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Applied Mathematics, Division of
34 matches found.
 | Lucien Bienenstock
Applied Mathematics, Division of
Neuroscience, Department of
Elie Bienenstock studies the mechanisms used by brains to create and compose complex representations. His research, focusing on models of vision, assumes that brains use compositional hierarchies of explicit and detailed representations of objects, parts, and relationships. With colleagues in neuroscience and applied math, he investigates the hypothesis that the fine temporal structure of cortical activity, e.g. the synchronous firing of neurons, plays an important role in these representations. |  | Frederic Bisshopp
Applied Mathematics, Division of
Professor Bisshopp's research work continues to make significant contributions to the fields of hydrodynamic stability, thermal convection, perturbation theory, rotating fluids, nonlinear waves and wavepackets. His work also involves the areas of electromagnetic theory, optimization, complex analysis, numerical analysis, computer graphics and partial differential equations. His other work in progress includes water waves, stratified flows, rotating flows, global circulation models, capillary waves on jets, waves on beaches, flow visualization, computer graphics and more numerical analysis. |  | Constantine Michael Dafermos
Applied Mathematics, Division of
I work on the interface between continuum mechanics and the theory of partial differential equations. In recent years, my research has focused on nonlinear hyperbolic systems of conservation laws, whose solutions spontaneously develop singularities that propagate as shock waves. I am interested in the interplay between thermodynamics and analysis, in the theory of these systems, and have been striving to elucidate the fundamental role of entropy, as a stabilizing agent. |  | Philip Davis
Applied Mathematics, Division of
Professor Davis' books, The Mathematical Experience and Descartes' Dream, written jointly with Reuben Hersh of the University of New Mexico, explore certain questions in the philosophy of mathematics, and the role of mathematics in society. They have been translated into practically all major European and Oriental languages. His important writings in the philosophy of mathematics have been widely anthologized. The Mathematical Experience won an American Book Award for 1983. |  | Bo Dong
Applied Mathematics, Division of
I am interested in numerical methods for partial differential equations. Currently, I am particularly interested in the analysis of the discontinuous Galerkin methods, hybridized Galerkin methods and mixed methods for second-order elliptic equations, transport equations, biharmonic equations and KdV type equations. |  | Hongjie Dong
Applied Mathematics, Division of
My main research interest is in partial differential equations, including nonlinear elliptic and parabolic equations, the Navier-Stokes equations, the quasi-geostrophic equations, the reaction diffusion equations, the probability approaches of PDEs, and rates of convergence of finite difference approximations for elliptic and parabolic Bellman's equations. I am also interested in the probability theory and stochastic partial differential equations. |  | Paul Dupuis
Applied Mathematics, Division of
My main interests are in applications of probability and in the control of deterministic and stochastic processes. Tools used are large deviation theory, which explains how rare events occur in random processes, numerical methods such as Markov chain approximations and Monte Carlo simulation, and partial differential equations. |  | Peter Falb
Applied Mathematics, Division of
Professor Falb's research interests are in the areas of systems science and engineering, particularly algebraic and geometric methods, parametric dependence, numerical methods, multivariable linear systems, and infinite dimensional stochastic systems, as well as control and stability theory and mathematics of investment. |  | Wendell Fleming
Applied Mathematics, Division of
Fleming's current research interests are in stochastic control and related topics in applied probability and the theory of differential games. Areas of application include mathematical finance: in particular, stochastic control models of investment, production, and consumption. |  | Walter Freiberger
Applied Mathematics, Division of
Please consult my complete list of publications and theses supervised (below) for an indication of my research interests. More recently, these have included computational and statistical molecular biology. |  | Stuart Geman
Applied Mathematics, Division of
What are the basic principles of representation and computation in the nervous system? Cognitive scientists have argued for a theory based upon compositionality, which refers to the evident ability of brains to represent objects, scenes, thoughts and actions in a hierarchical structure. I am studying a mathematical formulation for compositionality, and the implications of this formulation for interpreting neural activity patterns and for building computer vision systems. |  | Basilis Gidas
Applied Mathematics, Division of
The research interests of Professor Basilis Gidas the past eight years have been in transcriptional regulatory networks, signal transduction pathways,and ab initio protein folding, using Bayesian statistics and Chomsky type grammars. The work emphasizes: Myc regulatory networks and pathways in cell-growth, cell proliferation, and apoptosis, using Microarray and ChIp-chip data, and cross-species comparison; finding phosphorylation site motifs via tandem mass spectrometry, and structural information of kinases and substrates; ab initio protein folding using compositional/syntactic representations of proteins. |  | Ulf Grenander
Applied Mathematics, Division of
Professor Grenander's research involves a broad range of seminal contributions within the area of Applied Mathematics, and upon the ongoing development of a remarkable Pattern Theory and its applications to image analysis.
