added all my stuff
This commit is contained in:
142
pointprocesses/lecture/Makefile
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142
pointprocesses/lecture/Makefile
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BASENAME=pointprocesses
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TEXFILE=$(BASENAME).tex
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DVIFILE=$(BASENAME).dvi
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PSFILE=$(BASENAME).ps
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PDFFILE=$(BASENAME).pdf
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FOILSFILE=foils.pdf
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THUMBNAILSFILE=thumbnails.pdf
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HTMLBASENAME=$(BASENAME)h
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HTMLTEXFILE=$(BASENAME)h.tex
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HTMLDIR=$(BASENAME)h
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GPTFILES=$(wildcard *.gpt)
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GPTTEXFILES=$(GPTFILES:.gpt=.tex)
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all: ps pdf talk again watchps watchpdf foils thumbs html html1 epsfigs clean cleanup cleanplots help
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.PHONY: epsfigs
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# thumbnails:
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thumbs: $(THUMBNAILSFILE)
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$(THUMBNAILSFILE): $(TEXFILE) $(GPTTEXFILES)
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sed -e 's/setboolean{presentation}{true}/setboolean{presentation}{false}/; s/usepackage{crop}/usepackage[frame]{crop}/' $< > thumbsfoils.tex
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pdflatex thumbsfoils | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && pdflatex thumbsfoils || true
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pdfnup --nup 2x4 --no-landscape --paper a4paper --trim "-1cm -1cm -1cm -1cm" --outfile $@ thumbsfoils.pdf '1-19'
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rm thumbsfoils.*
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# transparencies:
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foils: $(FOILSFILE)
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$(FOILSFILE): $(TEXFILE) $(GPTTEXFILES)
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sed -e 's/setboolean{presentation}{true}/setboolean{presentation}{false}/' $< > tfoils.tex
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pdflatex tfoils | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && pdflatex tfoils || true
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pdfnup --nup 1x2 --orient portrait --trim "-1mm -1mm -1mm -1mm" --frame true --delta "1cm 1cm" --paper a4paper --outfile tfoils2.pdf tfoils.pdf
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pdfnup --nup 1x1 --orient portrait --trim "-2cm -2cm -2cm -2cm" --paper a4paper --outfile $@ tfoils2.pdf
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rm tfoils.* tfoils2.pdf
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# talk:
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talk: $(PDFFILE)
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pdf: $(PDFFILE)
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$(PDFFILE): $(TEXFILE) $(GPTTEXFILES)
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pdflatex -interaction=scrollmode $< | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && pdflatex -interaction=scrollmode $< || true
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# batchmode (no output, no stop on error)
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# nonstopmode / scrollmode (no stop on error)
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# errorstopmode (stop on error)
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again :
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pdflatex $(TEXFILE)
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watchpdf :
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while true; do ! make -q pdf && make pdf; sleep 0.5; done
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# html
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html : $(HTMLTEXFILE) $(GPTTEXFILES)
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rm -f $(HTMLDIR)/*
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htlatex $<
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mkdir -p $(HTMLDIR)
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mv $(HTMLBASENAME).html $(HTMLDIR)
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mv $(HTMLBASENAME)*.* $(HTMLDIR)
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mv z*.gif $(HTMLDIR)
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cd $(HTMLDIR); for i in *.gif; do convert -page +0+0 $$i tmp.gif; mv tmp.gif $$i; done; rmtex $(HTMLBASENAME)
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#$(HTMLTEXFILE) : $(TEXFILE) Makefile
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# sed 's/setboolean{html}{false}/setboolean{html}{true}/; s/\\colorbox{white}{\(.*\)}/\1/g' $< > $@
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html1 : $(HTMLTEXFILE) $(GPTTEXFILES)
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latex2html -dir $(HTMLDIR) -mkdir -subdir -nonavigation -noinfo -image_type png -notransparent -white -split 0 $<
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sed 's-<I>Date:</I>--' $(HTMLDIR)/$(HTMLDIR).html > tmp.html
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cp tmp.html $(HTMLDIR)/index.html
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mv tmp.html $(HTMLDIR)/$(HTMLDIR).html
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$(HTMLTEXFILE) : $(TEXFILE)
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sed '/^%nohtml/,/^%endnohtml/d; s/\\colorbox{white}{\(.*\)}/\1/g' $< > $@
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# eps of all figures:
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epsfigs:
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mkdir -p epsfigs; \
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for i in $(GPTFILES); do \
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{ sed -n -e '1,/\\begin{document}/p' $(TEXFILE); echo "\texpicture{$${i%%.*}}"; echo "\end{document}"; } > tmp.tex; \
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latex tmp.tex; \
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dvips tmp.dvi; \
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ps2eps tmp.ps; \
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mv tmp.eps epsfigs/$${i%%.*}.eps; \
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rm tmp.*; \
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done
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# plots:
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%.tex: %.gpt whitestyles.gp
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gnuplot whitestyles.gp $<
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epstopdf $*.eps
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clean :
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rm -f *~
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rmtex $(BASENAME)
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rm -f $(GPTTEXFILES)
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cleanup :
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rm -f *~
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rmtex $(BASENAME)
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rm -f $(PSFILE) $(PDFFILE) $(FOILSFILE) $(THUMBNAILSFILE)
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rm -f $(GPTTEXFILES)
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rm -f -r $(HTMLDIR)
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cleanplots :
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sed -n -e '/\\begin{document}/,/\\end{document}/p' $(TEXFILE) | fgrep '\input{' | grep -v '^%' | sed 's/.*input{\(.*\).tex}.*/\1.gpt/' > plot.fls
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mkdir -p unusedplots
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for i in *.gp*; do \
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grep -q $$i plot.fls || { grep -q $$i $$(<plot.fls) && echo $$i || mv $$i unusedplots; }; \
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done >> plot.fls
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for i in $$(<plot.fls); do \
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sed "s/\([^'\" ]*\.dat\)/\n\1\n/g;" $$i | fgrep .dat; \
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done | sort | uniq > dat.fls
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mkdir -p unuseddata
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for i in *.dat; do \
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grep -q $$i dat.fls || mv $$i unuseddata; \
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done
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rm dat.fls plot.fls
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help :
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@echo -e \
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"make pdf: make the pdf file of the talk.\n"\
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"make foils: make black&white postscript foils of the talk.\n"\
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"make thumbs: make color thumbnails of the talk.\n"\
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"make again: run latex and make the pdf file of the talk,\n"\
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" no matter whether you changed the .tex file or not.\n\n"\
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"make watchpdf: make the pdf file of the talk\n"\
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" whenever the tex file is modified.\n"\
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"make html: make a html version of the paper (in $(HTMLDIR)).\n\n"\
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"make clean: remove all intermediate files,\n"\
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" just leave the source files and the final .ps and .pdf files.\n"\
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"make cleanup: remove all intermediate files as well as\n"\
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" the final .ps and .pdf files.\n"\
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"make cleanplots: move all unused .gpt and .dat files\n"\
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" into unusedplots/ and unuseddata/, respectively."
