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DTSTART;TZID=America/Los_Angeles:20230207T121500
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DTSTAMP:20260518T154557
CREATED:20230202T190817Z
LAST-MODIFIED:20230202T190817Z
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SUMMARY:Orthogonality defect and coherence of cyclotomic lattices (Lenny Fukshansky\, CMC)
DESCRIPTION:There are two different measures of how far a given Euclidean lattice is from being orthogonal — the orthogonality defect and the average coherence. The first of these comes from the study of sphere packing while the second is motivated by frame theory\, but both of them have applications in digital communications\, especially in coding theory and cryptography. It is interesting to understand how the two are related. We investigate this question on an important class of cyclotomic lattices\, where some nice formulas can be derived and certain empirical observations can be made. Joint work with David Kogan.
URL:https://colleges.claremont.edu/ccms/event/orthogonality-defect-and-coherence-of-cyclotomic-lattices-lenny-fukshansky-cmc/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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DTSTART;TZID=America/Los_Angeles:20230208T161500
DTEND;TZID=America/Los_Angeles:20230208T173000
DTSTAMP:20260518T154557
CREATED:20230122T180304Z
LAST-MODIFIED:20230206T231015Z
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SUMMARY:The mathematics of neural networks: recent advances\, thoughts\, and the path forward (Prof. Mikhail Belkin\, UCSD)
DESCRIPTION:Title: The mathematics of neural networks: recent advances\, thoughts\, and the path forward \nSpeaker: Prof. Mikhail Belkin\, Department of Mathematics\, University of California San Diego \nAbstract: The recent remarkable practical achievements of neural networks have far outpaced our theoretical understanding of their properties. Yet\, it is hard to imagine that progress can continue indefinitely\, without deeper understanding of their fundamental principles and limitations. In this talk I will discuss some recent advances in the mathematics of neural networks and outline what\, in my opinion\, are some promising directions for future research. \n\n\n\n\n\nMikhail Belkin received his Ph.D. in 2003 from the Department of Mathematics at the University of Chicago. His research interests are in theory and  applications of machine learning and data analysis. Some of his well-known work includes widely used Laplacian Eigenmaps\, Graph Regularization and Manifold Regularization algorithms\, which brought ideas from classical differential geometry and spectral analysis to data science. His recent work has been concerned with understanding remarkable mathematical and statistical phenomena observed in deep learning. This empirical evidence necessitated revisiting some of the basic concepts in statistics and optimization.  One of his key recent findings is the “double descent” risk curve that extends the textbook U-shaped bias-variance trade-off curve beyond the point of interpolation. Mikhail Belkin has served on the editorial boards of the Journal of Machine Learning Research\, IEEE Pattern Analysis and Machine Intelligence and SIAM Journal on Mathematics of Data Science.
URL:https://colleges.claremont.edu/ccms/event/prof-mikhail-belkin/
LOCATION:Argue Auditorium\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Colloquium
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DTSTART;TZID=America/Los_Angeles:20230209T163000
DTEND;TZID=America/Los_Angeles:20230209T173000
DTSTAMP:20260518T154557
CREATED:20230208T193627Z
LAST-MODIFIED:20230213T200028Z
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SUMMARY:Linear Multifractional Stable Sheets in the Broad Sense: Existence and Joint Continuity of Local Times (Qidi Peng\, Institute of Mathematical Sciences\, CGU)
DESCRIPTION:We introduce the notion of linear multifractional stable sheets in the broad sense (LMSS) to include both linear multifractional Brownian sheets and linear multifractional stable sheets. The purpose of the framework is to study the existence and joint continuity of the local times of LMSS\, and also the local Holder condition of the local times in the set variable. As the main results\, (1) we provide a sufficient and necessary condition for the existence of local times of LMSS; (2) we show a sufficient condition for the joint continuity of local times; and (3) we prove a sharp local Holder condition for the local times in the set variable. All these theorems improve significantly the existing results for the local times of multifractional Brownian sheets and linear multifractional stable sheets in the literature.
URL:https://colleges.claremont.edu/ccms/event/linear-multifractional-stable-sheets-in-the-broad-sense-existence-and-joint-continuity-of-local-times-qidi-peng-institute-of-mathematical-sciences-cgu/
LOCATION:Roberts North 105\, CMC\, 320 E. 9th St.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Analysis Seminar
ORGANIZER;CN="Asuman Aksoy":MAILTO:asuman.aksoy@claremontmckenna.edu
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