- Spectral Theory for Dynamics on Graphs containing Attractive and Repulsive Interactions, with Jared Bronski, submitted to SIAM Journal of Applied Mathematics, March 2013.
- Dynamics on Networks of Manifolds, with Eugene Lerman, submitted to Forum of Mathematics - Pi, February 2013.
- A Stochastic Hybrid Systems Framework for Analyzing Markov Reward Models, with Sairaj Dhople and Alejandro Domínguez-García, submitted to Performance Evaluation, October 2012.
Publications, accepted or in print
- 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, submitted
to Journal of the European Mathematical Society, accepted.
- 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
- 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.
- The Weighted Flow Algorithm (WFA) for stochastic particle coagulation, with Nicole Riemer and Matt West, Journal of Computational Physics, DOI: 10.1016/j.jcp.2011.07.027
- 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.
- Stability of a Stochastic
Two-Dimensional Non-Hamiltonian System, with Sri Namachchivaya
and Zoi Rapti, SIAM Journal of Applied
- 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/201052022009
- Stability of Distributed Algorithms in the face of Incessant Faults, with Sayan Mitra, 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS '09), to appear.2008
- Regular gaits and optimal velocities for motor proteins, with Eric Vanden-Eijnden, Biophysical Journal, 95 (6), 2681--2691, September 2008.
- Synchrony and asynchrony in a fully stochastic neural network, with Charles S. Peskin, Bulletin of Mathematical Biology, 70 (6), 1608--1633, August 2008.
- Analysis of a Renormalization Group Method for solving perturbed Ordinary Differential Equations, Physica D, 237 (2008) 1029--1052. (with Anthony Harkin, Matt Holzer, Krešimir Josić, and Tasso Kaper)
- Regularity and synchrony in motor proteins. Bulletin of Mathematical Biology, 70 (2):484--516, 2008. (with Eric Vanden-Eijnden)2007
- Method of multiple scales with three time scales. Proc. Appl. Math. Mech., 7: 2040031–2040032. doi: 10.1002/pamm.200700507 (with Peter Kramer, Adnan Khan, and Philip Stathos)
- Self-induced stochastic resonance for Brownian ratchets under load. Communications in Mathematical Sciences, 5 (2): 431--446 2007. (with Eric Vanden-Eijnden)
- Wavetrain response of an excitable medium to local stochastic forcing. Nonlinearity, 20 (2007), 51--74. (with Eric Vanden-Eijnden)
- Non--equilibrium statistics of a reduced model for energy transfer in waves. Communications on Pure and Applied Mathematics, 60 (2007), no. 3, 439--461. (with Paul Milewski, Ricardo Pignol, Esteban Tabak, and Eric Vanden-Eijnden) doi:10.1088/0951-7715/20/1/004.
- Nontrivial scaling limits for multiscale Markov chains. Journal of Statistical Physics, 126 (1): 75--94, Jan 2007. (with Eric Vanden-Eijnden)2006
- Non-meanfield deterministic limits in chemical reaction kinetics far from equilibrium. Journal of Chemical Physics, 124 (23): Article 231102, June 21, 2006. (with Cyrill Muratov and Eric Vanden-Eijnden)2005
- 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)
- Reduced Equations for models of Laminated Materials in Thin Domains. I. Asymptotic Analysis, 42 (2005) vol. 3--4, 263--309. (with C. Eugene Wayne)
- Reduced Equations for models of Laminated Materials in Thin Domains. II. Asymptotic Analysis, 42 (2005) vol 3--4, 311--346.2004 and before
- Brjuno Numbers and the Symbolic Dynamics of the Complex Exponential. Qualitative Theory of Dynamical Systems, 5 (2004), no. 1, 63--74.
- Accessible Points in the Julia Sets of Stable Exponentials. Discrete and Continuous Dynamical Systems. 1 (2001), no. 3, 299--318. (with Ranjit Bhattacherjee, Robert Devaney, Krešimir Josić, and Mónica Moreno-Rocha)
- Itineraries of Entire Functions. Journal of Difference Equations and Applications. 7 (2001), no. 2, 193--214.
- Reduced Equations for Hyperbolic Problems on Thin Domains , Ph. D. thesis, Boston University, (2001).
- 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
PresentationsList of Invited presentations -- HTML