**Yaser Abu-Mostafa**
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Professor of Electrical Engineering and Computer Science
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Machine learning applies to any situation where there is data that we are trying to make sense of, and a target function that we cannot mathematically pin down. The spectrum of applications is huge, going from financial forecasting to medical diagnosis to industrial inspection to recommendation systems, to name a few. The field encompasses neural networks, statistical inference, and data mining.

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**Aaron D. Ames**
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Bren Professor of Mechanical and Civil Engineering and Control and Dynamical Systems
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Professor Ames’ research interests center on robotics, nonlinear control, hybrid systems and cyber-physical systems, with special emphasis on foundational theory and experimental realization on robotic systems; his lab designs, builds and tests novel bipedal robots and prosthesis with the goal of achieving human-like bipedal robotic walking and translating these capabilities to robotic assistive devices.

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**Alan H. (Al) Barr**
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Professor of Computer Science
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Professor Barr's research involves (1) mathematical simulation methods for computer graphics (2) developing new types of mathematical and computational methods for the study of biophysical behaviors and structures and (3) technological leveraging for medical health care and new medical devices.

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**Oscar P. Bruno**
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Professor of Applied and Computational Mathematics
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Prof. Bruno's work focuses on development of accurate, high-performance numerical PDE solvers capable of modeling faithfully realistic scientific and engineering configurations. Major theoretical and computational difficulties arise in associated areas of PDE theory, numerical analysis and computational science as a result of intricate and/or singular geometries as well as solution singularities, resonances, nonlinearities, high-frequencies, dispersion, etc. Recently developed Fourier Continuation (FC) and integral-equation techniques, which can successfully tackle such challenges, have enabled accurate solution of previously intractable PDE problems of fundamental importance in science and engineering.

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**Joel W. Burdick**
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Richard L. and Dorothy M. Hayman Professor of Mechanical Engineering and Bioengineering; Jet Propulsion Laboratory Research Scientist
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Professor Burdick focuses on robotics, kinematics, mechanical systems and control. Active research areas include: robotic locomotion, sensor-based motion planning algorithms, multi-fingered robotic manipulation, applied nonlinear control theory, neural prosthetics, and medical applications of robotics.

**Venkat Chandrasekaran**
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Assistant Professor of Computing and Mathematical Sciences and Electrical Engineering
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Chandrasekaran’s research interests lie in mathematical optimization and its application to the information sciences.

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**Mathieu Desbrun**
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Carl F Braun Professor of Computing and Mathematical Sciences
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Applied geometry (geometry processing and computer graphics); Discrete differential modeling (differential, yet readily-discretizable tools for computational modeling).

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**John C. Doyle**
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Jean-Lou Chameau Professor of Control and Dynamical Systems, Electrical Engineering, and Bioengineering
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Doyle's research is on theoretical foundations for complex tech, bio, med, neuro, and social networks integrating control, communications, computing, and multiscale physics. Layered architectures such as brains integrate high level planning with fast lower level sensing, reflex, and action and facilitate learning, adaptation, augmentation (tools), and teamwork, despite being implemented in energy efficient hardware with sparse, quantized, noisy, delayed, and saturating sensing, communications, computing, and actuation, on time scales from milliseconds to minutes to days. We are developing a mathematical framework that deals with all of these features and constraints in a coherent and rigorous way with broad applications in science and technology.

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**Yizhao T. (Thomas) Hou**
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Charles Lee Powell Professor of Applied and Computational Mathematics
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Professor Hou focuses on multiscale problems arising from geophysical applications and fluid dynamics, the Millennium Problem on the 3D incompressible Navier-Strokes equations, model reduction for stochastic problems with high dimensional input variables, and adaptive data analysis.

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**Katrina A. Ligett**
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Assistant Professor of Computer Science and Economics
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Professor Ligett's research focuses on mathematical and computational approaches to fundamental problems in algorithmic game theory and in data privacy.

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**Steven H. Low**
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Professor of Computer Science and Electrical Engineering
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Power systems, cyber-physical systems, network architecture, energy-efficient networking.

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**Daniel I. (Dan) Meiron**
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Fletcher Jones Professor of Aeronautics and Applied and Computational Mathematics
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Professor Meiron's research focuses on computation and modelling of basic fluid mechanical phenomena. Particular interests include shock driven flow instabilities, turbulence, simulation approaches for high strain rate solid mechanics. He is also interested on development of adaptive numeriocal methods for such flows that are suitable for high performance computation.

Research Group
**Richard M. Murray**
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Thomas E. and Doris Everhart Professor of Control and Dynamical Systems and Bioengineering
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Research in Richard Murray's group is in the application of feedback and control to networked systems, with applications in biology and autonomy. Current projects include novel control system architectures, biomolecular feedback systems and networked control systems.

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**Houman Owhadi**
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Professor of Applied and Computational Mathematics and Control and Dynamical Systems
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Professor Owhadi focuses on the modeling and analysis of systems characterized by multiple scales, geometric structures, noise and uncertainties. At the center of his work are fundamental problems such as non-separated scales, anomalous diffusion, the geometric integration of multi-scale stochastic mechanical systems and the optimal quantification of uncertainties in presence of limited information.

