourier transform to the response of the neuron, the firing rate of the spike trains $r(t)$ resulted in $R(f)$.
\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.
The time-dependent response of the neuron was estimated from the spiking activity $x_k(t) = \sum_i\delta(t-t_{k,i})$ recorded for each stimulus presentation, $k$, by kernel convolution with a Gaussian kernel
\begin{equation}
K(t) = \scriptstyle \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{t^2}{2\sigma^2}}
\end{equation}
with $\sigma$ the standard deviation of the Gaussian which was set to 2.5\,ms if not stated otherwise. For each trial $k$ the $x_k(t)$ is convolved with the kernel $K(t)$
\begin{equation}
r_k(t) = x_k(t) * K(t) = \int_{-\infty}^{+\infty} x_k(t') K(t-t') \, \mathrm{d}t' \;,
\end{equation}
where $*$ denotes the convolution. $r(t)$ is then calculated as the across-trial average
\begin{equation}
r(t) = \left\langle r_k(t) \right\rangle _k.
\end{equation}
To quantify how strongly the neuron is driven by the stimulus we quantified the response modulation as the standard deviation $\sigma_{M} = \sqrt{\langle (r(t)-\langle r(t) \rangle)^2\rangle}$.
%, therefore the stimulusSecond-order susceptibility
\paragraph{Spectral analysis}\label{susceptibility_methods}%chapter 2In this score the stimulus $s(t)$ and the response $r(t)$ were set into relation.
The first-order and second-order susceptibility between the stimulus $s(t)$ and the response $r(t)$ were calculated (\eqnref{linearencoding_methods}, \eqnref{susceptibility}). The response $r(t)$ was the firing rate of the neuron, calculated as the binary spike train representation, with the sampling rate value when a spike occurred, zero everywhere else and the unit Hz. The noise stimulus $s(t)$ (see section \ref{rammethods}), was expressed in relation to the EOD and had no unit. A stimulus had a duration of 10\,s that were subdivided into $\n{}=20$ segments with no overlap, each with the duration of $T=0.5$\,s. Since the sampling rate $S_{r}$ varied between cell recordings (20\,kHz, 40\,kHz or 100\,kHz) $n_{\rm fft}$ was set to $S_{r}\cdot0.5$\,s, resulting in a frequency resolution of 2\,Hz for each cell.
\paragraph{Spectral analysis}\label{susceptibility_methods}
The neuron is driven by the stimulus and thus the neuronal response $r(t)$ depends on the stimulus $s(t)$. To investigate the relation between stimulus and response we calculated the first- and second-order susceptibility of the neuron to the stimulus in the frequency domain. The Fourier transforms of $s(t)$ and $r(t)$ are denoted as $\tilde s(\omega)$ and $\tilde r(\omega)$ and were calculated according to $\tilde x(\omega) = \int_{0}^{T} \, x(t) \cdot e^{- i \omega t}\,dt$, with $T$ being the signal duration. Stimuli had a duration of 10\,s and spectra of stimulus and response were calculated in separate segments of 0.5\,s with no overlap resulting in a spectral resolution of 2\,Hz. $r(t)$ was estimated by kernel convolution with a box kernel that had a width matching the sampling interval to preserve temporal accuracy as far as possible.
The Fourier transform of a time signal was calculated as $\tilde s(\omega) = \int_{0}^{T} \, s(t) \cdot e^{- i \omega t}\,dt$, with $T$ being the signal duration. The power spectrum was calculated as
The power spectrum was calculated as
\begin{equation}
\label{powereq}
\begin{split}
S_{ss}(\omega) = \frac{\langle \tilde s(\omega) \tilde s^* (\omega)\rangle}{T}
\end{split}
\end{equation}
with $\tilde s^* $ being the complex conjugate and $\langle ... \rangle$ the averaging over the segments.
