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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stdpscalingpaper
mod
infot.mod
intf6.mod
intfsw.mod *
misc.mod *
myfft.mod *
nstim.mod *
place.mod *
sampen.mod *
staley.mod *
stats.mod *
tsa.mod *
updown.mod *
vecst.mod *
bpf.h *
misc.h *
mkmod *
parameters.multi *
                            
: $Id: intfsw.mod,v 1.50 2009/02/26 18:24:34 samn Exp $ 

:* COMMENT
COMMENT
this file contains functions/utilities for computing the network/graph-theoretic
properties of INTF and other networks represented as adjacency lists
:** clustering coefficient functions

FUNCTION GetCCR(adj,outvec,[startid,endid,subsamp]) gets the clustering coefficient on a range
         of cells
FUNCTION GetCC -- gets clustering coefficient
FUNCTION GetCCSubPop -- get the clustering coefficient between 'sub-populations' of vertices

:** path length related functions

FUNCTION GetPathR -- gets path length on a range of cells at a time
FUNCTION GetWPath -- gets weighted path length , which may be weighted by synaptic weights &
         delays
FUNCTION GetPairDist -- computes distances between all pairs of vertices, self->self distance==
           distance of shortest loop
FUNCTION GetPathSubPop -- computes path lengths between sub-populations
FUNCTION GetLoopLength -- computes distance to loop back to each node
FUNCTION GetPathEV -- gets path length
FUNCTION CountNeighborsR -- counts the # of neighbors/outputs of a specified degree on a range
         of cells

:** miscellaneous functions
FUNCTION GetRecurCount -- counts # of recurrent connections
FUNCTION Factorial -- computes factorial, if input is too large uses approximation
FUNCTION perm - count # of permutations from set of N elements with R selections
ENDCOMMENT

:* NEURON blocks
NEURON {
  SUFFIX intfsw
  GLOBAL INSTALLED
  GLOBAL verbose
  GLOBAL edgefuncid : edge-weight-function for GetWPath,0=weightdelaydist,1=weightdist,2=delaydist
}

PARAMETER {
  INSTALLED=0
  verbose=0
  edgefuncid=0
}

VERBATIM
#include "misc.h"

typedef struct {
  int isz;
  int imaxsz;
  double* p;  
} myvec;

myvec* allocmyvec (int maxsz){
  myvec* pv = (myvec*)malloc(sizeof(myvec));
  if(!pv) return 0x0;
  pv->isz=0;
  pv->imaxsz=maxsz;
  pv->p=(double*)malloc(sizeof(double)*maxsz);
  if(!pv->p) { free(pv); return 0x0; }
  return pv;
}

int freemyvec (myvec** pps) {
  if(!pps || !pps[0]) return 0;
  myvec* ps = pps[0];
  if(ps->p)free(ps->p);
  free(ps);
  pps[0]=0x0;
  return 1;
}

double popmyvec (myvec* pv) {
  if(pv->isz<1) {
    printf("popmyvec ERRA: can't pop empty stack!\n");
    return 0.0;
  }
  double d = pv->p[pv->isz-1]; pv->isz--;
  return d;
}

void popallmyvec (myvec* pv) {
  pv->isz=0;
}

double pushmyvec (myvec* ps,double d) {
  if(ps->isz==ps->imaxsz) {
    printf("pushmyvec realloc\n");
    ps->imaxsz*=2;
    ps->p=(double*)realloc(ps->p,sizeof(double)*ps->imaxsz);
    if(!ps->p){ printf("pushmyvec ERRA: myvec out of memory %d!!\n",ps->imaxsz); return 0.0; }
  }
  ps->p[ps->isz++]=d; 
  return 1.0;  
}

double appendmyvec (myvec* ps,double d) {
  return pushmyvec(ps,d);
}

typedef struct myqnode_ {
  struct myqnode_* pnext;  
  struct myqnode_* pprev;
  int dd;
} myqnode;

myqnode* allocmyqnode() {
  myqnode* p = (myqnode*)malloc(sizeof(myqnode));
  p->pnext=0x0;
  p->pprev=0x0;
  return p;
}

typedef struct {
  myqnode* pfront;
  myqnode* pback;
} myq;

myq* allocmyq() {
  myq* pq = (myq*)malloc(sizeof(myq));
  pq->pfront = pq->pback = 0x0;
  return pq;
}

int freemyq(myq** ppq) {
  myq* pq = *ppq;
  myqnode* ptmp=pq->pback;
  while(pq->pback){
    if(pq->pback->pprev==0x0){
      free(pq->pback);
      pq->pback=0x0;
      pq->pfront=0x0;
      break;
    } else {
      ptmp=pq->pback->pprev;
      free(pq->pback);    
    }
  }
  free(pq);
  ppq[0]=0;
  return 1;
}

int printfrontmyq (myq* pq) {
  if(pq && pq->pfront) {
    printf("front=%d  ",pq->pfront->dd);
    return 1;
  }
  printf("printfrontmyq ERRA: empty front!\n");
  return 0;
}

int printbackmyq (myq* pq) {
  if(pq && pq->pback) {
    printf("back=%d  ",pq->pback->dd);
    return 1;
  }
  printf("printbackmyq ERRA: empty back!\n");
  return 0;
}

int printmyq (myq* pq, int backwards) {
  if(pq){
    int i=0;
    if(backwards){
      myqnode* pnode = pq->pback;
      while(pnode){
        printf("val %d from back = %d\n",i++,pnode->dd);
        pnode = pnode->pprev;
      }
    } else {
      myqnode* pnode = pq->pfront;
      while(pnode){
        printf("val %d from front = %d\n",i++,pnode->dd);
        pnode = pnode->pnext;
      }
    }
    return 1;
  }
  printf("printmyq ERRA: null pointer!\n");
  return 0;
}

int enqmyq (myq* pq,int d) {
  if(pq->pfront==pq->pback) {
    if(!pq->pfront){
      pq->pfront = allocmyqnode();
      pq->pback = pq->pfront;
      pq->pfront->dd=d;
    } else {
      pq->pback = allocmyqnode();
      pq->pback->dd=d;
      pq->pback->pprev = pq->pfront;
      pq->pfront->pnext = pq->pback;
    }
  } else {
    myqnode* pnew = allocmyqnode();
    pnew->dd = d;
    pq->pback->pnext = pnew; 
    pnew->pprev = pq->pback;
    pq->pback = pnew;
  }
  return 1;
}

int emptymyq (myq* pq) {
  if(pq->pfront==0x0) return 1;
  return 0;
}

int deqmyq (myq* pq) {
  if(pq->pfront == pq->pback){
    if(!pq->pfront){
      printf("deqmyq ERRA: can't deq empty q!\n");
      return -1.0;
    } else {
      int d = pq->pfront->dd;
      free(pq->pfront);
      pq->pfront=pq->pback=0x0;
      return d;
    }
  } else {
    myqnode* tmp = pq->pfront;
    int d = tmp->dd;
    pq->pfront = pq->pfront->pnext;
    pq->pfront->pprev = 0x0;
    free(tmp);
    return d;
  }
}

ENDVERBATIM

FUNCTION testmystack () {
VERBATIM
  myvec* pv = allocmyvec(10);
  printf("created stack with sz %d\n",pv->imaxsz);
  int i;
  for(i=0;i<pv->imaxsz;i++) {
    double d = 41.0 * (i%32) + rand()%100;
    printf("pushing %g onto stack of sz %d\n",d,pv->isz);
    pushmyvec(pv,d);
  }
  printf("test stack realloc by pushing 123.0\n");
  pushmyvec(pv,123.0);
  printf("stack now has %d elements, %d maxsz. contents:\n",pv->isz,pv->imaxsz);
  for(i=0;i<pv->isz;i++)printf("s[%d]=%g\n",i,pv->p[i]);
  printf("popping %d elements. contents:\n",pv->isz);
  while(pv->isz){
    double d = popmyvec(pv);
    printf("popped %g, new sz = %d\n",d,pv->isz);
  }
  printf("can't pop stack now, empty test: ");
  popmyvec(pv);
  freemyvec(&pv);
  printf("freed stack\n");
  return 1.0;
ENDVERBATIM
}

FUNCTION testmyq () {
VERBATIM
  myq* pq = allocmyq();
  printf("created q, empty = %d\n",emptymyq(pq));
  printf("enqueing 10 values:\n");
  int i;
  for(i=0;i<10;i++){
    int d = 41 * (i%32) + rand()%252;
    printf("enqueuing %d...",d);
    enqmyq(pq,d);
    printfrontmyq(pq);
    printbackmyq(pq); printf("\n");
  }
  printf("printing q in forwards order:\n");
  printmyq(pq,0);
  printf("printing q in backwards order:\n");
  printmyq(pq,1);
  printf("testing deq:\n");
  while(!emptymyq(pq)){
    printf("b4 deq: ");
    printfrontmyq(pq); 
    printbackmyq(pq); printf("\n");
    int d = deqmyq(pq);
    printf("dequeued %d\n",d);
    printf("after deq: ");
    printfrontmyq(pq); 
    printbackmyq(pq); printf("\n");
  }
  freemyq(&pq);
  printf("freed myq\n");
  return 1.0;
ENDVERBATIM
}

