Eventshttp://www.cam.cornell.eduEventsSat, 21 Oct 2017 17:09:15 -0400CAM Colloquium: Austin Benson (CS, Cornell University) - Spacey random walksAbstract: Random walks are a fundamental model in applied mathematics and are a common example of a Markov chain. A standard way to compute the stationary distribution for a random walk on a finite set of states is to compute the Perron vector of the associated transition probability matrix. There are algebraic analogues of the Perron vector in terms of z-eigenvectors of transition probability tensors whose entries come from higher-order Markov chains. These vectors look stochastic, but they are derived from an algebraic substitution in the stationary distribution equation of higher-order Markov chains and do not carry a probabilistic interpretation. In this talk, I will present the spacey random walk, a non-Markovian stochastic process whose stationary distribution is given by a dominant z eigenvector of the transition probability tensor. The process itself is a vertex-reinforced random walk, and its discrete dynamics are related to a continuous dynamical system. We analyze the convergence properties of these dynamics and discuss numerical methods for computing the stationary distribution. We also provide several applications of the spacey random walk model in population genetics, ranking, and clustering data, and we use the process to analyze taxi trajectory data in New York. Bio: Austin Benson is currently a postdoctoral associate in the department of Computer Science at Cornell. He will join the faculty of Computer Science at Cornell in July 2018. Before coming to Cornell, he received his PhD in 2017 from the Institute for Computational and Mathematical Engineering at Stanford University. Before that, he received undergraduate degrees in computer science and applied mathematics from UC-Berkeley. Outside of the university, he has also spent time as an intern at Google Research, Sandia National Laboratories, and HP Labs.http://www.cam.cornell.edu/news/colloquium.cfm?event=18165
http://www.cam.cornell.edu/news/colloquium.cfm?event=18165
Fri, 27 Oct 2017 15:30:00 -0400CAM Colloquium: Rahul Roy (Indian Statistical Institute, New Delhi) - Two laws of drainage networks: a Brownian web approachAbstract: Two empirically observed laws of river geomorphology are the Hack's law and the Horton-Strahler ordering. Hack's law says that the drainage area of a river network up to a point of its divide is proportional to a power of the length of the river till its divide. Horton-Strahler ordering gives a weightage of the river vis-a-vis its tributaries. We study these laws for a mathematical model of river networks known as the Howard's model. The approach is via the Brownian web, which is realized as the diffusive scaling of Howard's model. (This is a joint work with Kumarjit Saha and Anish Sarkar.) Bio: Rahul Roy is a professor at the Indian Statistical Institute, New Delhi. He works in probability theory and, more particularly, in percolation theory and random graphs. He is also interested in the history of mathematics. He is a fellow of the Indian Academy of Sciences, and he obtained his Ph.D. from Cornell University.http://www.cam.cornell.edu/news/colloquium.cfm?event=18182
http://www.cam.cornell.edu/news/colloquium.cfm?event=18182
Fri, 03 Nov 2017 15:30:00 -0400CAM Alumni Panel DiscussionSpeaker TBAhttp://www.cam.cornell.edu/news/colloquium.cfm?event=17989
http://www.cam.cornell.edu/news/colloquium.cfm?event=17989
Fri, 10 Nov 2017 15:30:00 -0400CAM Colloquium: Notable Alumni Series, Mason Porter (UCLA)Details TBAhttp://www.cam.cornell.edu/news/colloquium.cfm?event=17992
http://www.cam.cornell.edu/news/colloquium.cfm?event=17992
Fri, 17 Nov 2017 15:30:00 -0400CAM Colloquium: No Colloquium - Thanksgiving BreakCAM Colloquium: No Colloquium - Thanksgiving Breakhttp://www.cam.cornell.edu/news/colloquium.cfm?event=17991
http://www.cam.cornell.edu/news/colloquium.cfm?event=17991
Fri, 24 Nov 2017 15:30:00 -0400CAM Colloquium: Stephen Ellner (EEB, Cornell University) - Who gets into the 1%, and why: integrodifference equations as models for individuals, populations, and communitiesAbstract: In humans “the 1%” refers to inequality in wealth. Many animal and plant populations have similarly extreme inequality in lifetime reproductive success: a small fraction of the current generation produces most of the offspring that make up the next generation. Who gets to be one of these lucky few? Integrodifference equation models for structured populations, parameterized from empirical data, can be used to address questions like this. Assuming first that individuals are not intrinsically different, I consider two ways of identifying what distinguishes the lucky few: comparing life trajectories of lucky and unlucky, and comparing the impact of good outcomes at different ages, stages, or sizes. When there are persistent differences among individuals (e.g., different genotypes) we can ask how much of the variability in outcomes is due to sheer luck, rather than differences in individual quality. The role of luck often turns out to be surprisingly large. Time permitting, I will mention some open mathematical questions about these models. Bio: Stephen Ellner is a CAM graduate (PhD 1982) and Horace White Professor of Ecology and Evolutionary Biology at Cornell. He is a Fellow of the Ecological Society of America, and received the 2017 Presidential Award (for outstanding paper) from the American Society of Naturalists. Before coming to Cornell in 2000 he was a faculty member at University of Tennessee (mathematics) and NC State (biomathematics & statistics). His research interests have centered on environmental and within-species variability, including species coexistence in random environments, evolution of bet-hedging strategies, interactions between ecological and evolutionary dynamics on similar time scales, and pathogen spread through multispecies communities.http://www.cam.cornell.edu/news/colloquium.cfm?event=18188
http://www.cam.cornell.edu/news/colloquium.cfm?event=18188
Fri, 01 Dec 2017 15:30:00 -0400CAM Colloquium: John Urschel (MIT) - Learning Determinantal Point Processes with Moments and CyclesAbstract: Determinantal Point Processes (DPPs) are a family of probabilistic models that have a repulsive behavior, and lend themselves naturally to many tasks in machine learning in which returning a diverse set of objects is important. While there are fast algorithms for sampling, marginalization and conditioning, much less is known about learning the parameters of a DPP. Our contribution is twofold: (i) we establish the optimal sample complexity achievable in this problem and show that it is governed by a natural parameter, which we call the \emph{cycle sparsity}; (ii) we propose a provably fast combinatorial algorithm that implements the method of moments efficiently and achieves optimal sample complexity. Finally, we give experimental results that confirm our theoretical findings. (Joint work with Victor-Emmanuel Brunel, Ankur Moitra and Philippe Rigollet.) Bio: John Urschel is a doctoral candidate in applied mathematics at MIT, and an adjunct research associate in mathematics at Penn State. His research areas include spectral graph theory, numerical PDE's, matrix algebra, computational finance and mathematical physics. His work with L. Zikatanov regarding the connectedness of nodal decompositions of Fiedler vectors led to the Urschel-Zikatanov Theorem, and he currently has the fastest eigensolver for minimal Laplacian eigenvectors. Recently, he published a paper in SIAM Journal of Numerical Analysis on centroidal Voronoi tessellations.http://www.cam.cornell.edu/news/colloquium.cfm?event=18187
http://www.cam.cornell.edu/news/colloquium.cfm?event=18187
Fri, 02 Feb 2018 15:30:00 -0400