Started using the online collaborative LaTeX editor sharelatex.com. Tried a number of other ones, and this one seems about the best. Really like the history feature, but for me, one of the best features is dropbox integration so I can edit on my own machines with emacs. 

Time Series Analysis of Simulated fMRI Signals - 2010

A wavelet decomposition allows us to decompose a set of signals into different detail levels. Each detail level encompasses a unique range of amplitudes and frequencies of the original signal. This type of decomposition is may provide considerable insight when applied in the analysis of neural signals which are composed of numerous overlapping and most likely interacting signals.

This paper deals with a simulated data set: a set of 47 time series. The simulation is intended to model the BOLD signal obtained from an fMRI. It is suspected that this simulation might exhibit similar overlapping signals to a real fMRI signal. Although a set of real signals do exist, the data set is very large, and will not be analyzed here. 

Time Series Analysis of Simulated fMRI Signals

Stochastic Bi-Stability Analysis - 2010

A stochastic bistable system is simulated and analyzed. A master equation and Gillespie's algorithm are derived, and the system is simulated using Gillespie's algorithm and the resulting probability distributions are compared to the deterministic solutions.

Stochastic Bi-Stability Analysis

Hopfield and Potts-Hopfield Networks - 2010

In this article, I follow the standard derivation of free energy for such a network. Next, I in- troduce my extension, the “Potts-Hopfield” network, which I argue behaves more like a biological system than the original Hopfield network. I next discuss the details of the program I wrote to test and evaluate both networks, mine and Hopfield’s, trained on and matching a variety of patterns. Finally, I display and discuss the results of various experiments with both networks.

Hopfield and Potts-Hopfield Networks

Numerical Investigation Of A Central Pattern Generator Network - 2009

Dynamical systems theory can help in understanding biological nervous systems and in designing artificial ones. Dynamical systems theory deals with the long-term qualitative behavior of dynamical systems. Its the focus is not necessarily on finding precise solutions, but rather on analyzing what types of behaviors a dynamical system will produce based on a set of parameters. A central pattern generator (CPG) is one of the simplest examples of a neural circuit that is useful in and of itself and can be studied in isolation. The goal of this paper is to examine a single isolated central pattern generator model based on that of a lamprey originally investigated by James Buchanan  and analyze what range range of parameters produce what kinds of behavior.

Numerical Investigation Of A Central Pattern Generator Network