:* utility functions: copynz(), nnmeandbl(), gzmeandbl(), gzmean(), nnmean() 
VERBATIM
//copy values in valarray who's corresponding entry in binarray != 0 into this vector
//copynz(valvec,binvec)
static double copynz (void* vv) {
  double* pV;
  int n = vector_instance_px(vv,&pV) , iCount = 0 , idx=0;
  int iStartIDx = 0, iEndIDx = n - 1;
  if(ifarg(2)){
    iStartIDx = (int)*getarg(1);
    iEndIDx = (int) *getarg(2);
  }
  if(iEndIDx < iStartIDx || iStartIDx >= n || iEndIDx >= n
                         || iStartIDx<0    || iEndIDx < 0){
    printf("copynz ERRA: invalid indices start=%d end=%d size=%d\n",iStartIDx,iEndIDx,n);
    return -1.0;
  }

  double* pVal,*pBin;

  if(vector_arg_px(1,&pVal)!=n || vector_arg_px(2,&pBin)!=n){
    printf("copynz ERRB: vec args must have size %d!",n);
    return 0.0;
  }

  int iOutSz = 0;
  for(idx=iStartIDx;idx<=iEndIDx;idx++){
    if(pBin[idx]){
      pV[iOutSz++]=pVal[idx];
    }
  }

  vector_resize(pV,iOutSz);

  return (double)iOutSz;
}

//** nnmeandbl()
static double nnmeandbl (double* p,int iStartIDX,int iEndIDX) {
  int iCount=0,idx=0;
  double dSum = 0.0;
  for(idx=iStartIDX;idx<=iEndIDX;idx++){
    if(p[idx]>=0.0){
      dSum+=p[idx];
      iCount++;
    }
  }
  if(iCount>0) return dSum / iCount;
  return -1.0;
} 

//** gzmeandbl()
static double gzmeandbl (double* p,int iStartIDX,int iEndIDX) {
  int iCount=0,idx=0;
  double dSum = 0.0;
  for(idx=iStartIDX;idx<=iEndIDX;idx++){
    if(p[idx]>0.0){
      dSum+=p[idx];
      iCount++;
    }
  }
  if(iCount>0) return dSum / iCount;
  return -1.0;
}

//** gzmean() mean for elements in Vector > 0.0
static double gzmean (void* vv) {
  double* pV;
  int n = vector_instance_px(vv,&pV) , iCount = 0 , idx=0;
  int iStartIDx = 0, iEndIDx = n - 1;
  if(ifarg(2)){
    iStartIDx = (int)*getarg(1);
    iEndIDx = (int) *getarg(2);
  }
  if(iEndIDx < iStartIDx || iStartIDx >= n || iEndIDx >= n
                         || iStartIDx<0    || iEndIDx < 0){
    printf("gzmean ERRA: invalid indices start=%d end=%d size=%d\n",iStartIDx,iEndIDx,n);
    return -1.0;
  }
  return gzmeandbl(pV,iStartIDx,iEndIDx);
}


//** nnmean() mean for elements in Vector >= 0.0
static double nnmean (void* vv) {
  double* pV;
  int n = vector_instance_px(vv,&pV) , iCount = 0 , idx=0;
  int iStartIDx = 0, iEndIDx = n - 1;
  if(ifarg(2)){
    iStartIDx = (int)*getarg(1);
    iEndIDx = (int) *getarg(2);
  }
  if(iEndIDx < iStartIDx || iStartIDx >= n || iEndIDx >= n
                         || iStartIDx<0    || iEndIDx < 0){
    printf("nnmean ERRA: invalid indices start=%d end=%d size=%d\n",iStartIDx,iEndIDx,n);
    return -1.0;
  }
  return nnmeandbl(pV,iStartIDx,iEndIDx);
}
ENDVERBATIM

:* GetCCR(adj,outvec,[startid,endid,subsamp]) 
FUNCTION GetCCR () {
  VERBATIM
  ListVec* pList = AllocListVec(*hoc_objgetarg(1));
  if(!pList){
    printf("GetCC ERRA: problem initializing first arg!\n");
    return 0.0;
  }

  int iCells = pList->isz;
  if(iCells<2){
    printf("GetCC ERRB: size of List < 2 !\n");
    FreeListVec(&pList);
    return 0.0;
  }

  double** pLV = pList->pv;
  int* pLen = pList->plen;

  //init vector of distances to each cell , 0 == no path found
  int* pNeighbors = (int*)calloc(iCells,sizeof(int));
  int i = 0, iNeighbors = 0;
  if(!pNeighbors){
    printf("GetCCR ERRE: out of memory!\n");
    FreeListVec(&pList);
    return 0.0;
  }  

  //init vector of avg distances to each cell , 0 == no path found
  double* pCC; 
  int iVecSz = vector_arg_px(2,&pCC);
  if(!pCC || iVecSz < iCells){
    printf("GetCCR ERRE: arg 2 must be a Vector with size %d\n",iCells);
    FreeListVec(&pList);
    return 0.0;
  }  
  memset(pCC,0,sizeof(double)*iVecSz);//init to 0

  //start/end id of cells to find path to
  int iStartID = ifarg(3) ? (int)*getarg(3) : 0,
      iEndID = ifarg(4) ? (int)*getarg(4) : iCells - 1;

  if(iStartID < 0 || iStartID >= iCells ||
     iEndID < 0 || iEndID >= iCells ||
     iStartID >= iEndID){
       printf("GetCCR ERRH: invalid ids start=%d end=%d numcells=%d\n",iStartID,iEndID,iCells);
       FreeListVec(&pList);
       free(pNeighbors);
       return 0.0;
  }

  double dSubsamp = ifarg(5)?*getarg(5):1.0;
  if(dSubsamp<0.0 || dSubsamp>1.0){
    printf("GetCCR ERRH: invalid subsamp = %g , must be btwn 0 and 1\n",dSubsamp);
    FreeListVec(&pList);
    free(pNeighbors);
    return 0.0;
  }

  unsigned int iSeed = ifarg(7)?(unsigned int)*getarg(7):INT_MAX-109754;

  double* pUse = 0; 
  
  if(dSubsamp<1.0){ //if using only a fraction of the cells
     pUse = (double*)malloc(iCells*sizeof(double));
     mcell_ran4(&iSeed, pUse, iCells, 1.0);
  }

  //get id of cell to find paths from
  int myID;

  int* pNeighborID = (int*)calloc(iCells,sizeof(int));

  if( verbose > 0 ) printf("searching from id: ");

  for(myID=0;myID<iCells;myID++) pCC[myID]=-1.0; //set invalid

  for(myID=iStartID;myID<=iEndID;myID++){

    if(verbose > 0 && myID%1000==0)printf("%d ",myID);

    //only use dSubSamp fraction of cells, skip rest
    if(pUse && pUse[myID]>=dSubsamp) continue;

    int idx = 0, youID = 0, youKidID=0 , iNeighbors = 0;

    //mark neighbors of distance == 1
    for(idx=0;idx<pLen[myID];idx++){
      youID = pLV[myID][idx];
      if(youID>=iStartID && youID<=iEndID){
        pNeighbors[youID]=1;      
        pNeighborID[iNeighbors++]=youID;
      }
    }

    if(iNeighbors < 2){
      for(i=0;i<iNeighbors;i++)pNeighbors[pNeighborID[i]]=0;
      continue;
    }

    int iConns = 0 ; 
  
    //this checks # of connections between neighbors of node
    for(i=0;i<iNeighbors;i++){
      if(!pNeighbors[pNeighborID[i]])continue;
      youID=pNeighborID[i];
      for(idx=0;idx<pLen[youID];idx++){
        youKidID=pLV[youID][idx];
        if(youKidID >= iStartID && youKidID <= iEndID && pNeighbors[youKidID]){
          iConns++;
        }
      }
    }
    pCC[myID]=(double)iConns/((double)iNeighbors*(iNeighbors-1));
    for(i=0;i<iNeighbors;i++)pNeighbors[pNeighborID[i]]=0;
  }
 
  free(pNeighborID);
  free(pNeighbors);
  FreeListVec(&pList);
  if(pUse)free(pUse);

  if( verbose > 0 ) printf("\n");

  return  1.0;
  ENDVERBATIM
}

:* usage GetCentrality(adjlist,outvec)
: based on code from http://www.inf.uni-konstanz.de/algo/publications/b-fabc-01.pdf
: and python networkx centrality.py implementation (brandes betweenness centrality)
FUNCTION GetCentrality () {
  VERBATIM

  ListVec* pList = AllocListVec(*hoc_objgetarg(1));
  if(!pList){
    printf("GetCentrality ERRA: problem initializing first arg!\n");
    return 0.0;
  }

  int iCells = pList->isz;
  if(iCells<2){
    printf("GetCentrality ERRB: size of List < 2 !\n");
    FreeListVec(&pList);
    return 0.0;
  }

  double** pLV = pList->pv;
  int* pLen = pList->plen;