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**Lior S. Pachter**
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Bren Professor of Computational Biology and Computing and Mathematical Sciences
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Professor Patcher is a computational biologist working in genomics. His career began in comparative genomics, and initially was interested in genome alignment, annotation, and the determination of conserved regions using phylogenetic methods. More recently he's become focused on functional genomics, which includes answering questions about the function and interaction of DNA, RNA and protein products. He's particularly interested in applications of high-throughput sequencing to RNA biology. Genomics requires the development of algorithms, statistical methodology and mathematical foundations, and a major part of his research is therefore on methods.

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**Niles A. Pierce**
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Professor of Applied and Computational Mathematics and Bioengineering
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Engineering small conditional DNAs and RNAs for signal transduction in vitro, in situ, and in vivo; computational algorithms for the analysis and design of nucleic acid systems; programmable molecular instruments for readout and regulation of cell state.

Research Group
**Peter Schroeder**
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Shaler Arthur Hanisch Professor of Computer Science and Applied and Computational Mathematics
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Professor Schröder is interested in the design of efficient and reliable algorithms for problems in computer graphics. These range from geometric modeling (effective methods to model the shape of objects) to animation (simulation of physical phenomena such as the deformation of cloth). His emphasis is on an area known as "Discrete Differential Geometry." Its goals are to rebuild the foundations of classical differential geometry in a discrete setting which makes it immediately useful for computation.

**Leonard J. Schulman**
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Professor of Computer Science
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Algorithms and Communication Protocols; Combinatorics and Probability; Coding and Information Theory; Quantum Computation.

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**Andrew M. Stuart**
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Bren Professor of Computing and Mathematical Sciences
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Professor Stuart's research is focused on the development of mathematical and algorithmic frameworks for the seamless integration of models with data. He works in the Bayesian formulation of inverse problems, and in data assimilation for dynamical systems. Quantification of uncertainty plays a significant role in this work. Current applications of interest include a variety of problems in the geophysical sciences, and in graph-based learning.

**Joel A. Tropp**
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Steele Family Professor of Applied and Computational Mathematics
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Joel Tropp's work lies at the interface of applied mathematics, electrical engineering, computer science, and statistics. This research concerns the theoretical and computational aspects of data analysis, sparse modeling, randomized linear algebra, and random matrix theory.

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**Christopher M. (Chris) Umans**
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Professor of Computer Science
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Professor Umans is interested in theoretical computer science, and especially computational complexity. He enjoys problems with an algebraic flavor, and this often leads to research questions in derandomization and explicit combinatorial constructions, algebraic algorithms, coding theory, and hardness of approximation.

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**Thomas G. Vidick**
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Associate Professor of Computing and Mathematical Sciences
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Thomas Vidick's research is situated at the interface of theoretical computer science, quantum information and cryptography. He is interested in using complexity theory as a lens to approach fundamental problems in quantum computing. He has investigated the role of entanglement in multi-prover interactive proof systems and obtained the first substantial computational hardness results on the power of entangled provers. He has made important contributions to the field of device-independent cryptography, where the property of entanglement monogamy plays a key role. His work also demonstrates that insights from quantum information theory can be productively transferred to yield novel perspectives on fundamental techniques in theoretical computer science such as semidefinite programming and approximation algorithms.

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**Adam Wierman**
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Professor of Computing and Mathematical Sciences; Executive Officer for Computing and Mathematical Sciences; Director, Information Science and Technology
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Adam Wierman's research focuses on three seemingly distinct areas: networks, economics, and energy. Though diverse, the areas are each essential to his broader research goal: easing the incorporation of renewable energy into IT and, more generally, into the electricity grid. His work toward this goal is diverse in both area and technique. It not only draws on tools from algorithms, networking, operations research, economics, and control -- starting from theory and continuing through implementation to industrial transfer.

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**Erik Winfree**
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Professor of Computer Science, Computation and Neural Systems, and Bioengineering
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Professor Winfree's research involves theoretical and experimental aspects of molecular programming. Models of computation are developed that incorporate essential features of molecular folding, molecular self-assembly, biochemical circuits, and molecular robotics. These models are studied to determine their expressiveness for programming molecular-level tasks including decision-making, memory, behavior, and morphogenesis. Methods for compiling abstract molecular programs into actual molecules are developed and tested in the laboratory.

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**Yisong Yue**
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Assistant Professor of Computing and Mathematical Sciences
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Yisong Yue's research interests lie primarily in the theory and application of statistical machine learning. He is particularly interested in developing novel methods for structured prediction, spatiotemporal reasoning, adaptive learning systems, and learning with humans in the loop. In the past, his research has been applied to information retrieval, content recommendation, text classification, learning from rich user interfaces, analyzing implicit human feedback, data-driven animation, sports analytics, policy learning in robotics, and adaptive routing and allocation problems.

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