Publications

Most Recent

Michael Batista, Patrick Murphy, Oleg A. Igoshin, Misha Perepelitsa, Ilya Timofeyev ``Role of Non-Exponential Reversal times in Aggregation Models of Bacterial Populations", submitted to Mathematical Biosciences [2024].   Preprint

Robert Azencott, Brett Geiger, Ilya Timofeyev "Rare Events Analysis in Stochastic Models for Bacterial Evolution", submitted to J. Stat. Phys. [2024].   Preprint

Ilya Timofeyev, Alexey Schwarzmann, Dmitri Kuzmin ``Application of Machine Learning and Convex Limiting to Subgrid Flux Modeling in the Shallow-Water Equations", submitted to Mathematics and Computers in Simulation [2024].   Preprint

Patrick Murphy, Oleg Igoshin, Misha Perepelitsa, Ilya Timofeyev ``Existence of weak solutions for the kinetic models of motion of myxobacteria with alignment and reversals", Kinetic and Related Models [2025].   Preprint   Publication

Yingxue Su, Brett Geiger, Ilya Timofeyev, Andreas Mang, Robert Azencott, ``Rare Events Analysis and Computation for Stochastic Evolution of Bacterial Populations", Stochastic Analysis and Applications 43(1), 1-29 [2024].   Preprint   Publication

Mohammad Daneshvar, Richard C. Barnard, Cory Hauck, Ilya Timofeyev, ``Modeling Information Flow with a Multi-Stage Queuing Model", Accepted Physica D 471, 134446 [2025].   Preprint   Publication

Patrick Murphy, Mikhail Perepelitsa, Ilya Timofeyev, Brandon Islas, Matan Lieber-Kotz, and Oleg A. Igoshin, ``Breakdown of Boltzmann-type Models for Self-propelled Rods'', Mathematical Biosciences 376, 109226 [2024].   Preprint   Publication

Machine Learning

Ilya Timofeyev, Alexey Schwarzmann, Dmitri Kuzmin ``Application of Machine Learning and Convex Limiting to Subgrid Flux Modeling in the Shallow-Water Equations", submitted to Mathematics and Computers in Simulation [2024].   Preprint

J. Alcala and I. Timofeyev, "Subgrid-scale parametrization of unresolved scales in forced Burgers equation using Generative Adversarial Networks (GAN)", Theor. Comp. Fluid Dyn. 35, 875-894 [2021].   Preprint   Publication

Xiaoqian Chen, Balu T. Nadiga, and I. Timofeyev, "Predicting Shallow Water Dynamics using Echo-State Networks with Transfer Learning", submitted to Int. J. on Geomath. (GEM) 13, 20 [2022].   Publication,   Preprint
The model code for this project is publicly available at github in the repository Timofeyev/SWE_ESN and on zenodo

Mathematical Biology

Patrick Murphy, Mikhail Perepelitsa, Ilya Timofeyev, Brandon Islas, Matan Lieber-Kotz, and Oleg A. Igoshin, ``Breakdown of Boltzmann-type Models for Self-propelled Rods'', Mathematical Biosciences 376, 109226 [2024].   Preprint   Publication   DOI

Misha Perepelitsa, Ilya Timofeyev, Patrick Murphy, Oleg A. Igoshin, ``A mean-field model for nematic alignment of self-propelled rods'', Phys. Rev E 106, 034613 [2022].   Publication,   Preprint,   DOI

P. Bedekar, I. Timofeyev, A. Warmflash, M. Perepelitsa, "Reaction-diffusion models for morphological patterning of hESCs", J. Math. Biol. 83, 55 [2021].   Preprint,   Publication,   DOI

B. Karamched, W. Ott, I. Timofeyev, R. N. Alnahhas, M. R. Bennett, K. Josic, "Moran model of spatial alignment in microbial colonies", Physica D 395, 1-6, [2019].   Preprint   Original Article

Estimation of SDEs, Sub-Sampling, Mathematical Finance

Xi Chen and I. Timofeyev, "Non-parametric estimation of Stochastic Differential Equations from stationary time-series", J. Stat. Phys. 186, 1 [2022].   Preprint   Publication