His current research interests focus on the the creation of a new theory of regular structure (pattern theory) and its application to the actual and man-made world. Also of interest is the development of the theory of statistical inference on stochastic processes and abstract spaces, by functional analytic methods. Work is directed toward the development of algorithms for medical image processing, and a unified theory of automatic target recognition. |  | Yan Guo
Applied Mathematics, Division of
Professor Guo's research is concerned with the rigorous mathematical study of partial differential equations arising in various scientific applications, such as kinetic and fluid models for plasma physics, vortices in classical field theory (superconductivity and superfluidity), and stability problems in stellar dynamics, and other physical problems. |  | Johnny Guzman
Applied Mathematics, Division of
My main research interest lies in the area of numerical approximations to partial differential equations (PDEs). I work in devising new numerical methods for various PDEs and analyzing new or existing numerical methods. |  | Matthew Harrison
Applied Mathematics, Division of
My research has focused primarily on applications related to neuroscience, information theory and computer vision. These topics provide ample opportunities to participate in collaborative, interdisciplinary research, something that I value and enjoy, and they relate to a subject that I find fascinating: the mathematical and computational foundations of learning and intelligence. They also provide an endless supply of interesting mathematical and statistical problems. |  | Jan Hesthaven
Applied Mathematics, Division of
The research interests of Prof Hesthaven can broadly be defined as the development, analysis, and application of high-order accurate methods for the solution of partial differential equations. Particular emphasis is on high-order finite difference and spectral methods, and spectral element and discontinuous Galerkin methods, in particular for problems in complex geometries. Applications include gas dynamics, electromagnetic scattering, micro optics and photonics, plasma physics, and cosmology. |  | George Karniadakis
Applied Mathematics, Division of
Professor Karniadakis's research interests include diverse topics in computational science both on algorithms and applications. A main current thrust is stochastic multiscale modeling of physical and biological systems. |  | Harold Kushner
Applied Mathematics, Division of
Professor Kushner's current research interests include stochastic control and stochastic systems theory, approximation methods, limit theorems and optimization methods for complex stochastic systems and stochastic networks (such as heavy traffic theory and control). Professor Kushner's work also involves nonlinear filtering, applications to adaptive and competitive learning processes and in communication theory. |  | Charles Lawrence
Applied Mathematics, Division of
Charles (Chip) Lawrence has been involved in computational biology research since the early 1980's. His research now specifically focuses on the application of Bayesian algorithms that he and his collaborators have developed, leading to biological insights on transcription regulation and identification of regulatory motifs in prokaryotic and eukaryotic sequences, comparative genomics, antisense oligonucleotide and siRNA design, the composition of nucleotide sequences and detailed analyses of several protein families. |  | John Mallet-Paret
Applied Mathematics, Division of
Professor Mallet-Paret studies ordinary and functional differential equations. |  | Martin Maxey
Applied Mathematics, Division of
Professor Maxey's research in fluid dynamics is focused on dispersed two-phase flows such as suspensions of particles in liquids. Current applications of interest include self-assembly in micro-scale flows, swimming of single cell organisms and blood flow. Other research areas include turbulent flows and mixing with applications to physical and geophysical systems. |  | Donald McClure
Applied Mathematics, Division of
Donald McClure does research in the areas of image processing and computer vision, ill-posed inverse problems, and analysis of image sequences such as occur in film or progressive video. Current work includes the relationship between optimization problems for discrete probabilistic models of images and continuous variational counterparts of these problems that lead to PDEs. He is also working on methods of nonlinear function approximation that relate to image compression. |  | Govind Menon