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529
pointprocesses/lecture/UT_WBMW_Rot_RGB.pdf
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529
pointprocesses/lecture/UT_WBMW_Rot_RGB.pdf
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61
pointprocesses/lecture/beamercolorthemetuebingen.sty
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pointprocesses/lecture/beamercolorthemetuebingen.sty
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% Copyright 2007 by Till Tantau
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%
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% This file may be distributed and/or modified
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%
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% 1. under the LaTeX Project Public License and/or
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% 2. under the GNU Public License.
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||||
%
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% See the file doc/licenses/LICENSE for more details.
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\usepackage{color}
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\definecolor{karminrot}{RGB}{165,30,55}
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\definecolor{gold}{RGB}{180,160,105}
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\definecolor{anthrazit}{RGB}{50 ,65 ,75 }
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\mode<presentation>
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\setbeamercolor*{normal text}{fg=anthrazit,bg=white}
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\setbeamercolor*{alerted text}{fg=anthrazit}
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\setbeamercolor*{example text}{fg=anthrazit}
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\setbeamercolor*{structure}{fg=gold,bg=karminrot}
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\providecommand*{\beamer@bftext@only}{%
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\relax
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\ifmmode
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\expandafter\beamer@bftext@warning
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\else
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\expandafter\bfseries
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\fi
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}
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\providecommand*{\beamer@bftext@warning}{%
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\ClassWarning{beamer}
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||||
{Cannot use bold for alerted text in math mode}%
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||||
}
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||||
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||||
\setbeamerfont{alerted text}{series=\beamer@bftext@only}
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||||
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||||
\setbeamercolor{palette primary}{fg=karminrot,bg=white}
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||||
\setbeamercolor{palette secondary}{fg=gold,bg=white}
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\setbeamercolor{palette tertiary}{fg=anthrazit,bg=white}
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||||
\setbeamercolor{palette quaternary}{fg=black,bg=white}
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||||
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||||
\setbeamercolor{sidebar}{bg=karminrot!100}
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\setbeamercolor{palette sidebar primary}{fg=karminrot}
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\setbeamercolor{palette sidebar secondary}{fg=karminrot}
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||||
\setbeamercolor{palette sidebar tertiary}{fg=karminrot}
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\setbeamercolor{palette sidebar quaternary}{fg=karminrot}
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\setbeamercolor{item projected}{fg=black,bg=black!20}
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||||
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||||
\setbeamercolor*{block body}{}
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\setbeamercolor*{block body alerted}{}
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||||
\setbeamercolor*{block body example}{}
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||||
\setbeamercolor*{block title}{parent=structure}
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||||
\setbeamercolor*{block title alerted}{parent=alerted text}
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||||
\setbeamercolor*{block title example}{parent=example text}
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||||
\setbeamercolor*{titlelike}{parent=structure}
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||||
|
||||
\mode
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||||
<all>
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pointprocesses/lecture/lifadaptfano10-100ms.pdf
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pointprocesses/lecture/lifadaptisihdistr08-100ms.pdf
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pointprocesses/lecture/lifadaptisihdistr65-100ms.pdf
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pointprocesses/lecture/lifadaptreturnmap10-100ms.pdf
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pointprocesses/lecture/lifisih16.pdf
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pointprocesses/lecture/lifisihdistr16.pdf
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pointprocesses/lecture/lifouisihdistr16-100ms.pdf
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pointprocesses/lecture/lifreturnmap16.pdf
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pointprocesses/lecture/lifserial16.pdf
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pointprocesses/lecture/pifisihdistr01.pdf
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pointprocesses/lecture/pointprocesses.pdf
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pointprocesses/lecture/pointprocesses.pdf
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pointprocesses/lecture/pointprocesses.tex
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pointprocesses/lecture/pointprocesses.tex
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\documentclass{beamer}
|
||||
|
||||
%%%%% title %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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||||
\title[]{Scientific Computing --- Point Processes}
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||||
\author[]{Jan Benda}
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||||
\institute[]{Neuroethology}
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||||
\date[]{WS 14/15}
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||||
\titlegraphic{\includegraphics[width=0.3\textwidth]{UT_WBMW_Rot_RGB}}
|
||||
|
||||
%%%%% beamer %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\mode<presentation>
|
||||
{
|
||||
\usetheme{Singapore}
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||||
\setbeamercovered{opaque}
|
||||
\usecolortheme{tuebingen}
|
||||
\setbeamertemplate{navigation symbols}{}
|
||||
\usefonttheme{default}
|
||||
\useoutertheme{infolines}
|
||||
% \useoutertheme{miniframes}
|
||||
}
|
||||
|
||||
%\AtBeginSection[]
|
||||
%{
|
||||
% \begin{frame}<beamer>
|
||||
% \begin{center}
|
||||
% \Huge \insertsectionhead
|
||||
% \end{center}
|
||||
% \end{frame}
|
||||
%}
|
||||
|
||||
\setbeamertemplate{blocks}[rounded][shadow=true]
|
||||
\setcounter{tocdepth}{1}
|
||||
|
||||
%%%%% packages %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\usepackage[english]{babel}
|
||||
\usepackage{amsmath}
|
||||
\usepackage{bm}
|
||||
\usepackage{pslatex} % nice font for pdf file
|
||||
%\usepackage{multimedia}
|
||||
|
||||
\usepackage{dsfont}
|
||||
\newcommand{\naZ}{\mathds{N}}
|
||||
\newcommand{\gaZ}{\mathds{Z}}
|
||||
\newcommand{\raZ}{\mathds{Q}}
|
||||
\newcommand{\reZ}{\mathds{R}}
|
||||
\newcommand{\reZp}{\mathds{R^+}}
|
||||
\newcommand{\reZpN}{\mathds{R^+_0}}
|
||||
\newcommand{\koZ}{\mathds{C}}
|
||||
|
||||
%%%% graphics %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\usepackage{graphicx}
|
||||
\newcommand{\texpicture}[1]{{\sffamily\small\input{#1.tex}}}
|
||||
|
||||
%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\usepackage{listings}
|
||||
\lstset{
|
||||
basicstyle=\ttfamily,
|
||||
numbers=left,
|
||||
showstringspaces=false,
|
||||
language=Matlab,
|
||||
commentstyle=\itshape\color{darkgray},
|
||||
keywordstyle=\color{blue},
|
||||
stringstyle=\color{green},
|
||||
backgroundcolor=\color{blue!10},
|
||||
breaklines=true,
|
||||
breakautoindent=true,
|
||||
columns=flexible,
|
||||
frame=single,
|
||||
captionpos=b,
|
||||
xleftmargin=1em,
|
||||
xrightmargin=1em,
|
||||
aboveskip=10pt
|
||||
}
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\begin{document}
|
||||
|
||||
\begin{frame}[plain]
|
||||
\frametitle{}
|
||||
\vspace{-1cm}
|
||||
\titlepage % erzeugt Titelseite
|
||||
\end{frame}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\begin{frame}
|
||||
\frametitle{Content}
|
||||
\tableofcontents
|
||||
\end{frame}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section{Point processes}
|
||||
|
||||
\begin{frame}
|
||||
\frametitle{Point process}
|
||||
\vspace{-3ex}
|
||||
\texpicture{pointprocessscetchA}
|
||||
|
||||
A point process is a stochastic (or random) process that generates a sequence of events
|
||||
at times $\{t_i\}$, $t_i \in \reZ$.
