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DTSTART;TZID=America/Los_Angeles:20191104T161500
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SUMMARY:Markov Chains and Emergent Behavior in Programmable Matter given by Prof. Sarah Canon (CMC)
DESCRIPTION:Markov chains are widely used throughout mathematics\, statistics\, and the sciences\, often for modelling purposes or for generating random samples. In this talk I’ll discuss a different\, more recent application of Markov chains\, to developing distributed algorithms for programmable matter systems. Programmable matter is a material or substance that has the ability to change its features in a programmable\, distributed way; examples are diverse and include robot swarms and smart materials. We study an abstraction of programmable matter where particles independently move on a lattice according to simple\, local algorithms. We want to design these algorithms so that the system has a desired collective behavior\, such as compression of the particles into a shape with small perimeter or separation of differently colored particles. In our stochastic approach\, we describe a desired collective behavior using an energy function; design a Markov chain that uses local moves and converges to the Gibbs distribution for this energy function; and then turn the Markov chain into an asynchronous distributed algorithm that each particle can execute independently. In several of our algorithms\, changing just a single parameter results in a different\, but equally desirable\, emergent global behavior. To prove our algorithms are correct\, we must show this Gibbs distribution has the desired properties with high probability\, which we do using proof techniques from probability\, statistical physics\, and Markov chain analysis. This principled approach has been used to inform the design of real-world robot systems. Joint work with Marta Andres Arroyo\, Enis Aydin\, Joshua J. Daymude\, Bahnisikha Dutta\, Cem Gokmen\, Daniel I. Goldman\, Shengkai Li\, Dana Randall\, Andrea Richa\, William Savoie\, and Ross Warkentin.
URL:https://colleges.claremont.edu/ccms/event/applied-math-talk-given-by-sarah-canon-cmc/
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:20191111T161500
DTEND;TZID=America/Los_Angeles:20191111T171500
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CREATED:20191022T164250Z
LAST-MODIFIED:20191105T183518Z
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SUMMARY:Applied Math Talk: Stochastic similarity matrices and data clustering given by Prof. Denis Gaidashev (Uppsala University)
DESCRIPTION:Clustering in image analysis is a central technique that allows to classify elements of an image. We describe a simple clustering technique that uses the method of similarity matrices\, and an algorithm in which a collection of image elements is treated as a dynamical system. Efficient clustering in this framework   is achieved if the dynamical system admits a spectral gap. \nWe expand upon recent results in spectral analysis for Gaussian mixture distributions\, and in particular\, provide conditions for the existence of a spectral gap between the leading and remaining eigenvalues for matrices with entries from a Gaussian mixture with two real univariate components.
URL:https://colleges.claremont.edu/ccms/event/applied-math-talk-given-by-prof-denis-gaidashev-uppsala-university/
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:20191121T120000
DTEND;TZID=America/Los_Angeles:20191121T130000
DTSTAMP:20260429T025237
CREATED:20191119T200348Z
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SUMMARY:Dynamics of a childhood disease model with isolation
DESCRIPTION:Joan Ponce \nPurdue University \nAbstract: One of the main challenges of mathematical modeling is the balance between simplifying assumptions and incorporating sufficient complexity for the model to provide more accurate and reliable outcomes. For mathematical simplicity\, many commonly used epidemiological models make restrictive modeling assumptions. Although models under such assumptions are capable of producing useful insights into the biological questions in many cases\, they may generate discrepancies in model outcomes. One of the common assumptions in infectious disease models is that the duration for disease stages is exponentially distributed. This may result in discrepancies in model outcomes between such a model and models with more realistic stage distribution assumptions such as gamma distributions with the shape parameter greater than one (Feng et al.\, 2007). In this talk\, I will present an ODE model with gamma-distributed infectious and isolated periods and compare it with a model with exponentially distributed stages. These models intend to show that\, for childhood diseases\, isolation of infected children may be a possible mechanism responsible for the observed oscillatory behavior in incidence. This is shown analytically by identifying a Hopf bifurcation with the isolation period as the bifurcation parameter. \nAn important result is that the threshold value for isolation to generate sustained oscillations from the model with gamma-distributed isolation period is much more realistic than the model assuming exponential distributions. \nAbout the speaker:  Joan Ponce is a graduate student from Purdue University
URL:https://colleges.claremont.edu/ccms/event/dynamics-of-a-childhood-disease-model-with-isolation/
LOCATION:Millikan 2141\, Pomona College
CATEGORIES:Applied Math Seminar
ORGANIZER;CN="Kathy Sheldon":MAILTO:ksheldon@pomona.edu
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DTSTART;TZID=America/Los_Angeles:20191125T161500
DTEND;TZID=America/Los_Angeles:20191125T171500
DTSTAMP:20260429T025237
CREATED:20190909T232742Z
LAST-MODIFIED:20191112T033822Z
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SUMMARY:Applied Math Talk: Patterns deformed by spatial inhomogeneity give by Prof. Jasper Weinburd (HMC)
DESCRIPTION:At the turn of the twentieth century\, physicist Henri Bénard heated a shallow plate of fluid from below. For temperatures above a critical value\, the fluid’s evenly heated state became unstable as thermal convection took hold; heated fluid rose in localized areas while cooler fluid fell nearby. The rising and falling fluid created hexagonal convection cells\, squares\, and stripes.\nSuppose that we modify Bénard’s experiment by heating only the left half plate. We expect the fluid on the right to remain stationary and only the the fluid on the left to form patterns. We confirm this intuition mathematically and\, more surprisingly\, find that the step-type inhomogeneity restricts the spatial period of the resulting patterns on the left. We examine this phenomenon using a universal partial differential equation model. The main difficulty arrises at the location of the discontinuous inhomogeneity because results on either side cannot be directly compared. We construct a transformation of variables that bridges this jump and allows a heteroclinic glueing argument from left to right. The explicit form of this transformation determines the widths of patterns that may occur in the inhomogeneous environment.
URL:https://colleges.claremont.edu/ccms/event/jasper-weinburd-pomona-college/
LOCATION:Emmy Noether Room\, Millikan 1021\, Pomona College\, 610 N. College Ave.\, Claremont\, California\, 91711
CATEGORIES:Applied Math Seminar
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