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DTSTART;TZID=America/Los_Angeles:20191104T161500
DTEND;TZID=America/Los_Angeles:20191104T171500
DTSTAMP:20260419T025935
CREATED:20190803T171420Z
LAST-MODIFIED:20191026T215438Z
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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:20191105T121500
DTEND;TZID=America/Los_Angeles:20191105T131000
DTSTAMP:20260419T025935
CREATED:20190910T234841Z
LAST-MODIFIED:20191101T153056Z
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SUMMARY:Differential spectra of power permutations (Daniel Katz\, CSUN)
DESCRIPTION:If $F$ is a finite field and $d$ is a positive integer relatively prime to $|F^\times|$\, then the power map $x \mapsto x^d$ is a permutation of $F$\, and so is called a power permutation of $F$. For any function $f: F \to F$\, and $a\, b \in F$\, we define the differential multiplicity of $f$ with respect to $a$ and $b$\, written $\delta_f(a\,b)$\, to be the number of pairs $(x\,y) \in F^2$ with $x-y=a$ and $f(x)-f(y)=b$.  We usually insist that $a\not=0$\, since it is immediate that $\delta_f(0\,0)=|F|$ and $\delta_f(0\,b)=0$ for $b\not=0$.  The differential spectrum of $f$\, written $\Delta_f$\, is defined as $\Delta_f=\{\delta_f(a\,b): a \in F^\times\, b \in F\}$. Differential spectra of power permutations are of interest in applications to cryptography and digital communications.  We are especially interested in fields $F$ and exponents $d$ such $f(x)=x^d$ is a power permutation over $F$ whose differential spectrum contains at most three values. We present computational experiments that suggest conjectures as to which $(F\,d)$ pairs produce such spectra.  This is joint work with Kyle Pacheco and Yakov Sapozhnikov.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-daniel-katz-csun-2/
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:20191105T150000
DTEND;TZID=America/Los_Angeles:20191105T160000
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CREATED:20191024T001849Z
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SUMMARY:Paper Strip Knots (David Bachman)
DESCRIPTION:I will discuss joint work with Jim Hoste\, where we prove that a unique folded strip of paper can follow any polygonal knot with odd stick number. In the even stick number case there are either infinitely many\, or none.
URL:https://colleges.claremont.edu/ccms/event/paper-strip-knots-david-bachman/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Topology Seminar
ORGANIZER;CN="Helen Wong":MAILTO:hwong@cmc.edu
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DTSTART;TZID=America/Los_Angeles:20191106T080000
DTEND;TZID=America/Los_Angeles:20191106T170000
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CREATED:20190826T235443Z
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SUMMARY:Science for the Greater Good: How a Math Professor Saved the Italian Coastline from Big Oil
DESCRIPTION:In 2007\, Dr. Maria D’Orsogna learned of proposed oil activities in her home region of Abruzzo\, Italy. Century-old wineries were to be uprooted to build clusters of oil wells\, refineries and pipelines\, turning scenic Abruzzo into an oil district. Although based in California\, 6\,000 miles away\, Dr. D’Orsogna took it upon herself to raise awareness and educate the public at large. She blended her scientific training\, her experience as a professor\, and her strong desire for social justice into an environmental movement that rapidly spread from Abruzzo across the country. Over the years\, she traveled from town to town in Italy\, educating citizens about environmental and health effects tied to hydrocarbon extraction\, debating Big Oil\, exposing political corruption\, engaging the Catholic Church\, putting pressure on decision makers to act for the common good. While in California she used social networks and blogging to expose wrongdoings of the oil and gas industry\, coordinate letter writings\, keep raising awareness and spur action. Thanks to public uproar\, spearheaded by Marias unwavering efforts\, Abruzzo banned oil drilling and for the first time ever\, the Italian parliament imposed a no-drill zone of 12 miles encompassing all of Italy’s 5\,000 mile coastline. Overall she helped stop at least 50 oil leases\, earning the nickname Erin Brockovich of Italy. Maria’s story is a testament of how\, by engaging with the community\, scientists and educators can truly make a difference.
URL:https://colleges.claremont.edu/ccms/event/tba-11/
LOCATION:Argue Auditorium\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Colloquium
ORGANIZER;CN="Blerta Shtylla":MAILTO:shtyllab@pomona.edu
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