The cross-spectrum was calculated with \eqnref{cross}, linear encoding was estimated with \eqnref{linearencoding_methods} and the higher-order cross-spectrum was calculated with \eqnref{crosshigh}.
with $\tilde s^* $ being the complex conjugate and $\langle ... \rangle$ denotes averaging over the segments. The cross-spectrum $S_{rs}(\omega)$ was calculated according to
\begin{equation}
\label{cross}
\begin{split}
S_{rs}(\omega) = \frac{\langle \tilde r(\omega) \tilde s^* (\omega)\rangle}{T}
\end{split}
\end{equation}
From $S_{rs}(\omega)$ and $ S_{ss}(\omega)$ we calculated the linear susceptibility (transfer function) as
\begin{equation}
\label{linearencoding_methods}
\begin{split}
\chi_{1}(\omega) = \frac{S_{rs}(\omega) }{S_{ss}(\omega) }
\end{split}
\end{equation}
The second-order cross-spectrum that depends on the two frequencies $\omega_1$ and $\omega_2$ was calculated according to
\begin{equation}
\label{crosshigh}
S_{rss} (\omega_{1},\omega_{2}) = \frac{\langle \tilde r (\omega_{1}+\omega_{2}) \tilde s^* (\omega_{1})\tilde s^* (\omega_{1}) \rangle}{T}
S_{rss} (\omega_{1},\omega_{2}) = \frac{\langle \tilde r (\omega_{1}+\omega_{2}) \tilde s^* (\omega_{1})\tilde s^* (\omega_{2}) \rangle}{T}
\end{equation}
The second-order susceptibility was calculated as
The second-order susceptibility was calculated by dividing the higher-order cross-spectrum by the spectral power at the respective frequencies.
\begin{equation}
\label{susceptibility0}
\begin{split}
%\begin{split}
\chi_{2}(\omega_{1}, \omega_{2}) = \frac{S_{rss} (\omega_{1},\omega_{2})}{2S_{ss} (\omega_{1}) S_{ss} (\omega_{2})}
\end{split}
\end{equation}
by dividing the higher-order cross-spectrum by the power spectra. Applying the Fourier transform this can be rewritten resulting in:
\begin{equation}
\label{susceptibility}
\begin{split}
\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{split}
%\end{split}
\end{equation}
% Applying the Fourier transform this can be rewritten resulting in:
% \begin{equation}
% \label{susceptibility}
% \begin{split}
% \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{split}
% \end{equation}
% \notejg{Wofuer genau brauchen wir equation 9?}
The absolute value of a second-order susceptibility matrix is visualized in \figrefb{model_full}. There the upper right and the lower left quadrants characterize the nonlinearity in the response $r(t)$ at the sum frequency of the two input frequencies. The lower right and upper left quadrants characterize the nonlinearity in the response $r(t)$ at the difference of the input frequencies.
%\subsection{First-order susceptibility} \label{linearencoding_methods}
% The lower right and upper left quadrants in the susceptibility matrix in \figrefb{model_full} were calculated as
%\begin{equation}
% \label{susceptibility2}
% \chi_{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}^{N} dt s_{n}(t)e^{-i \omega_{2}t} \int_{0}^{N} dt' s_{n}(t')e^{i \omega_{2}t'}}.
%\end{equation}
\paragraph{Nonlinearity index}\label{projected_method}%chapter 2
The structural changes in the absolute value of the second-order susceptibility (as the matrix in \figrefb{model_full}) were quantified in a nonlinearity index:
\paragraph{Nonlinearity index}\label{projected_method}
\notejg{use of $f_{Base}$ or $f_{base}$ or $f_0$ should be consistent throughout the manuscript.}
We expect to see non-linear susceptibility when $\omega_1 + \omega_2 = f_{Base}$. To characterize this we calculated the nonlinearity index (NLI) as
\begin{equation}
\label{nli_equation}
NLI(f_{0}) = \frac{\max_{f_{0}-5\,\rm{Hz} \leq f \leq f_{0}+5\,\rm{Hz}} D(f)}{\mathrm{med}(D(f))}
NLI(f_{Base}) = \frac{\max_{f_{Base}-5\,\rm{Hz} \leq f \leq f_{Base}+5\,\rm{Hz}} D(f)}{\mathrm{med}(D(f))}
\end{equation}
For this index, the second-order susceptibility matrix was projected on the diagonal $D(f)$, by taking the mean of the anti-diagonals. The peakedness of a frequency $f_{0}$ in $D(f)$ was quantified by finding the maximum of $D(f)$ in the range $f_{0} \pm 5$\,Hz (\subfigrefb{cells_suscept}\,\panel[vi]{A}, gray area) and dividing it by the median of $D(f)$. This was calculated for the frequencies \fbase{} and \fbasecorr{} resulting in \nli{} and \nlicorr{}.
