popular math

 

 

Software

A model of the VS network of the blowfly

James Trousdale and Sam Carroll developed some code that we obtained from Alexander Borst and Yishai Elyada.  You can find the code along with instructions on how to use it here.


Neuronal network simulations and linear response approximation to the resulting cross-correlations

This folder contains the code to simulate a network of EIF neurons.  It also includes code that computes the linear response kernels for the cells in the network.  The correlations between the cells in the network are computed both from simulations, and approximated using the linear response properties.  Instructions are provided here, and a full description of the problem and the methos can be found in this paper. 

Generation of spatio-temporally correlated spike trains

This code allows for the generation of spike trains with predefined temporal cross-correlation functions.  It accompanies this paper

Stochastic Integrate-and-Fire Neurons

An implementatioin of the finite volume method for the solution of the
Fokker-Planck equation described in the article with F. Marpeau and A. Barua
is available at SourceForge.

We have also extended the code to model two, potentially coupled neurons. The code is avalable here, and the accompanying documentation can be found here.

Imaging of ripples in neural tissue

Matlab code for the spatiotemporal patterns obtained using voltage sensitive dyes is available here . Documentation is available here.

Nonautonomous Differential Equations

You can find animations and Mathematica files that accompany my article with Robert Rosenbaum on nonautomous differential equations here.


Dynamics in One Complex Variable

Yakov Shapiro has written a java applet that illustrates the results in our paper on singularly perturbed quadratic maps. The applet can be found here.

The following is a program that Yakov Shapiro has developed while working with me in the summer of 2001. We were interested in studying the bifurcations of the reversible, area preserving complex Henon Map. The program is in principle able to parse all quadratic polynomial maps in C^2. You can download the .txt files for information on how to install and use the program.

The program StCurve.exe will draw the intersection of the stable manifold of the saddle point of the Henon Map with a plane that can be specified by the user.

This program will unfortunately only run on a PC.


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Current Address: Department of Mathematics, PGH Building, University of Houston, Houston, Texas 77204-3008
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Image designed by Graham Johnson, Graham Johnson Medical Media, Boulder, Colorado