M. Perepelitsa and I. Timofeyev, "Self-sustained price bubbles driven by Bitcoin innovations and adaptive behavior", SN Business & Economics 2, 30 [2022].   Preprint   Publication

M. Perepelitsa and I. Timofeyev, "Asynchronous stochastic price pump", Physica A 516, 356-364, [2019].   Preprint   Original Article

R. Azencott, P. Ren, I. Timofeyev, "Realized volatility and parametric estimation of Heston SDEs", Finance and Stochastics 24(3), 723-755, [2020].   DOI: 10.1007/s00780-020-00427-2   Preprint PDF

R. Azencott, P. Ren, I. Timofeyev, "Parametric Estimation from Approximate Data: Non-Gaussian Diffusions", J. Stat. Phys. 161(5), 1276-1298, [2015].   DOI: 10.1007/s10955-015-1379-6   Preprint PDF

R. Azencott, A. Beri, A. Jain, and I. Timofeyev, "Sub-sampling and Parametric Estimation for Multiscale Dynamics", Comm. Math. Sci. 11(4), 939-970, [2013].   Preprint PDF   Issue TOC

R. Azencott, A. Beri, and I. Timofeyev, "Parametric Estimation of Stationary Stochastic Processes under Indirect Observability" J. Stat. Phys. 144(1), 150-170, [2011].   Preprint PDF   Issue TOC

R. Azencott, A. Beri, and I. Timofeyev, "Adaptive Sub-sampling for Parametric Estimation of Gaussian Diffusions", J. Stat. Phys. 139(6), 1066-1089, [2010].   Preprint PDF   Issue TOC

Multi-Agent Systems

Mohammad Daneshvar, Richard C. Barnard, Cory Hauck, Ilya Timofeyev, ``Modeling Information Flow with a Multi-Stage Queuing Model", Submitted to Physica D [2024].   Preprint

W. Ott, I. Timofeyev, T. Weber, "Stochastic and Coarse-Grained Two-Dimensional Modeling of Directional Particle Movement", accepted to Physica D, 402,132209, [2020]   Original Article   Preprint

A. Chertock, A. Kurganov, A. Polizzi, and I. Timofeyev, "Pedestrian Flow Models with Slowdown Interactions", Mathematical Models and Methods in Applied Sciences 24(2), 249-275, [2014],   DOI: 10.1142/S0218202513400083,   Preprint PDF

C. Hauck and Y. Sun and I. Timofeyev, "On Cellular Automata Models of Traffic Flow with Look-Ahead Potential", Stochastics and Dynamics 14, 1350022, [2014],   DOI: 10.1142/S0219493713500226,   Preprint PDF

Y. Sun and I. Timofeyev, "Kinetic Monte Carlo simulations of 1D and 2D traffic flows: Comparison of two look-ahead potentials", Phys. Rev. E 89, 052810, [2014].   DOI: 10.1103/PhysRevE.89.052810,   Preprint PDF

Reduced Dynamics, Subgrid-Scale Parametrization, Geophysical Turbulence

M. Zacharuk, S. I. Dolaptchiev, U. Achatz, I. Timofeyev, "Stochastic subgrid-scale parameterization for one-dimensional shallow water dynamics using stochastic mode reduction", Q.J.R. Meteorol. Soc. Vol 144, Issue 715, July 2018 part B, 1975-1990 [2018]   Preprint   Original Article

A. Jain, I. Timofeyev, E. Vanden-Eijnden, "Stochastic Mode-Reduction in Models with Conservative Fast Sub-Systems", Comm. Math. Sci. 13(2), 297-314, [2015].   Issue TOC   Preprint PDF

S. I. Dolaptchiev, I. Timofeyev, U. Achatz, "Subgrid-scale closure for the inviscid Burgers-Hopf equation" Comm. Math Sci. 11(3), 757-777, [2013].   Issue TOC   Preprint PDF

S. I. Dolaptchiev, U. Achatz, and I. Timofeyev, "Stochastic closure for local averages in the finite-difference discretization of the forced Burgers equation" Theor. Comput. Fluid Dyn. 27(3-4), 297-317, [2013],   DOI: 10.1007/s00162-012-0270-1   Preprint PDF

