Gregor Kovacic

Professor
Department of Mathematical Sciences
Rensselaer Polytechnic Institute
Troy, New York 12180-3590

E-mail: kovacg at rpi dot edu
Telephone: (518) 276-6908
Fax: (518) 276-4824


Ph.D. California Institute of Technology, Applied Mathematics, 1990


  • Research Interests
  • Honors and Awards
  • Graduate Students
  • Postdocs
  • Publications
  • Courses
  • Links


    Research Interests

    Matematical neuroscience, wave dynamics, integrable systems, nonlinear resonant optics.


    Honors and Awards

    Alfred P. Sloan Fellowship, 1996
    NSF CAREER Award, 1995
    Director's Funded Postdoctoral Fellowship, Los Alamos National Laboratory, 1989
    Preseren's Student Prize, University of Ljubljana, Slovenia, 1985


    Graduate Students

    Jennifer Kile, Christina Lee, Katelyn Plaisier-Leisman, Michael Schwartz, Paulina Volosov, Current Ph.D. Students
    Rafail Abramov, 2002
    Mehmet Baran, 2003
    Victor Barranca, 2013
    Julie Byrne, 2000
    Ibrahim Fatkullin, 2002
    Laura Gross, 1997
    Katherine Newhall, 2011
    Pamela Pyzza, 2015
    Kathryn Rasmussen, 2008
    Ilya Timofeyev, 1998
    Thomas A. Wettergren, 1995.


    Postdocs

    Michael Jenkinson, 2015-present
    Maxim Shkarayev, 2007-2010
    Joseph Biello, 2000-03
    Lee DeVille, 2001-04
    Melinda Koelling, 2001-02


    Publications

    V. J. Barranca, G. Kovacic, D. Zhou, and D. Cai [2016]. Improved Compressive Sensing of Natural Scenes Using Localized Random Sampling, to appear in Nature Scientific Reports.

    V. J. Barranca, G. Kovacic, D. Zhou, and D. Cai [2016]. Efficient Image Processing Via Compressive Sensing of Integrate-And-Fire Neuronal Network Dynamics, Neurocomputing 171, 1313-1322.

    D. Kraus, G. Biondini, and G. Kovacic [2015]. The focusing Manakov system with nonzero boundary conditions, Nonlinearity 28(9), 3101.

    K. A. Newhall, M. S. Shkarayev, P. R. Kramer, G. Kovacic, and D. Cai [2015]. Synchrony in Stochastically Driven Neuronal Networks with Complex Topologies, Phys. Rev. E 91, 052806.

    V. J. Barranca, G. Kovacic, D. Zhou, and D. Cai [2014]. Network Dynamics for Optimal Compressive Sensing Input Signal Recovery, Phys. Rev. E 90, 042908.

    V. J. Barranca, G. Kovacic, D. Zhou, and D. Cai [2014]. Sparsity and Compressed Coding in Sensory Systems, PLOS Comput. Biol. 10(8), e1003793.

    G. Biondini and G. Kovacic [2014]. Inverse scattering transform for the focusing nonlinear Schroedinger equation with nonzero boundary conditions, J. Math. Phys. 55(3), 031506.

    V. J. Barranca, D. C. Johnson, J. L. Moyher, J. P. Sauppe, M. S. Shkarayev, G. Kovacic, and D. Cai [2014]. Dynamics of the Exponential Integrate-and-Fire Model with Slow Currents and Adaptation, J. Comput. Neurosci. 37(1), 161-180.

    A. O. Korotkevich, K. E. Rasmussen, G. Kovacic, V. Roytburd, A. I. Maimistov, and I. Gabitov [2013]. Optical Pulse Dynamics in Active Metamaterials with Positive and Negative Refractive Index, JOSA B 30(4), 1077-1084.

    K. A. Newhall, E. P. Atkins, P. R. Kramer, G. Kovacic, and I. Gabitov [2013]. Random Polarization Dynamics in a Resonant Optical Medium, Opt. Lett. 38(6), 893-895.

    W. Lee, G. Kovacic, and D. Cai [2013]. Generation of Dispersion in Non-Dispersive Nonlinear Waves in Thermal Equilibrium, Proc. Natl. Acad. Sci. U.S.A. 110(9), 3237-3241.

    E. P. Atkins, P. R. Kramer, G. Kovacic, and I. Gabitov [2012]. Stochastic Pulse Switching in a Degenerate Resonant Optical Medium, Phys. Rev. A 85, 043834.

    M. S. Shkarayev, G. Kovacic, and D. Cai [2012]. Topological effects on dynamics in complex pulse-coupled networks of integrate-and-fire type, Phys. Rev. E 85, 036104.

    D. Cai, L. Tao, M. S. Shkarayev, A. V. Rangan, D. W. McLaughlin, and G. Kovacic [2012]. The Role of Fluctuations in Coarse-Grained Descriptions of Neuronal Networks, Comm. Math. Sci., 10, 307-354.

    M. M. Crosskey, A. T. Nixon, L. M. Schick, and G. Kovacic [2011]. Invisibility Cloaking via Non-Smooth Transformation Optics and Ray Tracing, Phys. Lett. A 375, 1903-1911.

    K. A. Newhall, G. Kovacic, P. R. Kramer, and D. Cai [2010]. Cascade-Induced Synchrony in Stochastically-Driven Neuronal Networks, Phys. Rev. E 82, 041903.

    K. A. Newhall, G. Kovacic, P. R. Kramer, D. Zhou, A. V. Rangan, and D. Cai [2010]. Dynamics of Current-Based, Poisson Driven, Integrate-and-Fire Neuronal Networks, Comm. Math. Sci., 8, 541-600.