|
||||
|
||||
For each point process there is an underlying continuous-valued
|
||||
process evolving in time. The associated point process occurs when
|
||||
the underlying continuous process crosses a threshold.
|
||||
Examples:
|
||||
\begin{itemize}
|
||||
\item Spikes/heartbeat: generated by the dynamics of the membrane potential of neurons/heart cells.
|
||||
\item Earth quakes: generated by the pressure dynamics between the tectonic plates on either side of a geological fault line.
|
||||
\item Onset of cricket/frogs/birds/... songs: generated by the dynamics of the state of a nervous system.
|
||||
\end{itemize}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}
|
||||
\frametitle{Point process}
|
||||
\texpicture{pointprocessscetchB}
|
||||
\end{frame}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section{Homogeneous Poisson process}
|
||||
|
||||
\begin{frame}
|
||||
\frametitle{Homogeneous Poisson process}
|
||||
The probability $p(t)\delta t$ of an event occuring at time $t$
|
||||
is independent of $t$ and independent of any previous event
|
||||
(independent of event history).
|
||||
|
||||
The probability $P$ for an event occuring within a time bin of width $\Delta t$
|
||||
is
|
||||
\[ P=\lambda \cdot \Delta t \]
|
||||
for a Poisson process with rate $\lambda$.
|
||||
\includegraphics[width=1\textwidth]{poissonraster100hz}
|
||||
\end{frame}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section{Interval statistics}
|
||||
|
||||
\begin{frame}
|
||||
\frametitle{Rate}
|
||||
Rate of events $r$ (``spikes per time'') measured in Hertz.
|
||||
\begin{itemize}
|
||||
\item Number of events $N$ per observation time $W$: $r = \frac{N}{W}$
|
||||
\item Without boundary effects: $r = \frac{N-1}{t_N-t_1}$
|
||||
\item Inverse interval: $r = \frac{1}{\mu_{ISI}}$
|
||||
\end{itemize}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}
|
||||
\frametitle{(Interspike) interval statistics}
|
||||
\begin{itemize}
|
||||
\item Histogram $p(T)$ of intervals $T$. Normalized to $\int_0^{\infty} p(T) \; dT = 1$
|
||||
\item Mean interval $\mu_{ISI} = \langle T \rangle = \frac{1}{n}\sum\limits_{i=1}^n T_i$
|
||||
\item Variance of intervals $\sigma_{ISI}^2 = \langle (T - \langle T \rangle)^2 \rangle$\vspace{1ex}
|
||||
\item Coefficient of variation $CV_{ISI} = \frac{\sigma_{ISI}}{\mu_{ISI}}$
|
||||
\item Diffusion coefficient $D_{ISI} = \frac{\sigma_{ISI}^2}{2\mu_{ISI}^3}$
|
||||
\vfill
|
||||
\end{itemize}
|
||||
\includegraphics[width=0.45\textwidth]{poissonisih100hz}\hfill
|
||||
\includegraphics[width=0.45\textwidth]{lifisih16}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}
|
||||
\frametitle{Interval statistics of homogeneous Poisson process}
|
||||
\begin{itemize}
|
||||
\item Exponential distribution of intervals $T$: $p(T) = \lambda e^{-\lambda T}$
|
||||
\item Mean interval $\mu_{ISI} = \frac{1}{\lambda}$
|
||||
\item Variance of intervals $\sigma_{ISI}^2 = \frac{1}{\lambda^2}$
|
||||
\item Coefficient of variation $CV_{ISI} = 1$
|
||||
\end{itemize}
|
||||
\vfill
|
||||
\includegraphics[width=0.45\textwidth]{poissonisihexp20hz}\hfill
|
||||
\includegraphics[width=0.45\textwidth]{poissonisihexp100hz}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}
|
||||
\frametitle{Interval return maps}
|
||||
Scatter plot between succeeding intervals separated by lag $k$.
|
||||
\vfill
|
||||
Poisson process $\lambda=100$\,Hz:
|
||||
\includegraphics[width=1\textwidth]{poissonreturnmap100hz}\hfill
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}
|
||||
\frametitle{Serial interval correlations}
|
||||
Correlation coefficients between succeeding intervals separated by lag $k$:
|
||||
\[ \rho_k = \frac{\langle (T_{i+k} - \langle T \rangle)(T_i - \langle T \rangle) \rangle}{\langle (T_i - \langle T \rangle)^2\rangle} = \frac{{\rm cov}(T_{i+k}, T_i)}{{\rm var}(T_i)} \]
|
||||
\begin{itemize}
|
||||
\item $\rho_0=1$ (correlation of each interval with itself).
|
||||
\item Poisson process: $\rho_k =0$ for $k>0$ (renewal process!)
|
||||
\end{itemize}
|
||||
\vfill
|
||||
\includegraphics[width=0.7\textwidth]{poissonserial100hz}
|
||||
\end{frame}
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section{Count statistics}
|
||||
|
||||
\begin{frame}
|
||||
\frametitle{Count statistics}
|
||||
Histogram of number of events $N$ (counts) within observation window of duration $W$.
|
||||
|
||||
\vfill
|
||||
\includegraphics[width=0.48\textwidth]{poissoncounthist100hz10ms}\hfill
|
||||
\includegraphics[width=0.48\textwidth]{poissoncounthist100hz100ms}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}
|
||||
\frametitle{Count statistics of Poisson process}
|
||||
Poisson distribution:
|
||||
\[ P(k) = \frac{(\lambda W)^ke^{\lambda W}}{k!} \]
|
||||
|
||||
\vfill
|
||||
\includegraphics[width=0.48\textwidth]{poissoncounthistdist100hz10ms}\hfill
|
||||
\includegraphics[width=0.48\textwidth]{poissoncounthistdist100hz100ms}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}
|
||||
\frametitle{Count statistics --- Fano factor}
|
||||
Statistics of number of events $N$ within observation window of duration $W$.
|
||||
\begin{itemize}
|
||||
\item Mean count: $\mu_N = \langle N \rangle$
|
||||
\item Count variance: $\sigma_N^2 = \langle (N - \langle N \rangle)^2 \rangle$
|
||||
\item Fano factor (variance divided by mean): $F = \frac{\sigma_N^2}{\mu_N}$
|
||||
\item Poisson process: $F=1$
|
||||
\end{itemize}
|
||||
\vfill
|
||||
Poisson process $\lambda=100$\,Hz:
|
||||
\includegraphics[width=1\textwidth]{poissonfano100hz}
|
||||
\end{frame}
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section{Integrate-and-fire models}
|
||||
|
||||
\begin{frame}
|
||||
\frametitle{Integrate-and-fire models}
|
||||
Leaky integrate-and-fire model (LIF):
|
||||
\[ \tau \frac{dV}{dt} = -V + RI + D\xi \]
|
||||
Whenever membrane potential $V(t)$ crosses the firing threshold $\theta$, a spike is emitted and
|
||||
$V(t)$ is reset to $V_{reset}$.
