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Lee DeVille

Associate Professor, Mathematics
University of Illinois
344 B Illini Hall M/C 382
Urbana, IL  61801
rdeville@illinois.edu

Biographical Information

Professional Preparation

• Tulane University, B. S. in Mathematics, May 1996
• Boston University, M. A. in Mathematics, May 2001
• Boston University, Ph. D. in Mathematics, May 2001
• Rensselaer Polytechnic Institute, VIGRE Postdoctoral Research Associate, 2001 – 2004
• Courant Institute of Mathematical Sciences, Associate Research Scientist, 2004 – 2005
• Courant Institute of Mathematical Sciences, Courant Instructor, 2005 – 2007

Appointments

• July 2013 – present. Associate Professor, Department of Mathematics, University of Illinois
at Urbana-Champaign.
• August 2007 – June 2013. Assistant Professor, Department of Mathematics, University of
Illinois at Urbana-Champaign.
• August 2009 – present. Affiliate faculty, Institute for Genomic Biology, University of Illinois at Urbana-Champaign.                                                                                                                                                          • August 2010 – present. Affiliate faculty, Neuroscience Program, University of Illinois at Urbana-Champaign.                                                    

Research

Prof. DeVille is a mathematician whose research focus lies in the intersection of probability theory, stochastic processes, and dynamical systems. He is particularly interested in applications of these theories to various problems in the physical and life sciences. His most recent work has focused on nonlinear dynamical systems defined on networks with a view towards characterizing stable or metastable dynamics on these networks, but Prof. DeVille has also considered a variety of applications in the life sciences, including neuroscience and biophysics.

Selected Publications

Stability/metastability on networks

Spectral Theory for Dynamics on Graphs containing Attractive and Repulsive Interactions, with Jared Bronski, submitted to SIAM Journal of Applied Mathematics, March 2013.

Fully Synchronous Solutions and the Synchronization Phase Transition for the Finite N Kuramoto Model, with Jared Bronski and Moon Jip Park, Chaos, 22, 033133 (2012). DOI:10.1063/1.4745197 (17 pages).

Transitions amongst synchronous solutions in the stochastic Kuramoto model, Nonlinearity, 25 (2012) 1473-1494. DOI:10.1088/0951-7715/25/5/1473 4. Analysis of Power System Dynamics Subject to Stochastic Power Injections , with Sairaj Dhople and Alejandro Domínguez-García, IEEE Transactions on Circuits and Systems, accepted April 2013.

Dynamics on networks I. Modular continuous-time systems, with Eugene Lerman, Journal of the European Mathematical Society, accepted 2013.

Neuroscience

Universal critical dynamics in high resolution neuronal avalanche data, with Nir Friedman, Shinya Ito, Braden Brinkman, Nori Shimono, Karin A. Dahmen, John M. Beggs, and Thomas C. Butler, Physical Review Letters, accepted Mar 20 2012. DOI:10.1103/PhysRevLett.108.208102

Synchrony and asynchrony for neuronal dynamics defined on complex networks, with Charles S. Peskin, Bulletin of Mathematical Biology, DOI:10.1007/s11538-011-9674-0.

Synchrony and asynchrony in a fully stochastic neural network, with Charles S. Peskin, Bulletin of Mathematical Biology, 70 (6), 1608--1633, August 2008.

Dynamics of stochastic neuronal networks and the connections to random graph theory, with Charles S. Peskin and Joel H. Spencer, Mathematical Modeling of Natural Phenomena 5 (2010), no. 2, 26–66.  DOI:10.1051/mmnp/20105202

Biophysics and biochemistry

Regular gaits and optimal velocities for motor proteins, with Eric Vanden-Eijnden, Biophysical Journal, 95 (6), 2681--2691, September 2008.

Regularity and synchrony in motor proteins. Bulletin of Mathematical Biology, 70 (2):484--516, 2008. (with Eric Vanden-Eijnden)

Two distinct mechanisms of coherence in randomly perturbed dynamical systems. Physical Review E, 72, 031105 (2005) (10 pages). (with Cyrill Muratov and Eric Vanden-Eijnden)

Self-induced stochastic resonance for Brownian ratchets under load.  Communications in Mathematical Sciences, 5 (2): 431--446 2007. (with Eric Vanden-Eijnden)