    I. Fatkullin, G. Kovacic, and E. VandenEijnden [2010]. Reduced dynamics of stochastically perturbed gradient flows, Comm. Math. Sci., 8, 439-461.

    M. S. Shkarayev, G. Kovacic, A. V. Rangan, and D. Cai [2009]. Architectural and functional connectivity in scale-free integrate-and-fire networks, Europhys. Lett. 88, 50001.

    G. Kovacic, L. Tao, A. V. Rangan, and D. Cai [2009]. Fokker-Planck Description of Conductance-Based Integrate-and-Fire Neuronal Networks, Phys. Rev. E 80, 021904.

    A. V. Rangan, L. Tao, G. Kovacic, and D. Cai [2009]. Large-scale computational modeling of the primary visual cortex, in Coherent Behavior in Neuronal Networks, K. Josic, M. Matias, R. Romo, J. Rubin Eds., Springer Series in Computational Neuroscience , Vol. 3, Springer-Verlag.

    W. Lee, G. Kovacic, and D. Cai [2009]. Renormalized Resonance Quartets in Dispersive Wave Turbulence, Phys. Rev. Lett. 103, 024502.

    A. V. Rangan, L. Tao, G. Kovacic, and D. Cai [2009]. Multi-scale modeling of the primary visual cortex, IEEE Engineering in Medicine and Biology Magazine 28(3), 19-24.

    A. V. Rangan, G. Kovacic, and D. Cai [2008]. Kinetic theory for neuronal networks with fast and slow excitatory conductances driven by the same spike train, Phys. Rev. E 77, 041915.

    G. Kovacic, L. Tao, D. Cai, and M. J. Shelley [2008]. Theoretical analysis of reverse-time correlation for idealized orientation tuning dynamics, J. Comput. Neurosci. 25(3), 401-438.

    J. A. Byrne, G. Kovacic, and I. R. Gabitov [2003]. Polarization switching of light interacting with a degenerate two-level optical medium, Physica D 186, 69-92.

    R. V. Abramov, G. Kovacic, and A. J. Majda [2003]. Hamiltonian structure and statistically relevant conserved quantities for the truncated Burgers-Hopf equation, Commun. Pure Appl. Math. 56 (1), 1-46.

    M. Frankel, G. Kovacic, V. Roytburd, and I. Timofeyev [2000]. Finite-dimensional dynamical system modeling thermal instabilities, Physica D 137, 295-315.

    R. Camassa, G. Kovacic, and S.-K. Tin [1998]. A Melnikov method for homoclinic orbits with many pulses, Arch. Rat. Mech. Anal. 143, 105-193.

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

    T. J. Kaper and G. Kovacic [1996]. Multi-bump orbits homoclinic to resonance bands, Trans. AMS 348, 3835-3887.

    D. D. Holm, G. Kovacic, and T. A. Wettergren [1996]. Homoclinic orbits in the Maxwell-Bloch equations with a probe, Phys. Rev. E 54, 243-256.

    G. Kovacic and T. A. Wettergren [1996]. Homoclinic orbits in the dynamics of resonantly driven coupled pendula, ZAMP 47, 221-264.

    G. Kovacic [1995]. Singular perturbation theory for homoclinic orbits in a class of near-integrable dissipative systems, SIAM J. Math. Anal. 26, 1611-1643.

    D. D. Holm, G. Kovacic and T. A. Wettergren [1995]. Near-integrability and chaos in a resonant-cavity laser model, Phys. Lett. A 200, 299-307.

    T. J. Kaper and G. Kovacic [1994]. A geometric criterion for adiabatic chaos, J. Math. Phys. 35 (3), 1202-1218.

    G. Kovacic [1993]. Singular perturbation theory for homoclinic orbits in a class of near-integrable Hamiltonian systems, J. Dynamics Diff. Eqns. 5, 559-597.

    G. Kovacic [1992]. Dissipative dynamics of orbits homoclinic to a resonance band, Phys. Lett. A 167, 143-150.

    G. Kovacic [1992]. Hamiltonian dynamics of orbits homoclinic to a resonance band, Phys. Lett. A 167, 137-142.

    G. Kovacic and S. Wiggins [1992]. Orbits homoclinic to resonances with an application to chaos in a model of the forced and damped Sine-Gordon equation, Physica D 57, 185-225.

    D. D. Holm and G. Kovacic [1992]. Homoclinic chaos in a laser-matter system, Physica D 56, 270-300.

    A. Aceves, D. D. Holm, and G. Kovacic [1992]. Homoclinic chaos due to competition among degenerate modes in a ring-cavity laser, Phys. Lett. A 161, 499-505.

    D. D. Holm, G. Kovacic, and B. Sundaram [1991]. Chaotic laser-matter interaction, Phys. Lett. A 154, 346-352.

    D. D. Holm and G. Kovacic [1991]. Homoclinic chaos for ray optics in a fiber, Physica D 51, 177-188.

    G. Kovacic [1991]. Lobe area via action formalism in a class of Hamiltonian systems, Physica D 51, 226-233.


    Courses

    MATH-4100, Linear Algebra, Fall 2016.

    MATH-6600, Methods of Applied Mathematics, Fall 2016.


    Links

    Discrete and Continuous Dynamical Systems - Series S, for which I am on the editorial commitee.

    A picture of the current, past, and honorary RPI mathematics team members at the IMACS conference in Athens, GA, 2015.

    Poems by my wife, Miriam Herrera.


    RPI Math Faculty List