|
||||
\begin{itemize}
|
||||
\item $\tau$: membrane time constant (typically 10\,ms)
|
||||
\item $R$: input resistance (here 1\,mV (!))
|
||||
\item $D\xi$: additive Gaussian white noise of strength $D$
|
||||
\item $\theta$: firing threshold (here 10\,mV)
|
||||
\item $V_{reset}$: reset potential (here 0\,mV)
|
||||
\end{itemize}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}
|
||||
\frametitle{Integrate-and-fire models}
|
||||
Discretization with time step $\Delta t$: $V(t) \rightarrow V_i,\;t_i = i \Delta t$.\\
|
||||
Euler integration:
|
||||
\begin{eqnarray*}
|
||||
\frac{dV}{dt} & \approx & \frac{V_{i+1} - V_i}{\Delta t} \\
|
||||
\Rightarrow \quad V_{i+1} & = & V_i + \Delta t \frac{-V_i+RI_i+\sqrt{2D\Delta t}N_i}{\tau}
|
||||
\end{eqnarray*}
|
||||
$N_i$ are normally distributed random numbers (Gaussian with zero mean and unit variance)
|
||||
--- the $\sqrt{\Delta t}$ is for white noise.
|
||||
|
||||
\includegraphics[width=0.82\textwidth]{lifraster16}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}
|
||||
\frametitle{Interval statistics of LIF}
|
||||
Interval distribution approaches Inverse Gaussian for large $I$:
|
||||
\[ p(T) = \frac{1}{\sqrt{4\pi D T^3}}\exp\left[-\frac{(T-\langle T \rangle)^2}{4DT\langle T \rangle^2}\right] \]
|
||||
where $\langle T \rangle$ is the mean interspike interval and $D$
|
||||
is the diffusion coefficient.
|
||||
\vfill
|
||||
\includegraphics[width=0.45\textwidth]{lifisihdistr08}\hfill
|
||||
\includegraphics[width=0.45\textwidth]{lifisihdistr16}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}
|
||||
\frametitle{Interval statistics of PIF}
|
||||
For the perfect integrate-and-fire (PIF)
|
||||
\[ \tau \frac{dV}{dt} = RI + D\xi \]
|
||||
(the canonical model or supra-threshold firing on a limit cycle)\\
|
||||
the Inverse Gaussian describes exactly the interspike interval distribution.
|
||||
\vfill
|
||||
\includegraphics[width=0.45\textwidth]{pifisihdistr01}\hfill
|
||||
\includegraphics[width=0.45\textwidth]{pifisihdistr10}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}
|
||||
\frametitle{Interval return map of LIF}
|
||||
LIF $I=15.7$:
|
||||
\includegraphics[width=1\textwidth]{lifreturnmap16}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}
|
||||
\frametitle{Serial correlations of LIF}
|
||||
LIF $I=15.7$:
|
||||
\includegraphics[width=1\textwidth]{lifserial16}\\
|
||||
Integrate-and-fire driven with white noise are still renewal processes!
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}
|
||||
\frametitle{Count statistics of LIF}
|
||||
LIF $I=15.7$:
|
||||
\includegraphics[width=1\textwidth]{liffano16}\\
|
||||
Fano factor is not one!
|
||||
\end{frame}
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\begin{frame}
|
||||
\frametitle{Interval statistics of LIF with OU noise}
|
||||
\begin{eqnarray*}
|
||||
\tau \frac{dV}{dt} & = & -V + RI + U \\
|
||||
\tau_{OU} \frac{dU}{dt} & = & - U + D\xi
|
||||
\end{eqnarray*}
|
||||
Ohrnstein-Uhlenbeck noise is lowpass filtered white noise.
|
||||
\includegraphics[width=0.45\textwidth]{lifouisihdistr08-100ms}\hfill
|
||||
\includegraphics[width=0.45\textwidth]{lifouisihdistr16-100ms}\\
|
||||
More peaky than the inverse Gaussian!
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}
|
||||
\frametitle{Interval return map of LIF with OU noise}
|
||||
LIF $I=15.7$, $\tau_{OU}=100$\,ms:
|
||||
\includegraphics[width=1\textwidth]{lifoureturnmap16-100ms}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}
|
||||
\frametitle{Serial correlations of LIF with OU noise}
|
||||
LIF $I=15.7$, $\tau_{OU}=100$\,ms:
|
||||
\includegraphics[width=1\textwidth]{lifouserial16-100ms}\\
|
||||
OU-noise introduces positive interval correlations!
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}
|
||||
\frametitle{Count statistics of LIF with OU noise}
|
||||
LIF $I=15.7$, $\tau_{OU}=100$\,ms:
|
||||
\includegraphics[width=1\textwidth]{lifoufano16-100ms}\\
|
||||
Fano factor increases with count window duration.
|
||||
\end{frame}
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\begin{frame}
|
||||
\frametitle{Interval statistics of LIF with adaptation}
|
||||
\begin{eqnarray*}
|
||||
\tau \frac{dV}{dt} & = & -V - A + RI + D\xi \\
|
||||
\tau_{adapt} \frac{dA}{dt} & = & - A
|
||||
\end{eqnarray*}
|
||||
Adaptation $A$ with time constant $\tau_{adapt}$ and increment $\Delta A$ at spike.
|
||||
\includegraphics[width=0.45\textwidth]{lifadaptisihdistr08-100ms}\hfill
|
||||
\includegraphics[width=0.45\textwidth]{lifadaptisihdistr65-100ms}\\
|
||||
Similar to LIF with white noise.
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}
|
||||
\frametitle{Interval return map of LIF with adaptation}
|
||||
LIF $I=10$, $\tau_{adapt}=100$\,ms:
|
||||
\includegraphics[width=1\textwidth]{lifadaptreturnmap10-100ms}\\
|
||||
Negative correlation at lag one.
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}
|
||||
\frametitle{Serial correlations of LIF with adaptation}
|
||||
LIF $I=10$, $\tau_{adapt}=100$\,ms:
|
||||
\includegraphics[width=1\textwidth]{lifadaptserial10-100ms}\\
|
||||
Adaptation with white noise introduces negative interval correlations!