If the same frozen noise was recorded several times in a cell, each noise repetition resulted in a separate second-order susceptibility matrix. The mean of the corresponding \nli{} and \nlicorr{} values was used for the population statistics in \figref{data_overview_mod} and \figrefb{data_overview}. The second-order susceptibility matrices depicted in \figrefb{cells_suscept}, \figrefb{ampullary}, \figrefb{burst_cells_suscept} and \figrefb{cells_eigen} were calculated based on the first frozen noise repeat.
% \includegraphics[width=\columnwidth]{cells_eigen} % {ampullary}{burst_cells_suscept}, {cells_eigen}
%\nli{} and \nlicorr{} scores shown in were calculated as the mean of the \nli{} and \nlicorr{} values for all frozen noise RAM repetitions in a cel
\notejg{sollte es $D(\omega)$ sein?}
For this index, the second-order susceptibility matrix was projected onto the diagonal $D(f)$, by taking the mean of the anti-diagonals. The peakedness at the frequency $f_{Base}$ in $D(f)$ was quantified by finding the maximum of $D(f)$ in the range $f_{Base} \pm 5$\,Hz (\subfigrefb{cells_suscept}\,\panel[vi]{A}, gray area) and dividing it by the median of $D(f)$.
If the same frozen noise was recorded several times in a cell, each noise repetition resulted in a separate second-order susceptibility matrix. The mean of the corresponding \nli{} values was used for the population statistics in \figref{data_overview_mod}.
\notejg{should go to the legend: calculated based on the first frozen noise repeat.}
\subsection{Leaky integrate-and-fire models}\label{lifmethods}
Leaky integrate-and-fire (LIF) models with a carrier were constructed to reproduce the specific firing
properties of P-units \citep{Chacron2001,Sinz2020}. The input into the P-unit model during baseline was the fish's own EOD
\begin{equation}
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{eod}
x(t) = x_{EOD}(t) = \cos(2\pi f_{EOD} t)
\end{equation}
with EOD frequency $f_{EOD}$ and amplitude normalized to one.
with the EOD frequency $f_{EOD}$ and an amplitude normalized to one.
In the model, the input $x(t)$ was first thresholded.
In the model, the input $x(t)$ was then first thresholded to model the synapse between the primary receptor cells and the afferent.
\begin{equation}
\label{threshold2}
\lfloor x(t) \rfloor_0 = \left\{ \begin{array}{rcl} x(t) & ; & x(t) \ge 0 \\ 0 & ; & x(t) < 0 \end{array} \right.
\end{equation}
$\lfloor x(t) \rfloor_{0}$ denotes the threshold operation that sets negative values to zero (box left to \subfigrefb{flowchart}\,\panel[i]{A}). Thresholding potentially happens at the synapse between the receptor cells and the afferent.
$\lfloor x(t) \rfloor_{0}$ denotes the threshold operation that sets negative values to zero (box left to \subfigrefb{flowchart}\,\panel[i]{A}).
The resulting signal was then low-pass filtered with a time constant $\tau_{d}$ by the afferent's dendrite (box left to \subfigrefb{flowchart}\,\panel[ii]{A}).
The resulting receptor signal was then low-pass filtered to approximate passive signal conduction in the afferent's dendrite (box left to \subfigrefb{flowchart}\,\panel[ii]{A}).
\begin{equation}
\label{dendrite}
\tau_{d} \frac{d V_{d}}{d t} = -V_{d}+ \lfloor x(t) \rfloor_{0}^{p}
\tau_{d} \frac{d V_{d}}{d t} = -V_{d}+ \lfloor x(t) \rfloor_{0}
\end{equation}
Dendritic low-pass filtering was necessary to reproduce the loose coupling of P-unit spikes to the EOD while maintaining high
sensitivity to small amplitude modulations. Because the input was unitless, the dendritic voltage was unitless, too. $p$ was set to one resulting in a pure threshold. This thresholding and low-pass filtering extracted the amplitude modulation of the input $x(t)$.
with $\tau_{d}$ as the dendritic time constant. Dendritic low-pass filtering was necessary to reproduce the loose coupling of P-unit spikes to the EOD while maintaining high sensitivity at small amplitude modulations. Because the input was dimensionless, the dendritic voltage was dimensionless, too. The combination of threshold and low-pass filtering extracts the amplitude modulation of the input $x(t)$.
