Math Sciences Colloquia - Spring 2005

All Math Sciences colloquia take place on Wednesdays from 12pm to 1pm in 657 Rhodes Hall. Pizza will be served during the talks.

• February 16 - Jesus Rodriguez, CAM, "Valuation of Energy Derivatives"
  
• March 2 - Retsef Levi, ORIE, "Approximation Algorithms for Stochastic Inventory Control Models with Correlated Demand"
  Abstract: In this talk, we address the long-standing problem of finding computationally efficient and provably good inventory control policies in supply chains with correlated and non-stationary (time-dependent) stochastic demands. This problem arises in many domains and has many practical applications in supply chain management. We consider two classical models, the periodic-review stochastic inventory control problem and the stochastic lot-sizing problem with correlated and non-stationary demands. Here the correlation is inter-temporal, i.e., what we observe in period s changes our forecast for the demand in future periods.
  We provide what we believe to be the first computationally efficient policies with constant worst-case performance guarantees; that is, there exists a constant C such that, for any instance of the problem, the expected cost of the policy is at most C times the expected cost of an optimal policy.
  The dominant paradigm in almost all of the existing literature has been to formulate these models using a dynamic programming framework. This approach has turned out to be very successful in characterizing the structure of the optimal policies, which follow simple forms of state-dependent base-stock policies and state-dependent (s,S) policies. However, in case the demands over time are non-stationary and correlated, computing these optimal policies is likely to be intractable.
  We present a novel approach to give general approximation algorithms with constant performance guarantee for these classical models. Our approach is based on several novel ideas: we present a new (marginal) cost accounting for stochastic inventory models; we use cost-balancing techniques; and we consider non state-dependent policies that are extremely easy to implement on-line. Our results are valid for all of the currently known approaches in the literature to model correlation and non-stationarity of demands over time.
  This is joint work with Martin Pal, Robin Roundy and David Shmoys.
• March 16 - A. Deniz Sezer, ORIE, "Filtration Shrinkage: Modelling Information Reduction"
  Abstract: (To preserve the symbols used in this abstract, please view it in pdf format.)
• March 30 - Jeffrey Pang, CAM, "Set intersection theorems and existence of optimal solutions"
  Abstract: The question of nonemptiness of the intersection of a nested sequence of closed sets is fundamental in a number of important optimization topics, including the existence of optimal solutions, the validity of the minimax inequality in zero sum games, and the absence of a duality gap in constrained optimization. We introduce the new notion of an asymptotic direction of a sequence of closed sets, and the associated notions of retractive, horizon, and critical directions, and we provide several conditions that guarantee the nonemptiness of the corresponding intersection. We show how these conditions can be used to obtain simple proofs of some known results on existence of optimal solutions, and to derive some new results, including an extension of the Frank-Wolfe Theorem for (nonconvex) quadratic programming.
• April 6 - Robert Clewley, CAM, "A small-world network study into the origin of epileptic activity"
  Abstract: I will motivate and describe some exciting work in understanding the origin of epileptic activity in the Hippocampus of mammalian brains, using simple but carefully-reduced dynamical models of electrical activity in small-world networks. Small-world networks are of growing interest in neuroscience as a more statistically realistic model of large-scale connectivity between neurons, compared to purely random networks or regular lattices (see a graphical introduction to small-worlds in the Introduction section of http://www.bu.edu/ndl/people/netoff/SWN/SWN.html).
  The talk is non-technical from a neurolophysiological point of view, and heavy on graphical descriptions of our models and their results --- so that it's also mathematically accessible.
• April 12 - Jose M. Gutierrez, University of La Rioja (Spain), "Some ways of 'rediscovering' an iterative method"
  NOTE CHANGE OF DAY -- Tuesday for this week only; talk held at noon with pizza served during the talk.
  Abstract: Iterative methods are a powerful tool for approximating the roots of nonlinear equations. Newton's method is by far the most studied and used in practice amongst these root-finding algorithms. But is not the only one. In this talk some other iterative methods are presented as well as different constructions for them. In particular, we analyse with special emphasis the case of Halley's method, perhaps the most rediscovered iteration function in the literature.
• April 20 - Niranjan Nagarajan, Computer Science, "Techniques for efficient p-value estimation with error guarantees"
  Abstract: The increasing use of probabilistic models in Bioinformatics has created a need for efficient and accurate algorithms for significance testing. Fast and reliable p-value computation is a critical component in a wide variety of areas like motif finding, sequence alignment and microarray analysis. Many of the existing algorithms for significance testing work by computing convolutions or characteristic functions. We present techniques that can potentially be applied to such algorithms to get faster algorithms that produce reliable estimates. In addition, we also present techniques for providing error guarantess for the computed estimates. We illustrate our ideas by presenting an improved algorithm to compute the p-value of the multinomial log-likehood ratio statistic.
  This is joint work with Dr. Uri Keich.
• April 27 - An-Swol Clement Hu, ECE, "Cooperative Time Synchronization in Pulse-Connected Networks"
  
• May 4 - Matt Dimmic, BSCB (Biological Statistics and Computational Biology), "Detecting coevolving amino acid sites using Bayesian mutational mapping"
  Abstract: The evolution of protein sequences is constrained by complex interactions between amino acid residues. Because harmful substitutions may be compensated by other substitutions at neighboring sites, residues can coevolve. We describe a Bayesian phylogenetic approach to the detection of coevolving residues in protein families. This method, Bayesian mutational mapping (BMM), assignsmutations to the branches of the evolutionary tree stochastically, and then test statistics are calculated to determine whether a coevolutionary signal exists in the mapping. Posterior predictive P-values provide an estimate of significance, and specificity is maintained by integrating over uncertainty in the estimation of the tree topology, branch lengths, and substitution rates. A coevolutionary Markov model for codon substitution is also described, and this model is used as the basis of several test statistics.
  Results on simulated coevolutionary data indicate that the BMM method can successfully detect nearly all coevolving sites when the model has been correctly specified, and that nonparametric statistics such as mutual information are generally less powerful than parametric statistics. On a dataset of eukaryotic proteins from the phosphoglycerate kinase (PGK) family, interdomain site contacts yield a significantly greater coevolutionary signal than interdomain non-contacts, an indication that the method provides information about interacting sites.