  //init vector of avg distances to each cell , 0 == no path found
  double* pCE; 
  int iVecSz = vector_arg_px(2,&pCE);
  if(!pCE || iVecSz < iCells){
    printf("GetCCR ERRE: arg 2 must be a Vector with size %d\n",iCells);
    FreeListVec(&pList);
    return 0.0;
  }  
  memset(pCE,0,sizeof(double)*iVecSz);//init to 0

  double dSubsamp = ifarg(3)?*getarg(3):1.0;
  if(dSubsamp<0.0 || dSubsamp>1.0){
    printf("GetCCR ERRH: invalid subsamp = %g , must be btwn 0 and 1\n",dSubsamp);
    FreeListVec(&pList);
    return 0.0;
  }

  unsigned int iSeed = ifarg(4)?(unsigned int)*getarg(4):INT_MAX-109754;

  double* pUse = 0; 
  
  if(dSubsamp<1.0){ //if using only a fraction of the cells
     pUse = (double*)malloc(iCells*sizeof(double));
     mcell_ran4(&iSeed, pUse, iCells, 1.0);
  }

  int s,w,T,v,idx;

  myvec* S = allocmyvec(iCells*2);
  myvec** P = (myvec**)malloc(sizeof(myvec*)*iCells);
  myvec* d = allocmyvec(iCells);
  myvec* sigma = allocmyvec(iCells);
  myvec* di = allocmyvec(iCells);
  for(w=0;w<iCells;w++) P[w]=allocmyvec(iCells);
  for(s=0;s<iCells;s++){
    if(verbose && s%100==0) printf("s=%d\n",s);
    S->isz=0;//empty stack    
    for(w=0;w<iCells;w++) P[w]->isz=0;//empty list
    for(T=0;T<iCells;T++) sigma->p[T]=0; sigma->p[s]=1;
    for(T=0;T<iCells;T++) d->p[T]=-1; d->p[s]=0;
    myq* Q = allocmyq();
    enqmyq(Q,s);
    while(!emptymyq(Q)){
      v = deqmyq(Q);
      pushmyvec(S,v);
      for(idx=0;idx<pLen[v];idx++){
        w = (int) pLV[v][idx];
        if(d->p[w]<0){
          enqmyq(Q,w);
          d->p[w] = d->p[v] + 1;
        }
        if(d->p[w] == d->p[v] + 1){
          sigma->p[w] = sigma->p[w] + sigma->p[v];
          appendmyvec(P[w],v);
        }
      }
    }
    freemyq(&Q);
    for(v=0;v<iCells;v++) di->p[v]=0;
    while(S->isz){
      w = popmyvec(S);
      for(idx=0;idx<P[w]->isz;idx++){
        v=P[w]->p[idx];
        di->p[v] = di->p[v] + (sigma->p[v]/sigma->p[w])*(1.0+di->p[w]);
      }
      if(w!=s) pCE[w] = pCE[w] + di->p[w];
    }
  }

  int N = 0;
  for(s=0;s<iCells;s++) if(pLen[s]) N++;
  if(N>2){
    double scale = 1.0/( (N-1.0)*(N-2.0) );
    for(v=0;v<iCells;v++) if(pLen[v]) pCE[v] *= scale;
  }
  
CEFREE:
  freemyvec(&S);
  for(w=0;w<iCells;w++) freemyvec(&P[w]);
  free(P);
  freemyvec(&d);
  freemyvec(&sigma);
  freemyvec(&di);
  if(pUse)free(pUse);  
  return 1.0;

  ENDVERBATIM
}

:* usage GetCC(adjlist,myid,[startid,endid])
: adjlist == list of vectors specifying connectivity - adjacency list : from row -> to entry in column
: myid == id of cell to get clustering coefficient for
: startid == min id of cells search can terminate on or go through
: endid   == max  '    '   '  '   '  '  '  '  ' '  '  '  '  '  ' 
FUNCTION GetCC () {
  VERBATIM
  ListVec* pList = AllocListVec(*hoc_objgetarg(1));
  if(!pList){
    printf("GetCC ERRA: problem initializing first arg!\n");
    return -1.0;
  }

  int iCells = pList->isz;
  if(iCells<2){
    printf("GetCC ERRB: size of List < 2 !\n");
    FreeListVec(&pList);
    return -1.0;
  }

  double** pLV = pList->pv;
  int* pLen = pList->plen;

  //init vector of distances to each cell , 0 == no path found
  int* pNeighbors = (int*)calloc(iCells,sizeof(int));
  int i = 0, iNeighbors = 0;
  if(!pNeighbors){
    printf("GetCC ERRE: out of memory!\n");
    FreeListVec(&pList);
    return -1.0;
  }  

  //get id of cell to find paths from
  int myID = (int) *getarg(2);
  if(myID < 0 || myID >= iCells){
    printf("GetCC ERRF: invalid id = %d\n",myID);
    FreeListVec(&pList);
    free(pNeighbors);
    return -1.0;
  }

  //start/end id of cells to find path to
  int iStartID = ifarg(3) ? (int)*getarg(3) : 0,
      iEndID = ifarg(4) ? (int)*getarg(4) : iCells - 1;

  if(iStartID < 0 || iStartID >= iCells ||
     iEndID < 0 || iEndID >= iCells ||
     iStartID >= iEndID){
       printf("GetCC ERRH: invalid ids start=%d end=%d numcells=%d\n",iStartID,iEndID,iCells);
       FreeListVec(&pList);
       free(pNeighbors);
       return -1.0;
     }

  int idx = 0, iDist = 1 , youID = 0, youKidID=0;

  int* pNeighborID = (int*)calloc(iCells,sizeof(int));

  //mark neighbors of distance == 1
  for(idx=0;idx<pLen[myID];idx++){
    youID = pLV[myID][idx];
    if(youID>=iStartID && youID<=iEndID){
      pNeighbors[youID]=1;      
      pNeighborID[iNeighbors++]=youID;
    }
  }

  if(iNeighbors < 2){
    FreeListVec(&pList);
    free(pNeighbors);
    return -1.0;
  }

  int iConns = 0; 

  //this checks # of connections between neighbors of node starting from
  for(i=0;i<iNeighbors;i++){
    if(!pNeighbors[pNeighborID[i]])continue;
    youID=pNeighborID[i];
    for(idx=0;idx<pLen[youID];idx++){
      youKidID=pLV[youID][idx];
      if(youKidID >= iStartID && youKidID <= iEndID && pNeighbors[youKidID]){
        iConns++;
      }
    }
  }
 
  free(pNeighborID);
  free(pNeighbors);
  FreeListVec(&pList);

  return  (double)iConns/((double)iNeighbors*(iNeighbors-1));
  
  ENDVERBATIM
}

:* usage CountNeighborsR(adjlist,outvec,startid,endid,degree,subsamp])
: adjlist == list of vectors specifying connectivity - adjacency list : from row -> to entry in column
: outvec == vector of distances
: startid == min id of cells search can terminate on or go through
: endid   == max  '    '   '  '   '  '  '  '  ' '  '  '  '  '  ' 
: degree == distance of neighbors -- counts # of neighbors of EXACT distance specified ONLY
: subsamp == specifies fraction btwn 0 and 1 of starting nodes to search
FUNCTION CountNeighborsR () {
  VERBATIM
  ListVec* pList = AllocListVec(*hoc_objgetarg(1));
  if(!pList){
    printf("CountNeighborsR ERRA: problem initializing first arg!\n");
    return 0.0;
  }
 
  int iCells = pList->isz; 
  if(iCells < 2){
    printf("CountNeighborsR ERRB: size of List < 2 !\n");
    FreeListVec(&pList);
    return 0.0;
  }

  double** pLV = pList->pv;
  int* pLen = pList->plen;

  //init vector of avg distances to each cell , 0 == no path found
  double* pVD; 
  int iVecSz = vector_arg_px(2,&pVD) , i = 0;
  if(!pVD || iVecSz < iCells){
    printf("CountNeighborsR ERRE: arg 2 must be a Vector with size %d\n",iCells);
    FreeListVec(&pList);
    return 0.0;
  }  
  memset(pVD,0,sizeof(double)*iVecSz);//init to 0

  //get id of cell to find paths from
  int myID = (int) *getarg(3);
  if(myID < 0 || myID >= iCells){
    printf("CountNeighborsR ERRF: invalid id = %d\n",myID);
    FreeListVec(&pList);
    return 0.0;
  }

  //start/end id of cells to search for neighbors of degree iDist 
  int iStartID = (int)*getarg(3),
      iEndID =   (int)*getarg(4),
      iSearchDegree =    (int)*getarg(5);

  double dSubsamp = ifarg(6)?*getarg(6):1.0;

  unsigned int iSeed = ifarg(7)?(unsigned int)*getarg(7):INT_MAX-109754;

  if(iStartID < 0 || iStartID >= iCells ||
     iEndID < 0 || iEndID >= iCells ||
     iStartID >= iEndID){
       printf("CountNeighborsR ERRH: invalid ids start=%d end=%d numcells=%d\n",iStartID,iEndID,iCells);
       FreeListVec(&pList);
       return 0.0;
     }

  //check search degree
  if(iSearchDegree<=0){
    printf("CountNeighborsR ERRI: invalid searchdegree=%d\n",iSearchDegree);
    FreeListVec(&pList);
    return 0.0;
  }