The dendritic voltage $V_d(t)$ was the input to a leaky integrate-and-fire (LIF) model
\begin{equation}
\label{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 $V_{d}$, and $\sqrt{2D}\xi(t)$ is a white noise with strength $D$. All state variables in the LIF are unitless. The output of the model is in seconds.
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 $D$. All state variables except $\tau_m$ are dimensionless.
The adaptation current $A$ followed
\begin{equation}
@ -913,18 +799,18 @@ The adaptation current $A$ followed
\end{equation}
with adaptation time constant $\tau_A$.
Whenever the membrane voltage $V_m(t)$ crossed the 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}\,\panel[iv]{A}).
Whenever the membrane voltage $V_m(t)$ crossed 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}\,\panel[iv]{A}).
\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 static nonlinearity $f(V_m)$ was equal to zero for the LIF. In the case of an exponential integrate-and-fire model (EIF), this function was set to
\begin{equation}
\label{eifnl}
f(V_m)= \Delta_V \text{e}^{\frac{V_m-1}{\Delta_V}}
\end{equation}
\citep{Fourcaud-Trocme2003}, where $\Delta_V$ was varied from 0.001 to 0.1.
% The static nonlinearity $f(V_m)$ was equal to zero for the LIF. In the case of an exponential integrate-and-fire model (EIF), this function was set to
% \begin{equation}
% \label{eifnl}
% f(V_m)= \Delta_V \text{e}^{\frac{V_m-1}{\Delta_V}}
% \end{equation}
% \citep{Fourcaud-Trocme2003}, where $\Delta_V$ was varied from 0.001 to 0.1.
%, \figrefb{eif}
\begin{figure*}[hb!]
@ -933,72 +819,43 @@ The static nonlinearity $f(V_m)$ was equal to zero for the LIF. In the case of a
\end{figure*}
%\figitem[i]{C}$RAM(t)$
\subsection{Numerical implementation}
The ODEs were integrated by the Euler forward method with a time-step of $\Delta t = 0.00005$\,s.
For the intrinsic noise $\xi(t)$ (\eqnref{LIF}, \subfigrefb{flowchart}\,\panel[iii]{A}) in each time step $i$ a random number was drawn from a normal distribution $\mathcal{N}(0,\,1)$ with zero mean and standard deviation of one. This number was multiplied with $\sqrt{2D}$ and divided by $\sqrt{\Delta t}$:
The model's ODEs were integrated by the Euler forward method with a time-step of $\Delta t = 0.00005$\,s. The intrinsic noise $\xi(t)$ (\eqnref{LIF}, \subfigrefb{flowchart}\,\panel[iii]{A}) 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 $\sqrt{\Delta t}$:
\begin{equation}
\label{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}
\subsection{Model parameters}\label{paramtext}
The 8 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 baseline activity (mean baseline firing rate, CV of ISIs, serial correlation of ISIs at lag one, and vector
strength of spike coupling to EOD) and responses to step increases and
decreases in EOD amplitude (onset-state and steady-state responses,
effective adaptation time constant) of 42 specific P-units for a fixed power of $p=1$ (table~\ref{modelparams}, \citealp{Ott2020}). When modifying
the model (e.g. varying the threshold nonlinearity or the power $p$ in \eqnref{dendrite}) the bias current $\mu$ was adapted to restore the original mean baseline firing rate. For each stimulus repetition the start parameters $A$, $V_{d}$ and $V_{m}$ were drawn randomly from a starting value distribution, retrieved from a 100\,s baseline, recorded in the model after a 100\,s transient.
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 baseline activity (mean baseline firing rate, CV of ISIs, serial correlation of ISIs at lag one, and vector strength of spike coupling to EOD) and responses to step increases and decreases in EOD amplitude (onset-state and steady-state responses,
effective adaptation time constant) of 42 specific P-units for a fixed power of $p=1$ (table~\ref{modelparams}, \citealp{Ott2020}). When modifying the model (e.g. varying the threshold nonlinearity or the power $p$ in \eqnref{dendrite}) the bias current $\mu$ was adapted to restore the original mean baseline firing rate. For each stimulus repetition the start parameters $A$, $V_{d}$ and $V_{m}$ were drawn randomly from a starting value distribution, retrieved from a 100\,s baseline simulation after an initial 100\,s transient that was dicarded.
\subsection{Stimuli for the model}
The model neurons were driven with similar stimuli as the real neurons in the original experiments. To mimic the interaction with one or two foreign animals the receiving fish's EOD (eq. \,\ref{eod}) was normalized to an amplitude of one and the respective EODs of a second or third fish were added.
