Synaptic scaling balances learning in a spiking model of neocortex (Rowan & Neymotin 2013)

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Accession:147141
Learning in the brain requires complementary mechanisms: potentiation and activity-dependent homeostatic scaling. We introduce synaptic scaling to a biologically-realistic spiking model of neocortex which can learn changes in oscillatory rhythms using STDP, and show that scaling is necessary to balance both positive and negative changes in input from potentiation and atrophy. We discuss some of the issues that arise when considering synaptic scaling in such a model, and show that scaling regulates activity whilst allowing learning to remain unaltered.
Reference:
1 . Rowan MS,Neymotin SA (2013) Synaptic Scaling Balances Learning in a Spiking Model of Neocortex Adaptive and Natural Computing Algorithms, Tomassini M, Antonioni A, Daolio F, Buesser P, ed. pp.20
Model Information (Click on a link to find other models with that property)
Model Type: Realistic Network;
Brain Region(s)/Organism: Neocortex;
Cell Type(s): Neocortex V1 pyramidal corticothalamic L6 cell; Neocortex V1 pyramidal intratelencephalic L2-5 cell; Neocortex V1 interneuron basket PV cell; Neocortex fast spiking (FS) interneuron; Neocortex spiny stellate cell; Neocortex spiking regular (RS) neuron; Neocortex spiking low threshold (LTS) neuron; Abstract integrate-and-fire adaptive exponential (AdEx) neuron;
Channel(s):
Gap Junctions:
Receptor(s): GabaA; AMPA; NMDA;
Gene(s):
Transmitter(s): Gaba; Glutamate;
Simulation Environment: NEURON; Python;
Model Concept(s): Synaptic Plasticity; Long-term Synaptic Plasticity; Learning; STDP; Homeostasis;
Implementer(s): Lytton, William [billl at neurosim.downstate.edu]; Neymotin, Sam [samn at neurosim.downstate.edu]; Rowan, Mark [m.s.rowan at cs.bham.ac.uk];
Search NeuronDB for information about:  Neocortex V1 pyramidal corticothalamic L6 cell; Neocortex V1 pyramidal intratelencephalic L2-5 cell; Neocortex V1 interneuron basket PV cell; GabaA; AMPA; NMDA; Gaba; Glutamate;
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// $Id: spkts.hoc,v 1.86 2010/07/10 02:32:11 samn Exp $

print "Loading spkts.hoc..."

// ancillary programs for handling vectors

{load_file("decvec.hoc")}
{load_file("decnqs.hoc")}


//* transfer a file into a list of strings
// usage 'f2slist(list,file)'
proc f2slist() { local i
  $o1.remove_all
  if (! tmpfile.ropen($s2)) { print "Can't open ",$s2
    return }
  while (tmpfile.gets(temp_string_)>0) {
    sfunc.head(temp_string_,"\n",temp_string_) // chop
    tmpobj = new String(temp_string_)
    $o1.append(tmpobj)
  }
}

//* spkts(attrnum[,flag,min,max]) graph spikes from the vectors

thresh = -20    // threshold for deciding which are spikes
burstlen = 1.4  // duration of spike or burst, don't accept another till after this time

proc spkts_call() {}// callback function stub
proc spkts () { local cnt, attrnum, ii, pstep, jj, num, time0, flag, min, max, tst
  revec(vec,vec1) // store times and indices respectively
  if (numarg()==0) { print "spkts(attrnum[,flag,min,max])\n\tflag 0: graph, flag 1: save vec1,vec to veclist, flag 2: save inds (vec1) and times (vec)" // infomercial
    return }
  attrnum=$1
  panobj = GRV[attrnum]
  if (attrnum==0) { cnt=printlist.count() } else { cnt = panobj.llist.count() }
  pstep = panobj.printStep
  if (numarg()>1) { flag = $2 } else { flag = 0 }
  if (numarg()>2) { min = $3 } else { min = 0 }
  if (numarg()>3) { max = $4 } else { max = cnt-1 }
  if (flag==0){
    newPlot(0,1,0,1)
    panobj.glist.append(graphItem)
  }
  for ii=min,max {
    if (attrnum==0) { 
      vrtmp.copy(printlist.object(ii).vec) 
      if (panobj.printStep==-2) tvec = printlist.object(ii).tvec
      if (panobj.printStep==-1) tvec = panobj.tvec
    } else {
      panobj.rv_readvec(ii,vrtmp)  // pick up vector from file
      if (panobj.printStep<0) tvec = panobj.tvec
    }
    if (panobj.printStep>=0) { // make a tvec
      if (!isobj(tvec,"Vector")) { print "ERR0 spkts(): tvec not a vector" return }
      tvec.resize(vrtmp.size)
      tvec.indgen(pstep)
    }
    spkts1(tvec,vrtmp,vec,vec1,ii)

