| source Brown University (X) |
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department |
Review of the theory of stochastic differential equations and reflected SDEs, and of the ergodic and stability theory of these processes. Introduction to the theory of weak convergence of probability measures and processes. Concentrates on applications to the probabilistic modeling, control, and approximation of modern communications and queuing networks; emphasizes the basic methods, which are fundamental tools throughout applications of probability. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
Advanced Statistical Inference. Emphasis on the theoretical aspects of the subject. Frequentist and the Bayesian approaches, and their interplay. Topics include: general theory of inference, point and set estimation, hypothesis testing, and modern computational methods (E-M Algorithm, Markov Chain Monte Carlo, Bootstrap). Students should have prior knowledge of probability theory, at the level of APMA 2630 or higher. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
The course provides a solid presentation of modern nonparametric statistical methods. Topics include: density estimation, adaptive smoothing, cross-validation, bootstrap, classification and regression trees and their connection to the Huffman code, projection pursuit, the ACE algorithm for time series prediction, support vector machines, and learning theory; the course will provide the mathematical underpinnings, but it will also touch upon some applications in computer vision/speech recognition, and biological, neural, and cognitive sciences. Prerequisite: APMA 2670 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Prerequisites: Graduate level APMA 2670 Minimum Grade of S Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
No description available. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Do not Schedule Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
No description available. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Do not Schedule Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
Information theory and its relationship with probability, statistics, and data compression. Entropy. The Shannon-McMillan-Breiman theorem. Shannon's source coding theorems. Statistical inference; hypothesis testing; model selection; the minimum description length principle. Information-theoretic proofs of limit theorems in probability: Law of large numbers, central limit theorem, large deviations, Markov chain convergence, Poisson approximation, Hewitt-Savage 0-1 law. Prerequisites: Am 263; AM 171. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
The courses mentioned below are graduate level seminars. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Do not Schedule Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
Provides an up-to-date presentation of the main problems and algorithms in bioinformatics. Emphasis is given to statistical/ probabilistic methods for various molecular biology tasks, including: comparison of genomes of different species, finding genes and motifs, understanding transcription control mechanisms, analyzing microarray data for gene clustering, and predicting RNA structure. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
Provides an up-to-date presentation of problems and algorithms in bioinformatics, beginning with an introduction to biochemistry and molecular genetics. Topics include: proteins and nucleic acids, the genetic code, the central dogma, the genome, gene expression, metabolic transformations, and experimental methods (gel electrophoresis, X-ray crystallography, NMR). Also, algorithms for DNA sequence alignment, database search tools (BLAST), and DNA sequencing. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
No description available. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
No description available. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
No description available. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
No description available. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
No description available. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
No description available. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
We shall present on some models in the quantum chemistry field (Thomas Fermi and related, Hartree Fock, Kohn Sham) the basic tools of functional analysis for the study of their solutions. Then some of the discretization methods and iterative algorithms to solve these problems will be presented and analyzed. Some of the open problems that flourish in this field will also be presented all along the lectures. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
No description available. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
Develops the ideas of algebraic geometry in the context of control theory. The first semester examines scalar linear systems and affine algebraic geometry while the second semester addresses multivariable linear systems and projective algebraic geometry. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
No description available. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
Nonlinear instabilities as well as boundary effects in a collisionless plasmas; Stable galaxy configurations; A nonlinear energy method in the Boltzmann theory will also be introduced. Self-contained solutions to specific concrete problems. Focus on ideas but not on technical aspects. Open problems and possible future research directions will then be discussed so that students can gain a broader perspective. Prerequisite: One semester of PDE (graduate level) is required. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
Aspects of the theory on nonlinear evolution equations, which includes kinetic theory, nonlinear wave equations, variational problems, and dynamical stability. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
This course develops the theory and some applications of stochastic differential equations. Topics include: stochastic integral with respect to Brownian motion, existence and uniqueness for solutions of SDEs, Markov property of solutions, sample path properties, Girsanov's Theorem, weak existence and uniqueness, and connections with partial differential equations. Possible additional topics include stochastic stability, reflected diffusions, numerical approximation, and stochastic control. Prerequisite: APMA 2640 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
Basic concepts of asymptotic approximations with examples with examples such as evaluation of integrals and functions. Regular and singular perturbation problems for differential equations arising in fluid mechanics, wave propagation or nonlinear oscillators. Methods include matched asymptotic expansions and multiple scales. Methods and results will be discussed in the context of applications to physical problems. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
In this seminar course we will cover the algorithm formulation, stability analysis and error estimates, and implementation and applications of discontinuous Galerkin finite element methods for solving hyperbolic conservation laws, convection diffusion equations, dispersive wave equations, and other linear and nonlinear partial differential equations. Prerequisite: AM 255 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
The course presents computational and statistical methods for gene and protein networks and structural proteomics; it emphasizes: (1) Probablistic models for gene regulatory networks via microarray, chromatin immunoprecipitation, and cis-regulatory data; (2) Signal transduction pathways via tandem mass spectrometry data; (3) Molecular Modeling forligand-receptor coupling and docking. The course is recommended for graduate students. 1.000 Credit Hours 1.000 Lecture hours Levels: Graduate, Undergraduate Schedule Types: Primary Meeting Graduate School College Applied Mathematics Department Return to Previous New Search
Score: 5.0149603 Details | Listing | Web page
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