\subsection{Stimuli for the model}%analysis of the
For the beat protocols, the stimulus was the EOD of the receiving fish, normalized to an
amplitude of one plus the EOD of a second or third fish. If not stated
otherwise, a superposition of cosine waves was used to
mimic the EODs (\eqnref{beat}).
The input for the model during RAM stimulation was the EOD multiplied with a random amplitude modulation $RAM(t)$:
\begin{equation}
The random amplitude modulation (RAM) input to the model created using the same random sequences as were used in the electrophysiological experiments. The input to the model was then
\begin{equation}
\label{ram_equation}
x(t) = (1+ RAM(t)) \cdot \cos(2\pi f_{EOD} t)
\end{equation}
The $RAM(t)$ was generated by drawing random numbers for each frequency up to 300\,Hz in Fourier space. After back transformation, the resulting signal was scaled to the desired standard deviation relative to the EOD carrier, which was termed contrast. %Rectified $x(t)$ with RAM contrasts of $2$ and $20\,\%$ are depicted in \subfigrefb{flowchart}\,\panel[i]{B},\,\panel[i]{C}.%$f_{EOD}/2$
\subsection{Second-order susceptibility analysis of the model}
%\subsubsection{Model second-order nonlinearity}
The second-order susceptibility in the model was calculated with \eqnref{susceptibility}, resulting in matrices as in \figrefb{model_and_data} and \figrefb{model_full}. For this, the model neuron was presented the input $x(t)$ for 2\,s, with the first second being dismissed as the transient. The second-order susceptibility calculation was performed on the last second, resulting in a frequency resolution of 1\,Hz.
\end{equation}
% \subsection{Second-order susceptibility analysis of the model}
% %\subsubsection{Model second-order nonlinearity}
% The second-order susceptibility in the model was calculated with \eqnref{susceptibility}, resulting in matrices as in \figrefb{model_and_data} and \figrefb{model_full}. For this, the model neuron was presented the input $x(t)$ for 2\,s, with the first second being dismissed as the transient. The second-order susceptibility calculation was performed on the last second, resulting in a frequency resolution of 1\,Hz.
\subsection{Model noise split into a noise and a stimulus component}\label{intrinsicsplit_methods}
Based on the Novikov-Furutsu Theorem \citep{Novikov1965, Furutsu1963} the total noise of a LIF model can be split up into several independent noise processes with the same correlation function. Based on this theorem a weak input signal to the LIF model can be approximated with no input signal but instead, a split of the total noise into a noise component and a signal component (\citealp{Egerland2020}). This signal component can be used for the cross-spectrum calculation in \eqnref{susceptibility}, where it is not a weak signal anymore. This approach has the advantage that the signal-to-noise ratio is increased and the number of noise stimulus realizations \n, which would be required in case of a weak input signal for the same signal-to-noise ratio, is reduced. The signal component is regulated by $c_{signal}$ in \eqnref{ram_split} and the noise component is regulated by $c_{noise}$ in \eqnref{Noise_split_intrinsic}.
\notejg{This has large overlaps with the results text... where to keep it?}
Based on the Novikov-Furutsu Theorem \citep{Novikov1965, Furutsu1963} the total noise of a LIF model can be split up into several independent noise processes with the same correlation function. Based on this theorem the internal noise can be split into two parts. One part can then be treated as (additional) input signal and used to calculate the cross-spectra \eqnref{susceptibility}. While maintaining the variability in the system, the effective signal-to-noise ratio can thus be increased. The relation of the total noise treated as signal and the noise is regulated by $c_{signal}$ in \eqnref{ram_split} and the noise component is regulated by $c_{noise}$ in \eqnref{Noise_split_intrinsic}.
\begin{equation}
\begin{equation}
\label{ram_split}
x(t) = (1+ \sqrt{\rho \, 2D \,c_{signal}} \cdot RAM(t)) \cdot \cos(2\pi f_{EOD} t)
\end{equation}
\end{equation}
\begin{equation}
\label{Noise_split_intrinsic_dendrite}
\tau_{d} \frac{d V_{d}}{d t} = -V_{d}+ \lfloor x(t) \rfloor_{0}^{p}
\tau_{d} \frac{d V_{d}}{d t} = -V_{d}+ \lfloor x(t) \rfloor_{0}
\end{equation}