    if (panobj.printStep<0) { // a tvec
      tst = vec.max
    } else {
      tst = pstep*vrtmp.size()         // calc the tst
    }
  }
  if (flag==1) { savevec(vec1) savevec(vec) }
  if (flag<=0) {
    vec1.mark(graphItem,vec,"O",panobj.line)  // graph all the times
    printf("\n")
    graphItem.size(0,tst,min,max)
    graphItem.xaxis(0)
    graphItem.label(0.1,0.9,panobj.filename)
  }
}

// spkts1(tvec,vec,timev,indexv,index)
proc spkts1 () { local ind,tm,ix
  ind=tm=allocvecs(2) tm+=1
  spkts_call()  // place to reset thresh or do other manipulations
  mso[tm].resize($o2.size)
  mso[tm].xing($o2,$o1,thresh) // times
  if (numarg()==5) {
    mso[ind].resize(mso[tm].size)  // scratch vector stores index
    mso[ind].fill($5)
    $o3.append(mso[tm])     // add the times for this to end of vec
    $o4.append(mso[ind])  // add same index for each spk to end of vec1
  } else {
    vlk(mso[tm])
  }
  dealloc(ind)
}

//* parse_spkts()
// pull the vec and vec1 files from spkts apart and put in alloc'ed vectors
func parse_spkts () { local p,q
  p=allocvecs(vec1.max+2) q=p+1
  for (ii=0;ii<=vec1.max;ii+=1) {
    mso[p].indvwhere(vec1,"==",ii)
    mso[q].index(vec,mso[p]) 
    q += 1
  }
  return p+1
}

proc line_spkts () { local ii,min,max,xmax,skip
  skip = $1
  if (numarg()==3) { min=$2 max=$3 } else {
    min = int(graphItem.size(3)+1) max = int(graphItem.size(4)) }
  xmax = graphItem.size(2)
  for (ii=min;ii<max;ii=ii+skip) {
    graphItem.beginline()
    graphItem.line(0,ii)
    graphItem.line(xmax,ii)
  }
  graphItem.xaxis()
}

burst_time=0
burst_maxfreq = 30
calc_ave = 0

//** calcspkts(flag,index)
// run after spkts() so vec contains the times, vec1 contains the
// indices
proc calcspkts () { local ii,jj,flag,index,p1,p2,mn,mx
  p1 = allocvecs(2,1000) p2 = p1+1
  if (numarg()==0) {
    print "To be run after spkts(). \
Assumes times in vec, indices in vec1. \
calcspkts(flag,min,max)\nflags:\t1\tspk times\n\t2\tspk freq \
\t3\tburst times\n\t4\tburst freq\nset calc_ave to get averages for freqs"
    return
  }
  // vec contains the times, vec1 contains the indices
  flag = $1
  mn = $2
  if (numarg()==3) { mx=$3 } else { mx=mn }
  for index=mn,mx {
    mso[p2].resize(0)
    mso[p1].indvwhere(vec1,"==",index)
    mso[p1].index(vec,mso[p1])
    if (flag==1) {  
      printf("SPKS for #%d: ",index)
      for jj=0,mso[p1].size()-1 {printf("%g ",mso[p1].x[jj])}
      printf("\n")
    } else if (flag==2) {  
      printf("FREQ for #%d: ",index)
      for jj=0,mso[p1].size()-2 { 
        pushvec(mso[p2],1000./(mso[p1].x[jj+1]-mso[p1].x[jj])) }
      if (calc_ave) { print mso[p2].mean } else { vlk(mso[p2]) }
    } else if (flag==3) {  
      printf("BTIMES for #%d: ",index)
      burst_time = mso[p1].x[0]
      for jj=1,mso[p1].size()-1 {
        if (1000./(mso[p1].x[jj]-burst_time) < burst_maxfreq) {
          printf("%g ",burst_time)
          burst_time = mso[p1].x[jj]
        } 
      }
      printf("\n")
    } else if (flag==4) {  
      printf("BFREQ for #%d: ",index)
      burst_time = mso[p1].x[0]
      for jj=1,mso[p1].size()-1 {
        // should keep track of spike times in case of very long bursts
        if (1000./(mso[p1].x[jj]-burst_time) < burst_maxfreq) {
          pushvec(mso[p2],1000./(mso[p1].x[jj]-burst_time))
          burst_time = mso[p1].x[jj]
        } 
      }
      if (calc_ave) { print mso[p2].mean } else { mso[p2].printf }
    }
  }
  dealloc(p1)
}

