Brown University Center for Statistical Sciences Seminar
Abstract: Using the notion of local ancillary to describe the robustness of estimating functions, we develop a functional modeling approach for inference in regression models containing measurement error in the covariates. Suppose interest is on the model $ E(Y | u, w)$ for response $ Y $, the observed data are $ (y, x, w), X $ is a mismeasured surrogate for $ u $, and $ u $ is treated as a fixed unknown nuisance parameter. Beginning with quasiscores for both the regression parameter and $ u $, a bias-corrected quasiscore for the regression parameter is derived that is second order locally ancillary for the nuisance $ u $. When an estimator for $ u $ is plugged into the corrected quasiscore, local approximations show that the bias is small. The method requires only the correct specification of the mean and variance functions for $ Y $ and $ X $ in terms of $ u, w $ and the regression parameter. Extensions to longitudinal data regression models, which are suggested by the quasilikelihood modeling framework, are explored and discussed. Simulations and a small example using real data are presented, using log-linear and logistic regression models.
Joint Seminar - Fluids, Thermal and Chemical Processes and The Center for Fluid Mechanics
Massachusetts Institute of Technology, Cambridge, MA | |
Abstract: Vascular endothelial cells have been subjected to mechanical forces such as fluid shear stress and stretching of the substrate to which they are attached. The objective of these experiments has been to determine the cellular response to each different type of force. This talk will review some of the notable fluid flow experiments and their outcomes, and attempt to interpret these results from the point of view of the internal structure of the cell.
Actin filaments within the cell form an interconnected meshwork whose typical dimension is about 100 nm. This structure is in a continual state of dissolution and rebuilding; this allows the cells to change shape and be motile. Recent experiments show that the rate of actin turnover depends on the state of the cell as well as the forces applied to it. Confluent endothelial cells with no external forces are relatively quiescent, with long actin turnover times and little cell motion. The turnover rate increases when the cells are subjected to fluid shear stress or when cell-cell contacts are compromised. By studying the kinetics of actin polymerization (McGrath et al., to be submitted), it is possible to determine what reactions are promoted by the application of mechanical forces.
We postulate that it is stresses on the membrane-cytoskeleton attachment complexes that produce the changes in actin kinetics that are observed. The kinetic changes in turn lead to different internal structural configurations and actin turnover rates. While the exact signaling pathways are still somewhat elusive, the observed effects are reproducible and consistent with the postulated mechanism.
Special Seminars on PDE and Fluids
Brown Applied Mathematics Pattern Theory and Vision Seminar
Abstract: I will begin with a brief, biophysically motivated derivation of an integro-differential equation system describing electrical activity in a synaptically coupled network of cortical neurons along a single spatial dimension. The existence and structure of traveling front and pulse solutions will be examined using singular perturbation construction, shooting arguments, and other analytic techniques. both the results as well as the strategies employed lead to specific experimental questions. Wave-speed analysis, for instance, identifies the strength and pattern of connectivity as key determinants of wave-speed. Singular perturbation construction suggests that the initiation, propagation, and termination of pulses may entail three distinct underlying mechanisms. Using an in-vitro slice preparation from rodent somatosensory cortex, recent experimental data will be presented verifying both of these predictions. I will conclude with a few experimental 'surprises' and, time permitting, indicate how the mathematics might be modified in order to capture and analyze the new phenomena.
Brown Analysis Seminar
Special Brown Analysis/PDE Seminar
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