Research Area

  • Partial Differential Equations, Applied Analysis, Applied Probability, and Statistics

Research Interests

  • Computational and Mathematical Biology
    • Population genomics, including stochastic modeling and inference
    • Population dynamics, including structured populations
  • Partial differential equations with applications to
    • Materials science, including elastodynamics and gas dynamics
    • Singularity formations: vacuums, cavities and fractures
    • Hyperbolic balance laws, including shocks
  • Statistics with applications to Data Science

Collaborators

Publications

    Papers in Preparation
  • A. Miroshnikov, M. Steinrücken, Computing transition functions for Piecewise Deterministic Markov Processes and Applications to Computational Genomics.
  • A. Miroshnikov, M. Steinrücken, Accurate and Efficient Inference of Population Size History from Genomic Sequence Data of Multiple Individuals.
  • A. Miroshnikov, R. Young, Weak* Solutions III: a Convergent Front Tracking Scheme.
  • A. Miroshnikov, E. Savelev, Stability and Convergence of Fully-discrete Entropic Variational Schemes for One-dimensional Equations of Elastodynamics.
    Submitted Papers and Preprints
  • [pdf] A. Miroshnikov, E. Savelev, Asymptotic properties of parallel Bayesian kernel density estimators. In revision (2017), arXiv:1611.02874.
  • [pdf] A. Miroshnikov, K. Kotsiopoulos, E. Conlon, Asymptotic properties and approximation of Bayesian logspline density estimators for communication-free parallel methods. Preprint (2017). arXiv:1710.09071.
  • [pdf] A. Miroshnikov, Stability of Fully Discrete Variational Schemes for Elastodynamics with a Polyconvex Stored Energy. Preprint (2017), arXiv:1611.02888.
    Published and Accepted Papers
  • [pdf] A. Miroshnikov, M. Steinrücken, Computing the joint distribution of the total tree length across loci in populations with variable size. Theoretical Population Biology. (2017). Vol. 118, p.1-19.
  • [pdf] P.-E. Jabin, A. Miroshnikov, R. Young, Cellulose Biodegradation Models; an Example of Cooperative Interactions in Structured Populations. ESAIM: Mathematical Modelling and Numerical Analysis. In press (2017). DOI:10.1051/m2an/2017021. arXiv:1411.7476.
  • [pdf] A. Miroshnikov, R. Young, Weak* Solutions II: The Vacuum in Lagrangian Gas Dynamics. SIAM Journal on Mathematical Analysis (2017), 49(3), 1810-1843.
  • [pdf] A. Miroshnikov, R. Young, Weak* Solutions I: A New Perspective on Solutions to Systems of Conservation Laws. Methods and Applications of Analysis. In press (2017). arXiv:1511.02579.
  • [pdf] A. Miroshnikov, K. Trivisa, Stability and Convergence of Relaxation Schemes to Hyperbolic Balance Laws via a Wave Operator, Journal of Hyperbolic Differential Equations (2015), Vol. 12, No. 1, 189-219.
  • [pdf] A. Miroshnikov, A. Tzavaras, On the Construction and Properties of Weak Solutions Describing Dynamic Cavitation, Journal of Elasticity (2015), 118-2, 141-185.
  • [pdf] A. Miroshnikov, Z. Wei, E. Conlon, Parallel Markov Chain Monte Carlo for Non-Gaussian Posterior Distributions, Stat (2015), Vol. 4, Issue 1, 304-319. DOI:10.1002/sta4.97.
  • [pdf] J. Philips, A. Miroshnikov, P.-J. Haest, D. Springael and E. Smolders, Motile Geobacter Dechlorinators Migrate into a Model Source Zone of Trichloroethene Dense Non-aqueous Phase Liquid: Experimental Evaluation and Modeling, Journal of Contaminant Hydrology (2014), 170, 28-38.
  • [pdf] A. Miroshnikov, E. Conlon, parallelMCMCcombine: An R Package for Bayesian Methods for Big Data and Analytics, PLoS ONE (2014), 9(9): e108425. DOI:10.1371/journal.pone.0108425.
  • [pdf] A. Miroshnikov, K. Trivisa, Relative Entropy in Hyperbolic Relaxation for Balance Laws, Communications in Mathematical Sciences (2014), 12-6, 1017-1043.
  • [pdf] A. Miroshnikov, A. Tzavaras, Convergence of Variational Approximation Schemes for Elastodynamics with Polyconvex Energy," with A.  Tzavaras, Journal of Analysis and its Applications (ZAA) (2014), 33-1, 43-64.
  • [pdf] J. Giesselmann, A. Miroshnikov, A. Tzavaras, The problem of Dynamic Cavitation in Nonlinear Elasticity, Séminaire Laurent Schwartz - EDP et applications (2012-2013), Exp. No. 14, 1-17.
  • [pdf] A. Miroshnikov, A. Tzavaras, A Variational Approximation Scheme for Radial Polyconvex Elasticity That Preserves the Positivity of Jacobians, Communications in Mathematical Sciences (2012), 10-1, 87-115.
    Software Publications
  • R-package parallelMCMCcombine: Methods for combining independent subset Markov chain Monte Carlo (MCMC) posterior samples to estimate a posterior density given the full data set. (with E. Conlon) (2014).
  • R-package BayesSummaryStatLM: Methods for generating Markov Chain Monte Carlo (MCMC) posterior samples of Bayesian linear regression model parameters that require only summary statistics of data as input. (with E. Conlon and E. Savelev) (2015).

