Increased computational accuracy in multi-compartmental cable models (Lindsay et al. 2005)

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Accession:129149
Compartmental models of dendrites are the most widely used tool for investigating their electrical behaviour. Traditional models assign a single potential to a compartment. This potential is associated with the membrane potential at the centre of the segment represented by the compartment. All input to that segment, independent of its location on the segment, is assumed to act at the centre of the segment with the potential of the compartment. By contrast, the compartmental model introduced in this article assigns a potential to each end of a segment, and takes into account the location of input to a segment on the model solution by partitioning the effect of this input between the axial currents at the proximal and distal boundaries of segments. For a given neuron, the new and traditional approaches to compartmental modelling use the same number of locations at which the membrane potential is to be determined, and lead to ordinary differential equations that are structurally identical. However, the solution achieved by the new approach gives an order of magnitude better accuracy and precision than that achieved by the latter in the presence of point process input.
Reference:
1 . Lindsay AE, Lindsay KA, Rosenberg JR (2005) Increased computational accuracy in multi-compartmental cable models by a novel approach for precise point process localization. J Comput Neurosci 19:21-38 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell;
Brain Region(s)/Organism:
Cell Type(s):
Channel(s): I Na,t; I K;
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: NEURON; C or C++ program;
Model Concept(s): Methods;
Implementer(s):
Search NeuronDB for information about:  I Na,t; I K;
/
LindsayEtAl2005
readme.txt
03-192.pdf
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BitsAndPieces.c
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ExactSolution.dat
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GenCom.c
GenCom1.c
GenCom2.c
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GenerateInput.c
GenerateInputText.c
GenRan.ran
GetNodeNumbers.c
Info100.dat
Info20.dat
Info200.dat
Info30.dat
Info300.dat
Info40.dat
Info400.dat
Info50.dat
Info500.dat
Info60.dat
Info70.dat
Info80.dat
Info90.dat
InputCurrents.dat
InputDendrite.dat
JaySpikeTrain.c
JayTest1.dat
JayTest100.dat
KenSpikeTrain.c
KenTest1.dat *
KenTest10.dat
KenTest100.dat *
KenTest10p.dat
KenTest1p.dat *
KenTest2.dat
KenTest2p.dat
KenTest3.dat
KenTest3p.dat
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KenTest7.dat
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LU.c
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Mean500.dat
mosinit.hoc
NC.pdf
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NC1.tex
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NC3.tex
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NC6.tex
NCFig2.eps *
NCFig3.eps *
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NCFig5a.eps *
NCFig5b.eps *
NCFig6.eps *
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NeuronDriver.hoc
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NewComp3.tex
NewComp4.tex
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NewComp6.tex
NewCompFig1.eps
NewCompFig2.eps *
NewCompFig3.eps *
NewCompFig4.eps *
NewCompFig5a.eps *
NewCompFig5b.eps *
NewCompFig6.eps *
NewCompPics.tex
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out.res
principles_01.tex
rand
Ratio.dat
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ReviewOfSpines.pdf
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TestCell4.d3
testcellnew2.hoc
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[Squeakfoundation]Unrandom Random (was Two fixes I would like!)
Ken G. Brown squeakfoundation@lists.squeakfoundation.org
Wed, 4 Dec 2002 13:27:09 -0700

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An associate of mine has previously run into problems with utilizing underlying platform random number generation for encryption and
security and had come across a site that plotted noise spheres for various RNG's. Unfortunately, the site is no longer accessible.
He ended up going with the attached 'C' code for RNG, for use in the algorithms.
When asked for a pointer to the www site, he said:

> The site in question is no longer up. What it did was plot the "noise
> sphere" of the output of numerous RNG's from different OS's to give a
> measure of how good any encryption would be. Noise spheres of higher
> dimensions are used to rate high-order correlations between samples in
> sequences. I would suggest doing a search on "noise sphere". (if I recall
> correctly, either the 'mathworks' site and/or the 'wolfram' (mathematica)
> site(s) have a good discussion on the use of "noise spheres".)
>
> The DDJ mag (Doctor Dobb's Journal) site also used to have a good discussion
> on the difficulty of artificially generated randomness as well.
>
> Windows 98/ME/NT4 did rate as among the poorest RNGs; Windows 2000 was much
> improved and Windows XP rates as equivalent to many UNIX's. In any case, the
> MAC (OS7 and later) and Linux (2.4 kernel) rated as among the best.
>
<snip>
>We ended up using a RNG we found in the 95-03 version of 'snippets'. I have
> included them here.

Perhaps this information may help with the RNG considerations.