func rvwheres () { local ii
  if ($1!=0) {
    for ii=0,panobjl.object($1).llist.count()-1 {
      if (sfunc.substr(panobjl.object($1).llist.object(ii).name,$s2)==0) {
        return ii }
    }
    errorMsg("String not found in rvwheres.")
  }
  return -2
}

supind = 0
//* spkhist assume spk times in vec 
// allows superimposing of graphs
// spkhist(bin_size)
proc spkhist () { local ii,jj,min,max,diff
  if (numarg()==0) { print "spkhist(bin_size)" return }
  if (numarg()==3) { min=$2 max=$3 } else { min=0 max=tstop }
  diff = max-min
  vrtmp.hist(vec,min,max,$1)
  vec0.resize(4*diff/$1)
  vec1.resize(4*diff/$1)
  vec0.fill(0) vec1.fill(0)
  for (ii=min;ii<int(diff/$1);ii=ii+1) {
    jj=ii*4
    vec0.x[jj+0] = ii*$1
    vec0.x[jj+1] = ii*$1
    vec0.x[jj+2] = (ii+1)*$1
    vec0.x[jj+3] = (ii+1)*$1
    vec1.x[jj+0] = 0
    vec1.x[jj+1] = vrtmp.x[ii]
    vec1.x[jj+2] = vrtmp.x[ii]
    vec1.x[jj+3] = 0
  }
  if (panobj.super==0) {
    newPlot(min,max,0,vrtmp.max)
    panobj.glist.append(graphItem)  
  } else { graphItem = panobjl.object(panobj.remote).glist.object(supind) 
    supind = supind+1 }
  vec1.line(graphItem,vec0)
  sprint(temp_string_,"Hist: %s %d",panobj.filename,$1)
  graphItem.label(0.1,0.9,temp_string_)
}

//** truncvec (vec1,margin) 
// truncate a thresholded time vector so that only one time is given for each spike
// vec1 has thresholded times, margin is duration of a spike
proc truncvec () { local a,ii,num,marg,time0 localobj vs
  marg = $2
  a=allocvecs(vs)
  num=0 time0=-1e3
  vs.resize($o1.size())
  vs.fill(-2)
  for ii=0,$o1.size()-1 {
    if ($o1.x[ii] > time0+marg) { 
      vs.x[ii] = $o1.x[ii]
      time0 = $o1.x[ii]
    }
  }
  $o1.where(vs,">",-1)
  dealloc(a)
}

//** redundkeep(vec) keeps sequential redundent entries
// destructive
proc redundkeep () { local x,ii
  $o1.sort
  x = $o1.x[0]
  for ii=1,$o1.size-1 {
    if ($o1.x[ii]!=x) { $o1.x[ii-1]=-1e20 x=$o1.x[ii] }
  }
  $o1.where($o1,">",-1e20)
}

//** after running spkall can see which cells are responsible for spks
// assumes spk times in vec, spk identities in vec1
// uses ind and vec0
proc whichspked () { local ii
  ind.indvwhere(vec,"()",$1,$2) // a range
  vec0 = vec1.ind(ind)
  ind = vec.ind(ind)
  for ii=0,ind.size()-1 { printf("%d %g\n",vec0.x[ii],ind.x[ii]) }
}

