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Unless otherwise noted, talks will be at 3:50 PM in O'Connor 204. Also, there will be refreshments before each talk in O'Connor 31 at 3:40 PM.
Tuesday April 17, O'Connor 204
Speaker: Kay Giesecke, Stanford University
Title: Large Portfolio Asymptotics for Loss From Default
Abstract: We prove a law of large numbers for the loss from default and use it for approximating the distribution of the loss from default in large, potentially heterogenous portfolios. The density of the limiting measure is shown to solve a non-linear stochastic PDE, and certain moments of the limiting measure are shown to satisfy an infinite system of SDEs. The solution to this system leads to the distribution of the limiting portfolio loss, which we propose as an approximation to the loss distribution for a large portfolio. Numerical tests illustrate the accuracy of the approximation, and highlight its computational advantages over a direct Monte Carlo simulation of the original stochastic system. This is joint work with Kostas Spiliopoulos, Richard Sowers, and Justin Sirignano.
Tuesday, April 24, O'Connor 204
Speaker: Nicolette Meshkat, Santa Clara University
Title: The Differential Algebra Approach to Identifiability
Abstract: Parameter identifiability analysis for dynamic system ODE models concerns finding which unknown parameters can be quantified from given input-output data. If all the parameters of a model have a finite number of solutions, then the model is said to be identifiable. A model is called unidentifiable if the parameters can take on an infinite number of values and yet result in identical input-output data. The differential algebra approach has been an effective method for analyzing identifiability properties, in particular, for proving global identifiability. In this talk, we examine unidentifiable models and a method for finding globally identifiable parameter combinations using Groebner Bases. We show that a set of algebraically independent identifiable parameter combinations can always be found from the Groebner Bases and can be used to reparameterize the model's input-output equations. We also discuss computational difficulties in finding these identifiable parameter combinations and explore possible improvements to our algorithm.
Tuesday, May 1, O'Connor 204
Speaker: Nancy Rodriguez, Stanford University
Title: Traveling Wave Solutions in a Reaction-Diffusion Model for Criminal Activity
Abstract: Recently, there has been much interest in the use of mathematical tools to obtain insight into the phenomena of crime. In this work we study a reaction-diffusion system of PDEs, which can be taken as a basic model for criminal activity, to explore the effect of a populations "natural tendencies'' towards crime. In this talk, I will first discuss the effect these natural tendencies have in the propagation of crime by studying the existence of traveling wave solutions. Secondly, I will consider the problem of preventing the propagation of crime using a minimum number of resources.
Tuesday, May 15, O'Connor 204
Speaker: Kelli Talaska, UC Berkeley
Title: Determinants and path counting
Abstract: If we have a network with some sources and sinks (think of a
Background needed: Very basic linear algebra (determinants). A little
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