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Research in evolutionary computation at our department focuses on the design, analysis, and applications of the genetic and evolutionary algorithms that can solve difficult problems in a robust and scalable manner. The following faculty are involved in evolutionary computation research: Uday Chakraborty, Mark Hauschild, Cezary Janikow.
Computer Graphics and Image Manipulations
Research in computer graphics and image manipulations in the Department of Mathematics and Computer Science focuses on mathematical modeling and analysis, as well as algorithm and software development for various problems in both image-based and object-based computer graphics. Our research directions include mathematics of imaging, surface subdivision schemes, non-photorealistic rendering, image-based rendering, terrain modeling, meshleess wavelet compression, point-based graphics, image database indexing, storage, and retrieval. The following faculty are involved in the graphics-related research: Sanjiv Bhatia, Charles Chui, Wenjie He, Qingtang Jiang, Henry Kang.
Networking and Communications
Research in networking and communications in the Department of Mathematics and Computer Science focuses on designing cutting-edge protocols and architectures for current and future Internet, improving the performance, security and reliability of mobile and fixed networks, and providing innovative methods for future network services. Our research directions include future Internet architecture, mobile and cloud computing, cyber security, network function virtualization (NFV), Internet of Things (IoTs), energy efficiency in smart buildings, and Smart Grids. The following faculty are involved in networking and communications research: Jianli Pan
Algebra, Geometry and Topology
Faculty in this group focus on algebraic geometry, group theory, topology and string theory. Adrian Clingher does research on string theory, moduli spaces, K3 surfaces and Calabi-Yau manifolds. Ronald Dotzel does research on transformation groups and invariants of topological spaces. Prabhakar Rao and Ravindra Girivaru do research on algebraic vector bundles, hypersurfaces and varieties in projective spaces.
Faculty in this group, including Charles Chui, Wenjie He, and Qingtang Jiang are active researchers in Computational Harmonic Analysis, Computer-aided Geometric Design, and Approximation Theory, with emphasis on the theory and methods of Multivariate Splines and Wavelets. They are also members of the Institute of Computational Harmonic Analysis which is an integrated unit of the department.
Probability and Statistics
Research in Probability and Statistics in the Department of Mathematics and Computer Science is focused on theoretical as well as on the computational aspects of these disciplines. Haiyan Cai conducts research in Statistics and Probability with focus in the areas of statistical modeling, statistical computations, spatial statistics, Markov random fields, and their applications. Nevena Marić does research in Probability and Stochastic Processes including subjects as Interacting Particle Systems, Point Processes, and Perfect simulation techniques. Yuefeng Wu conducts research in Bayes data analysis, non-parametric method, and inference on dynamic system.
Advances in the biological sciences are accelerating at an unparalleled rate, producing massive amounts of data and providing unprecedented opportunities for major dvances in medical and environmental domains. Sophisticated computer science, statistical, and mathematical tools are indispensable for reasoning about these data and unveiling hidden truths that are unreachable using experimental and theoretical approaches alone. Computational biology, biostatistics, and bioinformatics are overlapping fields aimed at filling this demand. More broadly, the adaptation and fusion of combinatorial optimization, artificial intelligence, statistics and applied mathematics, imaging, evolutionary computation, machine learning, mathematical programming, and data mining techniques provide potential for the production of novel specialized solutions. The integration of mathematics and computer science in our department makes us well poised for the interdisciplinary demands and rapidly evolving challenges this field presents. Our current research includes network modeling, mixed integer linear programming, statistics, and clustering applied to combinatorial genetics, gene co-expression, combinatorial proteomics, and haplotype inference problems arising in the research of Alzheimer disease, psoriasis, hypertensive heart failure, vitamin D metabolism, and human population genetics. The following faculty are involved in biological data research: Sharlee Climer