// firebtwn(ind,time,min,max) list of cells that fire between times min and max
proc firebtwn () { local ii,p1,p2,p3
  p1 = allocvecs(3) p2=p1+1 p3=p2+1
  mso[p3].indvwhere($o2,"[]",$3,$4)
  mso[p1].index($o1,mso[p3]) // indices
  mso[p2].index($o2,mso[p3]) // times
  printf("%d hits\n",mso[p3].size)
  for vtr2(&x,&y,mso[p1],mso[p2]) {
      printf("%4d::%6.2f ",x,y)
      if ((ii+1)%5==0) { print "" }
  }
  print ""
  dealloc(p1)
//  dealloc(p2) // to save the indexes
}

// elimind(ind,time,min,max) take out cells with nums between min,max
// destructive
proc elimind () { local ii,p1
  p1 = allocvecs(1)
  mso[p1].indvwhere($o1,"[]",$3,$4)
  vecelim($o1,mso[p1]) vecelim($o2,mso[p1])
  dealloc(p1)
}

// index/time graph
// tigr(ind,vec,size,marker)
proc tigr () { local sz
  if (numarg()==0) { print "tigr(Yvec,Xvec,marker size,marker type)" 
    print "Marker types: \"o\",t,s,O,T,S,+ (circ, tri, square; CAP is filled)"
    return }
  if (numarg()>2) { sz=$3 } else { sz=6 }
  if (numarg()>3) { temp_string_=$s4 } else { temp_string_="O" }
  nvplt($o2)
  graphItem.size($o2.min,$o2.max,$o1.min,$o1.max)
  $o1.mark(graphItem,$o2,temp_string_,sz,panobj.curcol) 
}

//* p2nqs(#,panobj,nqs) -- copy an entry into an nqs
proc p2nqs () { local x,a localobj v1,q,p
  x=$1 p=$o2 q=$o3
  q.resize(0)
  a=allocvecs(v1)
  p.rv_readvec(x,v1)
  q.resize("time",p.tvec,"ind",v1)
  dealloc(a)
}

//** spkboth() determines how many cells spike in 2 time periods
proc spkboth () { local a,t1,t2,t3,t4,s1,s2,s3 localobj v1,v2,v3,o
  o=$o1 t1=$2 t2=$3 t3=$4 t4=$5
  printf("MAY NEED DEBUGGING SINCE NQS.getcol() CHANGED\n")
  a=allocvecs(v1,v2,v3,1e4)
  o.verbose=0
  o.select("time","()",t1,t2) v1.redundout(o.getcol("ind"))
  o.select("time","()",t3,t4) v2.redundout(o.getcol("ind"))
  v3.insct(v1,v2)
  s1=v1.size s2=v2.size s3=v3.size
  printf("P1: %d, P2: %d, Both: %d (%d%%, %d%%)\n",s1,s2,s3,s3/s1*100,s3/s2*100)
  o.verbose=1
  dealloc(a)
}

//returns NQS containing ID,Type,SpikeT
//doesn't check if cell is dead or alive, assumes input is valid
//$o1 = spike vitem
//or
//$o1 = spike vitem, $2 == skipI
//or
//$o1 = time vec , $o2 = id vec
obfunc SpikeNQS(){ local idx,skipI localobj vec,tvec,nq
  if(ce==nil) return nil
  skipI=0
  if(numarg()==1){
    vec = $o1.vec tvec = $o1.tvec
  } else if(numarg()==2){
    if(argtype(1)==1 && argtype(2)==1){
      tvec=$o1 vec=$o2
    } else {
      vec = $o1.vec tvec=$o1.tvec skipI=$2
    }
  } else {
    printf("SpikeNQS ERRA: invalid args!\n")
    return nil
  }
  nq = new NQS("ID","Type","SpikeT")
  if(skipI){
    for idx=0,2 { nq.v[idx].resize(vec.size) nq.v[idx].resize(0) }
    for idx=0,vec.size-1 {
      if(ice(ce.o(vec.x(idx)).type)) continue
      nq.append(vec.x(idx),ce.o(vec.x(idx)).type,tvec.x(idx))
    }
  } else {
    nq.v[0].copy(vec)
    nq.v[2].copy(tvec)
    nq.v[1].resize(vec.size)
    for idx=0,vec.size-1 nq.v[1].x(idx)=ce.o(vec.x(idx)).type
  }
  return nq
}

