Center for Statistical Sciences Seminar
Abstract: Most neurophysiological experiments entail activating a system with a putative stimulus and recording the responses of individual neurons one at a time. From a statistical perspective, the analysis of a neurophysiological experiment is a highly structured regression problem in which the responses are neural spike trains (point processes) and the experimentalist often has substantial control over the putative stimuli (regressors or covariates). Despite the long-standing use of the single neuron recording paradigm, the response characteristics of individual neurons to putative stimuli remain poorly characterized from a quantitative standpoint. We demonstrate how point process theory combined with the generalized linear model (GLM) makes it possible to analyze the responses of individual neurons to putative stimuli. We show how use of the point process- GLM framework leads to a principled way of estimating important neural characteristics such as, the nature of the stimulus specific response, absolute and relative refractory periods, bursting propensity, network effects and the challenging concept of a neuron's signal-to-noise ratio. We illustrate these ideas in the analysis of neural activity from hippocampal, auditory, thalamic and visual single neuron recordings.
Generous support for this lecture provided by the Sidney E. Frank Invitational Seminar Fund November 10, 2008 Image Credit: Adrian Humphrey
For additional information: Contact sfurtado@stat.brown.edu or Visit www.stat.brown.edu/grad The Biostatistics Graduate Program and Division of Biology and Medicine
Applied Math Colloquium
Abstract: The current theory of global attractors for the Navier-Stokes equations on thin 3D domains is motivated by the desire to better understand the theory of heat transfer in the oceans of the Earth. (In this context, the thinness refers to the aspect ratio - depth divided by expanse - of the oceans.) The issue of heat transfer is, of course, closely connected with many of the major questions concerning the climate. In order to exploit the tools of modern dynamical systems in this study, one needs to know that the global attractors are "good" in the sense that the nonlinearities are Frechet differentiable on these attractors. About 20 years ago, it was discovered that on certain thin 3D domains, the Navier-Stokes equations did possess good global attractors. This discovery, which was itself a major milestone in the study of the 3D Navier-Stokes equations, left open the matter of extending the theory to cover oceanic-like regions with the appropriate physical boundary behavior. In this lecture, we will review this theory, and the connections with climate modeling, while placing special emphasis on the recent developments for fluid flows with the Navier (or slip) boundary conditions.
CCMB Seminar Series
Abstract: Understanding how biological sequences encode structural and functional information is a fundamental scientific challenge. For RNA viral genomes, the information encoded in the sequence extends well-beyond their protein coding role to the role of intra-sequence base pairing in viral packaging, replication, and gene expression. Working with the Pariacoto virus as a model sequence, we investigate the compatibility of predicted base pairings with the dodecahedral cage known from crystallographic studies. To build a putative secondary structure, we first analyze different possible configurations using a combinatorial model of RNA folding. We give results on the trade-offs among types of loop structures, the asymptotic degree of branching in typical configurations, and the characteristics of stems in "well-determined" substructures. These mathematical results yield insights into the interaction of local and global constraints in RNA secondary structures, and suggest new directions in understanding the folding of RNA viral genomes.
LCDS Seminar Lecture
Abstract: In this lecture special emaphasis will be placed on the dynamical systems aspect of the study of the Navier-Stokes equations on thin 3D domains. The focus will be on the role of the Navier (or slip) boundary conditions, and the connection with the 2D Reduced Problem, which arises as the thinness goes to 0.
Scientific Computing Seminar
PDE Seminar
Abstract: We will recall a certain number of pathological behaviors of solutions of Euler and Navier-Stokes-like equations. Related to these behaviors is the intuitive or statistical notion of turbulence. Then we will compare the principles of statistical turbulence with the description of weak limits in terms of Wigner measures.
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