  //init array of cells/neighbors to check
  int* pCheck = (int*)malloc(sizeof(int)*iCells);
  if(!pCheck){
    printf("CountNeighborsR ERRG: out of memory!\n");
    FreeListVec(&pList);
    return 0.0;
  }

  int iCheckSz = 0, idx = 0, iDist = 1 , youID = 0, youKidID=0, iTmpSz = 0, jdx = 0, iMatches = 0;

  double* pVDTmp = 0, dgzt = 0.0; 
  int* pTmp = 0;
  double* pUse = 0; 
  
  if(dSubsamp<1.0){ //if using only a fraction of the cells
     pUse = (double*)malloc(iCells*sizeof(double));
     mcell_ran4(&iSeed, pUse, iCells, 1.0);
  }

  if( verbose > 0 ) printf("searching from id: ");

  pVDTmp = (double*)calloc(iCells,sizeof(double));
  pTmp = (int*)calloc(iCells,sizeof(int)); 

  for(myID=iStartID;myID<=iEndID;myID++){

    if(verbose > 0 && myID%1000==0)printf("%d ",myID); 

    //only use dSubSamp fraction of cells, skip rest
    if(pUse && pUse[myID]>=dSubsamp) continue;

    iMatches = 0;

    iCheckSz = 0; idx = 0; iDist = 1; youID = 0; youKidID = 0;

    //mark neighbors of distance == 1
    for(idx=0;idx<pLen[myID];idx++){
      youID = pLV[myID][idx];
      if(youID>=iStartID && youID<=iEndID && !pVDTmp[youID]){
        pVDTmp[youID]=(double)iDist;
        pCheck[iCheckSz++]=youID;
      }
    }

    if(iSearchDegree == iDist){
      pVD[myID] = iCheckSz;
      for(idx=0;idx<iCheckSz;idx++) pVDTmp[pCheck[idx]]=0; //reset for next cell
      continue;
    }

    pVDTmp[myID]=1;

    iTmpSz = 0;  jdx=0;

    iDist++;
  
    //this does a breadth-first search but avoids recursion
    while(iCheckSz>0 && iDist<=iSearchDegree){
      iTmpSz = 0;
      for(idx=0;idx<iCheckSz;idx++){
        youID=pCheck[idx];
        for(jdx=0;jdx<pLen[youID];jdx++){
          youKidID=pLV[youID][jdx];
          if(youKidID >= iStartID && youKidID <=iEndID && !pVDTmp[youKidID]){ 
            pTmp[iTmpSz++] = youKidID; //save id of cell to search it's kids on next iteration
            pVDTmp[youKidID]=(double)iDist; //this cell is at iDist away, even if it is also @ a shorter distance
          }
        }
      }
      iCheckSz = iTmpSz;
      
      if(iSearchDegree == iDist){
        pVD[myID] = iCheckSz;
        memset(pVDTmp,0,sizeof(double)*iCells); //reset to 0 for next cell
        break;
      } 

      if(iCheckSz) memcpy(pCheck,pTmp,sizeof(int)*iCheckSz);
      iDist++;
    }
  }

  if(pUse) free(pUse); 
  free(pCheck);
  FreeListVec(&pList);  
  free(pVDTmp); free(pTmp);

  if( verbose > 0 ) printf("\n");

  return 1.0;
  ENDVERBATIM
}

:* utility functions: maxval(), weightdelaydist(), weightdist(), delaydist(), printedgefunc()
VERBATIM
double maxval(double* p,int sz)
{
  double dmax = p[0];
  int i = 1;
  for(;i<sz;i++) if(p[i]>dmax) dmax = p[i];
  return dmax;
}

double weightdelaydist(double w,double d)
{
  if(w < 0)
    return -w/d;
  if(w > 0)
    return d/w;
  return DBL_MAX; // no connection means infinite distance
}

double weightdist(double w,double d)
{
  if(w < 0)
    return -w;
  if(w > 0)
    return 1/w;
  return DBL_MAX; // no connection means infinite distance
}

double delaydist(double w,double d)
{
  return d;
}

void printedgefunc(int id)
{
  switch(id){
    case 0:
     printf("weightdelaydist\n");
     break;
    case 1:
     printf("weightdist\n");
     break;
    case 2:
     printf("delaydist\n");
     break;
    default:
     printf("unknown!\n");
     break;
  }
}

ENDVERBATIM

:* FUNCTION predgefunc()
FUNCTION predgefunc () {
  VERBATIM
  int i;
  if(ifarg(1)){ printf("%d=",(int)*getarg(1)); printedgefunc((int)*getarg(1)); printf("\n"); }    
  else for(i=0;i<3;i++){ printf("%d=",i); printedgefunc(i); printf("\n"); }
  return 0.0;
  ENDVERBATIM
}

:* usage GetWPath(preid,poid,weights,delays,outvec,[subsamp])
: preid == list of presynaptic IDs
: poid == list of postsynaptic IDs
: weights == list of weights, excit > 0 , inhib < 0
: delays == list of delays 
: outvec == vector of distances
: subsamp == only use specified fraction of synapses , optional
FUNCTION GetWPath () {
  VERBATIM

  double* ppre = 0, *ppo = 0, *pwght = 0, *pdel = 0, *pout = 0;
  int iSz,iTmp,i,j,k,l;
  void* voi;

  iSz = vector_arg_px(1,&ppre);

  if(iSz < 1)
  { printf("GetWPath ERRO: invalid size for presynaptic ID Vector (arg 1) %d!\n",iSz);
    return -666.666;
  }

  if( (iTmp=vector_arg_px(2,&ppo)) != iSz)
  { printf("GetWPath ERRA: incorrectly sized postsynaptic ID Vector (arg 2) %d %d!",iSz,iTmp);
    return -666.666;
  }
  if( (iTmp=vector_arg_px(3,&pwght)) != iSz)
  { printf("GetWPath ERRB: incorrectly sized weight Vector (arg 3) %d %d!\n",iSz,iTmp);
    return -666.666;
  }
  if( (iTmp=vector_arg_px(4,&pdel)) != iSz)
  { printf("GetWPath ERRC: incorrectly sized delay Vector (arg 4) %d %d!\n",iSz,iTmp);
    return -666.666;
  }

  int maxid = maxval(ppre,iSz);

  iTmp = maxval(ppo,iSz);
  if(iTmp > maxid) maxid=iTmp;

  voi = vector_arg(5);

  if( (iTmp=vector_arg_px(5,&pout))!= maxid+1 && 0)
  { printf("GetWPath ERRD: incorrectly sized output Vector (arg 5) %d %d!\n",maxid+1,iTmp);
    return -666.666;
  }
  memset(pout,0,sizeof(double)*iTmp);//init to 0

  double (*EdgeFunc)(double,double) = &weightdelaydist;
  int iEdgeFuncID = (int)edgefuncid; 
  if(iEdgeFuncID < 0 || iEdgeFuncID > 2)
  {  printf("GetWPath ERRK: invalid edgedfunc id %d!\n",iEdgeFuncID);
     return -666.666;
  } else if(iEdgeFuncID == 1) EdgeFunc = &weightdist;
    else if(iEdgeFuncID == 2) EdgeFunc = &delaydist;
  if(verbose) printedgefunc(iEdgeFuncID);

 int** adj = (int**) calloc(maxid+1,sizeof(int*));
 if(!adj)
 { printf("GetWPath ERRE: out of memory!\n");
   return -666.666;
 }

 //stores weight of each edge
 //incident from edge is index into pdist
 //incident to edge id is stored in ppo
 double** pdist = (double**) calloc(maxid+1,sizeof(double*));

 int* pcounts = (int*) calloc(maxid+1,sizeof(int));

 //count divergence from each presynaptic cell
 for(i=0;i<iSz;i++)
 { //check for multiple synapses from same source to same target
   if(i+1<iSz && ppre[i]==ppre[i+1] && ppo[i]==ppo[i+1])
   { if(verbose>1) printf("first check double synapse i=%d\n",i);
     while(1)
     { if(i+1>=iSz) break;
       if(ppre[i]!=ppre[i+1] || ppo[i]!=ppo[i+1])
       { //new synapse?
         i--;//move back 1 so get this synapse on next for loop step
         break;
       }
       i++; //move to next synapse
     }      
   }
   pcounts[(int)ppre[i]]++;    //count this one and continue
 }

 //allocate memory for adjacency & distance lists
 for(i=0;i<maxid+1;i++){
   if(pcounts[i]){
     adj[i] = (int*)calloc(pcounts[i],sizeof(int));
     pdist[i] = (double*)calloc(pcounts[i],sizeof(double));
   }
 }

 //index for locations into adjacency lists
 int* pidx = (int*) calloc(maxid+1,sizeof(int));

 //set distance values based on weights and neighbors in adjacency lists based on postsynaptic ids
 for(i=0;i<iSz;i++)
 { int myID = (int)ppre[i];
   if(!pcounts[myID]) continue;//skip cells with 0 divergence
   double dist = EdgeFunc(pwght[i],pdel[i]);
   j=i; //store index of current synapse
   //check for multiple synapses from same source to same target
   if(i+1<iSz && ppre[i]==ppre[i+1] && ppo[i]==ppo[i+1])
   { if(verbose>1) printf("check double syn i=%d\n",i);
     while(1)
     { if(i+1>=iSz) break;
       if(ppre[i]!=ppre[i+1] || ppo[i]!=ppo[i+1])
       { //new synapse?
         i--;//move back 1 so get right synapse on next for loop step
         break;
       }
       if(j!=i) //if didn't count this synapse yet
         dist += EdgeFunc(pwght[i],pdel[i]);
       i++; //move to next synapse to see if it's the same pre,post pair
     }      
   }
   pdist[myID][pidx[myID]] = dist;
   adj[myID][pidx[myID]] = ppo[i];
   pidx[myID]++;
 }

 free(pidx);

