- Synchronization conditions in the Kuramoto model and their relationship to seminorms, with Jared Bronski and Thomas Carty, submitted.
- Symbiosis, Stability, and Persistence, with Shinhae Park and Zoi Rapti, submitted.
Publications, accepted or in print
- The generalized distance spectrum of a graph and applications, Linear and Multilinear Algebra, DOI.
- Consensus on simplicial complexes: Results on stability and synchronization , Chaos, 31, 023137 (2021) DOI.
- Circulant Type Formulas for the Eigenvalues of Linear Network Maps,
with Eddie Nijholt, Linear Algebra and its Applications, Volume 610, 1 February 2021, Pages 379-439. DOI.
- Convergence of a generalized Weighted Flow Algorithm for stochastic particle coagulation, with Nicole Riemer and Matthew West, accepted in Journal of Computational Dynamics.
- Optimizing Gershgorin
for Symmetric Matrices, accepted in Linear Algebra and its Applications.
- Synchronization and Stability for Quantum Kuramoto, accepted in Journal of Statistical Physics.
- Configurational stability for the Kuramoto-Sakaguchi model, with Jared Bronski and Thomas Carty, accepted in Chaos.
- Stable Configurations in Social Networks, with Jared
Bronski, Tim Ferguson, and Michael Livesay, accepted at Nonlinearity.
- Finite-size effects and switching times for Moran dynamics with mutation, with Meghan Galiardi, Journal of Mathematical Biology, April 2017, Volume 74, Issue 5, pp 1197--1222. DOI
- Math PhD careers: New opportunities emerging amidst crisis, with
Yuliy Baryshnikov and Richard Laugesen, Notices of the American
Mathematical Society, 64 (3) Published March 1 2017, 260--264.
- Phase-locked Patterns of the Kuramoto Model on 3-Regular Graphs, with Bard Ermentrout, Chaos 26, 094820 (2016). DOI
- Graph Homology and
Stability of Coupled Oscillator Networks, with Jared Bronski and
Timothy Ferguson, SIAM Journal of Applied Mathematics 76(3), 1126--1151. (26 pages).
- Moment closure and finite-time blowup for Piecewise Deterministic Markov Processes , with Jiangmeng Zhang, Sairaj Dhople and Alejandro Domínguez-García, SIAM Journal on Applied Dynamical Systems, accepted December 2015.
- Modular dynamical systems on networks, with Eugene Lerman, Journal of the European Mathematical Society, Volume 17, Issue 12, 2015, pp. 2977–3013. DOI
- Multi-dimensional niche construction and diversification in trait-based Lotka-Volterra models , with Tommaso Biancalani and Nigel Goldenfeld, Physical Review E, 91, 052107 -- Published 7 May 2015. DOI
- Dynamics on Networks of
Manifolds, with Eugene Lerman, SIGMA 11 (2015), 022, 21
pages, March 2015. DOI
- A Maximum Entropy Approach to the Moment Closure Problem for Stochastic Hybrid Systems at Equilibrium, with Jiangmeng Zhang, Sairaj Dhople and Alejandro Domínguez-García, 53rd IEEE Conference on Decision and Control, December 2014. DOI
- Synchrony and Periodicity in Excitable Neural Networks with Multiple Subpopulations, with Yi Zeng, SIAM Journal of Applied Dynamical Systems, accepted, May 2014. DOI
- Spectral Theory for Dynamics on Graphs containing Attractive and Repulsive Interactions, with Jared Bronski, SIAM Journal of Applied Mathematics, 74 (1), 2014, pp. 83--105. DOI
- A Stochastic Hybrid
Systems Framework for Analyzing Markov Reward Models, with Sairaj
Dhople and Alejandro Domínguez-García,
Reliability Engineering & System Safety, 123,
158--170, March 2014.
- Analysis of Power
System Dynamics Subject to Stochastic Power Injections
, with Yu Chen, Sairaj Dhople and Alejandro
IEEE Transactions on Circuits and Systems,
60 (12), 3341--3353, December
2013. DOI: http://dx.doi.org/10.1109/TCSI.2013.2265972.
- 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