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DTSTART;TZID=America/Los_Angeles:20220125T123000
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DTSTAMP:20260406T091230
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SUMMARY:Questions on Symmetric Chains (Shahriar Shahriari\, Pomona)
DESCRIPTION:The set of subsets {1\, 3}\, {1\, 3\, 4}\, {1\, 3\, 4\, 6} is a symmetric chain in the partially ordered set (poset) of subsets of {1\,…\,6}. It is a chain\, because each of the subsets is a subset of the next one. It is symmetric because the collection has as many subsets with less than 3 elements as it has subsets with more than 3 elements (3 is half of 6\, the size of the original set). It is straightforward to partition the set of all subsets of {1\,…\,6} into symmetric chains. Such a partition is called a symmetric chain decomposition of the poset. We are interested in the following—admittedly curious sounding—question. What is the maximum integer k\, such that given any collection of k disjoint symmetric chains in the poset of subsets of a finite set\, we can enlarge the collection to a symmetric chain decomposition of the poset? I don’t know the answer\, but in this talk\, I will discuss a special case\, a number of related results and questions\, and provide some background on why symmetric chain decompositions are useful.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-shahriar-shahriari-pomona/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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DTSTART;TZID=America/Los_Angeles:20220126T161500
DTEND;TZID=America/Los_Angeles:20220126T173000
DTSTAMP:20260406T091230
CREATED:20220121T013826Z
LAST-MODIFIED:20220121T212036Z
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SUMMARY:Using Stitching for faster sampling (Prof. Mark Huber)
DESCRIPTION:Title: Using Stitching for faster sampling \nSpeaker: Mark Huber\, Department of Mathematics\, Claremont McKenna College \nAbstract: Point processes are used to model location data\, such as the locations of trees in a forest\, or cities in a plain.  Repulsive point processes modify the basic model in order to obtain points that are farther apart from each other than would be expected if they were placed uniformly at random.  In order to understand the behavior of these models\, Monte Carlo methods are used\, which draw samples from the probabilistic model.  In this talk\, I’ll show how to draw from a particular example of a repulsive point process called the Strauss process for parameters that were never possible before.  The method is called stitching\, and is a type of divide-and-conquer algorithm that is surprisingly effective for these types of problems. \n\nHuber got his start in data science (before it was called that) at HMC (’94).  He then headed to Cornell and obtained his Ph.D. from the Operations Research and Industrial Engineering department.  After a postdoc at Stanford and a position at Duke\, he returned to the West Coast and is now the Fletcher Jones Foundation Professor of Mathematics and Statistics and George R. Roberts Fellow\, and the Program Director of Data Science and Computer Science at Claremont McKenna.  His third book\, “Probability Adventures”\, is now available.
URL:https://colleges.claremont.edu/ccms/event/using-stitching-for-faster-sampling-prof-mark-huber/
LOCATION:CA
CATEGORIES:Colloquium
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DTSTART;TZID=America/Los_Angeles:20220131T161500
DTEND;TZID=America/Los_Angeles:20220131T171500
DTSTAMP:20260406T091230
CREATED:20220116T203846Z
LAST-MODIFIED:20220118T032454Z
UID:2533-1643645700-1643649300@colleges.claremont.edu
SUMMARY:APPLIED MATH SEMINAR: Archetypal analysis by Professor Braxton Osting (University of Utah)
DESCRIPTION:Archetypal analysis is an unsupervised learning method that uses a convex polytope to summarize multivariate data. For fixed k\, the method finds a convex polytope with k vertices\, called archetype points\, such that the polytope is contained in the convex hull of the data and the mean squared distance between the data and the polytope is minimal. In this talk\, I’ll give an overview of the method and discuss connections to matrix factorization\, SVD/PCA\, and the k-means clustering method. I’ll discuss our recent results proving the consistency of archetypal analysis and describe probabilistic methods for approximate archetypal analysis. This is joint work with Ruijian Han\, Dong Wang\, Yiming Xu\, and Dominique Zosso.
URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-braxton-osting-university-of-utah/
LOCATION:CA
CATEGORIES:Applied Math Seminar
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