Ken



> -----Original Message-----
> From: squeakfoundation-admin@lists.squeakfoundation.org
> [mailto:squeakfoundation-admin@lists.squeakfoundation.org]On Behalf Of
> Tim Rowledge
> Sent: December 3, 2002 4:28 PM
> To: squeakfoundation@lists.squeakfoundation.org
> Subject: Re: [Squeakfoundation]Two fixes I would like!
>
>
> John M McIntosh <johnmci@smalltalkconsulting.com> is claimed by the authorities to have written:
>
> > One of the issues is that on the mac the millisecond clock starts from
> > zero at application start time, so this code
>
> Possible simple improvement; add a prim to return a seed. Each platform
> can do whatever it can plausibly do (sounds like some OSs have some sort
> of facility for random) and returns a number. Is a SmallInt good enough
> or should we allow LPIs?
>
> If the prim fails then we fall back to the current case and nobody is
> any worse off.
>
> tim
> --
> Tim Rowledge, tim@sumeru.stanford.edu, http://sumeru.stanford.edu/tim
> Strange OpCodes: SDS: Sort of Do Something
>
> _______________________________________________
> Squeakfoundation mailing list
> Squeakfoundation@lists.squeakfoundation.org
> http://lists.squeakfoundation.org/listinfo/squeakfoundation

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/********************************************************************
          The McGill Super-Duper Random Number Generator
             G. Marsaglia, K. Ananthanarayana, N. Paul

    Incorporating the Ziggurat method of sampling from decreasing
              or symmetric unimodal density functions.
                      G. Marsaglia, W.W. Tsang

                 Rewritten into C by E. Schneider
 *********************************************************************/

static unsigned long mcgn, srgn;

#define MULT 69069L

void rstart (long i1, long i2)
{
      mcgn = (unsigned long)((i1 == 0L) ? 0L : i1 | 1L);
      srgn = (unsigned long)((i2 == 0L) ? 0L : (i2 & 0x7FFL) | 1L);
}

long uni(void)
{
      unsigned long r0, r1;

      r0 = (srgn >> 15);
      r1 = srgn ^ r0;
      r0 = (r1 << 17);
      srgn = r0 ^ r1;
      mcgn = MULT * mcgn;
      r1 = mcgn ^ srgn;
      return (r1 >> 1);
}

long vni(void)
{
      unsigned long r0, r1;

      r0 = (srgn >> 15);
      r1 = srgn ^ r0;
      r0 = (r1 << 17);
      srgn = r0 ^ r1;
      mcgn = MULT * mcgn;
      r1 = mcgn ^ srgn;
      return r1;
}

/*
"Anyone who consider arithmetic means of producing random number is,
 of course, in a state of sin" - John Von Neumann
*/

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/************************************************************************
 This random number generator originally appeared in "Toward a Universal
 Random Number Generator" by George Marsaglia and Arif Zaman.
 Florida State University Report: FSU-SCRI-87-50 (1987)

 It was later modified by F. James and published in "A Review of Pseudo-
 random Number Generators"

 Converted from FORTRAN to C by Phil Linttell, James F. Hickling
 Management Consultants Ltd, Aug. 14, 1989.

 THIS IS THE BEST KNOWN RANDOM NUMBER GENERATOR AVAILABLE.
       (However, a newly discovered technique can yield
         a period of 10^600. But that is still in the development stage.)

 It passes ALL of the tests for random number generators and has a period
   of 2^144, is completely portable (gives bit identical results on all
   machines with at least 24-bit mantissas in the floating point
   representation).

 The algorithm is a combination of a Fibonacci sequence (with lags of 97
   and 33, and operation "subtraction plus one, modulo one") and an
   "arithmetic sequence" (using subtraction).

 On a Vax 11/780, this random number generator can produce a number in
    13 microseconds.
************************************************************************/

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>

#define TRUE    1
#define FALSE   0

float u[97], c, cd, cm;
int i97, j97, test;

int rmarin(int ij, int kl);
int ranmar(float rvec[], int len);


int main()
{

        float temp[100];
        int i;
        int ij, kl, len;

        /*These are the seeds needed to produce the test case results*/

        ij = 1802;
        kl = 9373;

        /*Do the initialization*/

        if (1 == rmarin(ij,kl))
                return 1;

        /*Generate 20000 random numbers*/

        len = 100;
        for ( i=0; i<=199 ; i++)
                if (1 == ranmar(temp, len))
                        return 1;

        /*If the random number generator is working properly,
          the next six random numbers should be:

            6533892.0  14220222.0   7275067.0
            6172232.0   8354498.0  10633180.0
        */

        len = 6;
        if (1 == ranmar(temp, len))
                return 1;

        for ( i=0; i<=5; i++)
                printf("%12.1f\n",4096.0*4096.0*temp[i]);

        return 0;
}


/************************************************************************
 This is the initialization routine for the random number generator RANMAR()
 NOTE: The seed variables can have values between:    0 <= IJ <= 31328
                                                      0 <= KL <= 30081
 The random number sequences created by these two seeds are of sufficient
 length to complete an entire calculation with. For example, if several
 different groups are working on different parts of the same calculation,
 each group could be assigned its own IJ seed. This would leave each group
 with 30000 choices for the second seed. That is to say, this random
 number generator can create 900 million different subsequences -- with
 each subsequence having a length of approximately 10^30.