//returns NQS with refractory % of cell types vs time -- assumes all cells of a type
//have the same refractory period
//$o1 = nqs from SpikeNQS, $2 = dt, optional, $3=skip inhib cells, optional
obfunc refracNQ () { local ct,tt,dt,s,skipI,dotypes localobj snq,nr,vid
  snq=$o1  nr=new NQS("Type","t","r")  ct=0
  if(numarg()>1)dt=$2 else dt=0.25
  if(numarg()>2)skipI=$3 else skipI=1
  if(numarg()>3)dotypes=$4 else dotypes=0
  for(tt=0;tt<=tmax_INTF;tt+=dt){
    for ctt(&ct) if(skipI && !ice(ct)) {
      if(snq.select("Type",ct,"SpikeT","[]",tt-ce.o(ix[ct]).refrac,tt)){
        vid=snq.getcol("ID")//after select, so will use output
        s=vid.uniq
      } else {
        s=0
      }
      nr.append(ct,tt,s/numc[ct])
    }
  }
  return nr
}

//returns nqs with % of cells of each type that have activated by time=t
obfunc PActNQS () { local tinc,winsz,idx,ct,tt,tm,spks,cells,spksE,spksI,nE,nI,cellsE,cellsI\
                   localobj nqt,va,vspk,snq
  snq=$o1
  //time start,end,cell type,activated:0-1,spikes,cells:abs,cells:0-1
  nqt=new NQS("ts","te","ct","act","spks","cells","cellsn")
  if(numarg()>1)tinc=$2 else tinc=0.25
  if(numarg()>2)winsz=$3 else winsz=0.5
  va=new Vector(CTYPi+1)//keep track of % of cells of a type that have spiked
  va.fill(0)
  {vspk=new Vector(allcells) vspk.fill(0)}//keep track of which cells have spiked
  snq.verbose=0
  snq.tog("DB") tm=snq.getcol("SpikeT").max
  for(tt=0;tt<tm;tt+=tinc) {
    spksE=spksI=nE=nI=cellsE=cellsI=0
    for ctt(&ct) {
      if((spks=snq.select("Type",ct,"SpikeT","[]",tt,tt+winsz))) {
        for vtr(&idx,snq.getcol("ID"))vspk.x(idx)=1 
        if(ice(ct)) spksI+=spks else spksE+=spks
      }
      va.x(ct) = vspk.sum(ix[ct],ixe[ct]) / numc[ct]
      if(spks>0) cells=snq.out.getcol("ID").uniq else cells=0
      if(ice(ct)) {
        nI+=va.x(ct)*numc[ct]
        cellsI+=cells
      } else {
        nE+=va.x(ct)*numc[ct]
        cellsE+=cells
      }
      nqt.append(tt,tt+winsz,ct,va.x(ct),spks,cells,cells/numc[ct])
    }
    nqt.append(tt,tt+winsz,-1,nE/ecells,spksE,cellsE,cellsE/ecells)
    nqt.append(tt,tt+winsz,-2,nI/icells,spksI,cellsI,cellsI/icells)
  }
  snq.verbose=1
  return nqt
}

//$o1=nqs from PActNQS , gets peaks & intervals of cell activity levels,
//ct == -1 for E cells, ct == -2 for I cells
obfunc GetPeakNQ () { local idx,ct localobj vi,nqp,vc,nqpo,nqin
  nqin=$o1 nqin.tog("DB") vc=new Vector(nqin.size(-1)) nqin.getcol("ct").uniq(vc)
  nqin.verbose=0
  nqpo=new NQS("ct","ts","x","y","dx","dy")
  for vtr(&ct,vc) {
    nqin.select("ct",ct) vi=nqin.getcol("spks")
    nqp=new NQS("ct","ts","x","y") 
    for idx=1,vi.size-2 {
      if(vi.x(idx)>vi.x(idx-1) && vi.x(idx)>vi.x(idx+1)) {
        nqp.append(ct,nqin.getcol("ts").x(idx),idx,vi.x(idx))
      }
    }
    nqp.resize("dx") nqp.resize("dy")
    nqp.v[nqp.m-2]=Deriv(nqp.getcol("x"))
    nqp.v[nqp.m-1]=Deriv(nqp.getcol("y"))
    nqpo.append(nqp)
    nqsdel(nqp)
  }
  nqin.verbose=1
  return nqpo
}


