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DTSTART;TZID=America/Los_Angeles:20260126T160000
DTEND;TZID=America/Los_Angeles:20260126T170000
DTSTAMP:20260512T081602
CREATED:20260121T185658Z
LAST-MODIFIED:20260121T185658Z
UID:3967-1769443200-1769446800@colleges.claremont.edu
SUMMARY:Fractional Brownian Motion: Small Increments and First Exit Time from One-sided Barrier (Qidi Peng\, CGU)
DESCRIPTION:Abstract: The talk introduces a conjecture on the first exit time of fractional Brownian motion: the upper-tail probability for a fractional Brownian motion to first exit a positive-valued barrier over time T has the exact asymptotic rate T^(H-1)\, where H is the Hurst parameter of the fractional Brownian motion. The talk tries to understand this conjecture by providing several equivalent statements. We then introduce the best effort made in the current literature towards solving this conjecture.
URL:https://colleges.claremont.edu/ccms/event/fractional-brownian-motion-small-increments-and-first-exit-time-from-one-sided-barrier-qidi-peng-cgu/
LOCATION:Emmy Noether Room\, Estella 1021\, Pomona College\,\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Applied Math Seminar
ORGANIZER;CN="Ryan Aschoff":MAILTO:ryan.aschoff@cgu.edu
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DTSTART;TZID=America/Los_Angeles:20260129T161500
DTEND;TZID=America/Los_Angeles:20260129T171500
DTSTAMP:20260512T081602
CREATED:20260129T221950Z
LAST-MODIFIED:20260129T222543Z
UID:3979-1769703300-1769706900@colleges.claremont.edu
SUMMARY:Sampling from the proper colorings of a graph using a number of colors linear in the maximum degree in expected linear time (Mark Huber\, CMC)
DESCRIPTION:Abstract: A proper coloring of a graph is an assignment of colors from \( \{1\, 2\, \ldots\, k\} \) to each node of a graph such that no two nodes connected by an edge receive the same color. Let \( \Delta \) denote the maximum degree of the graph. If \( k \geq \Delta + 1 \) then at least one proper coloring always exists. However\, counting the number of proper colorings of an arbitrary graph is a #P-complete problem\, even when \( \Delta = 3 \). This means finding a polynomial time exact algorithm is unlikely to be found. On the other hand\, if a user can sample uniformly at random from the proper colorings of a graph\, then it becomes possible to approximately count the number of proper colorings to arbitrary precision in polynomial time. This work presents the first algorithm that has an expected running time that is linear in the size of the graph under the condition that \( k > 3.637 \Delta \). Joint work with Kritika Bhandari.
URL:https://colleges.claremont.edu/ccms/event/sampling-from-the-proper-colorings-of-a-graph-using-a-number-of-colors-linear-in-the-maximum-degree-in-expected-linear-time-mark-huber-cmc/
LOCATION:Emmy Noether Room\, Estella 1021\, Pomona College\,\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Applied Math Seminar
ORGANIZER;CN="Ryan Aschoff":MAILTO:ryan.aschoff@cgu.edu
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