Brown University Center for Statistical Sciences Seminar
Wharton School, University of Pennsylvania | |
1st Floor Conference Room #106 (Coffee at 3:45 p.m.) |
Abstract: Instrumental variables (IV) regression is a method for overcoming problems of unobserved confounders and measurement error in estimating causal relationships. The ability of IV regression to overcome these problems rests on the proposed instruments satisfying certain assumptions. Often there is a degree of uncertainty about whether the proposed instruments satisfy these assumptions. Two useful methods for incorporating such uncertainty into a statistical analysis are the following: (i) when the number of instruments is greater than than the number of included endogenous variables, the validity of the instruments (i.e., whether the instruments satisfy the needed assumptions) can be tested via an ``overidentifying restrictions test''; (ii) a sensitivity analysis can be carried out to examine how much the results differ when plausible violations of the assumptions are entertained. After a brief review of applications of IV regression in biostatistics, we discuss methods of sensitivity analysis for IV regression that incorporate the information provided by the overidentifying restrictions. Our methods provide insight into the circumstances under which failure to reject the validity of the instruments via an overidentifying restrictions test increases confidence in the results from an IV regression. We illustrate our methods through an empirical study of the income elasticity of demand for food among Philippine rural households.
Brown University
Joint Materials/Solid Mechanics Seminar Series
Abstract: Many bacteria use rotating helical flagella to swim. A flagellum has three parts: a rotary motor, a thin helical filament that acts as a propeller, and a curved "hook" which joins the filament to the motor. The filaments undergo polymorphic transformations in which the magnitude and sign of the helical pitch change abruptly.
These transformations may arise in response to mechanical loading, changes in environmental conditions such as temperature and ionic strength, and point substitutions in the amino acid sequence of the protein subunits that make up the flagellar filament. To explain polymorphism, we propose a new coarse-grained continuum rod theory based on the structure of the subunits. These subunits are arranged in eleven proto- filaments that gently wind around each other to form the filament. We assign to each subunit a double-well potential for extension along the protofilament. Curved filament shapes arise in our model because the bonds in the inner core of the filament may prefer a subunit spacing which differs from both of the spacings preferred by the double-well potential. There is also a double-well potential for twist, arising from lateral interactions between neighboring protofilaments. Cooperative interactions between neighboring subunits within a protofilament are necessary to ensure the uniqueness of helical ground states. We calculate a phase diagram for filament shapes, finding discontinuous transitions between helical states as well as straight states, and we show how the curvature and twist change as parameters of the model vary.
Special Joint PDE and Dynamical Systems Seminar
**Please Note Special Day, Time, and Room for This Week Only** |
Scientific Computing Seminar
Abstract: The study of 2D shapes and their similarities is a central problem in the field of vision. It arises in particular from the task of classifying and recognizing objects from their observed silhouette. Defining natural distances between 2D shapes creates a metric space of shapes, whose mathematical structure is inherently relevant to the classification task. One intriguing metric space comes from using conformal mappings of 2D shapes into each other, via the theory of Teichmuller spaces. In this space every simple closed curve in the plane (a "shape") is represented by a 'fingerprint' which is a diffeomorphism of the unit circle to itself (a differentiable and invertible, periodic function). The shortest path between each two shapes is unique, and is given by a geodesic connecting them. Their distance from each other is given by integrating the Weil-Petersson norm along that geodesic. In this talk I will concentrate on solving the "welding" problem of "sewing" together conformally the interior and exterior of the unit circle, glued on the unit circle by a given diffeomorphism, to obtain the unique 2D shape associated with this diffeomorphism. This will allow us to go back and forth between 2D shapes and their representing diffeomorphisms in this "space of shapes". I will also demonstrate computation of geodesics.
This is a joint work with David Mumford
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