|8:15||9:00||Registration & breakfast|
|9:15||9:45||Invited talk, J. Johnson: "ECCAD Past and Future"|
|9:45||10:30||Invited talk, M.A. Burr: "Certified Subdivision Algorithms in Computer Algebra"|
|10:30||11:00||Coffee break & poster session|
|11:00||11:45||Invited talk, A. Mahdi: "Computer Algebra in Dynamical Systems and Biology"|
|12:00||1:45||Lunch at the R. David Thomas Center (sponsored by Duke CS)|
|1:45||2:15||Invited talk, A.S. Iliopoulos: "Sparse and Structured Embeddings in Matrix Algebra: Analysis & Applications"|
|2:15||3:00||Invited talk, M.C. Lin: "Computer Algebra in Physics-based Modeling"|
|3:00||3:30||Coffee break & poster session|
|3:30||5:00||Panel discussion: Emerging directions & thesis topics|
|Tour of Duke chapel and gardens|
Professor of Computer Science and Electrical & Computer Engineering
Title: "ECCAD Past
Abstract: This year marks the 20th anniversary of East Coast Computer Algebra Day (ECCAD), which was first held at Drexel University in Philadelphia and was inspired by Bruce Char's goal to establish a regional low cost venue for computer algebra researchers to share recent results and to discuss problems. The one day meeting was arranged around a mixture of invited talks and poster sessions with plenty of time for informal discussion. Student participation was emphasized, with a desire to attract new researchers to the field and to give them a venue to learn about computer algebra and to promote their work. In this talk we review the history, highlights, and challenges of the past 20 years of ECCAD conferences and discuss ideas for sustaining ECCAD well into the future.
Professor Johnson's research interests include algebraic algorithms, computer algebra systems, problem-solving environments, programming languages and compilers, high performance computing, hardware generation, and automated performance tuning. He has co-founded SPIRAL, a joint research project with Carnegie Mellon University, University of Illinois at Urbana-Champaign, and ETH Zürich, to develop techniques for automatically implementing and optimizing signal processing algorithms. Furthermore, he directs the Applied Symbolic Computing Lab (ASYM) whose projects pertain to signal processing, communications, scientific computing, computer algebra, as well as power systems funded by DARPA, NSF, DOE, and Intel. He has served as chair of the ACM special-interest group on symbolic and algebraic manipulation (SIGSAM), and the Franklin Institute Computer and Cognitive Science cluster in the Committee on Science and the Arts. Professor Johnson co-hosted, together with Professor Char and Professor Lakshman, the first ECCAD, held at Drexel University.
Assistant Professor of Mathematical Sciences
Title: "Certified Subdivision Algorithms
in Computer Algebra"
Abstract: Subdivision algorithms iteratively subdivide subsets of real or complex space until a local, terminal condition is reached. The prototypical example of such algorithms is the marching cubes algorithm. In computer algebra, subdivision algorithms have appeared in the root isolation algorithms based on Sturm sequences, Descartes' rule of signs, and continued fractions. Subdivision algorithms are of current interest because they are (1) often simple recursive algorithms and (2) they allow the interaction of global symbolic data with local numerical data. These algorithms, therefore, may be practical because they are efficient, easy to implement, and can use local data to circumvent symbolic bottlenecks. In this talk, we will discuss recent progress in subdivision algorithms for approximating algebraic varieties whose output is certified to be correct. We will also examine a general method for computing the complexity of these algorithms based on the new technique of continuous amortization.
Prior to joining Clemson University, Professor Burr held the position of Peter M. Curran Visiting Research Instructor at Fordham University. He got his Ph.D. in 2010, under Professor Fedor Bogomolov at the Courant Institute of Mathematical Sciences. His thesis topic was Asymptotic Cohomological Vanishing Theorems and Applications of Real Algebraic Geometry to Computer Science.
Professor Burr's research interests include algebraic geometry, algebraic topology, algorithms, and computational and discrete geometry. His recent work includes new forms of the classical amortization techniques, namely algebraic and continuous amortization, for complexity analysis. Algebraic amortization is used to bound the distance between roots of a polynomial while continuous amortization has been used to compute the number of subdivisions performed by an algorithm. It is hoped that these techniques will become part of the standard toolbox of algorithms for researchers interested in complexity analysis.
Research Assistant Professor of Mathematics
North Carolina State University
Title: "Computer Algebra in
Dynamical Systems and Biology"
Abstract: The study of the stability properties is of fundamental importance in dynamical systems. For a steady state, one typically considers the linear part of a (nonlinear) system and examines the corresponding eigenvalues. Unfortunately, when the real part of one of the eigenvalues is zero, the local stability cannot be deduced form the linearization as higher order terms must be taken into account. In this talk we show how to use computer algebra to determine the stability of a steady state in the presence of purely imaginary eigenvalues. An important ingredient of the method is the computation of the so-called focus quantities, usually large polynomials in the coefficients of the system. Focus quantities also contain information about limit cycles ("isolated" periodic orbits) that can bifurcate from the steady state, which will also be discussed in this talk. Limit cycles are important objects in many branches of science including engineering and biology, and are the main concern of the well-known, unsolved, Hilbert's 16th problem.