// returns list containing spike times for each cell
// $o1 == raster vitem
obfunc spikelist () { local idx localobj ls,vec,tvec
  vec=$o1.vec tvec=$o1.tvec
  ls=new List()
  for idx=0,allcells-1 ls.append(new Vector())
  for idx=0,vec.size-1 ls.o(vec.x(idx)).append(tvec.x(idx))
  return ls
}

// plot a single cell's spike times
// $o1 == snq, $2 == cell id, $3 == color, $4 == size, $5==drawR
proc plotcellst () { local cid,st,clr,a,sz,drawR localobj snq,vt,vx,vy
  snq=$o1 cid=$2 clr=$3 sz=$4
  if(numarg()>4)drawR=$5 else drawR=0
  a=allocvecs(vx,vy)
  snq.select("ID",cid)
  gvmarkflag=1
  vt=snq.out.v[2]//SpikeT
  for vtr(&st,vt) vx.append(st) vy.append(cid)
  if(drawR) for vtr(&st,vt) drline(st+.05,cid,st+ce.o(cid).refrac,cid,g,1,1)
  vy.mark(g,vx,"O",sz,clr,1)
  dealloc(a)
}

//draw fancier raster
//$o1=nqs from SpikeNQS, $2==draw refractory periods, $3==skip inhib cells
proc drawrastw () { local idx,skipI,drawR,maxID,a,c,sz,drlt localobj snq,vx,vy,vtype,vc,vtu
  a=allocvecs(vx,vy) drlt=drlflush drlflush=0
  vc=new Vector(CTYP.count+1) vc.fill(0)
  snq=$o1 snq.tog("DB") maxID=snq.v[0].max//max ID
  vtype=new Vector() vtype.copy(snq.v[1])//Type
  if(numarg()>1)drawR=$2 else drawR=0
  if(numarg()>2)skipI=$3 else skipI=0
  if(numarg()>3)sz=$4 else sz=2
  vtu=new Vector(vtype.size) vtype.uniq(vtu)
  c=2
  for vtr(&idx,vtu) if(!skipI || !ice(idx)) {
    vc.x(idx)=c
    c+=1
  }
  if(skipI){
    for idx=0,maxID if(!ice(ce.o(idx).type)) {
      plotcellst(snq,idx,vc.x(ce.o(idx).type),sz,drawR)
    }
  } else {
    for idx=0,maxID {
      plotcellst(snq,idx,vc.x(ce.o(idx).type),sz,drawR)
    }
  }
  dealloc(a) drlflush=drlt  
  if(name_declared("rasterlines"))rasterlines()
  g.flush
}



// plot inhib cells in rast
// $o1 == snq, $2==color, $3==size
proc plotIrast () { local idx,clr,sz localobj xo,snq
  snq=$o1 clr=$2 sz=$3 idx=0
  for ltr(xo,ce,&idx) if(ice(xo.type)) plotcellst(snq,idx,clr,sz)
}