 Use IJ = 1802 & KL = 9373 to test the random number generator. The
 subroutine RANMAR should be used to generate 20000 random numbers.
 Then display the next six random numbers generated multiplied by 4096*4096
 If the random number generator is working properly, the random numbers
 should be:
           6533892.0  14220222.0   7275067.0
           6172232.0   8354498.0  10633180.0
************************************************************************/

int rmarin(int ij, int kl)
{

        float s, t;
        int i, j, k, l, m;
        int ii, jj;

        /* Change FALSE to TRUE in the next statement to test the
           random routine.*/

        test = TRUE;

        if ( ( ij < 0 || ij > 31328 ) ||
                ( kl < 0 || kl > 30081 ) )
        {
                printf ("RMARIN: The first random number seed must have a "
                        "value between 0 and 31328\n");
                printf ("        The second random number seed must have a "
                        "value between 0 and 30081");
                return 1;
        }

        i = (int)fmod(ij/177.0, 177.0) + 2;
        j = (int)fmod(ij      , 177.0) + 2;
        k = (int)fmod(kl/169.0, 178.0) + 1;
        l = (int)fmod(kl      , 169.0);

        for ( ii=0; ii<=96; ii++ )
        {
                s = (float)0.0;
                t = (float)0.5;
                for ( jj=0; jj<=23; jj++ )
                {
                        m = (int)fmod( fmod(i*j,179.0)*k , 179.0 );
                        i = j;
                        j = k;
                        k = m;
                        l = (int)fmod( 53.0*l+1.0 , 169.0 );
                        if ( fmod(l*m,64.0) >= 32)
                                s = s + t;
                        t = (float)(0.5 * t);
                }
                u[ii] = s;
        }

        c  = (float)(  362436.0 / 16777216.0);
        cd = (float)( 7654321.0 / 16777216.0);
        cm = (float)(16777213.0 / 16777216.0);

        i97 = 96;
        j97 = 32;

        test = TRUE;

        return 0;
}

int ranmar(float rvec[], int len)
{
        float uni;
        int ivec;

        if ( !test )
        {
                printf ("RANMAR: Call the initialization routine (RMARIN) "
                        "before calling RANMAR.\n");
                return 1;
        }

        for ( ivec=0; ivec < len; ivec++)
        {
                uni = u[i97] - u[j97];
                if ( uni < 0.0F )
                        uni = uni + 1.0;
                u[i97] = uni;
                i97--;
                if ( i97 < 0 )
                        i97 = 96;
                j97--;
                if ( j97 < 0 )
                        j97 = 96;
                c = c - cd;
                if ( c < 0.0F )
                        c = c + cm;
                uni = uni - c;
                if ( uni < 0.0F )
                        uni = uni + 1.0;
                rvec[ivec] = uni;
        }
        return 0;
}

/* I use the following procedure in TC to generate seeds:

  The sow() procedure calculates two seeds for use with the random number
  generator from the system clock.  I decided how to do this myself, and
  I am sure that there must be better ways to select seeds; hopefully,
  however, this is good enough.  The first seed is calculated from the values
  for second, minute, hour, and year-day; weighted with the second most
  significant and year-day least significant.  The second seed weights the
  values in reverse.
*/

void sow( seed1, seed2 )
int *seed1, *seed2;
{
        struct tm *tm_now;
        float s_sig, s_insig, maxs_sig, maxs_insig;
        long secs_now;
        int s, m, h, d, s1, s2;

        time(&secs_now);
        tm_now = localtime(&secs_now);

        s = tm_now->tm_sec + 1;
        m = tm_now->tm_min + 1;
        h = tm_now->tm_hour + 1;
        d = tm_now->tm_yday + 1;

        maxs_sig   = (float)(60.0 + 60.0/60.0 + 24.0/60.0/60.0 +
              366.0/24.0/60.0/60.0);
        maxs_insig = (float)(60.0 + 60.0*60.0 + 24.0*60.0*60.0 +
              366.0*24.0*60.0*60.0);

        s_sig      = (float)(s + m/60.0 + h/60.0/60.0 + d/24.0/60.0/60.0);
        s_insig    = (float)(s + m*60.0 + h*60.0*60.0 + d*24.0*60.0*60.0);

        s1 = (int)(s_sig   / maxs_sig   * 31328.0);
        s2 = (int)(s_insig / maxs_insig * 30081.0);

        *seed1 = s1;
        *seed2 = s2;
}

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