 //perform bellman-ford single source shortest path algorithm once for each vertex
 //can improve efficiency by using johnson's algorithm, which uses dijkstra's alg  -- will do later
 double* d = (double*) malloc( (maxid+1)*sizeof(double) ); //distance vector for bellman ford algorithm
 for(i=0;i<=maxid;i++)
 { if(i%100==0) printf("%d ",i);
   if(!pcounts[i])continue;
   for(j=0;j<=maxid;j++) d[j] = DBL_MAX; //initialize distances to +infiniti
   d[i] = 0.0; //distance to self == 0.0
   int changed = 0;
   for(j=0;j<maxid;j++)//apply edge relaxation loop # of vertex-1 times
   { changed=0;
     for(k=0;k<=maxid;k++) //this is just to go thru all edges
     { for(l=0;l<pcounts[k];l++) //go thru all edges of vertex k
       {  if(d[adj[k][l]] > d[k] + pdist[k][l]){//perform edge relaxation
            d[adj[k][l]] = d[k] + pdist[k][l];
            changed=1;
          }
       }
     }
     if(!changed){ if(verbose>1) printf("early term @ j=%d\n",j); break; }
   }

//  int ok = 1;   //make sure no negative cycles
//  for(j=0;j<=maxid && ok;j++)
//  { for(k=0;k<=maxid && ok;k++)
//    { for(l=0;l<pcounts[k];l++)
//      { if( d[adj[k][l]] > d[k] + pdist[k][l] )
//        { ok = 0;
//          break;
//        }
//      }
//    }
//   }
   double avg = 0.0;   //get average distance from vertex i to all other vertices
   int N = 0;
   for(j=0;j<=maxid;j++)
   { if(j!=i && d[j] < DBL_MAX)
     { avg += d[j];
       N++;
     }
   }
   if(N) pout[i] = avg / (double) N;
 }

 free(d);

 //free memory
 free(pcounts);

 for(i=0;i<=maxid;i++){
   if(adj[i]) free(adj[i]);
   if(pdist[i]) free(pdist[i]);
 }

 free(adj);
 free(pdist);

 vector_resize(voi,maxid+1); // pass void* (Vect* ) instead of double*

 return gzmeandbl(pout,0,maxid);

 ENDVERBATIM
}

:* usage GetPathR(adjlist,outvec,[startid,endid,maxdist,subsamp])
: adjlist == list of vectors specifying connectivity - adjacency list : from row -> to entry in column
: outvec == vector of distances
: startid == min id of cells search can terminate on or go through
: endid   == max  '    '   '  '   '  '  '  '  ' '  '  '  '  '  ' 
: maxdist == max # of connections to allow hops over
: subsamp == perform calculation on % of cells, default == 1
FUNCTION GetPathR () {
  VERBATIM
  ListVec* pList = AllocListVec(*hoc_objgetarg(1));
  if(!pList){
    printf("GetPathEV ERRA: problem initializing first arg!\n");
    return 0.0;
  }
 
  int iCells = pList->isz; 
  if(iCells < 2){
    printf("GetPathEV ERRB: size of List < 2 !\n");
    FreeListVec(&pList);
    return 0.0;
  }

  double** pLV = pList->pv;
  int* pLen = pList->plen;

  //init vector of avg distances to each cell , 0 == no path found
  double* pVD; 
  int iVecSz = vector_arg_px(2,&pVD) , i = 0;
  if(!pVD || iVecSz < iCells){
    printf("GetPathEV ERRE: arg 2 must be a Vector with size %d\n",iCells);
    FreeListVec(&pList);
    return 0.0;
  }  
  memset(pVD,0,sizeof(double)*iVecSz);//init to 0

  //start/end id of cells to find path to
  int iStartID = ifarg(3) ? (int)*getarg(3) : 0,
      iEndID = ifarg(4) ? (int)*getarg(4) : iCells - 1,
      iMaxDist = ifarg(5)? (int)*getarg(5): -1;

  double dSubsamp = ifarg(6)?*getarg(6):1.0;

  unsigned int iSeed = ifarg(7)?(unsigned int)*getarg(7):INT_MAX-109754;

  if(iStartID < 0 || iStartID >= iCells ||
     iEndID < 0 || iEndID >= iCells ||
     iStartID >= iEndID){
       printf("GetPathEV ERRH: invalid ids start=%d end=%d numcells=%d\n",iStartID,iEndID,iCells);
       FreeListVec(&pList);
       return 0.0;
     }

  //check max distance
  if(iMaxDist==0){
    printf("GetPathEV ERRI: invalid maxdist=%d\n",iMaxDist);
    FreeListVec(&pList);
    return 0.0;
  }

  //init array of cells/neighbors to check
  int* pCheck;
  pCheck = (int*)malloc(sizeof(int)*iCells);
  if(!pCheck){
    printf("GetPathEV ERRG: out of memory!\n");
    FreeListVec(&pList);
    return 0.0;
  }

  int iCheckSz = 0, idx = 0, iDist = 1 , youID = 0, youKidID=0, iTmpSz = 0, jdx = 0;

  double* pVDTmp = 0, dgzt = 0.0; 
  int* pTmp = 0;
  double* pUse = 0; 
  
  if(dSubsamp<1.0){ //if using only a fraction of the cells
     pUse = (double*)malloc(iCells*sizeof(double));
     mcell_ran4(&iSeed, pUse, iCells, 1.0);
  }

  pTmp = (int*)calloc(iCells,sizeof(int)); 

  if( verbose > 0 ) printf("searching from id: ");

  pVDTmp = (double*)calloc(iCells,sizeof(double));

  int myID;

  for(myID=iStartID;myID<=iEndID;myID++){

    if(verbose > 0 && myID%1000==0)printf("%d ",myID); 

    //only use dSubSamp fraction of cells, skip rest
    if(pUse && pUse[myID]>=dSubsamp) continue;

    iCheckSz = 0; idx = 0; iDist = 1; youID = 0; youKidID = 0;

    pVDTmp[myID]=1;

    //mark neighbors of distance == 1
    for(idx=0;idx<pLen[myID];idx++){
      youID = pLV[myID][idx];
      if(youID>=iStartID && youID<=iEndID && !pVDTmp[youID]){
        pVDTmp[youID]=(double)iDist;
        pCheck[iCheckSz++]=youID;
      }
    }

    iTmpSz = 0;  jdx=0;

    iDist++;
  
    //this does a breadth-first search but avoids recursion
    while(iCheckSz>0 && (iMaxDist==-1 || iDist<=iMaxDist)){
      iTmpSz = 0;
      for(idx=0;idx<iCheckSz;idx++){
        youID=pCheck[idx];
        for(jdx=0;jdx<pLen[youID];jdx++){
          youKidID=pLV[youID][jdx];
          if(youKidID >= iStartID && youKidID <=iEndID && !pVDTmp[youKidID]){ //found a new connection
            pTmp[iTmpSz++] = youKidID; //save id of cell to search it's kids on next iteration
            pVDTmp[youKidID]=(double)iDist;
          }
        }
      }
      iCheckSz = iTmpSz;
      if(iCheckSz) memcpy(pCheck,pTmp,sizeof(int)*iCheckSz);
      iDist++;
    }

    pVDTmp[myID]=0.0; // distance to self == 0.0
    if((dgzt=gzmeandbl(pVDTmp,iStartID,iEndID))>0.0) pVD[myID]=dgzt;// save mean path length for given cell

    memset(pVDTmp,0,sizeof(double)*iCells);
  }
  
  free(pTmp);
  if(pUse) free(pUse); 
  free(pCheck);
  FreeListVec(&pList);  
  free(pVDTmp);

  if( verbose > 0 ) printf("\n");

  return 1.0;
  ENDVERBATIM
}

:* usage GetCCSubPop(adjlist,outvec,startids,endids[,subsamp])
: computes clustering cofficient between sub-populations
: adjlist == list of vectors specifying connectivity - adjacency list : from row -> to entry in column
: outvec == vector of distances
: startid == binary vector of ids of cells to start search from (from population)
: endid   == binary vector of ids of cells to terminate search on (to population)
: subsamp == perform calculation on ratio of cells btwn 0-1, default == 1
FUNCTION GetCCSubPop () {
  VERBATIM
  ListVec* pList = AllocListVec(*hoc_objgetarg(1));
  if(!pList){
    printf("GetCCSubPop ERRA: problem initializing first arg!\n");
    return 0.0;
  }
 
  int iCells = pList->isz; 
  if(iCells < 2){
    printf("GetCCSubPop ERRB: size of List < 2 !\n");
    FreeListVec(&pList);
    return 0.0;
  }

  double** pLV = pList->pv;
  int* pLen = pList->plen;