K. Nimsaila and I. Timofeyev, "Markov Chain Stochastic Parametrizations of Essential Variables", SIAM Mult. Mod. Simul. 8(5), 2079-2096, [2010].   PDF

I. Timofeyev, "Systematic Deviations from Gaussianity in Models of Quasi-Geostrophic Turbulence", Phys. Fluids, 19, 116603, [2007].   PDF

Truncated Burgers-Hopf System

A. J. Majda, and I. Timofeyev, "Statistical mechanics for truncations of the Burgers-Hopf equation: A model for intrinsic stochastic behavior with scaling", Milan Journal of Mathematics, 70(1), 39-96, [2002].   PDF

A. J. Majda, and I. Timofeyev, "Remarkable Statistical Behavior for Truncated Burgers-Hopf Dynamics", Proc. Natl. Acad. Sci. USA, 97(23), 12413-12417, [2000].   PDF

Stochastic Mode-Reduction

A. J. Majda, I. Timofeyev, and E. Vanden-Eijnden, "Stochastic Models for Selected Slow Variables in Large Deterministic Systems", Nonlinearity, 19, 769-794, [2006].   PDF

A. J. Majda and I. Timofeyev, "Low-dimensional chaotic dynamics versus intrinsic stochastic noise: a paradigm model", Physica D, 199, 339-368, [2004].   PDF

A. J. Majda, I. Timofeyev, and E. Vanden-Eijnden, "Systematic Strategies for Stochastic Mode Reduction in Climate", Journal of the Atmospheric Sciences, 60(14), 1705-1722, [2003].   PDF

A. J. Majda, I. Timofeyev, and E. Vanden-Eijnden, "A priori Tests of a Stochastic Mode Reduction Strategy", Physica D, 170, 206-252, [2002].   PDF

A. J. Majda, I. Timofeyev, and E. Vanden-Eijnden, "A Mathematical Framework for Stochastic Climate Models", Comm. Pure App. Math., 54(8), 891-974, [2001].   PDF

A. J. Majda, I. Timofeyev, and E. Vanden-Eijnden, "Models for stochastic climate prediction", Proc. Natl. Acad. Sci. USA, 96(26), 14687-14691, [1999].   PDF

Misc

Y. Zhou, P. Tsiamyrtzis, P. Lindner, I. Timofeyev, and I. Pavlidis, "Spatio-Temporal Smoothing as a Basis for Facial Tissue Tracking in Thermal Imaging", TBME, DOI: 10.1109/TBME.2012.2232927, [2012].   Publication Link

S. Burtsev, R. Camassa and I. Timofeyev, "Numerical Algorithms for the Direct Spectral Transform with Applications to Nonlinear Schrodinger Type Systems", J. Comp. Phys., 147, 166-186, [1998].   PDF

A.Aceves, D. D. Holm, G. Kovacic, and I. Timofeyev, "Homoclinic orbits and chaos in a second-harmonic generating optical cavity", Physics Letters A, 233, 203-208, [1997].   PDF

N. Barlas and I. Timofeyev, "Application of the Stochastic Mode-Reduction Strategy and a-priori Prediction of Symmetry Breaking in Stochastic Systems with Underlying Symmetry", Comm. Math. Sci., 8(2), 393-408, [2010].   PDF

N. Barlas, K. Josic, S. Lapin and I. Timofeyev, "Non-Uniform Decay of Predictability and Return of Skill in Stochastic Oscillatory Models", Physica D, 232(2), 116-127, [2007].   PDF

A. L. Alejandro-Quinones, K. E. Bassler, M. Field, J. L. McCauley, M. Nicol, I. Timofeyev, A. Torok and G. H. Gunaratne, "A theory of fluctuations in stock prices", Physica A, 363(2), 383-392, [2006].   PDF

R. Kleeman, A. J. Majda, and I. Timofeyev, "Quantifying predictability in a model with statistical features of the atmosphere", Proc. Natl. Acad. Sci. USA, 99(24), 15291-15296, [2002].   PDF

M. L. Frankel, G. Kovacic, V. Roytburd, and I. Timofeyev, "Finite-Dimensional Dynamical System Modeling Thermal Instabilities", Physica D, 137, 295-315, [2000].   PDF