****CANCELLED****Center for Statistical Sciences Seminar
Abstract:
We discuss the general problem of clustering non-Gaussian time series, giving
examples from several application domains. In the first example, we look at
clustering series in which each observation represents proportions of counts
across a set of categories, with application to clustering projects based on
similarity of skill types required each week of the project. The second example
focuses on clustering time series of actual counts modeled as Poisson random
variables, where some series may exhibit excess zeros. The technique is
illustrated through an application to clustering of pollutant monitoring
stations based on counts of exceedances above a specified tolerance threshold.
While the first two examples rely on model-based clustering approaches, the
third example introduces nonparametric methods for clustering non-linear time
series based on bispectral divergence measures. We provide an overview of the
approach and initial simulation results assessing the effectiveness of the
method under various conditions. We leave time for discussion as to
applicability of the three techniques for investigating interesting issues
in the neurosciences.
* The topics in the talk represent results of collaborations with multiple
colleagues, both within and outside IBM, including Jianying Hu (IBM Research),
Sarah Thomas and Katherine Ensor (Rice University), Jane Harvill (Baylor
University), and Nalini Ravishanker (Univ. Connecticut).
Lefschetz Center for Dynamical Systems Seminar
Abstract: We examine the topology and morphology of interfaces produced following phase separation in systems with conserved and nonconserved order parameters. These processes produce complex bicontinuous phases that have interfaces with spatially varying curvature. The conserved order parameter evolves by the Cahn-Hilliard equation and the nonconserved order parameter evolves by the Allen- Cahn equation. The morphology of these interfaces is determined using the interfacial shape distribution, the probability of finding a patch of interface with a given pair of principal curvatures, and the topology is quantified by the genus. The interface shape distribution is a function of the volume fraction of the phases and the dynamics used to produce the structures. However, these structures have the same scaled-genus, suggesting a universal value of the genus for a system undergoing self-similar coarsening. We also characterize the spatial correlations of the interfacial curvature. This analysis has indentified new characteristic length scales of these complex structures.
Center for Fluid Mechanics Seminar
Abstract: Recent cancer therapies have targeted tumor blood vessels with inconsistent results. Some treatments show promise while others fail, underscoring a frustrating lack of understanding of the mechanisms that control blood vessel formation, destruction and function . A major difficulty lies in the fact that the mechanisms of vessel formation and remodeling operate at multiple scales, each with its own set of controls, and each critical to the overall function of the blood vessel network. Most importantly, "rare" events occurring at the single cell level can dominate overall vessel network function, and therefore, tumor growth. We are developing analytical approaches--both experimental and computational-- that span the size scale from single cells to bulk tumor in order to incorporate the relevant parameters critical for understanding tumor growth. Experimentally, intravital microscopy allows determination of single-vessel hematocrit, blood velocity, permeability as well as vessel and network morphology over time. Mathematical models of blood flow, vessel growth & remodeling, and tumor growth and invasion span the size scale from cells to tissue to elucidate the cellular events that influence tissue-scale physiology. These tools provide a framework for studying the effects of anti-tumor therapies and improving their efficacy.
Stochastic Systems Seminar
Abstract: The two-dimensional stochastic Navier-Stokes equation with a fractional Brownian noise term is considered. The existence and uniqueness of solutions of the stochastic equation is proved. Fractional Brownian motions (fBms) are not semimartingales. Hence, suitable space-time stochastic integrals with respect to fBms are constructed in this study. Further properties of the solution will be discussed.
Boston University/Brown University PDE Seminar
Abstract: We prove the Wp1,2-solvability of second order parabolic equations in nondivergence form in the whole space for p? (1,?). The leading coefficients are assumed to be measurable in one spatial direction and have vanishing mean oscillation (VMO) in the orthogonal directions and the time variable in each small parabolic cylinder with the direction depending on the cylinder. This extends a recent result by Krylov for elliptic equations and removes the restriction that p>2.
CCMB Distinguished Lecture Series Seminar
Abstract: Large numbers of subjects are needed to obtain reproducible results relating disease characteristics to rare events or weak effects such as those measured for common genetic variants. Similarly large numbers are required to identify adverse events in currently marketed pharmaceuticals, identify new constellations of disease, and measure efficacy and quality in healthcare. Addressing the challenge of studying these large numbers will require use of information technology in ways that recognize the centrality of information processing at the heart of healthcare and biomedical research. This will be illustrated by reviewing our experience in three domains: a) genomic and pharmacovigilance studies of National Center for Biomedical Computing entitled "Informatics for Integrating Biology and the Bedside" (i2b2). b) mining the Internet for just-in-time public health intelligence (e.g. Healthmap.org) and c) using personal health records to allow patients greater autonomy in healthcare and greater participation and benefit from the research on their own data and biomaterials. These cases will illustrate why the recently announced NIH funding arising from the American Recovery & Reinvestment Act of 2009 has these technologies at their core.
Boston University/Brown University PDE Seminar
Abstract: I will speak on the dispersive character of waves on the interface between vacuum and water under the influence of gravity and surface tension. I will begin by giving a precise account of the formulation of the surface water-wave problem and discussion of its distinct features. They include the dispersion relation, the nonlinearity, traveling waves and the Hamiltonian structure. I will describe the recent work of Hans Christianson, Gigliola Staffilani and myself on the local smoothing effect of 1/4 derivative for the fully nonlinear problem under surface tension with some detail of the proof. If time permits, I will explore some open questions regarding long- time behavior and stability.