Applied Mathematics, Division of
I work on dynamical systems and partial differential equations arising in fluid mechanics, materials science and physical chemistry. My recent work has been on the scaling laws that appear in many guises in these areas. The main goal is to rigorously pin down these deceptively simple laws with methods from analysis and probability theory. |  | David Mumford
Applied Mathematics, Division of
Please visit my webpages at http://www.dam.brown.edu/people/mumford/index.html |  | Boris Rozovsky
Applied Mathematics, Division of
My main interests are in stochastic partial differential equations (SPDEs) and their applications. As its name suggests, SPDEs is an interdisciplinary area at the crossroads of stochastic processes and partial differential equations. In recent years, my research has focused on the development of spectral methods, in particular, the Wiener Chaos expansions for SPDEs. Applications of SPDEs to fluid dynamics in turbulent flows and nonlinear filtering (Hidden Markov Models) for spatial-temporal processes are the applications of SPDEs I am most interested in. |  | Bjorn Sandstede
Applied Mathematics, Division of
My recent research focuses on the formation and dynamics of patterns and nonlinear waves. More generally, my expertise is in
- Dynamics and stability of patterns and nonlinear waves
- Dynamical systems, ordinary and partial differential equations
- Homoclinic and heteroclinic phenomena
- Symmetry in dynamical systems
- Nonlinear optics |  | Chi-Wang Shu
Applied Mathematics, Division of
Professor Shu has a variety of research interests including: numerical solutions of conservation laws; convection dominated problems using finite difference (essentially non-oscillatory (ENO) methods and weighted ENO (WENO) methods); finite element discontinuous Galerkin methods and spectral methods; numerical solution of Hamilton-Jacobi type equations; computational fluid dynamics; and numerical solution of equations appearing in semi-conductor device simulations. |  | Suzanne Sindi
Applied Mathematics, Division of
Dr. Sindi's research area focuses on varied problems in applied non-linear dynamics. She is particularly interested in computational biology and genomics as well as ideas concerning the measure theoretic properties of dynamical systems. |  | Konstantinos Spiliopoulos
Applied Mathematics, Division of
My research has focused on asymptotic problems for stochastic
processes and PDE's, wave front propagation and probability theory. Other recent interests of mine are related to the use of asymptotics for stochastic equations and PDE's in analyzing models coming from applied problems (e.g., physics, mathematical biology and mathematical finance), asymptotic problems for stochastic partial differential equations and statistical inference for stochastic processes. |  | Chau-Hsing Su
Applied Mathematics, Division of
Current Research areas comprise the study of spatial random processes which satisfy bilateral second order dynamical systems. These processes are found to be governed by a modified Helmholtz equation. A number of covariant functions have been constructed in one and higher dimensions. Research also involves shock wave propagation under the influence of randomly moving objects and by rouge surfaces characterized by spatially random processes. |  | William Thompson
Applied Mathematics, Division of
To turn the genetic blueprint into a functional organism, genes must be expressed in a specific temporal and spatial pattern. Finding the signals that control this expression and understanding their interactions is a key to learning the language of the genes. One of the first steps in this process is locating the regulatory elements directly encoded in DNA sequences. The focus of my research is to develop computational methods to locate these key regulatory elements. |  | Ian Tice
Applied Mathematics, Division of
Dr. Tice's research focuses on partial differential equations, variational methods, the Ginzburg-Landau model, phase transitions, harmonic analysis, classical field theories, and high energy physics. |  | Hui Wang
Applied Mathematics, Division of
My research interest lies in the theory and applications of probabilistic methods. Recently, I have been working on game-theoretic importance sampling (IS). Importance sampling is a variance reduction technique in Monte Carlo simulation, and can be especially effective when the quantities of interest are largely determined by rare events. |
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