Publications
Publications, submitted
  1. Synchronization conditions in the Kuramoto model and their relationship to seminorms, with Jared Bronski and Thomas Carty, submitted.
  2. Symbiosis, Stability, and Persistence, with Shinhae Park and Zoi Rapti, submitted.
Publications, accepted or in print

    2020
  1. The generalized distance spectrum of a graph and applications, Linear and Multilinear Algebra, DOI.
  2. Consensus on simplicial complexes: Results on stability and synchronization , Chaos, 31, 023137 (2021) DOI.
  3. 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.

    2019
  4. Convergence of a generalized Weighted Flow Algorithm for stochastic particle coagulation, with Nicole Riemer and Matthew West, accepted in Journal of Computational Dynamics.
  5. Optimizing Gershgorin for Symmetric Matrices, accepted in Linear Algebra and its Applications.

    2018
  6. Synchronization and Stability for Quantum Kuramoto, accepted in Journal of Statistical Physics.
  7. Configurational stability for the Kuramoto-Sakaguchi model, with Jared Bronski and Thomas Carty, accepted in Chaos.
  8. Stable Configurations in Social Networks, with Jared Bronski, Tim Ferguson, and Michael Livesay, accepted at Nonlinearity.

    2017
  9. 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
  10. 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. DOI

    2016
  11. Phase-locked Patterns of the Kuramoto Model on 3-Regular Graphs, with Bard Ermentrout, Chaos 26, 094820 (2016). DOI
  12. 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). DOI

    2015
  13. 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.
  14. Modular dynamical systems on networks, with Eugene Lerman, Journal of the European Mathematical Society, Volume 17, Issue 12, 2015, pp. 2977–3013. DOI
  15. 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
  16. Dynamics on Networks of Manifolds, with Eugene Lerman, SIGMA 11 (2015), 022, 21 pages, March 2015. DOI

    2014
  17. 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
  18. Synchrony and Periodicity in Excitable Neural Networks with Multiple Subpopulations, with Yi Zeng, SIAM Journal of Applied Dynamical Systems, accepted, May 2014. DOI
  19. 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
  20. 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. DOI: http://dx.doi.org/10.1016/j.ress.2013.10.011

    2013
  21. Analysis of Power System Dynamics Subject to Stochastic Power Injections , with Yu Chen, Sairaj Dhople and Alejandro Domínguez-García, IEEE Transactions on Circuits and Systems, 60 (12), 3341--3353, December 2013. DOI: http://dx.doi.org/10.1109/TCSI.2013.2265972.

    2012
  22. 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).
  23. Transitions amongst synchronous solutions in the stochastic Kuramoto model, Nonlinearity, 25 (2012) 1473-1494. DOI:10.1088/0951-7715/25/5/1473
  24. 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

    2011
  25. 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
  26. 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.
  27. Stability of a Stochastic Two-Dimensional Non-Hamiltonian System, with Sri Namachchivaya and Zoi Rapti, SIAM Journal of Applied Math, DOI:10.1137/100782139

    2010
  28. 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

    2009
  29. 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
  30. Regular gaits and optimal velocities for motor proteins, with Eric Vanden-Eijnden, Biophysical Journal, 95 (6), 2681--2691, September 2008.
  31. Synchrony and asynchrony in a fully stochastic neural network, with Charles S. Peskin, Bulletin of Mathematical Biology, 70 (6), 1608--1633, August 2008.
  32. 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)
  33. Regularity and synchrony in motor proteins. Bulletin of Mathematical Biology, 70 (2):484--516, 2008. (with Eric Vanden-Eijnden)
    2007
  34. 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)
  35. Self-induced stochastic resonance for Brownian ratchets under load. Communications in Mathematical Sciences, 5 (2): 431--446 2007. (with Eric Vanden-Eijnden)
  36. Wavetrain response of an excitable medium to local stochastic forcing. Nonlinearity, 20 (2007), 51--74. (with Eric Vanden-Eijnden)
  37. 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.
  38. Nontrivial scaling limits for multiscale Markov chains. Journal of Statistical Physics, 126 (1): 75--94, Jan 2007. (with Eric Vanden-Eijnden)
    2006
  39. 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
  40. 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)
  41. Reduced Equations for models of Laminated Materials in Thin Domains.  I. Asymptotic Analysis, 42 (2005) vol. 3--4, 263--309. (with C. Eugene Wayne)
  42. Reduced Equations for models of Laminated Materials in Thin Domains.  II. Asymptotic Analysis, 42 (2005) vol 3--4, 311--346.
  43. 2004 and before
  44. Brjuno Numbers and the Symbolic Dynamics of the Complex Exponential. Qualitative Theory of Dynamical Systems, 5 (2004), no. 1, 63--74.
  45. 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)
  46. Itineraries of Entire Functions. Journal of Difference Equations and Applications. 7 (2001), no. 2, 193--214.
  47. Reduced Equations for Hyperbolic Problems on Thin Domains , Ph. D. thesis, Boston University, (2001).
Presentations
List of Invited presentations -- HTML