Brown University Center for Statistical Sciences Seminar
Abstract: A canonical problem in statistical signal and image processing is the detection of faint targets against complex backgrounds, which has been likened to the proverbial task of "finding a needle in a haystack". We consider the task of target detection when the `background' is neither one- nor two-dimensional but rather in the form of an association network. We model the acquisition of network data, including the potential presence of targets, using a system of sparse simultaneous equation models (SSEMs). In this context, detection is approached as a two-step procedure, involving (i) statistical inference and removal of `background' network structure, using tools of sparse inference, and (ii) outlier detection in the network-filtered residuals. Theoretical performance of the methodology can be characterized using a combination of tools and concepts from sparse inference, compressive sampling, random matrix theory, and spectral graph theory. We illustrate the practical capabilities of this approach using simulations and the problem of drug target detection in the context of a network of gene interactions.
Center for Fluid Mechanics Seminar
Stochastic Systems Seminar
***SPECIAL*** Stochastic Systems Seminar
Abstract: Recent research based autonomous sensing vehicles requires the consideration of their operation and control in stochastic environments. This is especially true in the case of sensing and analyzing ocean dynamics. In this talk, we will consider two types of stochastic dynamical systems. In the first part, we consider the loitering times of a single vehicle in a stochastic environment. We explicitly predict, using stochastic model reduction methods, loitering times, and we extend those times using simple control techniques. The second part of the talk will consider the dynamics of latency in swarms of vehicles, and how patterns are created. This work is done in collaboration with Dr. Eric Forgoston.
Joint Boston University/Brown University LCDS Seminar
Abstract: Stable spatially localized structures occur in many systems of physical interest. Examples can be found in the fields of optics, chemistry, fluid mechanics, and neuroscience to name a few. In this talk I will focus on one particular model, the Swift-Hohenberg equation, which arises in many of these applications. This equation contains a remarkable wealth of localized states, organized in a 'snakes-and-ladders' structure; a large number of these localized states are simultaneously stable. The talk will include an overview of the results for this model in both one and two spatial dimensions. The goal is to present a physical understanding of the mathematical and numerical results. Despite the simple model used in this analysis, there is evidence that the localized states observed in some experiments are organized in similar structures. Results will be presented for the example of natural doubly diffusive convection.
Joint Boston University/Brown University LCDS Seminar
Abstract: In numerical experiments involving nonlinear solitary waves propagating through nonhomogeneous media one observes "breathing" in the sense of the amplitude of the wave going up and down on a much faster scale than the motion of the wave. We investigate this phenomenon in the simplest case of stationary waves in which the evolution corresponds to relaxation to a nonlinear ground state. The particular model is the popular δ0 impurity in the cubic nonlinear Schrödinger equation on the line. We give asymptotics of the amplitude on a finite but relevant time interval and show their remarkable agreement with numerical experiments.
Scientific Computing Seminar
Abstract: I will first give a brief review on simple and robust central-upwind schemes for hyperbolic conservation laws. I will then discuss their application to the Saint-Venant system of (single layer) shallow water equations. This can be done in a straightforward manner, but then the resulting scheme may suffer from the lack of balance between the fluxes and (possibly singular) geometric source term, which may lead to a so-called numerical storm, and from appearance of negative values of the water height, which may destroy the entire computed solution. To circumvent these difficulties, we have developed a special technique, which guarantees that the designed second-order central-upwind scheme is both well-balanced and positivity preserving. Finally, I will show how the scheme can be extended to a more complicated case of a two-layer shallow water equations, which, in addition to the geometric source term, contains nonconservative interlayer exchange terms. It is well-known that such terms, which arise in many different multiphase models, are extremely sensitive to a particular choice their numerical discretization. To circumvent this difficulty, we rewrite the system in a different way so that the nonconservative terms are multiplied by a quantity, which is, in all practically meaningful cases, very small. We then apply the central-upwind scheme to the rewritten system and demonstrate robustness and superb performance of the proposed method on a number of one- and two-dimensional examples. The talk is based on a series of joint works with Guergana Petrova, Texas A&M University.
CCMB Seminar Series
Abstract: Molecular interaction networks generated by high-throughput whole-genome biological assays are highly intricate and difficult to interpret. Since cellular functions are carried out by modules of interacting molecules, reverse-engineering the modular structure of cellular interaction networks has the promise of significantly easing their analysis. We develop a top-down computational approach to identify building blocks of molecular interaction networks by (i) integrating gene expression measurements for a particular disease state (e.g., leukaemia) or experimental condition (e.g., treatment with growth serum) with molecular interactions to reveal an active network, which is the network of interactions perturbed in the cell in that disease state or condition and (ii) systematically combining active networks computed for different experimental conditions using set-theoretic formulae to reveal network legos, which are modules of coherently interacting genes and gene products in the wiring diagram. We propose methods to compute active networks, systematically mine candidate legos, assess the statistical significance of these candidates, arrange them in a directed acyclic graph (DAG), and exploit the structure of the DAG to identify true network legos. We assess the stability of our computations to changes in the input and our ability to recover active networks by composing network legos. We analyse two human datasets using our method. A comparison of three leukaemias demonstrates how a biologist can use our system to identify specific differences between these diseases. A larger-scale analysis of 13 distinct stresses illustrates our ability to compute the building blocks of the interaction networks activated in response to these stresses and to use these building blocks to identify differences in the response of fibroblasts and HeLa cells to endoplasmic reticulum stress. Refreshments will be served at 11:45 a.m.
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