) Not offered regularly; consult departmentUnits arranged [P/D/F]Can be repeated for credit. Grant, Same subject as STS.085[J] MATH5364. Prereq: Permission of instructor G (Spring)Units arrangedCan be repeated for credit. Basics of topology, Fundamental groups, covering spaces, Van Kampen's Theorem, categories and functors, singular homology, relative homology, Mayer-Vietoris sequence, cohomology, cup products, the cohomology ring of a space, CW complexes. Cost allocation. Cross-validation is a more statistically sound method for choosing the number of components in either PLSR or PCR. Topics include sorting; search trees, heaps, and hashing; divide-and-conquer; dynamic programming; greedy algorithms; amortized analysis; graph algorithms; and shortest paths. The package is implemented in MATLAB A least squares plane fit on a subset of displacement data is used to find the plane parameters in equations (13 Eberly D (2000) Least squares fitting of data. Prereq: None U (Fall, IAP, Spring, Summer)Units arranged [P/D/F]Can be repeated for credit. 3 Hours. Same subject as 2.78[J], HST.420[J]Prereq: Permission of instructor U (Fall)2-4-6 units. 3 Hours. You can also select a web site from the following list: Select the China site (in Chinese or English) for best site performance. constraints, First Choose Problem-Based or Solver-Based Approach, Nonnegative Linear Least Squares, Problem-Based, Large-Scale Constrained Linear Least-Squares, Problem-Based, Write Objective Function for Problem-Based Least Squares, Optimize Live Editor Task with lsqlin Solver, Nonnegative Linear Least Squares, Solver-Based, Jacobian Multiply Function with Linear Least Squares, Large-Scale Constrained Linear Least-Squares, Solver-Based, Code Generation in Linear Least Squares: Background, Optimization Code Generation for Real-Time Applications, Supported Operations for Optimization Variables and Expressions, Solve optimization problem or equation problem, Solve constrained linear least-squares problems, Solve nonnegative linear least-squares problem, Infinite bound support for code generation, Optimize or solve equations in the Live Editor. Introduces mathematical, algorithmic, and statistical tools needed to analyze geometric data and to apply geometric techniques to data analysis, with applications to fields such as computer graphics, machine learning, computer vision, medical imaging, and architecture. Particle methods and filtering. Topics include properties of limits of mappings, continuity of mappings, derivatives of mappings, and integrals of mappings from n-dimensional Euclidean space to m-dimensional Euclidean space. MATH1325. The solution provides the least squares solution z= Ax+ By+ C. 4 Hyperplanar Fitting of nD Points Using Orthogonal Regression It is also possible to t a plane using least squares where the errors are measured orthogonally to the proposed plane rather than measured vertically. Topics include conditional expectations, law of large numbers and central limit theorem, stochastic processes, including Poisson, renewal, birth-death, and Brownian motion. Prerequisites: MATH3321, MATH3335. Probability spaces, random variables, filtrations, conditional expectations, martingales, strong law of large numbers, ergodic theorem, central limit theorem, Brownian motion and its properties. The LMA is used in many software applications for solving generic curve-fitting problems. The Jacobian matrix as defined above is not (in general) a square matrix, but a rectangular matrix of size T Thus, PCR can lead to retaining variables that are unnecessary for prediction. MATH1421. D. M. Freeman, A. Hartz, L. P. Kaelbling, T. Lozano-Perez. Emphasizes construction of complete systems, including a five-axis robot arm, a fluorescent lamp ballast, a tomographic imaging station (e.g., a CAT scan), and a simple calculator. The use of mathematical software and calculators is required. That depends on what aspect of the model you consider. Topics include cameras and image formation, image processing and image representations, high-dynamic-range imaging, human visual perception and color, single view 3-D model reconstruction, morphing, data-rich photography, super-resolution, and image-based rendering. Introduces fundamental concepts of programming. MATH1327. Set design parameters and decisions as optimization variables. Fundamentals of digital signal processing with emphasis on problems in biomedical research and clinical medicine. Extension to moving materials. MATH4322. Teamwork skills include how to convene, launch, and develop various types of teams, including project teams. Bimatrix games and Nash equilibrium points. 