  //init vector of distances to each cell , 0 == no path found
  int* pNeighbors = (int*)calloc(iCells,sizeof(int));
  int i = 0, iNeighbors = 0;
  if(!pNeighbors){
    printf("GetCCSubPop ERRE: out of memory!\n");
    FreeListVec(&pList);
    return 0.0;
  }  

  //init vector of avg distances to each cell , 0 == no path found
  double* pCC; 
  int iVecSz = vector_arg_px(2,&pCC);
  if(!pCC || iVecSz < iCells){
    printf("GetCCSubPop ERRE: arg 2 must be a Vector with size %d\n",iCells);
    FreeListVec(&pList);
    return 0.0;
  }  
  memset(pCC,0,sizeof(double)*iVecSz);

  double* pStart,  // bin vec of ids to search from 
          *pEnd;   // bin vec of ids to terminate search on

  if( vector_arg_px(3,&pStart) < iCells || vector_arg_px(4,&pEnd) < iCells){
    printf("GetCCSubPop ERRF: arg 3,4 must be Vectors with size >= %d\n",iCells);
    FreeListVec(&pList);
    return 0.0;
  }
  double dSubsamp = ifarg(5)?*getarg(5):1.0;

  unsigned int iSeed = ifarg(6)?(unsigned int)*getarg(6):INT_MAX-109754;

  double* pUse = 0; 
  
  if(dSubsamp<1.0){ //if using only a fraction of the cells
     pUse = (double*)malloc(iCells*sizeof(double));
     mcell_ran4(&iSeed, pUse, iCells, 1.0);
  }

  //get id of cell to find paths from
  int myID;

  int* pNeighborID = (int*)calloc(iCells,sizeof(int));

  if( verbose > 0 ) printf("searching from id: ");

  for(myID=0;myID<iCells;myID++) pCC[myID]=-1.0; //set invalid

  for(myID=0;myID<iCells;myID++){

    if(!pStart[myID]) continue;

    if(verbose > 0 && myID%1000==0)printf("%d ",myID);

    //only use dSubSamp fraction of cells, skip rest
    if(pUse && pUse[myID]>=dSubsamp) continue;

    int idx = 0, youID = 0, youKidID=0 , iNeighbors = 0;

    //mark neighbors of distance == 1
    for(idx=0;idx<pLen[myID];idx++){
      youID = pLV[myID][idx];
      if(pEnd[youID] && !pNeighbors[youID]){
        pNeighbors[youID]=1;      
        pNeighborID[iNeighbors++]=youID;
      }
    }

    if(iNeighbors < 2){
      for(i=0;i<iNeighbors;i++)pNeighbors[pNeighborID[i]]=0;
      continue;
    }

    int iConns = 0 ; 
  
    //this checks # of connections between neighbors of node
    for(i=0;i<iNeighbors;i++){
      if(!pNeighbors[pNeighborID[i]])continue;
      youID=pNeighborID[i];
      for(idx=0;idx<pLen[youID];idx++){
        youKidID=pLV[youID][idx];
        if(pEnd[youKidID] && pNeighbors[youKidID]){
          iConns++;
        }
      }
    }
    pCC[myID]=(double)iConns/((double)iNeighbors*(iNeighbors-1));
    for(i=0;i<iNeighbors;i++)pNeighbors[pNeighborID[i]]=0;
  }
 
  free(pNeighborID);
  free(pNeighbors);
  FreeListVec(&pList);
  if(pUse)free(pUse);

  if( verbose > 0 ) printf("\n");

  return  1.0;

  ENDVERBATIM
}
:* usage GetRecurCount(adjlist,outvec,fromids,thruids)
: counts # of A -> B -> A patterns in adj adjacency list , using from ids as A
: and thruids as B. fromids/thruids should have size of adjacency list and have a 
: 1 in index iff using that cell, same with thruids
FUNCTION GetRecurCount () {
  VERBATIM
  ListVec* pList;
  int iCells,*pLen,iFromSz,iThruSz,idx,myID,youID,jdx,iCheckSz,*pVisited,*pCheck;
  double **pLV,*pFrom,*pThru,*pR;

  pList = AllocListVec(*hoc_objgetarg(1));
  if(!pList){
    printf("GetRecurCount ERRA: problem initializing first arg!\n");
    return 0.0;
  }
 
  iCells = pList->isz; 
  if(iCells < 2){
    printf("GetRecurCount ERRB: size of List < 2 !\n");
    FreeListVec(&pList);
    return 0.0;
  }

  pLV = pList->pv;
  pLen = pList->plen;

  pFrom=pThru=0;
  iFromSz = vector_arg_px(3,&pFrom); iThruSz = vector_arg_px(4,&pThru);
  
  if( iFromSz <= 0 || iThruSz <= 0){
    printf("GetRecurCount ERRF: arg 3,4 bad (fromsz,thrusz)=(%d,%d)\n",iFromSz,iThruSz);
    FreeListVec(&pList);
    return 0.0;
  }

  pVisited = (int*)calloc(iCells,sizeof(int));//which vertices already marked to have children expanded

  pCheck = (int*)malloc(sizeof(int)*iCells);

  pR = vector_newsize(vector_arg(2),iCells);
  memset(pR,0,sizeof(double)*iCells); //zero out output first

  for(myID=0;myID<iCells;myID++) {
    if(!pFrom[myID]) continue;
    iCheckSz = 0; 
    for(idx=0;idx<pLen[myID];idx++){//mark neighbors of distance == 1
      youID = pLV[myID][idx];
      if(!pThru[youID] || pVisited[youID]) continue;
      pCheck[iCheckSz++]=youID;
      pVisited[youID]=1;
    }
    for(idx=0;idx<iCheckSz;idx++) {
      youID = pCheck[idx];
      for(jdx=0;jdx<pLen[youID];jdx++) {
        if(pLV[youID][jdx]==myID) pR[myID]++;
      }
    }
    memset(pVisited,0,sizeof(int)*iCells);
  }
  

  free(pCheck);
  FreeListVec(&pList);  
  free(pVisited);

  if( verbose > 0) printf("\n");

  return 1.0;

  ENDVERBATIM
}

:* usage GetPairDist(adjlist,outvec,startid,endid[subsamp,seed])
: computes distances between all pairs of vertices, self->self distance == distance of shortest loop
: adjlist == list of vectors specifying connectivity - adjacency list : from row -> to entry in column
: outvec == vector of distances from vertex i in outvec.x(i)
: startid == first id to check
: endid   == last id to check
FUNCTION GetPairDist () {
  VERBATIM
  ListVec* pList = AllocListVec(*hoc_objgetarg(1));
  if(!pList){
    printf("GetPairDist ERRA: problem initializing first arg!\n");
    return 0.0;
  }
 
  int iCells = pList->isz; 
  if(iCells < 2){
    printf("GetPairDist ERRB: size of List < 2 !\n");
    FreeListVec(&pList);
    return 0.0;
  }

  double** pLV = pList->pv;
  int* pLen = pList->plen;

  double* pFrom = 0, *pTo = 0;
  int iFromSz = vector_arg_px(3,&pFrom) , iToSz = vector_arg_px(4,&pTo);
  
  if( iFromSz <= 0 || iToSz <= 0){
    printf("GetPairDist ERRF: arg 3,4 bad (fromsz,tosz)=(%d,%d)\n",iFromSz,iToSz);
    FreeListVec(&pList);
    return 0.0;
  }

  int iMinSz = iFromSz * iToSz;

  //init vector of avg distances to each cell , 0 == no path found
  double* pVD; 
  pVD = vector_newsize(vector_arg(2),iMinSz);
  memset(pVD,0,sizeof(double)*iMinSz); //zero out output first

  //init array of cells/neighbors to check
  int* pCheck;
  pCheck = (int*)malloc(sizeof(int)*iCells);
  if(!pCheck){
    printf("GetPairDist ERRG: out of memory!\n");
    FreeListVec(&pList);
    return 0.0;
  }

  int iCheckSz = 0, idx = 0, iDist = 1 , youID = 0, youKidID=0, iTmpSz = 0, jdx = 0;

  int* pTmp = (int*)calloc(iCells,sizeof(int)); 

  if( verbose > 0 ) printf("searching from id: ");

  int myID , iOff = 0 , kdx = 0;

  int* pVisited = (int*)calloc(iCells,sizeof(int)); //which vertices already marked to have children expanded
  int* pUse = (int*)calloc(iCells,sizeof(int)); //which 'TO' vertices
  int* pMap = (int*)calloc(iCells,sizeof(int)); //index of 'TO' vertices to output index
  for(idx=0;idx<iToSz;idx++){
    pUse[(int)pTo[idx]]=1;
    pMap[(int)pTo[idx]]=idx;
  }

  for(kdx=0;kdx<iFromSz;kdx++,iOff+=iToSz){
    myID=pFrom[kdx];
    if(verbose > 0 && myID%100==0)printf("%d\n",myID);

    iCheckSz = 0; idx = 0; iDist = 1; youID = 0; youKidID = 0;
      
