Georgia Institute of Technology College of Sciences

Problem: describe the asymptotic behavior of the coefficients a_{ij} of the Taylor series for 1/Q(x,y) where Q is a polynomial. This problem is the simplest of a number of such problems arising in analytic combinatorics whose answer was not until recently known. In joint work with J. van der Hoeven and T. DeVries, we give a solution that is completely effective and requires only assumptions that are met in the generic case. Symbolic algebraic computation and homotopy continuation tools are required for implementation.

Motivated by a problem in the synthesis of nanowires, a sequential space filling design, called Sequential Minimum Energy Design (SMED), is proposed for exploring and searching for the optimal conditions in complex black-box functions. The SMED is a novel approach to generate designs that are model independent, can quickly carve out regions with no observable nanostructure morphology, allow for the exploration of complex response surfaces, and can be used for sequential experimentation. It can be viewed as a sequential design procedure for stochastic functions and a global optimization procedure for deterministic functions. The basic idea has been developed into an implementable algorithm, and guidelines for choosing the parameters of SMED have been proposed. Convergence of the algorithm has been established under certain regularity conditions. Performance of the algorithm has been studied using experimental data on nanowire synthesis as well as standard test functions.(Joint work with V. R. Joseph, Georgia Tech and T. Dasgupta, Harvard U.)

Consider any dynamical system with the phase space (set of all states) M. One gets an open dynamical system if M has a subset H (hole) such that any orbit escapes ("disappears") after hitting H. The question in the title naturally appears in dealing with some experiments in physics, in some problems in bioinformatics, in coding theory, etc. However this question was essentially ignored in the dynamical systems theory. It occurred that it has a simple and counter intuitive answer. It also brings about a new characterization of periodic orbits in chaotic dynamical systems. Besides, a duality with Dynamical Networks allows to introduce dynamical characterization of the nodes (or edges) of Networks, which complements such static characterizations as centrality, betweenness, etc. Surprisingly this approach allows to obtain new results about such classical objects as Markov chains and introduce a hierarchy in the set of their states in regard of their ability to absorb or transmit an "information". Most of the results come from a finding that one can make finite (rather than traditional large) time predictions on behavior of dynamical systems even if they do not contain any small parameter. It looks plausible that a variety of problems in dynamical systems, probability, coding, imaging ... could be attacked now. No preliminary knowledge is required. The talk will be accessible to students.

Information encoded in a bar code can be read using a laser scanner or a camera-based scanner. For one-dimensional bar codes, which are in most prevalent use, the information that needs to be extracted are the widths of the black and white bars. The collection of black and white bars may be viewed as a binary one-dimensional image. The signal measured at the scanner amounts to the convolution of the binary image with a smoothing kernel. The challenge is that the smoothing kernel, in addition to the binary image, is also unknown. This presentation will review the technology behind bar code scanning and present several approaches to the decoding problem.