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}
|
||||
\frametitle{Count statistics of LIF with adaptation}
|
||||
LIF $I=10$, $\tau_{adapt}=100$\,ms:
|
||||
\includegraphics[width=1\textwidth]{lifadaptfano10-100ms}\\
|
||||
Fano factor decreases with count window duration.
|
||||
\end{frame}
|
||||
|
||||
|
||||
\end{document}
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section{Non stationary}
|
||||
\subsection{Inhomogeneous Poisson process}
|
||||
\subsection{Firing rate}
|
||||
\subsection{Instantaneous rate}
|
||||
\subsection{Autocorrelation}
|
||||
\subsection{Crosscorrelation}
|
||||
\subsection{Joint PSTH}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section{Renewal process}
|
||||
\subsection{Superthreshold firing}
|
||||
\subsection{Subthreshold firing}
|
||||
\section{Non-renewal processes}
|
||||
\subsection{Bursting}
|
||||
\subsection{Resonator}
|
||||
|
||||
|
||||
\subsection{Standard distributions}
|
||||
\subsubsection{Gamma}
|
||||
\subsubsection{How to read ISI histograms}
|
||||
refractoriness, poisson tail, sub-, supra-threshold, missed spikes
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section{Correlation with stimulus}
|
||||
\subsection{Tuning curve}
|
||||
\subsection{Linear filter}
|
||||
\subsection{Spatiotemporal receptive field}
|
||||
\subsection{Generalized linear model}
|
||||
|
||||
\begin{frame}
|
||||
\end{frame}
|
||||
500
pointprocesses/lecture/pointprocessscetchA.eps
Normal file
500
pointprocesses/lecture/pointprocessscetchA.eps
Normal file
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||||
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|
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hpt2 neg 0 V Opaque stroke} def
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hpt neg vpt -1.62 mul V
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hpt neg vpt 1.62 mul V
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translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
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Opaque stroke grestore} def
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hpt 0 360 arc Opaque stroke} def
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currentrgbcolor
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/ColG ColG Fillden mul Fillden sub 1 add def
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% XX = 0/1 for no/yes cross-hatch
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%
|
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|
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PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add translate
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clip
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currentlinewidth 0.5 mul setlinewidth
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/PFs PFa 2 get dup mul PFa 3 get dup mul add sqrt def
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0 0 M PFa 5 get rotate PFs -2 div dup translate
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||||
0 1 PFs PFa 4 get div 1 add floor cvi
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||||
{PFa 4 get mul 0 M 0 PFs V} for
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||||
0 PFa 6 get ne {
|
||||
0 1 PFs PFa 4 get div 1 add floor cvi
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{PFa 4 get mul 0 2 1 roll M PFs 0 V} for
|
||||
} if
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stroke grestore} def
|
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%
|
||||
/languagelevel where
|
||||
{pop languagelevel} {1} ifelse
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2 lt
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{/InterpretLevel1 true def}
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{/InterpretLevel1 Level1 def}
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%
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%
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bind def
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<< Tile8x8
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>> matrix makepattern
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/Pat1 exch def
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<< Tile8x8
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>> matrix makepattern
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/Pat2 exch def
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<< Tile8x8
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/PaintProc {0.5 setlinewidth pop 0 0 M 0 8 L
|
||||
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>> matrix makepattern
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<< Tile8x8
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<< Tile8x8
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||||
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>> matrix makepattern
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<< Tile8x8
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/PaintProc {0.5 setlinewidth pop -2 8 M 4 -4 L
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||||
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||||
>> matrix makepattern
|
||||
/Pat6 exch def
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<< Tile8x8
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/PaintProc {0.5 setlinewidth pop -2 0 M 4 12 L
|
||||
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>> matrix makepattern
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<< Tile8x8
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||||
12 0 M -4 8 L 12 4 M 0 10 L stroke}
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<< Tile8x8
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|
||||
-4 0 M 12 8 L -4 4 M 8 10 L stroke}
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/Pat9 exch def
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/Pattern1 {PatternBgnd KeepColor Pat1 setpattern} bind def
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||||
} def
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%
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%
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||||
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%
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% Substitute for Level 2 pattern fill codes with
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%
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|
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||||
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|
||||
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|
||||
SDict begin [
|
||||
/Title (pointprocessscetchA.tex)
|
||||
/Subject (gnuplot plot)
|
||||
/Creator (gnuplot 4.6 patchlevel 4)
|
||||
/Author (jan)
|
||||
% /Producer (gnuplot)
|
||||
% /Keywords ()
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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doclip
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0 setgray
|
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newpath
|
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|
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LCb setrgbcolor
|
||||
0.00 0.00 0.00 C 1.000 UP
|
||||
LTb
|
||||
LCb setrgbcolor
|
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LTb
|
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1.000 UL
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LTb
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528 824 M
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5680 0 V
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stroke
|
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|
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0.00 0.00 0.00 C 10.000 UL
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0.00 0.00 0.00 C 910 573 M
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end
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showpage
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||||
%%Trailer
|
||||
62
pointprocesses/lecture/pointprocessscetchA.gpt
Normal file
62
pointprocesses/lecture/pointprocessscetchA.gpt
Normal file
@@ -0,0 +1,62 @@
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||||
set term epslatex size 11.4cm, 3cm
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set out 'pointprocessscetchA.tex'
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set border 0
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set lmarg 4
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set rmarg 1
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set tmarg 1
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unset xtics
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unset ytics
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set label 1 at graph -0.07, graph 1.1
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|
||||
set arrow 1 from 0, 0.5 to 11, 0.5 head filled
|
||||
set label 2 'Time' at 11, -0.3 center
|
||||
set label 3 "$t_{1}$" at 0.724649, -0.6 center
|
||||
set label 4 "$t_{2}$" at 1.67586, -0.6 center
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set label 5 "$t_{3}$" at 3.02389, -0.6 center
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||||
set label 6 "$t_{4}$" at 3.57466, -0.6 center
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set label 7 "$t_{5}$" at 4.15121, -0.6 center
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||||
set label 8 "$t_{6}$" at 5.00412, -0.6 center
|
||||
set label 9 "$t_{7}$" at 6.64549, -0.6 center
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||||
set label 10 "$t_{8}$" at 7.81657, -0.6 center
|
||||
set label 11 "$t_{9}$" at 9.77964, -0.6 center
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||||
plot '-' w l lt 1 lc rgb 'black' lw 10
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0.724649 1
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1.67586 0
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3.57466 1
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5.00412 1
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6.64549 1
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7.81657 0
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7.81657 1
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9.77964 0
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9.77964 1
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||||
e
|
||||
unset label 3
|
||||
unset label 4
|
||||
unset label 5
|
||||
unset label 6
|
||||
unset label 7
|
||||
unset label 8
|
||||
unset label 9
|
||||
unset label 10
|
||||
unset label 11
|
||||
BIN
pointprocesses/lecture/pointprocessscetchA.pdf
Normal file
BIN
pointprocesses/lecture/pointprocessscetchA.pdf
Normal file
Binary file not shown.
