My current research projects are focused on the analysis of biological rhythms, model estimation algorithms, qualitative reasoning for continuous-time dynamical systems, the utilization of dynamical systems theory to analyze and reduce complex neuroscience models, and software for neuroinformatics. This work is supported by an NSF grant from the Emerging Models and Technologies program of the Division of Computer and Communication Foundations. The title is "A Computational Framework for Inferring Self-Regulatory Properties from High-Dimensional Dynamic Models of Biological Systems".
Introductions to some of these topic areas at the following links to Wikipedia and Scholarpedia: computational neuroscience, neuroinformatics, phase response curves (general oscillators), phase response curves (neural dynamics) and neuronal parameter optimization.
I co-organized a minisymposium on "Multi-level Modeling of Dynamical Systems" at the SIAM Dynamical Systems 2011 meeting in Snowbird, UT, featuring Yannis Kevrekidis, Steve Cox, and Alona Ben-Tal.
I received two internal grants (URSA Research Initiation Grant and Brains & Behavior Seed Grant) to support research initiation in 2008, my first year at Georgia State. In 2011 I received an URSA RIG as co-PI with Drs. Iman Chahine and Mark Grinshpon, and a B&B Seed Grant as co-PI with Drs. Brad Cooke in the NI and Steve Potter at Georgia Tech.
I am the primary developer for the PyDSTool dynamical systems software package, which implements various ideas being developed in my research through the Python language. This software is open-source freeware, is actively maintained, and is available at Sourceforge. Here are the slides from a recent presentation I gave at Georgia Tech about scientific computing with Python and PyDSTool. I also belong to the Neural Ensemble online community, which focuses on python software tools for neuroscience.
I run the Spineless Neural Systems forum that meets regularly to share research ideas and skills across the Atlanta metro region.
I collaborate with Don Edwards, with whom I co-mentor two PhD students: Bryce Chung and Jarod Collens.
I belong to the INCF Task Force for a Standard Language in Neural Network Modeling, working on the NineML markup language. (INCF stands for International Neuroinformatics Coordinating Facility). Related resources in this vein are the NeuroML markup language, the BioModels SED-ML markup language. The ModelDB database at Yale is a good repository for neural models. Correspondingly, NeuronDB and NeuronBank at GSU are good repositories for neural data.
I compiled and edit the Guide to good practice for research in experimentally data-driven computational modeling and simulation.
I wrote and maintain a handy little XPP-Matlab interface between Bard Ermentrout's XPP-AUT software and Matlab. This simple code makes batch-running from external scripts very easy!
I contribute to the SoftWare Interest Group at Georgia State, and have helped Gennady Cymbalyuk organize recent local workshops on the Dynamics of Bursting Activity.
I have an open PhD position to work in the area of mathematical neuroscience and computational modeling. Applications should be made either through the Math and Stats Department or the Neuroscience Institute, depending on the applicant's background. Contact me for further details, attaching a copy of your resume and information about your interests.
Undergraduates interested in learning about neural computation may also wish to spend a semester rotating in my computational lab, working on a variety of data analysis, numerical analysis, and dynamical systems related projects using the Python programming language. I share the lab with Dr. Andrey Shilnikov, where we have several undergraduates and graduate students working with us on collaborative projects.
Ron Calabrese and Rob Butera gave interesting Long View seminars at GSU in 2008.
This Topics In Neuroscience graduate class is not a remedial math class for bioscientists. It is intended to lower the barrier for bio-science students to effectively communicate with mathematically-oriented researchers in the field. The course is based on discussions around journal articles and book chapters on "big picture" topics such as small world networks, evolutionary stable strategies, pattern formation, and others.
I received GSU STEM Faculty Fellowship awards in the Summers of 2009 and 2010 to develop materials for a more science-focused version of the standard Calculus I class that we offer. This class is expected to be offered specially for science majors in Spring 2012.
Development of the calculus curriculum has continued with a 2011 Research Initiation Grant with Drs. Iman Chahine of the College of Education, and Dr. Mark Grinshpon in the department of Math and Stats.
Fall 2009. Details on this course can be found here.
A useful tool in learning the basics of computer arithmetic is this python module, which simulates binary floating point representation to IEEE 754 standards of arbitrary fixed precision, or to infinite precision.
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