//simple coefficient of variation of interspike interval synch measure from tiesinga03.pdf
//$o1 = spike nqs from SpikeNQS()
//$2 = interval time
//$3 = slide time
//$4 = skip inhib cells [optional] default == 1
obfunc CVPNQS(){ local idx,startt,endt,midt,N,intt,slidet,ct,skipI,CVp localobj snq,cvpnq,vs,vi,vu
  snq=$o1 intt=$2 slidet=$3 if(numarg()>3)skipI=$4 else skipI=1
  vs=new Vector(allcells*2) vi=new Vector(allcells*2)
  vs.resize(0) vi.resize(0) snq.verbose=0
  cvpnq=new NQS("Type","startt","endt","midt","sync","N","CVp","sync2")
  startt=0 endt=intt midt=intt/2
  vu=new Vector(allcells)
  for(startt=0;startt<=tmax_INTF+1-intt;startt+=slidet){
    endt=startt+intt
    if(endt>=tmax_INTF) endt=tmax_INTF
    midt=(startt+endt)/2
    if( (N=snq.select("SpikeT",">=",startt,"SpikeT","<",endt)) > 2 ){
      if(N>vu.size)vu.resize(N)
      snq.out.getcol("ID").uniq(vu) N=vu.size //# of active cells
      vs.copy(snq.out.getcol("SpikeT")) //spike times
      vs.sort //sort spike times to make ISI for all active cells
      vi.resize(0)
      for idx=0,vs.size-2 vi.append(vs.x(idx+1)-vs.x(idx))
      CVp=vi.stdev/vi.mean
      cvpnq.append(0,startt,endt,midt,(CVp-1.)/sqrt(N),N,CVp,(CVp-1.)/sqrt(vi.size))
    } else {
      cvpnq.append(0,startt,endt,midt,0,0,0,0)
    }
    for ctt(&ct) {
      if(skipI && ice(ct)) continue
      if( (N=snq.select("Type",ct,"SpikeT",">=",startt,"SpikeT","<",endt)) > 2 ){
        if(N>vu.size)vu.resize(N)
        snq.out.getcol("ID").uniq(vu) N=vu.size //# of active cells
        vs.copy(snq.out.getcol("SpikeT")) //spike times
        vs.sort //sort spike times to make ISI for all active cells
        vi.resize(0)
        for idx=0,vs.size-2 vi.append(vs.x(idx+1)-vs.x(idx))
        CVp=vi.stdev/vi.mean
        cvpnq.append(ct,startt,endt,midt,(CVp-1.)/sqrt(N),N,CVp,(CVp-1.)/sqrt(vi.size))
      } else {
        cvpnq.append(ct,startt,endt,midt,0,0,0,0)
      }
    }
  }
  snq.verbose=1
  return cvpnq
}

//return spike frequency NQS
//$o1=spike nqs from SpikeNQS()
//$2=interval [optional]
//$3=just do types with interval [optional]
//$4=skipI [optional] default==1
//$5=stop time [optional]
//$6=start time [optional]
//$7=slide time [optional]
obfunc FreqNQS(){ local idx,startt,endt,intt,ct,dotypes,starttime,stoptime,sp,slidet,skipI\
                 localobj fnq,snq
  snq=$o1 intt=$2
  if(numarg()>2) dotypes=$3 else dotypes=0
  if(numarg()>3) skipI=$4 else skipI=1
  if(numarg()>4) stoptime=$5 else stoptime=tstop
  if(numarg()>5) starttime=$6 else starttime=0
  if(numarg()>6) slidet=$7 else slidet=intt
  if(!dotypes){
    fnq=new NQS("ID","Type","Freq","StartT","EndT")
    intt=$2 startt=starttime endt=startt+intt
    for(;startt<stoptime;startt+=slidet){
      endt=startt+intt
      //check length of interval, make sure it's within time bounds of run
      if(endt >= stoptime) endt = stoptime
      if(startt>=endt)endt=startt+1
      for idx=0,allcells-1{
        if(skipI && ice(ce.o(idx).type))continue
        sp=snq.select(-1,"ID",idx,"SpikeT",">=",startt,"SpikeT","<",endt)
        fnq.append(idx,ce.o(idx).type,1e3*sp/(endt-startt),startt,endt)
      }
    }
  } else {
    fnq=new NQS("Type","Freq","StartT","EndT")
    intt=$2 startt=starttime endt=startt+intt
    for(;startt<stoptime;startt+=slidet){
      endt=startt+intt
      //check length of interval, make sure it's within time bounds of run
      if(endt >= stoptime) endt = stoptime
      if(startt>=endt)endt=startt+1
      for ctt(&ct) { 
        if(skipI && ice(ct))continue
        sp=snq.select(-1,"Type",ct,"SpikeT",">=",startt,"SpikeT","<",endt)
        fnq.append(ct,1e3*sp/(numc[ct]*(endt-startt)),startt,endt)
      }
    }
  }
  return fnq
}