95
pointprocesses/lecture/pointprocessscetchA.tex
Normal file
95
pointprocesses/lecture/pointprocessscetchA.tex
Normal file
@@ -0,0 +1,95 @@
|
||||
% GNUPLOT: LaTeX picture with Postscript
|
||||
\begingroup
|
||||
\makeatletter
|
||||
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|
||||
\GenericError{(gnuplot) \space\space\space\@spaces}{%
|
||||
Package color not loaded in conjunction with
|
||||
terminal option `colourtext'%
|
||||
}{See the gnuplot documentation for explanation.%
|
||||
}{Either use 'blacktext' in gnuplot or load the package
|
||||
color.sty in LaTeX.}%
|
||||
\renewcommand\color[2][]{}%
|
||||
}%
|
||||
\providecommand\includegraphics[2][]{%
|
||||
\GenericError{(gnuplot) \space\space\space\@spaces}{%
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||||
Package graphicx or graphics not loaded%
|
||||
}{See the gnuplot documentation for explanation.%
|
||||
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||||
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|
||||
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||||
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||||
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736
pointprocesses/lecture/pointprocessscetchB.eps
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736
pointprocesses/lecture/pointprocessscetchB.eps
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SDict begin [
|
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|
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|
||||
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|
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|
||||
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|
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showpage
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%%Trailer
|
||||
204
pointprocesses/lecture/pointprocessscetchB.gpt
Normal file
204
pointprocesses/lecture/pointprocessscetchB.gpt
Normal file
@@ -0,0 +1,204 @@
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||||
set out 'pointprocessscetchB.tex'
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||||
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||||
set border 0
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|
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|
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|
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|
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set multiplot
|
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|
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|
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|
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unset label 7
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unset label 8
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unset label 9
|
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unset label 10
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unset label 11
|
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set origin 0, 0.4
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|
||||
set arrow 8 from 5.00412, 0.2 to 6.64549, 0.2 heads
|
||||
set label 9 "$T_{7}$" at 7.23103, -0.5 center
|
||||
set arrow 9 from 6.64549, 0.2 to 7.81657, 0.2 heads
|
||||
set label 10 "$T_{8}$" at 8.79811, -0.5 center
|
||||
set arrow 10 from 7.81657, 0.2 to 9.77964, 0.2 heads
|
||||
plot '-' w l lt 1 lc rgb 'black' lw 10
|
||||
0.724649 0
|
||||
0.724649 1
|
||||
|
||||
1.67586 0
|
||||
1.67586 1
|
||||
|
||||
3.02389 0
|
||||
3.02389 1
|
||||
|
||||
3.57466 0
|
||||
3.57466 1
|
||||
|
||||
4.15121 0
|
||||
4.15121 1
|
||||
|
||||
5.00412 0
|
||||
5.00412 1
|
||||
|
||||
6.64549 0
|
||||
6.64549 1
|
||||
|
||||
7.81657 0
|
||||
7.81657 1
|
||||
|
||||
9.77964 0
|
||||
9.77964 1
|
||||
e
|
||||
unset label 3
|
||||
unset label 4
|
||||
unset label 5
|
||||
unset label 6
|
||||
unset label 7
|
||||
unset label 8
|
||||
unset label 9
|
||||
unset label 10
|
||||
unset arrow 3
|
||||
unset arrow 4
|
||||
unset arrow 5
|
||||
unset arrow 6
|
||||
unset arrow 7
|
||||
unset arrow 8
|
||||
unset arrow 9
|
||||
unset arrow 10
|
||||
|
||||
set origin 0, 0
|
||||
set size 1, 0.4
|
||||
set border 2
|
||||
set yrange [-0.5:10.5]
|
||||
set ytics 2 nomirror out
|
||||
set arrow 1 from 0, 0.0 to 11, 0.0 head filled
|
||||
set label 2 'Time' at 11, -2.2 center
|
||||
set label 1 '\normalsize Event counts $\{ n_i \}$' at graph -0.07, graph 1.2
|
||||
plot '-' w l lt 1 lc rgb 'black' lw 3, \
|
||||
'-' w p lt 1 lc rgb 'black' pt 7 ps 1.5 lw 2, \
|
||||
'-' w p lt 1 lc rgb 'white' pt 7 ps 1.0 lw 2, \
|
||||
'-' w p lt 1 lc rgb 'black' pt 7 ps 1.5 lw 2
|
||||
0 0
|
||||
0.724649 0
|
||||
|
||||
0.724649 1
|
||||
1.67586 1
|
||||
|
||||
1.67586 2
|
||||
3.02389 2
|
||||
|
||||
3.02389 3
|
||||
3.57466 3
|
||||
|
||||
3.57466 4
|
||||
4.15121 4
|
||||
|
||||
4.15121 5
|
||||
5.00412 5
|
||||
|
||||
5.00412 6
|
||||
6.64549 6
|
||||
|
||||
6.64549 7
|
||||
7.81657 7
|
||||
|
||||
7.81657 8
|
||||
9.77964 8
|
||||
|
||||
9.77964 9
|
||||
10.7899 9
|
||||
e
|
||||
0.724649 0
|
||||
1.67586 1
|
||||
3.02389 2
|
||||
3.57466 3
|
||||
4.15121 4
|
||||
5.00412 5
|
||||
6.64549 6
|
||||
7.81657 7
|
||||
9.77964 8
|
||||
e
|
||||
0.724649 0
|
||||
1.67586 1
|
||||
3.02389 2
|
||||
3.57466 3
|
||||
4.15121 4
|
||||
5.00412 5
|
||||
6.64549 6
|
||||
7.81657 7
|
||||
9.77964 8
|
||||
e
|
||||
0.724649 1
|
||||
1.67586 2
|
||||
3.02389 3
|
||||
3.57466 4
|
||||
4.15121 5
|
||||
5.00412 6
|
||||
6.64549 7
|
||||
7.81657 8
|
||||
9.77964 9
|
||||
e
|
||||
|
||||
unset multiplot
|
||||
BIN
pointprocesses/lecture/pointprocessscetchB.pdf
Normal file
BIN
pointprocesses/lecture/pointprocessscetchB.pdf
Normal file
Binary file not shown.
130
pointprocesses/lecture/pointprocessscetchB.tex
Normal file
130
pointprocesses/lecture/pointprocessscetchB.tex
Normal file
@@ -0,0 +1,130 @@
|
||||
% GNUPLOT: LaTeX picture with Postscript
|
||||
\begingroup
|
||||
\makeatletter
|
||||
\providecommand\color[2][]{%
|
||||
\GenericError{(gnuplot) \space\space\space\@spaces}{%
|
||||
Package color not loaded in conjunction with
|
||||
terminal option `colourtext'%
|
||||
}{See the gnuplot documentation for explanation.%
|
||||
}{Either use 'blacktext' in gnuplot or load the package
|
||||
color.sty in LaTeX.}%
|
||||
\renewcommand\color[2][]{}%
|
||||
}%
|
||||
\providecommand\includegraphics[2][]{%
|
||||
\GenericError{(gnuplot) \space\space\space\@spaces}{%
|
||||
Package graphicx or graphics not loaded%
|
||||
}{See the gnuplot documentation for explanation.%
|
||||
}{The gnuplot epslatex terminal needs graphicx.sty or graphics.sty.}%
|
||||
\renewcommand\includegraphics[2][]{}%
|
||||
}%
|
||||
\providecommand\rotatebox[2]{#2}%
|
||||
\@ifundefined{ifGPcolor}{%
|
||||
\newif\ifGPcolor
|
||||
\GPcolortrue
|
||||
}{}%
|
||||
\@ifundefined{ifGPblacktext}{%
|
||||
\newif\ifGPblacktext
|
||||
\GPblacktexttrue
|
||||
}{}%
|
||||
% define a \g@addto@macro without @ in the name:
|
||||
\let\gplgaddtomacro\g@addto@macro
|
||||
% define empty templates for all commands taking text:
|
||||
\gdef\gplbacktext{}%
|
||||
\gdef\gplfronttext{}%
|
||||
\makeatother
|
||||
\ifGPblacktext
|
||||
% no textcolor at all
|
||||
\def\colorrgb#1{}%
|
||||
\def\colorgray#1{}%
|
||||
\else
|
||||
% gray or color?
