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DTSTART;TZID=America/Los_Angeles:20200210T161500
DTEND;TZID=America/Los_Angeles:20200210T171500
DTSTAMP:20260508T072145
CREATED:20200128T002046Z
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SUMMARY:Applied Math Talk: Robust Estimators for Monte Carlo data given by Prof.  Mark Huber (CMC)
DESCRIPTION:Data coming from Monte Carlo experiments is often analyzed in the same way as data from more traditional sources.  The unique nature of Monte Carlo data\, where it is easy to take a random number of samples\, allows for estimators where the user can control the relative error of the estimate much more precisely than with classical approaches.  In this talk I will discuss three such estimators useful in different problems.  The first is a user-specified-relative-error (USRE) estimate for the mean of a Bernoulli random variable.  This allows us to obtain exact error results while using slightly fewer samples than the CLT approximation.  The second is more general\, applying to any random variable where a bound on the relative error is known.  For this problem we give exact error bounds using a number of samples that is the same (to first order) as the CLT approximation requires.  In other words\, the new algorithm is the equivalent of always actually having normal data.  Finally\, we look at the problem of data with unknown variance and develop an algorithm that runs very close to the minimum number of samples established by results of Wald.  
URL:https://colleges.claremont.edu/ccms/event/applied-math-talk-given-by-prof-mark-huber/
LOCATION:Emmy Noether Room\, Millikan 1021\, Pomona College\, 610 N. College Ave.\, Claremont\, California\, 91711
CATEGORIES:Applied Math Seminar
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DTSTART;TZID=America/Los_Angeles:20200211T121500
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SUMMARY:Quandle module quivers (Sam Nelson\, CMC)
DESCRIPTION:Quandle coloring quivers categorify the quandle counting invariant. In this talk we enhance the quandle coloring quiver invariant with quandle modules\, generalizing both the quiver invariant and the quandle module polynomial invariant. This is joint work with Karma Istanbouli (Scripps College).
URL:https://colleges.claremont.edu/ccms/event/antc-talk-by-sam-nelson-cmc/
LOCATION:Emmy Noether Room\, Millikan 1021\, Pomona College\, 610 N. College Ave.\, Claremont\, California\, 91711
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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DTSTART;TZID=America/Los_Angeles:20200212T161500
DTEND;TZID=America/Los_Angeles:20200212T171500
DTSTAMP:20260508T072145
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SUMMARY:Applications of Markov Chains to Swarm Robotics and Political Redistricting
DESCRIPTION:What do swarm robotics and political redistricting have in common? One answer is Markov chains\, which have recently been used in very different ways to address problems in both these areas. To get a large swarm to exhibit a desired behavior\, one solution is to make each individual in the swarm fairly intelligent; another is to make the individuals simple\, but to let the desired behavior emerge as a result of their interactions. My collaborators and I recently used Markov chains and ideas from statistical physics to develop distributed algorithms that follow this second paradigm.  We also worked with physicists to create a physical robot system where each individual cannot compute anything\, but the system as a whole can still accomplish complex tasks. For political redistricting\, the main mathematical technique developed in the last few years for detecting gerrymandering is to compare a proposed plan to the space of all possible alternative plans; if the proposed plan is an outlier\, that’s an indicator it might be gerrymandered. However\, the space of all possible districting plans is far too large to ever be studied in its entirety.  Instead\, Markov chains are used to generate random samples of alternative plans\, where the hope is that the sampled plans are reasonably representative of all possible plans. This approach has already been used successfully in court cases around the country\, though questions still remain about what mathematical guarantees we can give about the randomly sampled districting plans.
URL:https://colleges.claremont.edu/ccms/event/tba-16/
LOCATION:Freeberg Forum\, LC 62\, Kravis Center\, CMC
CATEGORIES:Colloquium
ORGANIZER;CN="Blerta Shtylla":MAILTO:shtyllab@pomona.edu
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