    //mark neighbors of distance == 1
    for(idx=0;idx<pLen[myID];idx++){
      youID = pLV[myID][idx];
      if(pUse[youID]) pVD[ iOff + pMap[youID]  ] = 1; //mark 1st degree neighbor distance as 1
      if(!pVisited[youID]){ 
        pCheck[iCheckSz++]=youID;
        pVisited[youID]=1;
      }
    }

    iTmpSz = 0;  jdx=0;
      
    iDist++;
  
    //this does a breadth-first search but avoids recursion
    while(iCheckSz>0){
      iTmpSz = 0;
      for(idx=0;idx<iCheckSz;idx++){
        youID=pCheck[idx];
        for(jdx=0;jdx<pLen[youID];jdx++){
          youKidID=pLV[youID][jdx];
          if(pUse[youKidID] && !pVD[iOff + pMap[youKidID]])
            pVD[iOff + pMap[youKidID]] = iDist; 
          if(!pVisited[youKidID]){ //found a new connection
            pTmp[iTmpSz++] = youKidID; //save id of cell to search it's kids on next iteration
            pVisited[youKidID]=1;
          }
        }
      }
      iCheckSz = iTmpSz;
      if(iCheckSz) memcpy(pCheck,pTmp,sizeof(int)*iCheckSz);
      iDist++;
    }
    memset(pVisited,0,sizeof(int)*iCells);
  }
  
  free(pTmp);
  free(pCheck);
  FreeListVec(&pList);  
  free(pUse);
  free(pMap);
  free(pVisited);

  if( verbose > 0) printf("\n");

  return 1.0;
  ENDVERBATIM
}

:* usage GetPathSubPop(adjlist,outvec,startids,endids[subsamp,loop,seed])
: computes path lengths between sub-populations
: adjlist == list of vectors specifying connectivity - adjacency list : from row -> to entry in column
: outvec == vector of distances from vertex i in outvec.x(i)
: startid == binary vector of ids of cells to start search from (from population)
: endid   == binary vector of ids of cells to terminate search on (to population)
: subsamp == perform calculation on ratio of cells btwn 0-1, default == 1
: loop == check self-loops , default == 0
: seed == random # seed when using subsampling
FUNCTION GetPathSubPop () {
  VERBATIM
  ListVec* pList = AllocListVec(*hoc_objgetarg(1));
  if(!pList){
    printf("GetPathEV ERRA: problem initializing first arg!\n");
    return 0.0;
  }
 
  int iCells = pList->isz; 
  if(iCells < 2){
    printf("GetPathEV ERRB: size of List < 2 !\n");
    FreeListVec(&pList);
    return 0.0;
  }

  double** pLV = pList->pv;
  int* pLen = pList->plen;

  //init vector of avg distances to each cell , 0 == no path found
  double* pVD; 
  int iVecSz = vector_arg_px(2,&pVD) , i = 0;
  if(!pVD || iVecSz < iCells){
    printf("GetPathEV ERRE: arg 2 must be a Vector with size %d\n",iCells);
    FreeListVec(&pList);
    return 0.0;
  }  
  memset(pVD,0,sizeof(double)*iVecSz);

  double* pStart,  // bin vec of ids to search from 
          *pEnd;   // bin vec of ids to terminate search on

  if( vector_arg_px(3,&pStart) < iCells || vector_arg_px(4,&pEnd) < iCells){
    printf("GetPathSubPop ERRF: arg 3,4 must be Vectors with size >= %d\n",iCells);
    FreeListVec(&pList);
    return 0.0;
  }
  double dSubsamp = ifarg(5)?*getarg(5):1.0;

  int bSelfLoop = ifarg(6)?(int)*getarg(6):0;

  unsigned int iSeed = ifarg(7)?(unsigned int)*getarg(7):INT_MAX-109754;

  //init array of cells/neighbors to check
  int* pCheck = (int*)malloc(sizeof(int)*iCells);
  if(!pCheck){
    printf("GetPathEV ERRG: out of memory!\n");
    FreeListVec(&pList);
    return 0.0;
  }

  int iCheckSz = 0, idx = 0, iDist = 1 , youID = 0, youKidID=0, iTmpSz = 0, jdx = 0;

  double  dgzt = 0.0; 
  int* pTmp = 0;
  double* pUse = 0; 
  
  if(dSubsamp<1.0){ //if using only a fraction of the cells
     pUse = (double*)malloc(iCells*sizeof(double));
     mcell_ran4(&iSeed, pUse, iCells, 1.0);
  }

  pTmp = (int*)calloc(iCells,sizeof(int)); 

  if( verbose > 0 ) printf("searching from id: ");

  int* pVDTmp = (int*)calloc(iCells,sizeof(int)) , myID;

  for(myID=0;myID<iCells;myID++){

    if(!pStart[myID]) continue;

    if(verbose > 0 && myID%1000==0)printf("%d ",myID); 

    //only use dSubSamp fraction of cells, skip rest
    if(pUse && pUse[myID]>=dSubsamp) continue;

    unsigned long int iSelfLoopDist = LONG_MAX;
    int bFindThisSelfLoop = bSelfLoop && pEnd[myID]; // search for self loop for this vertex?

    iCheckSz = 0; idx = 0; iDist = 1; youID = 0; youKidID = 0;

    pVDTmp[myID]=1;

    //mark neighbors of distance == 1
    for(idx=0;idx<pLen[myID];idx++){
      youID = pLV[myID][idx];
      if(bFindThisSelfLoop && youID==myID && iDist<iSelfLoopDist) iSelfLoopDist = iDist; //found a self-loop? 
      if(!pVDTmp[youID]){
        pVDTmp[youID]=iDist;
        pCheck[iCheckSz++]=youID;
      }
    }

    iTmpSz = 0;  jdx=0;

    iDist++;
  
    //this does a breadth-first search but avoids recursion
    while(iCheckSz>0){
      iTmpSz = 0;
      for(idx=0;idx<iCheckSz;idx++){
        youID=pCheck[idx];
        for(jdx=0;jdx<pLen[youID];jdx++){
          youKidID=pLV[youID][jdx];
          if(bFindThisSelfLoop && youKidID==myID && iDist<iSelfLoopDist) iSelfLoopDist = iDist; //found a self-loop? 
          if(!pVDTmp[youKidID]){ //found a new connection
            pTmp[iTmpSz++] = youKidID; //save id of cell to search it's kids on next iteration
            pVDTmp[youKidID]=iDist;
          }
        }
      }
      iCheckSz = iTmpSz;
      if(iCheckSz) memcpy(pCheck,pTmp,sizeof(int)*iCheckSz);
      iDist++;
    }

    if(bFindThisSelfLoop && iSelfLoopDist<LONG_MAX){//if checking for this vertex's self-loop dist. and found a self-loop
      pVDTmp[myID] = iSelfLoopDist;
    } else {
      pVDTmp[myID]=0; // distance to self == 0.0
    }
    pVD[myID] = 0.0;
    int N = 0; //take average path length (+ self-loop length if needed) from myID to pEnd cells
    for(idx=0;idx<iCells;idx++){
      if(pEnd[idx] && pVDTmp[idx]){
        pVD[myID] += pVDTmp[idx];
        N++;
      }
    }

    if(N) pVD[myID] /= (double) N; // save mean path (and maybe self-loop) length for given cell

    memset(pVDTmp,0,sizeof(int)*iCells);
  }
  
  free(pTmp);
  if(pUse) free(pUse); 
  free(pCheck);
  FreeListVec(&pList);  
  free(pVDTmp);

  if( verbose > 0 ) printf("\n");

  return 1.0;
  ENDVERBATIM
}

:* usage GetLoopLength(adjlist,outvec,loopids,thruids[,subsamp,seed])
: computes distance to loop back to each node
: adjlist == list of vectors specifying connectivity - adjacency list : from row -> to entry in column
: outvec == vector of distances
: loopids == binary vector of ids of cells to start/end search from/to
: thruids == binary vector of ids of cells thru which loop can pass
: subsamp == perform calculation on ratio of cells btwn 0-1, default == 1
: seed == random # seed when using subsampling
FUNCTION GetLoopLength () {
  VERBATIM
  ListVec* pList = AllocListVec(*hoc_objgetarg(1));
  if(!pList){
    printf("GetLoopLength ERRA: problem initializing first arg!\n");
    return 0.0;
  }
 
  int iCells = pList->isz; 
  if(iCells < 2){
    printf("GetLoopLength ERRB: size of List < 2 !\n");
    FreeListVec(&pList);
    return 0.0;
  }

  double** pLV = pList->pv;
  int* pLen = pList->plen;

  //init vector of avg distances to each cell , 0 == no path found
  double* pVD; 
  int iVecSz = vector_arg_px(2,&pVD) , i = 0;
  if(!pVD || iVecSz < iCells){
    printf("GetLoopLength ERRE: arg 2 must be a Vector with size %d\n",iCells);
    FreeListVec(&pList);
    return 0.0;
  }  
  memset(pVD,0,sizeof(double)*iVecSz);//init to 0

  double* pLoop,  // bin vec of ids to search from 
          *pThru;   // bin vec of ids to terminate search on

  if( vector_arg_px(3,&pLoop) < iCells || vector_arg_px(4,&pThru) < iCells){
    printf("GetLoopLength ERRF: arg 3,4 must be Vectors with size >= %d\n",iCells);
    FreeListVec(&pList);
    return 0.0;
  }
  double dSubsamp = ifarg(5)?*getarg(5):1.0;

  unsigned int iSeed = ifarg(6)?(unsigned int)*getarg(6):INT_MAX-109754;

