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Week$1$Lecture$Notes$$Points$of$clarification$and$fun$facts$re:$video$lectures$$L2:$Computational$Neuroscience:$Descriptive$Models$= Slide:$An$Example:$Models$of$“Receptive$Fields”$o If$you$want$to$see$more$examples$of$Hubel$and$Wiesel’s$experiments,$check$out:$http://www.youtube.com/watch?v=Cw5PKV9Rj3o$o Converting$the$electrical$activity$of$neurons$ to$an$audio$signal$is$a$common$practice$in$experimental$neuroscience,$as$it$allows$researchers$to$easily$and$immediately$tell$when$a$neuron$is$active.$In$a$typical$setup,$each$“pop”$in$the$signal$is$an$action$potential—when$neurons$fire$many$action$potentials$per$second,$the$sound$resembles$loud$static.$= Slide:$Descriptive$Model$of$Receptive$Fields$o When$we$talk$about$center=on,$surround=off,$or$center=off,$surround=on$cells,$remember$that$we’re$not$talking$about$the$center$and$“surround”$of$the$entire$retina,$but$rather$only$the$small$portion$of$it$associated$with$that$cell,$i.e.,$each$cell$generally$cares$only$about$what’s$going$on$in$a$very$small$region$of$the$visual$field,$and$these$regions$tend$to$be$on$the$order$of$a$degree$or$two$(though$the$size$of$the$RF$depends$on$its$location).$As$a$rough$approximation,$you$can$think$of$many$cells’$RFs$“tiling”$the$visual$scene$(in$reality,$there$is$quite$a$bit$of$overlap,$and$different$cells$may$have$different$color=tuning$properties,$etc.).$Smaller$RFs$near$the$center$of$the$visual$field$(the$fovea)$lead$to$“higher$resolution”$there$during$the$daytime.$$L3:$Computational$Neuroscience:$Mechanistic$and$Interpretive$Models$= Slide:$III.$Interpretive$Model$of$Receptive$Fields$(oriented$bars)$o Again,$remember$that$these$oriented$bars$do$not$span$the$entire$retina,$but$only$a$small$portion$of$it$(if$they$spanned$the$entire$retina,$you’d$only$be$able$to$make$asterisk=like$images).$Because$of$this,$you$can$linearly$combine$them$to$make$an$enormous$variety$of$images.$For$example,$can$you$think$of$the$combination$of$RFs$needed$to$make$a$square?$A$polygon?$A$duck?$= Slide:$III.$Interpretive$Model$of$Receptive$Fields$(RFs$from$natural$images)$o It’s$worth$emphasizing$that$the$RFs$on$this$slide$are$learned$only$from$the$set$of$natural$images$and$do$not$depend$at$all$on$any$experimental$data.$The$algorithm$that$learns$them$simply$chooses$the$ideal$set$of$RFs$for$natural$images$subject$to$two$constraints$(1.$Efficient$representation$(sparse$coding)—representing$images$using$as$few$components$as$possible,$2.$Faithful$representation—accurate$representation$of$important$image$features).$The$fact$that$the$RFs$found$by$the$algorithm$match$the$RFs$observed$experimentally$is$very$cool,$suggesting$that$perhaps$efficient$and$faithful$representation$were$also$the$optimization$criteria$“used”$during$the$evolution$of$V1.$$L$4:$The$Electrical$Personality$of$Neurons$= Slide:$The$Idealized$Neuron$o In$the$initial$EPSP$plots,$the$x=axis$is$time,$and$the$y=axis$is$electrical$potential$(voltage).$o It$is$important$to$note$that$an$action$potential$is$not$just$the$sum$of$several$EPSP’s,$but$is$rather$an$active$signal$generated$by$the$sum$of$the$EPSP’s$crossing$a$threshold.$Usually$this$threshold$is$around$30mV$above$the$neuron’s$resting$potential.$= Slide:$The$Electrical$Personality$of$a$Neuron$(ion$channels)$o While$pumps$and$other$components$are$indeed$needed$to$model$the$cell$as$a$complete$circuit$that$obeys$Kirchoff’s$laws,$etc.,$for$our$purposes,$we$can$just$think$of$pumps$as$having$the$sole$purpose$of$maintaining$the$steady=state$intra=$and$extracellular$ion$concentrations.$Channels,$on$the$other$hand$are$just$gates$that,$when$opened,$allow$ions$to$flow$down$their$concentration$gradients.$o It’s$worth$noting$that$the$properties$of$an$action$potential$can’t$be$derived$from$a$simple$application$of$Ohm’s$law.$This$is$because$current,$voltage,$and$membrane$conductance$all$change$as$a$function$of$time.$Instead,$an$action$potential$is$described$by$a$set$of$differential$equations$that$model$how$these$variables$change$with$time.$Hodgkin$and$Huxley$were$the$first$to$formulate$and$present$a$solution$to$this$set$of$equations,$as$will$be$discussed$in$later$lectures.$= Slide:$Active$Wiring:$Myelination$of$Axons$o Lossless$signal$propagation$is$very$important,$as$some$action$potentials$have$to$travel$very$long$distances$(think$of$the$axons$that$reach$down$to$your$toes,$for$example).$If$signal$propagation$were$based$on$passive$changes$in$membrane$potential,$then$signals$would$dissipate$much$too$fast$for$information$to$be$conveyed$over$long$distances.$$L$5:$Making$Connections:$Synapses$= Slide:$Long$Term$Depression$(LTD)$o


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UF CIS 4905 - Week 1 Lecture Notes

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