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Archive : Discrete Mathematics

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Po-Shen Loh, Carnegie Mellon UniversityPo-Shen Loh, Carnegie Mellon UniversityGore 116Title: Setting Personalized Learning Free <br> Abstract: Improving math and science education is a national priority. Personalized education is within reach and has the potential to transform current practices through the usage of data and algorithms. Po-Shen Loh will speak about the social enterprise he founded (expii.com) that will turn every smartphone into a free personalized learning system by combining crowdsourcing and mathematical algorithms. In a modern world where content is everywhere (but of varying quality, and disorganized), the central problem is to identify exactly which piece of content a particular learner should interact with at any given moment based upon the learner’s current knowledge base and long-term goals. Leveraging the Elo rating system from competitive chess, Expii introduces a new mathematical framework for answering this question, which casts the central problem into a graph algorithm problem. In this talk, Po-Shen Loh will speak about his experience translating the mathematics and algorithms from the research world to the practical world, through mission-driven entrepreneurship.4/20/2018 7:30:00 PM4/20/2018 9:00:00 PMFalse
Po-Shen Loh, Carnegie Mellon UniversityPo-Shen Loh, Carnegie Mellon UniversityMemorial Hall 123Title: Ramsey Theory and Paths <br> Abrstract: Starting from an innocent Ramsey-theoretic question regarding directed paths in graphs, we discover a series of rich and surprising connections that lead into the theory around a fundamental result in Combinatorics: Szemeredi's Regularity Lemma, which roughly states that every graph (no matter how large) can be well-approximated by a bounded-complexity pseudorandom object. Using these relationships, we prove that every coloring of the edges of the transitive N-vertex tournament using three colors contains a directed path of length at least sqrt(N) e^{log^* N} which entirely avoids some color. The unusual function log^* is the inverse function of the tower function (iterated exponentiation).4/20/2018 2:30:00 PM4/20/2018 3:30:00 PMFalse
Ariel Keller, Emory University Ariel Keller, Emory University Ewing 336Title; "On Cycles, Chorded Cycles, and Degree Conditions," <br></br> Abstract: Sufficient conditions to imply the existence of different substructures in a graph have long been of interest in graph theory, and conditions that guarantee a large set of cycles or chorded cycles are a recurring theme. This talk explores different degree sum conditions that are sufficient for finding a large set of vertex-disjoint cycles or a large set of vertexdisjoint chorded cycles in a graph. For an integer t ≥ 1, let σt(G) be the smallest sum of degrees of t independent vertices of G. We prove that if a graph G has sufficiently large order and degree sum condition σ4(G) ≥ 8k−3, with k ≥ 2, then the graph contains k vertex-disjoint cycles. We consider an equivalent condition for chorded cycles, and we prove that the degree sum condition in each result is sharp. Finally, we conjecture generalized degree sum conditions on σt(G) for t ≥ 2 sufficient to imply that G contains k vertex-disjoint cycles for k ≥ 2 and k vertex-disjoint chorded cycles for k ≥ 2. This is joint work with Ronald J. Gould and Kazuhide Hirohata.4/17/2018 7:30:00 PM4/17/2018 8:30:00 PMFalse
Novi Bong, University of DelawareNovi Bong, University of DelawareEwing 336Title: Degree/Diameter Problem <br></br> Abstract: The degree/diameter problem is a problem to determine the largest graphs or digraphs of given maximum degree and given diameter. The general upper bounds for this problem are called the Moore bounds and the graphs that attain the bounds are called Moore graphs. However, there are not many of them. The research in this area focuses on two approaches, which are finding a tighter upper bounds for the maximum possible number of vertices or constructing large graphs of given degree and diameter to improve the lower bounds. In this talk, I will give an overview about the degree/diameter problem. 4/10/2018 7:30:00 AM4/10/2018 8:30:00 AMFalse

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