Fronto-parietal visuospatial WM model with HH cells (Edin et al 2007)

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1) J Cogn Neurosci: 3 structural mechanisms that had been hypothesized to underlie vsWM development during childhood were evaluated by simulating the model and comparing results to fMRI. It was concluded that inter-regional synaptic connection strength cause vsWM development. 2) J Integr Neurosci: Given the importance of fronto-parietal connections, we tested whether connection asymmetry affected resistance to distraction. We drew the conclusion that stronger frontal connections are beneficial. By comparing model results to EEG, we concluded that the brain indeed has stronger frontal-to-parietal connections than vice versa.
1 . Edin F, Macoveanu J, Olesen P, Tegnér J, Klingberg T (2007) Stronger synaptic connectivity as a mechanism behind development of working memory-related brain activity during childhood. J Cogn Neurosci 19:750-60 [PubMed]
2 . Edin F, Klingberg T, Stödberg T, Tegnér J (2007) Fronto-parietal connection asymmetry regulates working memory distractibility. J Integr Neurosci 6:567-96 [PubMed]
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 U1 L2/6 pyramidal intratelencephalic GLU cell; Abstract Wang-Buzsaki neuron;
Gap Junctions: Gap junctions;
Simulation Environment: NEURON;
Model Concept(s): Working memory; Attractor Neural Network;
Search NeuronDB for information about:  Neocortex U1 L2/6 pyramidal intratelencephalic GLU cell;
function f = spm_Gpdf(x,h,l) 

% Probability Density Function (PDF) of Gamma distribution 

% FORMAT f = spm_Gpdf(g,h,l) 


% x - Gamma-variate   (Gamma has range [0,Inf) ) 

% h - Shape parameter (h>0) 

% l - Scale parameter (l>0) 

% f - PDF of Gamma-distribution with shape & scale parameters h & l 



% spm_Gpdf implements the Probability Density Function of the Gamma 

% distribution. 


% Definition: 


% The PDF of the Gamma distribution with shape parameter h and scale l 

% is defined for h>0 & l>0 and for x in [0,Inf) by: (See Evans et al., 

% Ch18, but note that this reference uses the alternative 

% parameterisation of the Gamma with scale parameter c=1/l) 


%           l^h * x^(h-1) exp(-lx) 

%    f(x) = --------------------- 

%                gamma(h) 


% Variate relationships: (Evans et al., Ch18 & Ch8) 


% For natural (strictly +ve integer) shape h this is an Erlang distribution. 


% The Standard Gamma distribution has a single parameter, the shape h. 

% The scale taken as l=1. 


% The Chi-squared distribution with v degrees of freedom is equivalent 

% to the Gamma distribution with scale parameter 1/2 and shape parameter v/2. 


% Algorithm: 


% Direct computation using logs to avoid roundoff errors. 


% References: 


% Evans M, Hastings N, Peacock B (1993) 

%       "Statistical Distributions" 

%        2nd Ed. Wiley, New York 


% Abramowitz M, Stegun IA , (1964) 

%       "Handbook of Mathematical Functions" 

%        US Government Printing Office 


% Press WH, Teukolsky SA, Vetterling AT, Flannery BP (1992) 

%       "Numerical Recipes in C" 

%        Cambridge 


% @(#)spm_Gpdf.m           2.2 Andrew Holmes 99/04/26 


%-Format arguments, note & check sizes 


if nargin<3, error('Insufficient arguments'), end 


ad = [ndims(x);ndims(h);ndims(l)]; 

rd = max(ad); 

as = [             [size(x),ones(1,rd-ad(1))];... 


                      [size(l),ones(1,rd-ad(3))]     ]; 

rs = max(as); 

xa = prod(as,2)>1; 

if sum(xa)>1 & any(any(diff(as(xa,:)),1)) 

                      error('non-scalar args must match in size'), end 




%-Initialise result to zeros 

f = zeros(rs); 

%-Only defined for strictly positive h & l. Return NaN if undefined. 

md = ( ones(size(x))  &  h>0  &  l>0 ); 

if any(~md(:)), f(~md) = NaN ; 

                      warning('Returning NaN for out of range arguments'), end 


%-Degenerate cases at x==0: h<1 => f=Inf; h==1 => f=l; h>1 => f=0 

ml = ( md  &  x==0  &  h<1 ); 
f(ml) = Inf; 
ml = ( md  &  x==0  &  h==1 ); if xa(3), mll=ml; else mll=1; end 
f(ml) = l(mll); 


%-Compute where defined and x>0 

Q  = find( md  &  x>0 ); 

if isempty(Q), return, end 
if xa(1), Qx=Q; else Qx=1; end 
if xa(2), Qh=Q; else Qh=1; end 
if xa(3), Ql=Q; else Ql=1; end 



f(Q) = exp( (h(Qh)-1).*log(x(Qx)) +h(Qh).*log(l(Ql)) - l(Ql).*x(Qx)... 
                                           -gammaln(h(Qh)) );


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