|
||||
\ifGPcolor
|
||||
\def\colorrgb#1{\color[rgb]{#1}}%
|
||||
\def\colorgray#1{\color[gray]{#1}}%
|
||||
\expandafter\def\csname LTw\endcsname{\color{white}}%
|
||||
\expandafter\def\csname LTb\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LTa\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT0\endcsname{\color[rgb]{1,0,0}}%
|
||||
\expandafter\def\csname LT1\endcsname{\color[rgb]{0,1,0}}%
|
||||
\expandafter\def\csname LT2\endcsname{\color[rgb]{0,0,1}}%
|
||||
\expandafter\def\csname LT3\endcsname{\color[rgb]{1,0,1}}%
|
||||
\expandafter\def\csname LT4\endcsname{\color[rgb]{0,1,1}}%
|
||||
\expandafter\def\csname LT5\endcsname{\color[rgb]{1,1,0}}%
|
||||
\expandafter\def\csname LT6\endcsname{\color[rgb]{0,0,0}}%
|
||||
\expandafter\def\csname LT7\endcsname{\color[rgb]{1,0.3,0}}%
|
||||
\expandafter\def\csname LT8\endcsname{\color[rgb]{0.5,0.5,0.5}}%
|
||||
\else
|
||||
% gray
|
||||
\def\colorrgb#1{\color{black}}%
|
||||
\def\colorgray#1{\color[gray]{#1}}%
|
||||
\expandafter\def\csname LTw\endcsname{\color{white}}%
|
||||
\expandafter\def\csname LTb\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LTa\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT0\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT1\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT2\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT3\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT4\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT5\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT6\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT7\endcsname{\color{black}}%
|
||||
\expandafter\def\csname LT8\endcsname{\color{black}}%
|
||||
\fi
|
||||
\fi
|
||||
\setlength{\unitlength}{0.0500bp}%
|
||||
\begin{picture}(6462.00,3740.00)%
|
||||
\gplgaddtomacro\gplbacktext{%
|
||||
\csname LTb\endcsname%
|
||||
\put(122,3587){\makebox(0,0)[l]{\strut{}\normalsize Event times $\{t_i\}$}}%
|
||||
\put(6329,2947){\makebox(0,0){\strut{}Time}}%
|
||||
\put(910,2865){\makebox(0,0){\strut{}$t_{1}$}}%
|
||||
\put(1412,2865){\makebox(0,0){\strut{}$t_{2}$}}%
|
||||
\put(2123,2865){\makebox(0,0){\strut{}$t_{3}$}}%
|
||||
\put(2413,2865){\makebox(0,0){\strut{}$t_{4}$}}%
|
||||
\put(2717,2865){\makebox(0,0){\strut{}$t_{5}$}}%
|
||||
\put(3167,2865){\makebox(0,0){\strut{}$t_{6}$}}%
|
||||
\put(4033,2865){\makebox(0,0){\strut{}$t_{7}$}}%
|
||||
\put(4650,2865){\makebox(0,0){\strut{}$t_{8}$}}%
|
||||
\put(5685,2865){\makebox(0,0){\strut{}$t_{9}$}}%
|
||||
}%
|
||||
\gplgaddtomacro\gplfronttext{%
|
||||
}%
|
||||
\gplgaddtomacro\gplbacktext{%
|
||||
\csname LTb\endcsname%
|
||||
\put(122,2465){\makebox(0,0)[l]{\strut{}\normalsize Intervals $\{T_i\}, \; T_i = t_{i+1} - t_i$}}%
|
||||
\put(6329,1825){\makebox(0,0){\strut{}Time}}%
|
||||
\put(1161,1770){\makebox(0,0){\strut{}$T_{1}$}}%
|
||||
\put(1767,1770){\makebox(0,0){\strut{}$T_{2}$}}%
|
||||
\put(2268,1770){\makebox(0,0){\strut{}$T_{3}$}}%
|
||||
\put(2565,1770){\makebox(0,0){\strut{}$T_{4}$}}%
|
||||
\put(2942,1770){\makebox(0,0){\strut{}$T_{5}$}}%
|
||||
\put(3600,1770){\makebox(0,0){\strut{}$T_{6}$}}%
|
||||
\put(4341,1770){\makebox(0,0){\strut{}$T_{7}$}}%
|
||||
\put(5168,1770){\makebox(0,0){\strut{}$T_{8}$}}%
|
||||
}%
|
||||
\gplgaddtomacro\gplfronttext{%
|
||||
}%
|
||||
\gplgaddtomacro\gplbacktext{%
|
||||
\colorrgb{0.00,0.00,0.00}%
|
||||
\put(333,268){\makebox(0,0)[r]{\strut{}$0$}}%
|
||||
\colorrgb{0.00,0.00,0.00}%
|
||||
\put(333,460){\makebox(0,0)[r]{\strut{}$2$}}%
|
||||
\colorrgb{0.00,0.00,0.00}%
|
||||
\put(333,652){\makebox(0,0)[r]{\strut{}$4$}}%
|
||||
\colorrgb{0.00,0.00,0.00}%
|
||||
\put(333,844){\makebox(0,0)[r]{\strut{}$6$}}%
|
||||
\colorrgb{0.00,0.00,0.00}%
|
||||
\put(333,1036){\makebox(0,0)[r]{\strut{}$8$}}%
|
||||
\colorrgb{0.00,0.00,0.00}%
|
||||
\put(333,1228){\makebox(0,0)[r]{\strut{}$10$}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(122,1487){\makebox(0,0)[l]{\strut{}\normalsize Event counts $\{ n_i \}$}}%
|
||||
\put(6329,57){\makebox(0,0){\strut{}Time}}%
|
||||
}%
|
||||
\gplgaddtomacro\gplfronttext{%
|
||||
}%
|
||||
\gplbacktext
|
||||
\put(0,0){\includegraphics{pointprocessscetchB}}%
|
||||
\gplfronttext
|
||||
\end{picture}%
|
||||
\endgroup
|
||||
BIN
pointprocesses/lecture/poissoncounthist100hz100ms.pdf
Normal file
BIN
pointprocesses/lecture/poissoncounthist100hz100ms.pdf
Normal file
Binary file not shown.
BIN
pointprocesses/lecture/poissoncounthist100hz10ms.pdf
Normal file
BIN
pointprocesses/lecture/poissoncounthist100hz10ms.pdf
Normal file
Binary file not shown.
BIN
pointprocesses/lecture/poissoncounthistdist100hz100ms.pdf
Normal file
BIN
pointprocesses/lecture/poissoncounthistdist100hz100ms.pdf
Normal file
Binary file not shown.
BIN
pointprocesses/lecture/poissoncounthistdist100hz10ms.pdf
Normal file
BIN
pointprocesses/lecture/poissoncounthistdist100hz10ms.pdf
Normal file
Binary file not shown.
BIN
pointprocesses/lecture/poissonfano100hz.pdf
Normal file
BIN
pointprocesses/lecture/poissonfano100hz.pdf
Normal file
Binary file not shown.
BIN
pointprocesses/lecture/poissonisih100hz.pdf
Normal file
BIN
pointprocesses/lecture/poissonisih100hz.pdf
Normal file
Binary file not shown.
