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DTSTART;TZID=America/Los_Angeles:20190211T041500
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SUMMARY:Community structure in networks: the effect of communities on a preferential attachment model and epidemic spreading (Emily Fischer\, Cornell)
DESCRIPTION:Online social networks and other networks of interest are known to exhibit community structure\, where a community is defined to be a highly interconnected group of nodes with possibly shared traits or features. However\, classic network models\, such as the preferential attachment model\, do not account for community structure. In this talk\, I will present the Community-Aware Preferential Attachment Model (CAPAM)\, which allows the user to specify community structure via edge probabilities. I will show that CAPAM retains desirable properties of the preferential attachment model\, namely a power-law degree distribution\, and further that the multivariate degree distribution is dependent upon the edge probabilities in an interesting way. I will show that community structure also plays a role in epidemic spreading processes. Under the SIS model\, the lifetime of a spreading process is constrained by the structure of the individual communities\, and the epidemic threshold is bounded closely around the threshold associated with the strongest community.
URL:https://colleges.claremont.edu/ccms/event/applied-math-talk-given-by-emily-fisher/
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:20190212T121500
DTEND;TZID=America/Los_Angeles:20190212T131000
DTSTAMP:20260409T160713
CREATED:20181227T132155Z
LAST-MODIFIED:20190120T184543Z
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SUMMARY:Subgraph statistics (Benny Sudakov\, ETH Zurich)
DESCRIPTION:Given integers $k\,l$  and a graph $G$\, how large can be the fraction of $k$-vertex subsets of $G$ which span exactly $l$ edges?  The systematic study of this very natural  question  was recently initiated by Alon\, Hefetz\, Krivelevich and Tyomkyn who also proposed several interesting conjectures on this topic. \n\nIn this talk we discuss a theorem which proves one of their conjectures and implies an asymptotic version of another.  We also make some first steps towards analogous question for hypergraphs. Our proofs involve some Ramsey-type arguments\, and a number of different probabilistic tools\, such as polynomial anticoncentration inequalities and  hypercontractivity. \nJoint work with M. Kwan and T. Tran.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-benny-sudakov-eth-zurich/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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DTSTART;TZID=America/Los_Angeles:20190213T161500
DTEND;TZID=America/Los_Angeles:20190213T171500
DTSTAMP:20260409T160713
CREATED:20190110T154812Z
LAST-MODIFIED:20190213T234043Z
UID:1004-1550074500-1550078100@colleges.claremont.edu
SUMMARY:Cracking the Code: Predicting Properties of Material Fracture Networks using Machine Learning (Allon Percus\, CGU)
DESCRIPTION:Understanding how fluid flows through heterogeneous materials\, and how it can make these materials fail\, are among the hardest challenges in materials science.  Experiments and simulations show that flow through subsurface rock is mostly limited to a small subnetwork\, or backbone\, of fractures.  Identifying this backbone would allow for a large speedup in flow and transport simulations\, but the process of identifying it can itself be computationally intensive.  I will discuss a machine learning approach\, developed in a CGU Math Clinic project with Los Alamos National Laboratory\, that rapidly finds relevant subnetworks based on graph structure and training data from simulations.  Time permitting\, I will also describe a method that uses graph convolutional neural networks to predict\, with high accuracy\, how fractures grow in brittle materials.  This provides an automated approach for learning how the fractures can radiate through the material\, and ultimately cause it to fail.
URL:https://colleges.claremont.edu/ccms/event/ccms-colloquium-allon-percus-cgu/
LOCATION:Shanahan B460\, Harvey Mudd College\, 301 Platt Blvd.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Colloquium
ORGANIZER;CN="Ali Nadim":MAILTO:ali.nadim@cgu.edu
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