Professor Mahdi's research interests include applied algebraic geometry, polynomial dynamical systems (periodic oscillations and stability, symbolic computation, structural identifiability), dynamical system theory, and applications to building computer models for cardiovascular dynamics (baroreflex, cerebral autoregulation, and Kalman filtering).
Professor Mahdi's work not only involves complex analysis of dynamical systems but also tackles the intricate task of integrating theory and complicated applications. In particular, he takes part in a highly interdisciplinary research project, The Virtual Physiological Rat Project, which aims to simulate the integrated cardiovascular functions of the rat, and to build validated computer models that account for genetic variation across rat strains and physiological responses to their environment (i.e. diet). In addition, new strains of genetically engineered rats will be developed with the ultimate goal of using computer models to predict the physiological characteristics of not-yet-realized genetic combinations, derive those combinations in the lab, and then test the predictions.
Ph.D. candidate of Computer Science
and Structured Embeddings in Matrix Algebra: Analysis
Abstract: We address sparse and structured embedding techniques for large-scale matrix computation. These emerging techniques help elucidate the numerical properties of certain algorithms for large-scale matrix computations, lead to the development of more efficient and stable algorithms, or both. We illustrate their efficacy in three important cases: (i) Numerical analysis of the modified Gram-Schmidt procedure for least-squares (LS) solutions by Björck et al, via embedding projections into orthogonal reflections. (ii) Efficient semi-symbolic computation of expansion coefficients in a solution to a Laplace equation in multi-layer cylindrical geometries, via a structured embedding. (iii) Fast direct solution of hierarchically semi-separable (HSS) systems by Ho and Greengard, and its extension to the sparse embedding for direct solution or preconditioning of dense systems that can be compressed by the fast multipole method (FMM). This is joint work with Xiaobai Sun, Nikos P. Pitsianis, and Robert D. Pearlstein.
Alexandros Iliopoulos commenced his graduate studies with a Fulbright scholarship, after receiving his Diploma in Electrical and Computer Engineering from the Aristotle University of Thessaloniki, Greece. In his second year as a graduate student, he was the recipient of a teaching and a research award from the department. In the three years since he was recruited to the Ph.D. program at Duke, Alexandros Iliopoulos has taken part and played a key role in three collaborative research projects: panoramic composition of snapshots from camera arrays under sparse, irregular, and noisy conditions of image overlap; modeling, simulation, and localization of electrical sources in the spinal cord; and image-guided estimation of tumor deformation for adaptive on-board radiation therapy.
John R. & Louise S. Parker Distinguished Professor of Computer Science
University of North Carolina at Chapel Hill
Algebra in Physics-based Modeling"
Abstract: From turbulent fluids to granular flows, many phenomena observed in nature and in society show complex emergent behavior on different scales. The modeling and simulation of such phenomena continues to intrigue scientists and researchers across different fields. Understanding and reproducing the visual appearance and dynamic behavior of such complex phenomena through simulation is valuable for enhancing the realism of virtual scenes and for improving the efficiency of design evaluation. This is especially important for applications, where it is impossible to manually animate all the possible interactions and responses beforehand. In this talk, we discuss the roles and applications of computer algebra used in geometric modeling of complex surfaces and physics-based simulation to solve inequality arising from various constraints in simulating such phenomena. Some of the example dynamical systems that I will describe include turbulent fluids, deformable tissues, granular flows, and crowd simulation. I will also discuss some research challenges in computer algebra for physics-based modeling and simulation.
Ming C. Lin is currently John R. & Louise S. Parker Distinguished Professor of Computer Science at the University of North Carolina (UNC), Chapel Hill and an Honorary Professor at Tsinghua University in Beijing, China. She obtained her B.S., M.S., and Ph.D. in Electrical Engineering and Computer Science from the University of California, Berkeley. She received several honors and awards, including the NSF Young Faculty Career Award in 1995, Honda Research Initiation Award in 1997, UNC/IBM Junior Faculty Development Award in 1999, UNC Hettleman Award for Scholarly Achievements in 2003, Beverly W. Long Distinguished Professorship 2007-2010, Carolina Women's Center Faculty Scholar in 2008, UNC WOWS Scholar 2009-2011, IEEE VGTC Virtual Reality Technical Achievement Award in 2010, and eight best paper awards at international conferences. She is a Fellow of ACM and IEEE.
Her research interests include physically-based modeling, virtual environments, sound rendering, haptics, robotics, and geometric computing. She has (co-)authored more than 240 refereed publications in these areas and co-edited/authored four books. She has served on over 120 program committees of leading conferences and co-chaired dozens of international conferences and workshops. She is currently the Editor-in-Chief (EIC) of IEEE Transactions on Visualization and Computer Graphics, a member of 6 editorial boards, and a guest editor for over a dozen of scientific journals and technical magazines. She also has served on several steering committees and advisory boards of international conferences, as well as government and industrial technical advisory committees.
Themes: Emerging directions & potential thesis topics.
Erich L. Kaltofen (moderator)
North Carolina State University
Ming C. Lin
University of North Carolina at Chapel Hill
Daniel S. Roche
United States Naval Academy
University of Delaware
Stephen M. Watt
University of Western Ontario