BIN
pointprocesses/lecture/poissonisihexp100hz.pdf
Normal file
BIN
pointprocesses/lecture/poissonisihexp100hz.pdf
Normal file
Binary file not shown.
BIN
pointprocesses/lecture/poissonisihexp20hz.pdf
Normal file
BIN
pointprocesses/lecture/poissonisihexp20hz.pdf
Normal file
Binary file not shown.
BIN
pointprocesses/lecture/poissonraster100hz.pdf
Normal file
BIN
pointprocesses/lecture/poissonraster100hz.pdf
Normal file
Binary file not shown.
BIN
pointprocesses/lecture/poissonreturnmap100hz.pdf
Normal file
BIN
pointprocesses/lecture/poissonreturnmap100hz.pdf
Normal file
Binary file not shown.
BIN
pointprocesses/lecture/poissonserial100hz.pdf
Normal file
BIN
pointprocesses/lecture/poissonserial100hz.pdf
Normal file
Binary file not shown.
BIN
pointprocesses/lecture/raster.pdf
Normal file
BIN
pointprocesses/lecture/raster.pdf
Normal file
Binary file not shown.
BIN
pointprocesses/lecture/thumbs.pdf
Normal file
BIN
pointprocesses/lecture/thumbs.pdf
Normal file
Binary file not shown.
67
pointprocesses/lecture/whitestyles.gp
Normal file
67
pointprocesses/lecture/whitestyles.gp
Normal file
@@ -0,0 +1,67 @@
|
||||
set tics scale 0.8
|
||||
set tics out
|
||||
set format '$%g$'
|
||||
unset grid
|
||||
unset key
|
||||
|
||||
# on white background:
|
||||
set style line 1 lt -1 lc rgb "black" lw 2 # border
|
||||
set border back ls 1
|
||||
set style line 2 lt 1 lc rgb "black" lw 4 pt 7 ps 2 # thick line
|
||||
set style line 3 lt 1 lc rgb "black" lw 2 # thin line
|
||||
set style line 4 lt 3 lc rgb "black" lw 1 # grid line
|
||||
|
||||
set style line 10 lt 1 lc rgb "#00DD00" lw 6 # stimulus thick, AM
|
||||
set style line 11 lt 1 lc rgb "#00DD00" lw 3 # stimulus thin, AM
|
||||
set style line 15 lt 1 lc rgb "black" lw 15 # stimulus bar
|
||||
|
||||
set style line 20 lt 1 lc rgb "yellow" lw 4 # thin spikes cell 1
|
||||
set style line 21 lt 1 lc rgb "orange" lw 4 # thin spikes cell 2
|
||||
set style line 22 lt 1 lc rgb "yellow" lw 6 # thick spikes cell 1
|
||||
set style line 23 lt 1 lc rgb "orange" lw 6 # thick spikes cell 2
|
||||
set style line 24 lt 1 lc rgb "blue" lw 22 # big sync spikes
|
||||
set style line 25 lt 1 lc rgb "blue" lw 6 # thick sync spikes
|
||||
set style line 26 lt 1 lc rgb "orange" lw 4 # all spikes
|
||||
|
||||
set style line 30 lt 1 lc rgb "dark-red" lw 6 pt 7 ps 2 # firing rate 1 thick
|
||||
set style line 31 lt 1 lc rgb "red" lw 6 pt 7 ps 2 # firing rate 2 thick
|
||||
set style line 32 lt 1 lc rgb "orange" lw 6 pt 7 ps 2 # firing rate 3 thick
|
||||
set style line 33 lt 1 lc rgb "blue" lw 6 pt 7 ps 2 # firing rate 4 thick
|
||||
set style line 34 lt 1 lc rgb "gray" lw 6 # firing rate gray thick
|
||||
set style line 35 lt 1 lc rgb "dark-red" lw 3 pt 7 ps 0.7 # firing rate 1 thin
|
||||
set style line 36 lt 1 lc rgb "red" lw 3 # firing rate 2 thin
|
||||
set style line 37 lt 1 lc rgb "orange" lw 3 # firing rate 3 thin
|
||||
set style line 38 lt 1 lc rgb "blue" lw 3 # firing rate 4 thin
|
||||
set style line 39 lt 1 lc rgb "gray" lw 3 # firing rate gray thin
|
||||
|
||||
set style line 40 lt 1 lc rgb "green" lw 6 pt 5 ps 2 # onset f-I curve thick
|
||||
set style line 41 lt 1 lc rgb "green" lw 3 pt 5 ps 2 # onset f-I curve thin
|
||||
set style line 42 lt 1 lc rgb "red" lw 6 pt 7 ps 2 # steady-state f-I curve thick
|
||||
set style line 43 lt 1 lc rgb "red" lw 3 pt 7 ps 2 # steady-state f-I curve thin
|
||||
set style line 44 lt 1 lc rgb "blue" lw 6 pt 9 ps 2 # adapted f-I curve thick
|
||||
set style line 45 lt 1 lc rgb "blue" lw 3 pt 9 ps 2 # adapted f-I curve thin
|
||||
set style line 47 lt 1 lc rgb "cyan" lw 6 # adaptation level thick
|
||||
set style line 48 lt 1 lc rgb "cyan" lw 3 # adaptation level thin
|
||||
set style line 49 lt 1 lc rgb "yellow" lw 3 pt 7 ps 4 # current adaptation point
|
||||
|
||||
set style line 50 lt 1 lc rgb "dark-red" lw 4 # membrane voltage 1
|
||||
set style line 51 lt 1 lc rgb "red" lw 4 # membrane voltage 2
|
||||
set style line 52 lt 1 lc rgb "orange" lw 4 # membrane voltage 3
|
||||
set style line 55 lt 1 lc rgb "orange" lw 4 # nerve potential
|
||||
|
||||
set style line 60 lt 1 lc rgb "blue" lw 4 # gating variable
|
||||
set style line 61 lt 1 lc rgb "cyan" lw 4 # gating variable average
|
||||
|
||||
set style line 70 lt 1 lc rgb "red" lw 4 # ionic current
|
||||
set style line 71 lt 1 lc rgb "orange" lw 4 # ionic current average
|
||||
|
||||
set style line 80 lt 1 lc rgb "#77FFFF" lw 4 pt 13 ps 2.4# baseline
|
||||
set style line 81 lt 1 lc rgb "#FF5533" lw 4 pt 9 ps 2.8 # beat
|
||||
set style line 82 lt 1 lc rgb "yellow" lw 4 pt 7 ps 2.4 # chirp
|
||||
set style line 83 lt 1 lc rgb "#FF7700" lw 4 pt 11 ps 2.8# beat shuffled
|
||||
set style line 84 lt 1 lc rgb "#FFAA00" lw 4 pt 5 ps 2.2 # chirp shuffled
|
||||
|
||||
set style line 90 lt 1 lc rgb "#77FFFF" lw 2 # EOD thin
|
||||
set style line 91 lt 1 lc rgb "#77FFFF" lw 4 # EOD thick
|
||||
|
||||
set term epslatex input color dashed rounded size 11.4cm, 6.6cm
|
||||
Reference in New Issue
Block a user