func binfindtidx () { local done,val,idx,m,lo,hi,t localobj vv
  vv=$o1 t=$2
  lo=0  hi=vv.size-1  m=int(vv.size/2) done=0
  while(!done){
    if(vv.x(m)>t){
      hi=m m=int((hi+lo)/2.0)
    } else if(vv.x(m)<t){
      lo=m m=int((hi+lo)/2.0)
    }
    if(hi==m || lo==m) return m
  }
}

obfunc estconmat () { local t1,t2,idx,jdx,kdx,del,st1,st2,tdx,df localobj ls,emat,vs1,vs2,vp
  ls=$o1 del=$2  emat=new List()
  for idx=0,ls.count-1 emat.append(new Vector(ls.count))
  estconmat_vc(ls,del,emat)
  return emat
}

// geteff -- get efficiency of $1 to $2 connections
// $1 == type 1 (from)
// $2 == type 2 (to)
// $o3 == ls from spikelist
// returns vector with access by index
obfunc geteff () { local idx,jdx,kdx,ldx,ty1,ty2,tot,cnt,tt,del,fctr,cntonce\
              localobj vt,vpo,vdel,vm,vt2,vtmp,ls,vid
  ty1=$1  ty2=$2  ls=$o3 
  if(numarg()>3) fctr=$4 else fctr=2
  if(numarg()>4) cntonce=$5 else cntonce=0
  vpo=new Vector(allcells)
  vdel=new Vector(allcells)
  vm=new Vector(allcells)
  vtmp=new Vector(allcells)
  vtmp.resize(0)
  for idx=ix[ty1],ixe[ty1]{
    if(idx%100==0)printf("%d.",idx)
    if(!ls.o(idx).size) continue
    vt=ls.o(idx)
    ce.o(idx).getdvi(vpo,vdel)
    tot=0
    for jdx=0,vpo.size-1 if(ce.o(vpo.x(jdx)).type==ty2) tot+=1
    if(!tot) continue
    vtmp.resize(0)
    for jdx=0,vt.size-1 { // go thru spikes
      tt=vt.x(jdx)
      cnt=0    
      for kdx=0,vpo.size-1{ // go thru outputs
        if(ce.o(vpo.x(kdx)).type!=ty2) continue
        del=vdel.x(kdx)
        vt2=ls.o(vpo.x(kdx))
        for ldx=0,vt2.size-1{ // check spiketimes of each output
          if(vt2.x(ldx) >= tt+del && vt2.x(ldx) <= tt+fctr*del){ // within range?
            cnt += 1
            if(cntonce) break // only count once? then break
          }
        }
      }
      vtmp.append(cnt/tot)
    }
    if(vtmp.size) vm.x(idx)=vtmp.mean
  }
  printf("\n")
  return vm
}

// get efficiency of excitatory connections between populations in a given path
// specified by $o1 , i.e. $o1 = new Vector(layer4,layer2,layer5,layer6,layer4)
// $o2 == ls , from spikelist(...)
// $3 == delay fctr for geteff
// returned as NQS
obfunc getpatheffnq () { local fctr,cntonce localobj vpath,nqp,ve,ls
  vpath=$o1
  ls=$o2
  fctr=$3
  if(numarg()>3) nqp=$o4 else nqp=new NQS("ID","from","to","e")
  if(numarg()>4) cntonce=$5 else cntonce=0
  for idx=0,vpath.size-2 {
    printf("eff from %s to %s: ",CTYP.o(vpath.x(idx)).s,CTYP.o(vpath.x(idx+1)).s)
    ve=geteff(vpath.x(idx),vpath.x(idx+1),ls,fctr,cntonce)
    for jdx=ix[vpath.x(idx)],ixe[vpath.x(idx)]{
      nqp.append(jdx,vpath.x(idx),vpath.x(idx+1),ve.x(jdx))
    }
  }
  return nqp
}

Rowan MS,Neymotin SA (2013) Synaptic Scaling Balances Learning in a Spiking Model of Neocortex Adaptive and Natural Computing Algorithms, Tomassini M, Antonioni A, Daolio F, Buesser P, ed. pp.20

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