Hotspots of dendritic spine turnover facilitates new spines and NN sparsity (Frank et al 2018)

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Model for the following publication: Adam C. Frank, Shan Huang, Miou Zhou, Amos Gdalyahu, George Kastellakis, Panayiota Poirazi, Tawnie K. Silva, Ximiao Wen, Joshua T. Trachtenberg, and Alcino J. Silva Hotspots of Dendritic Spine Turnover Facilitate Learning-related Clustered Spine Addition and Network Sparsity
1 . Frank AC, Huang S, Zhou M, Gdalyahu A, Kastellakis G, Silva TK, Lu E, Wen X, Poirazi P, Trachtenberg JT, Silva AJ (2018) Hotspots of dendritic spine turnover facilitate clustered spine addition and learning and memory. Nat Commun 9:422 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell; Connectionist Network;
Brain Region(s)/Organism:
Cell Type(s): Abstract integrate-and-fire leaky neuron with dendritic subunits;
Gap Junctions:
Receptor(s): NMDA;
Simulation Environment: C or C++ program; MATLAB;
Model Concept(s): Active Dendrites; Synaptic Plasticity;
Implementer(s): Kastellakis, George [gkastel at];
Search NeuronDB for information about:  NMDA;
function [N,X,sp] = histogram(varargin)
% HISTOGRAM generates a histogram using the "optimal" number of bins
% If called with no output argument, histogram plots into the current axes
% SYNOPSIS [N,X,sp] = histogram(data,factor,normalize)
%          [...] = histogram(data,'smooth')
%          [...] = histogram(axesHandle,...)
% INPUT    data: vector of input data
%          factor: (opt) factor by which the bin-widths are multiplied
%                   if 'smooth' (or 's'), a smooth histogram will be formed.
%                   (requires the spline toolbox). For an alternative
%                   approach to a smooth histogram, see ksdensity.m
%                   if 'discrete' (or 'd'), the data is assumed to be a discrete
%                   collection of values. Note that if every data point is,
%                   on average, repeated at least 3 times, histogram will
%                   consider it a discrete distribution automatically.
%                   if 'continuous' (or 'c'), histogram is not automatically
%                   checking for discreteness.
%          normalize : if 1 (default), integral of histogram equals number
%                       data points. If 0, height of bins equals counts.
%                       This option is exclusive to non-"smooth" histograms
%          axesHandle: (opt) if given, histogram will be plotted into these
%                       axes, even if output arguments are requested
% OUTPUT   N   : number of points per bin (value of spline)
%          X   : center position of bins (sorted input data)
%          sp  : definition of the smooth spline
% REMARKS: The smooth histogram is formed by calculating the cumulative
%           histogram, fitting it with a smoothening spline and then taking
%           the analytical derivative. If the number of data points is
%           markedly above 1000, the spline is fitting the curve too
%           locally, so that the derivative can have huge peaks. Therefore,
%           only 1000-1999 points are used for estimation.
%           Note that the integral of the spline is almost exactly the
%           total number of data points. For a standard histogram, the sum
%           of the hights of the bins (but not their integral) equals the
%           total number of data points. Therefore, the counts might seem
%           off.
%           WARNING: If there are multiples of the minimum value, the
%           smooth histogram might get very steep at the beginning and
%           produce an unwanted peak. In such a case, remove the
%           multiple small values first (for example, using isApproxEqual)
% c: 2/05 jonas

% test input
if nargin < 1
    error('not enough input arguments for histogram')

% check for axes handle
if length(varargin{1}) == 1 && ishandle(varargin{1});
    axesHandle = varargin{1};
    varargin(1) = [];
    % ensure compatibility to when axesHandle was given as last input
    if nargin == 3 && ishandle(varargin{end}) && varargin{end} ~= 0
        axesHandle = varargin{end};
        varargin(end) = [];
        axesHandle = 0;

% assign data
numArgIn = length(varargin);
data = varargin{1};
data = data(:);

% check for non-finite data points
data(~isfinite(data)) = [];

% check for "factor"
if numArgIn < 2 || isempty(varargin{2})
    factor = 1;
    factor = varargin{2};
if ischar(factor)
    switch factor
        case {'smooth','s'}
        factor = -1;
        case {'discrete','d'}
            factor = -2;
        case {'continuous','c'}
            factor = -3;
        error('The only string inputs permitted for histogram.m are ''smooth'',''discrete'', or ''continuous''')
    % check for normalize, but do so only if there is no "smooth". Note
    % that numArgIn is not necessarily equal to nargin
    if numArgIn < 3 || isempty(varargin{3})
        normalize = true;
        normalize = varargin{3};

% doPlot is set to 1 for now. We change it to 0 below if necessary.
doPlot = 1;

nData = length(data);
% check whether we do a standard or a smooth histogram
if factor ~= -1
    % check for discrete distribution
    [xx,nn] = countEntries(data);
    % consider the distribution discrete if there are, on average, 3
    % entries per bin
    nBins = length(xx);
    if factor == -2 || (factor ~= -3 && nBins*3 < nData) 
        % discrete distribution. 
        nn = nn';
        xx = xx';
        % not a discrete distribution
        if nData < 20
            warning('HISTOGRAM:notEnoughDataPoints','Less than 20 data points!')
            nBins = ceil(nData/4);
            % create bins with the optimal bin width
            % W = 2*(IQD)*N^(-1/3)
            interQuartileDist = diff(prctile(data,[25,75]));
            binLength = 2*interQuartileDist*length(data)^(-1/3)*factor;
            % number of bins: divide data range by binLength
            nBins = round((max(data)-min(data))/binLength);
            if ~isfinite(nBins)
                nBins = length(unique(data));
        % histogram
        [nn,xx] = hist(data,nBins);
        % adjust the height of the histogram
        if normalize
            Z = trapz(xx,nn);
            nn = nn * nData/Z;
    if nargout > 0
        N = nn;
        X = xx;
        doPlot = axesHandle;
    if doPlot
        if axesHandle
    % make cdf, smooth with spline, then take the derivative of the spline
    % cdf
    xData = sort(data);
    yData = 1:nData;
    % when using too many data points, the spline fits very locally, and
    % the derivatives can still be huge. Good results can be obtained with
    % 500-1000 points. Use 1000 for now
    step = max(floor(nData/1000),1);
    xData2 = xData(1:step:end);
    yData2 = yData(1:step:end);
    % spline. Use strong smoothing
    cdfSpline = csaps(xData2,yData2,1./(1+mean(diff(xData2))^3/0.0006));
    % pdf is the derivative of the cdf
    pdfSpline = fnder(cdfSpline);
    % histogram
    if nargout > 0
        xDataU = unique(xData);
        N = fnval(pdfSpline,xDataU);
        X = xDataU;
        % adjust the height of the histogram
        Z = trapz(X,N);
        N = N * nData/Z;
        sp = pdfSpline;
        % set doPlot. If there is an axesHandle, we will plot
        doPlot = axesHandle;
    % check if we have to plot. If we assigned an output, there will only
    % be plotting if there is an axesHandle.
    if doPlot
        if axesHandle

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