3 Hours. For nonstationary series, they include methods for detrending and filtering. Systemic methodology for device sizing and biasing. Familiarity with MATLAB recommended. Homework exercises are based on theoretical derivation and software implementation. Topics covered include: constraint satisfaction in discrete and continuous problems, logical representation and inference, Monte Carlo tree search, probabilistic graphical models and inference, planning in discrete and continuous deterministic and probabilistic models including MDPs and POMDPs. {\displaystyle \mathbf {J} ^{\text{T}}\mathbf {J} } Integrated overview of the biophysics of cells from prokaryotes to neurons, with a focus on mass transport and electrical signal generation across cell membrane. Labs designed to strengthen background in signal processing and machine learning. Explores case studies of existing engineered systems to understand implications of different system architectures. For more information on extracting camera intrinsic parameters, see Evaluating the Accuracy of Single Camera Calibration. Particular attention paid to concurrent and distributed systems. Proposals subject to departmental approval. Topics include: motivation for quantum engineering, qubits and quantum gates, rules of quantum mechanics, mathematical background, quantum electrical circuits and other physical quantum systems, harmonic and anharmonic oscillators, measurement, the Schrdinger equation, noise, entanglement, benchmarking, quantum communication, and quantum algorithms. Prerequisite: Prior approval of Project Director. INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS. Same subject as 15.070[J]Prereq: 6.3702, 6.7700[J], 18.100A, 18.100B, or 18.100Q G (Spring)3-0-9 units, G. Bresler, D. Gamarnik, E. Mossel,Y. Polyanskiy, Prereq: Calculus II (GIR) or permission of instructor U (Fall)4-4-4 units. Designed for graduate students not majoring in mathematics. Basic properties of various classes of systems: observability, controllability, stability, and oscillating systems; optimal control problems and applications. N. Gershenfeld, J. DiFrancesco, J. Lavallee, G. Darcey, Prereq: Physics II (GIR) or permission of instructor U (Fall, Spring)2-8-2 units. Acad Year 2023-2024: G (Fall)3-0-9 units. Web browsers do not support MATLAB commands. Prereq: None G (Fall)Units arrangedCan be repeated for credit. Prereq: 6.100A or permission of instructor U (Spring) Introduces principles, algorithms, and applications of machine learning from the point of view of modeling and prediction; formulation of learning problems; representation, over-fitting, generalization; clustering, classification, probabilistic modeling; and methods such as support vector machines, hidden Markov models, and neural networks. Meets with undergraduate subject 6.2530, but requires the completion of additional/different homework assignments and or projects. Topics include specifications and invariants; testing, test-case generation, and coverage; abstract data types and representation independence; design patterns for object-oriented programming; concurrent programming, including message passing and shared memory concurrency, and defending against races and deadlock; and functional programming with immutable data and higher-order functions. Exposes students to the latest research in computational fabrication. {\displaystyle i} For the problem-based approach, create problem variables, and then MULTIVARIATE STATISTICAL METHODS. Hypothesis testing; detection; matched filters. Prerequisite: consent of instructor. {\displaystyle \mathbf {J} _{i}} Prerequisite: MATH5317. A comprehensive study of basic data analysis, focused on reasoning process of statistical investigations from asking question and collecting data to analyzing data and drawing inferences. Prereq: 6.3900 and 18.06 G (Spring)3-0-9 units. This Friday, were taking a look at Microsoft and Sonys increasingly bitter feud over Call of Duty and whether U.K. regulators are leaning toward torpedoing the Activision Blizzard deal. Probability: distributions and probabilistic calculations, inference methods, laws of large numbers, and random processes. 