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Unless otherwise noted, talks will be at 3:50 PM in O'Connor 207. Also, there will be refreshments before each talk in O'Connor 31 at 3:30 PM.
Tuesday, 14 April
Speaker: Elizabeth Gross, San Jose State University
Title: Goodness-of-fit testing for network models
Abstract: When using statistical models for network data, we would like to know the goodness-of-fit of the model (i.e., how well the model fits the data). This question has proved particularly challenging even for relatively simple classes of network models, as it currently requires sampling graphs with the same sufficient statistics (e.g., number of edges, number of triangles, degree sequence, etc) as the observed network. In this talk, we will introduce statistical network models and present a method for goodness-of-fit testing for log-linear network models that is rooted in computational algebraic geometry. We will demonstrate the approach on the Holland-Leinhardt p_1 model for random directed graphs. This is joint work with Sonja Petrovic and Despina Stasi.
Tuesday, 28 April
Speaker: Matthew Holmes, Undergraduate student at Santa Clara University
Title: Enumerating Primitive Words and Images
Abstract: Primitive words are strings that are not repetitions of some simpler substrings. For example, the string 101010 is not primitive, while the string 10000 is. In this work, I will explain how to generalize this notion to rectangular images and prove a formula based on the Mobius function for counting the number of primitive images of dimensions (m x n) over an alphabet of size k. I will also discuss some upper and lower bounds for these formulas.
Tuesday, 5 May
Speaker: Richard Scott, Santa Clara University
Title: Cube complexes and generating functions
Abstract: Some of your favorite geometric objects can actually be constructed by gluing together cubes of various dimensions along their faces. A very useful way to study the topology of such an object is to pass to an infinite version called the "universal cover"which retains the original local geometry. In this talk we will partition the (infinitely many) vertices in the universal cover in such a way that we can count them. The result of this count is a generating function, the likes of which which you may have encountered in a combinatorics class. After computing a couple of these, we will connect topological properties of the original geometric object to algebraic properties of this generating function. I promise at least six pictures, at least three colors, at least two theorems, and at most one proof.
Tuesday, 26 May
Speaker: Jeff Calder, UC Berkeley
Title: Partial differential equations and continuum limits for discrete sorting problems
Abstract: Many problems in science and engineering involve the sorting, or ordering, of large amounts of data. A common sorting technique is to arrange the data into layers by repeatedly removing extremal points. Different definitions of extremality lead to different sorting algorithms. Two common examples are non-dominate sorting, and convex hull ordering, which are widely used in multi-objective optimization, machine learning, and robust statistics. Furthermore, non-dominated sorting is equivalent to the longest chain problem, and polynuclear growth, which are important problems in probability and combinatorics. In this talk, I will present some recent work showing that the layers obtained by sorting i.i.d. random variables converge almost surely in the large sample size limit to the level sets of a function that satisfies a partial differential equations (PDE). These PDE continuum limits open the door to very fast approximate sorting algorithms based on solving the PDE in place of the discrete sorting problem. I will give some applications of our work along these lines.
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