  //init array of cells/neighbors to check
  int* pCheck = (int*)malloc(sizeof(int)*iCells);
  if(!pCheck){
    printf("GetLoopLength ERRG: out of memory!\n");
    FreeListVec(&pList);
    return 0.0;
  }

  int iCheckSz = 0, idx = 0, iDist = 1 , youID = 0, youKidID=0, iTmpSz = 0, jdx = 0;

  double  dgzt = 0.0; 
  int* pTmp = 0 , found = 0;
  double* pUse = 0; 
  
  if(dSubsamp<1.0){ //if using only a fraction of the cells
     pUse = (double*)malloc(iCells*sizeof(double));
     mcell_ran4(&iSeed, pUse, iCells, 1.0);
  }

  pTmp = (int*)calloc(iCells,sizeof(int)); 

  if( verbose > 0 ) printf("searching loops from id: ");

  int* pVDTmp = (int*)calloc(iCells,sizeof(int)) , myID;

  for(myID=0;myID<iCells;myID++){

    if(!pLoop[myID]) continue;

    if(verbose > 0 && myID%1000==0)printf("%d ",myID); 

    //only use dSubSamp fraction of cells, skip rest
    if(pUse && pUse[myID]>=dSubsamp) continue;

    iCheckSz = 0; idx = 0; iDist = 1; youID = 0; youKidID = 0; found = 0;

    pVDTmp[myID]=1;

    //mark neighbors of distance == 1
    for(idx=0;idx<pLen[myID];idx++){
      youID = pLV[myID][idx];
      if(youID==myID) {
        found = 1;
        pVD[myID]=iDist;
        iCheckSz=0;
        break;
      }
      if(pThru[youID] && !pVDTmp[youID]){
        pVDTmp[youID]=iDist;
        pCheck[iCheckSz++]=youID;
      }
    }

    iTmpSz = 0;  jdx=0;

    iDist++;
  
    //this does a breadth-first search but avoids recursion
    while(iCheckSz>0){
      iTmpSz = 0;
      for(idx=0;idx<iCheckSz;idx++){
        youID=pCheck[idx];
        for(jdx=0;jdx<pLen[youID];jdx++){
          youKidID=pLV[youID][jdx];
          if(youKidID==myID){
            pVD[myID]=iDist;
            found = 1;
            break;
          }
          if(pThru[youKidID] && !pVDTmp[youKidID]){ //found a new connection
            pTmp[iTmpSz++] = youKidID; //save id of cell to search it's kids on next iteration
            pVDTmp[youKidID]=iDist;
          }
        }
      }
      if(found) break;
      iCheckSz = iTmpSz;
      if(iCheckSz) memcpy(pCheck,pTmp,sizeof(int)*iCheckSz);
      iDist++;
    }
    memset(pVDTmp,0,sizeof(int)*iCells);
  }
  
  free(pTmp);
  if(pUse) free(pUse); 
  free(pCheck);
  FreeListVec(&pList);  
  free(pVDTmp);

  if( verbose > 0 ) printf("\n");

  return 1.0;
  ENDVERBATIM
}

:* usage GetPathEV(adjlist,outvec,myid,[startid,endid,maxdist])
: adjlist == list of vectors specifying connectivity - adjacency list : from row -> to entry in column
: outvec == vector of distances
: myid == id of cell to start search from
: startid == min id of cells search can terminate on or go through
: endid   == max  '    '   '  '   '  '  '  '  ' '  '  '  '  '  ' 
FUNCTION GetPathEV () {
  VERBATIM
  ListVec* pList = AllocListVec(*hoc_objgetarg(1));
  if(!pList){
    printf("GetPathEV ERRA: problem initializing first arg!\n");
    return 0.0;
  }
 
  int iCells = pList->isz; 
  if(iCells < 2){
    printf("GetPathEV ERRB: size of List < 2 !\n");
    FreeListVec(&pList);
    return 0.0;
  }

  double** pLV = pList->pv;
  int* pLen = pList->plen;

  //init vector of distances to each cell , 0 == no path found
  double* pVD; 
  int iVecSz = vector_arg_px(2,&pVD) , i = 0;
  if(!pVD || iVecSz < iCells){
    printf("GetPathEV ERRE: arg 2 must be a Vector with size %d\n",iCells);
    FreeListVec(&pList);
    return 0.0;
  }  
  memset(pVD,0,sizeof(double)*iVecSz);//init to 0

  //get id of cell to find paths from
  int myID = (int) *getarg(3);
  if(myID < 0 || myID >= iCells){
    printf("GetPathEV ERRF: invalid id = %d\n",myID);
    FreeListVec(&pList);
    return 0.0;
  }

  //start/end id of cells to find path to
  int iStartID = ifarg(4) ? (int)*getarg(4) : 0,
      iEndID = ifarg(5) ? (int)*getarg(5) : iCells - 1,
      iMaxDist = ifarg(6)? (int)*getarg(6): -1;

  if(iStartID < 0 || iStartID >= iCells ||
     iEndID < 0 || iEndID >= iCells ||
     iStartID >= iEndID){
       printf("GetPathEV ERRH: invalid ids start=%d end=%d numcells=%d\n",iStartID,iEndID,iCells);
       FreeListVec(&pList);
       return 0.0;
     }

  //check max distance
  if(iMaxDist==0){
    printf("GetPathEV ERRI: invalid maxdist=%d\n",iMaxDist);
    FreeListVec(&pList);
    return 0.0;
  }

  //init array of cells/neighbors to check
  int* pCheck = (int*)malloc(sizeof(int)*iCells);
  if(!pCheck){
    printf("GetPathEV ERRG: out of memory!\n");
    FreeListVec(&pList);
    return 0.0;
  }
  int iCheckSz = 0, idx = 0, iDist = 1 , youID = 0, youKidID=0;

  pVD[myID]=1;

  //mark neighbors of distance == 1
  for(idx=0;idx<pLen[myID];idx++){
    youID = pLV[myID][idx];
    if(youID>=iStartID && youID<=iEndID && !pVD[youID]){
      pVD[youID]=(double)iDist;
      pCheck[iCheckSz++]=youID;
    }
  }

  int* pTmp = (int*)malloc(sizeof(int)*iCells);
  int iTmpSz = 0 , jdx=0;

  iDist++;
  
  //this does a breadth-first search but avoids deep nesting of recursive version
  while(iCheckSz>0 && (iMaxDist==-1 || iDist<=iMaxDist)){
    iTmpSz = 0;
    for(idx=0;idx<iCheckSz;idx++){
      youID=pCheck[idx];
      for(jdx=0;jdx<pLen[youID];jdx++){
        youKidID=pLV[youID][jdx];
        if(youKidID >= iStartID && youKidID <=iEndID && !pVD[youKidID]){ //found a new connection
          pTmp[iTmpSz++] = youKidID; //save id of cell to search it's kids on next iteration
          pVD[youKidID]=(double)iDist;
        }
      }
    }
    iCheckSz = iTmpSz;
    if(iCheckSz) memcpy(pCheck,pTmp,sizeof(int)*iCheckSz);
    iDist++;
  }

  pVD[myID]=0.0;
 
  free(pCheck);
  free(pTmp);
  FreeListVec(&pList);

  return 1.0;
  ENDVERBATIM
}

:* FUNCTION Factorial()
FUNCTION Factorial () {
  VERBATIM
  double N = (int)*getarg(1) , i = 0.0;
  double val = 1.0;
  if(N<=1) return 1.0;
  if(N>=171){
    double PI=3.1415926535897932384626433832795;
    double E=2.71828183;
    val=sqrt(2*PI*N)*(pow(N,N)/pow(E,N));
  } else {
    for(i=2.0;i<=N;i++) val*=i;
  }
  return (double) val;  
  ENDVERBATIM
}

:* FUNCTION perm()
:count # of permutations from set of N elements with R selections
FUNCTION perm () {
  VERBATIM
  if(ifarg(3)){
    double N = (int)*getarg(1);
    double R = (int)*getarg(2);
    double b = *getarg(3);
    double val = N/b;
    int i = 0;
    for(i=1;i<R;i++){
      N--;
      val*=(N/b);
    }
    return val;
  } else {
    int N = (int)*getarg(1);
    int R = (int)*getarg(2);
    int val = N;
    int i = 0;
    for(i=1;i<R;i++){
      N--;
      val*=N;
    }
    return (double)val;
  }
  ENDVERBATIM
}

:* install_intfsw
PROCEDURE install () {
 if(INSTALLED==1){
   printf("Already installed $Id: intfsw.mod,v 1.50 2009/02/26 18:24:34 samn Exp $ \n")
 } else {
 INSTALLED=1
 VERBATIM
 install_vector_method("gzmean" ,gzmean);
 install_vector_method("nnmean" ,nnmean);
 install_vector_method("copynz" ,copynz);
 ENDVERBATIM
 printf("Installed $Id: intfsw.mod,v 1.50 2009/02/26 18:24:34 samn Exp $ \n")
 }
}

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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