3 Hours. It's a little hard to see without being able to interactively rotate the figure, but the PLSR plot above shows points closely scattered about a plane. A comprehensive course including multiple linear regression, non-linear regression and logistic regression. It develops problem-solving and critical thinking skills. Acad Year 2023-2024: Not offered3-0-9 units. Prereq: Permission of instructor U (Fall, Spring)2-0-4 unitsCan be repeated for credit. Students taking graduate version complete additional assignments and an extended final project. MATHEMATICAL GAME THEORY. MATH5355. The application of electronics to energy conversion and control. Propositional calculus, sets and operations, functions, induction, counting, relations and matrices, equivalences and partial orders, graphs and shortest path algorithms, trees and minimal spanning trees, tree traversal, elements of boolean algebra. Boundary conditions and multi-region boundary-value problems. Topics include review of the basic properties of electromagnetic waves; coherence and interference; diffraction and holography; Fourier optics; coherent and incoherent imaging and signal processing systems; optical properties of materials; lasers and LEDs; electro-optic and acousto-optic light modulators; photorefractive and liquid-crystal light modulation; spatial light modulators and displays; near-eye and projection displays, holographic and other 3-D display schemes, photodetectors; 2-D and 3-D optical storage technologies; adaptive optical systems; role of optics in next-generation computers. % Set random seed to generate reproducible results. Machine learning: linear classification, fundamentals of supervised machine learning, deep learning, unsupervised learning, and generative models. Acad Year 2023-2024: G (Spring)3-1-8 units. Subject meets with 6.8800[J], 16.456[J], HST.582[J]Prereq: (6.3700 or permission of instructor) and (2.004, 6.3000, 16.002, or 18.085) U (Spring)3-1-8 units, Same subject as HST.580[J]Prereq: 6.3010 Acad Year 2022-2023: Not offered Limit theorems. {\displaystyle S\left({\boldsymbol {\beta }}\right)} Password confirm. Develops a common conceptual framework based on invariants, abstraction, and modularity applied to state and labeled transition systems. Prereq: None U (Fall, Spring) Topics may vary year to year. The objective is to bring students to the research frontier. Students taking graduate version complete different assignments. respectively. Prerequisite: MATH5307. Same subject as 7.33[J]Prereq: (6.100A and 7.03) or permission of instructor Acad Year 2022-2023: Not offered 3 Hours. Performance and robustness trade-offs. Begins with basic principles of networking. 3 Hours. Prereq: Permission of instructor G (Fall)2-0-4 units. x INTRODUCTION TO LINEAR ALGEBRA. Teams should have members with varying engineering, programming and mechanical backgrounds. Suboptimal methods. The HDL-64 sensor captures data as a set of PNG images and corresponding PCD point clouds. Subject meets with 2.796[J], 6.4822[J]Prereq: Physics II (GIR), 18.03, or permission of instructor Acad Year 2022-2023: Not offered MATHEMATICAL STATISTICS I. Similarly, the PCA loadings describe how strongly each component in the PCR depends on the original variables. Prerequisite: MATH5358/STATS5358 (Regression Analysis) or equivalent. INTRODUCTION TO MATHEMATICAL CONTROL THEORY. Preference to first-year students in the Gordon Engineering Leadership Program. {\displaystyle {\boldsymbol {\beta }}+{\boldsymbol {\delta }}} Solve linear least-squares problems subject to bound and linear constraints. Studies of the quasistatic fields and their sources through solutions of Poisson's and Laplace's equations. See description for 6.047. Applications to cost allocation, fair division, and voting power. + Focuses on the physics of the interaction of photons with semiconductor materials. {\displaystyle \lambda } {\displaystyle {\boldsymbol {a}}_{k}} FUNCTIONAL ANALYSIS II. empirical pairs The existence and properties of solution of differential equations. {\displaystyle {\boldsymbol {\beta }}} Covers a variety of topics in optimization, with a focus on non-convex optimization. Statistical analysis for data collected in several variables, topics including sampling from multivariate normal distribution, Hotelling's T'2, multivariate analysis of variance, discriminant analysis, principal components, and factor analysis.