# David Cai

### Professor of Mathematics and Neural Science

Current Research Interests

Neuroscience --- Modeling, Network Dynamics, Chaos, Kinetic Theories, and Numerical Methods

### Insect Olfactory Systems:

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A Large-scale Model of Locust Antennal Lobe, M. Patel, A.V. Rangan, and D. Cai,
published June 2009, DOI 10.1007/s10827-009-0169-z J. Comp. Neurosci. (2009)
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### Primary Visual Cortex:

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Multi-scale Modeling of the Primary Visual Cortex, A.V. Rangan, L. Tao, G. Kovacic, and D. Cai,
IEEE Engineering in Medicine and Biology, May/June issue, pp19-24 (2009)
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Large-Scale Computational Modeling of the Primary Visual Cortex, A.V. Rangan, L. Tao, G. Kovacic, and D. Cai,
invited review in Coherent Behavior in Neuronal Networks, ed. Kresimir Josic, (Springer, New York) in press (2009)
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Theoretical Analysis of Reverse-Time Correlation for Idealized Orientation Tuning Dynamics, G. Kovacic, L. Tao, D. Cai, and M.J. Shelley,
J. Comp. Neurosci. 25, 401-38 (2008)
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Orientation Selectivity in Visual Cortex by Fluctuation-Controlled Criticality, L. Tao, D. Cai, D.W. McLaughlin, M.J. Shelley, and R. Shapley,
Proc. Nat. Acad. Sci. 103, 12911 (2006)**** **

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Modeling the Spatiotemporal Cortical Activity Associated with the Line-Motion Illusion in Primary Visual Cortex, A.V. Rangan, D. Cai and D.W. McLaughlin,
Proc. Nat. Acad. Sci. 102, 18793 (2005)**** **

** More illusions
(supplementary material for Modeling the Spatiotemporal Cortical Activity Associated with the Line-Motion Illusion in Primary Visual Cortex)
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Architectural and Synaptic Mechanisms Underlying Coherent Spontaneous Activity in V1, D. Cai, A.V. Rangan and D.W. McLaughlin,
Proc. Nat. Acad. Sci. 102, 5868 (2005)
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### Chaos and Network Dynamics:

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Network-induced Chaos in integrate-and-fire neuronal ensembles, D. Zhou, A.V. Rangan, Y. Sun, and D. Cai,
Phys. Rev. E, 80, 031918 (2009)
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### Numerical Methods:

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Library-based Numerical Reduction of the Hodgkin-Huxley Neuron for Network Simulation, Y. Sun, D. Zhou, A.V. Rangan, and D. Cai,
DOI 10.1007/s10827-009-0151-9, published, J. Comp. Neurosci. (2009)
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Fast numerical methods for simulating large-scale integrate-and-fire neuronal networks, A.V. Rangan and D. Cai,
J. Comp. Neurosci, 22, 81, (2007)
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Numerical Methods for Solving Kinetic Equations of Neuronal Network Dynamics,A.V. Rangan, D. Cai, and L. Tao,
J. Comp. Phys. 221, 781 (2007)
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An Embedded Network Approach for Scale-up of Fluctuation-Driven Systems with Preservation of Spike Information, D. Cai, L. Tao and D.W. McLaughlin,
Proc. Nat. Acad. Sci. 101, 14288 (2004)
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### Statistical Physics Approach to Network Dynamics:

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Fokker-Planck description of conductance-based integrate-and-fire neuronal networks, G. Kovacic, A.V. Rangan, L. Tao, and D. Cai,
Phys. Rev. E, 80, 021904 (2009)**** **

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Kinetic Theory for Neuronal Networks with Fast and Slow Excitatory Conductances Driven by the Same Spike Train, A.V. Rangan, G. Kovacic, and D. Cai,
Phys. Rev. E 77, 041915 (2008)
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Maximum-Entropy Closures for Kinetic Theories of Neuronal Network Dynamics, A.V. Rangan and D. Cai,
Phys. Rev. Lett. 96, 178101 (2006)
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Kinetic Theory for Neuronal Network Dynamics, D. Cai, L. Tao, A.V. Rangan, and D.W. McLaughlin,
Comm. Math. Sci. 4, 97 (2006)
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A New Kinetic Representation of Fluctuation-Driven Neuronal Networks with Application to Simple & Complex Cells in Primary Visual Cortex, D. Cai, L. Tao, M. Shelley and D.W. McLaughlin,
Proc. Nat. Acad. Sci, 101, 7757 (2004) **** **

### Encoding and Decoding of Information:

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Quantifying Neuronal Newtork Dynamics through Coarse-grained Event Trees, A.V. Rangan, D. Cai, and D.W. McLaughlin,
Proc. Nat. Acad. Sci. 105, 10990 (2008)
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Neuronal information encoding and reduction of dimension in network dynamics, D. Cai, A.V. Rangan, and D.W. McLaughlin,
invited review, SIAM News, 40 (2), 16 (2007)
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Predictability

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A Framework for Predictability through Relative Entropy, A.J. Majda, R. Kleeman, and D. Cai,
Methods Appl. Anal., 9, 425 (2002)**** **

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Quantifying Predictability in a Simple Model with Complex Features, I: The Perfect Predictability Scenario,
D. Cai, K. Haven and A.J. Majda,
Stochastics and Dynamics, 4, 547 (2004)
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Active Media

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Dynamics of Bacterial Flow: Emergence of Spatiotemporal Coherent Structures, N. Sambelashvili, A.W.C. Lau, and D. Cai,
Phys. Lett. A. 360, 507 (2007)**** **

Nonlinear Dispersive Waves ---Spatiotemporal Chaos, Wave Turbulence

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

** Interactions of Renormalized Waves in Thermalized Fermi-Pasta-Ulam Chains, B. Gershgorin, Y. Lvov, and D. Cai,
Phys. Rev. E, 75, 046603 (2007)**** **

** Renormalized Waves and Discrete Breathers in beta-Fermi-Pasta-Ulam Chains, B. Gershgorin, Y. Lvov, and D. Cai,
Phys. Rev. Lett. 95, 264301 (2005)**** **

** The Nonlinear Schrödinger Equation as Both a PDE and a Dynamical System, D. Cai, D.W. McLaughlin, and K.T.R. McLaughlin,
Handbook of Dynamical Systems, 2, 599-675 (2002))**** **

** Dispersive Wave Turbulence in One Dimension, D. Cai, A.J. Majda, D.W. McLaughlin, E.G. Tabak,
Physica D, 152-153, 551 (2001)**** **

** Chaotic and Turbulent Behavior of Unstable One-dimensional Nonlinear Dispersive Waves, D. Cai, and D.W. McLaughlin,
Year 2000 special issue of Mathematical Physics -Past and Future, J. Math. Phys, 41, 4125 (2000)**** **

** Spectral Bifurcations in Dispersive Wave Turbulence, D. Cai, A.J. Majda, D.W. McLaughlin, E.G. Tabak,
Proc. Nat'l Acad. Sci (USA), 96, 14216 (1999)**** **

** Spatiotemporal Chaos and Effective Stochastic Dynamics for a Near-integrable Nonlinear System, D. Cai, D.W. McLaughlin, J. Shatah,
Phys. Lett. A, 253, 280 (1999)**** **

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