Talks &
Conferences

  • Broad Institute of MIT and Harvard, Cambridge, Massachusetts, 2017.
  • Analysis and PDE Seminar, University of Southern California, Los Angeles, California, 2017
  • PDE and Applied Mathematics Seminar, University of California, Davis, California, 2016
  • Level Set Collective Seminar, UCLA, Los Angeles, California, 2016
  • 11-th AIMS International Conference on Dynamical Systems, Differential Equations and Applications, Florida, 2016.
  • British Applied Mathematics Colloquium, University of Oxford, Oxford, UK, 2016.
  • SIAM-SEAS Conference, University of Alabama Birmingham, Alabama, 2015.
  • SAND Lab seminar, Massachusetts Institute of Technology, Cambridge, Massachusetts 2014.
  • Participant of IdeaLab 2014: Program for Early Career Researchers "Toward a more realistic model of ciliated and flagellated organisms," ICERM, Brown University, Providence, Rhode Island, 2014.
  • IMA Workshop: Mathematics at the Interface of Partial Differential Equations, the Calculus of Variations, and Materials Science, IMA, University of Minnesota, 2014.
  • AMS Spring Western Section Meeting, Albuquerque, University of New Mexico, 2014.
  • SIAM Conference on Analysis of Partial Differential Equations, Orlando, Florida. 2013.
  • PDE seminar, University of Connecticut, Connecticut. 2013.
  • PDE seminar, Brown University, Providence, Rhode Island. 2013.
  • SIAM Conference on Mathematical Aspects of Material Science, Philadelphia, Pennsylvania. 2013.
  • Research Workshop "Hyperbolic Conservation Laws and Infinite-Dimensional Dynamical Systems," Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania. 2012.
  • SIAM Conference on Analysis of PDE, San Diego, California. 2011.
  • AMS Fall Western Section Meeting, University of Utah, Salt Lake City, Utah. 2011
  • "Kinetic Description of Multiscale Phenomena: Modeling, Theory, and Computation," Annual Kinetic FRG meeting, University of Wisconsin-Madison, Madison, Wisconsin. 2011
  • "Conference on Hyperbolic Conservation Laws and Continuum Mechanics" in Honor of Constantine Dafermos' 70-th Birthday, Brown University, Providence, Rhode Island. 2011
  • Research Workshop "Hyperbolic Conservation Laws and Fluid Dynamics," Department of Mathematics, University of Parma, Parma, Italy. 2010
  • The 3rd Annual Meeting of Marie Curie Initial Training Network "DEASE", Institute of Applied and Computational Mathematics, FORTH, Crete, Greece. 2009.
  • PDE Seminar, Virginia Polytechnic Institute and State University, Blacksburg, Virginia. 2008.
  • Computational Aeroacoustics Seminar, Institute of Mathematical Modeling of Russian Academy of Science, Moscow, Russia. 2005.
  • SIAM Conference on Computational Science & Engineering, Orlando, Florida. 2005.
  • Mathematical Modeling Seminar, Institute of Mathematical Modeling of Russian Academy of Science, Moscow, Russia. 2002.
  • The 2nd International Conference of the Young Scientists and Students "Actual Problems of Modern Science," Samara, Russia. 2001.
  • Annual Conference, Moscow State Technological University "Stankin", Moscow, Russia. 2000.