Quarterly of Applied Mathematics

November 21, 2012

REFERENCE Patterns of Growth

The Faithful Copy Neuron J. Comput. Neurosci. Published Online 11 Structural Analysis of Biodiversity (with M.Y. Stoeckle and Y. Zhang), PLoS ONE, 4e:9266 (2010).

Dynamics of Neuronal Populations: Stability and Synchrony (with A. Omurtag & K. Lubliner) Network: Computation in Neural Systems, 17:3-29 (2006). Lays the theoretical foundation for describing the behavior of populations of cortical neurons.

Orientation and Spatial Frequency in Primary Visual Cortex. (with R. Uglesich) PNAS, 101: 6 (2004). Solves the long standing problem of how spatial frequency coding is organized in cortex.

A pattern analysis of the second Rehnquist U.S. Supreme Court. PNAS, 100:7432-7437 (2003). Applies methods of mathematical physics to the analysis of ’data’ generated by a long sitting court.

Dynamics of neuronal populations: Eigenfunction Theory, some solvable cases. Network: Comput. Neural Syst., 14:249-272 (2003).

Basic mathematical theory for models of neuronal populations. Analysis Methods for Optical Imaging. (with E. Kaplan)In: Methods for In Vivo Optical Imaging of the Central Nervous System, (R. Frostig, ed). CRC Press, pp. 43-76 (2002). A basic review of available methods for extracting information from image records.

Turbulent drag reduction by passive mechanisms. (with S. Karlsson) Nature, 388:753-755 (1997). This is a joint experimental/theoretical paper that presents a procedure for reducing turbulent drag. (U.S. Patent No. 5, 362, 179, and others).

Dynamical models of interacting neuron populations in visual cortex. (with B. Knight and D. Manin) In: Symposium on Robotics and Cybernetics; Computational Engineering in Systems Application. (Gerf, E.C. ed) Cite Scientifique, Lille, France (1996). This is the fundamental paper, in neuroscience, on the dynamics and modeling of neuronal populations.

Turbulence and the dynamics of coherent structures, Parts I, II, and III, Quarterly of Applied Mathematics, XLV:561-590 (1987). This, and related papers, by L. Sirovich established the field of low dimension dynamical models.

A low dimensional procedure for identifying human faces. (with M. Kirby) Journal of Optical Society A, 4:519 (March 1987). All basic technology for machine recognition of human faces is based on this paper. It also develops the framework for general image analysis.

Effect of boundaries on the response of a neural network. (with S.E. Brodie, B.W. Knight) Biophys. Journal, 28: 423-446 (1979). This is a joint experimental/theoretical paper describing the behavior of the horseshoe crab visual system at a boundary. It led to astonishingly good agreement between theory and experiment, and represents a solved problem in biophysics.

On the propagation of forced soundwaves in rarefied gas-dynamics. (with J. Thurber) Journal of the Acoustical Society, 37:30 (February 1965). This paper solved the long standing problem of how sound traveled in dilute gases.

Current Publications

Large Scale Species Delimitation Method for Hyperdiverse Groups (with N. Puillandre, M.V. Modica, Y. Zhang, M.-C. Boisselier, C. Cruaund, M. Holford, S. Samadi) to appear (2012).

Spiking Neurons and the First Passage Problem (with B.Knight), Neural Computation, 23:1675-1703 (2011).

A Scalable Method for Analysis and Display of DNA Sequences (with M.Y. Stoeckle and Y. Zhang), PLoS ONE, 4:e7051 (2009).

Symmetry, Probability, and Recognition in Face Space (with M. Meytlis) PNAS, 106:6895-6899 (2009).

Populations of Tightly Coupled Neurons: the RGC/LGN System Neural Computation, 20:1179-1210 (2008).

Survival and Apoptotic Pathways Initiated by TNF-α: Modeling and Predictions (with P. Rangamani) Biotechnology and Bioengineering, 97:1216-1229 (2007).

On the Dimensionality of Face Space (with M. Meytlis) IEEE Transactions of Pattern Analysis and Machine Intelligence, 29: 1262-1267 (2007).

Source: www.brown.edu

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