Eventshttp://www.cam.cornell.eduEventsThu, 14 Dec 2017 10:04:06 -0500CAM Colloquium: Jaakko Lehtomaa (Mathematics, Cornell University) - On heavy-tailed phenomena and the principle of a single big jumpAbstract: Heavy-tailed distributions have offered an active field of research in insurance mathematics, queuing theory and operations research for decades. This talk concentrates on phenomena that can be encountered in heavy-tailed models. Special emphasis is put on the so-called principle of a single big jump. It means that the most likely way for a sum of i.i.d. variables to be large is that one of the summands itself is very large. We discuss what properties cause the phenomenon of a single big jump. It turns out that eventual log-convexity or log-concavity of densities is the key ingredient in determining if the principle of a single big jump occurs. In general, well-behaved densities are typically log-convex with heavy tails and log-concave with light ones. We discuss a benchmark and a visual tool for distinguishing between the two cases. The study supplements modern non-parametric density estimation methods where log-concavity plays a main role, as well as heavy-tailed diagnostics such as the mean excess plot. Bio: Lehtomaa received his Ph.D. in 2016 from University of Helsinki. After a postdoctoral study period in Professor Soren Asmussen's group at University of Aarhus, he joined Professor Sid Resnick's group at Cornell University as a postdoctoral researcher. Lehtomaa's research interests have concentrated around the topic of heavy-tailed modeling in insurance and finance. His interests have gradually shifted towards applied problems with real data.http://www.cam.cornell.edu/news/colloquium.cfm?event=18260
http://www.cam.cornell.edu/news/colloquium.cfm?event=18260
Fri, 26 Jan 2018 15:30:00 -0500CAM 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 -0500CAM Colloquium: Jane Wang (Physics, Cornell University) - Insect Flight: from Newton’s Law to NeuronsAbstract: We have been seeking mechanistic explanations of the complex movement of insect flight. Our recent analyses of insects’ balancing act predict the role of a steering muscle of a fly in regulating flight stability. The physics of flight informs us about the function of insect’s internal machinery that orchestrate its flight, and sheds light on the neural feedback circuitries underlying insects’ fast reflexes for balancing in air. In this talk, I will discuss how a dragonfly recovers from falling upside down and how a fly makes minute wing adjustments to stay upright. Bio: Jane Wang is a professor of Physics and a professor of Mechanical and Aerospace engineering at Cornell University. She has devoted much of her work to understand how insects fly and why they fly the way they do. Her recent work makes new connections to neural science in the study of flight reflexes.http://www.cam.cornell.edu/news/colloquium.cfm?event=18257
http://www.cam.cornell.edu/news/colloquium.cfm?event=18257
Fri, 09 Feb 2018 15:30:00 -0500CAM Colloquium: Philippe Sosoe (Mathematics, Cornell University) - Dispersive Equations with Random Initial DataAbstract: Beginning the 1980s, there has been interest in considering certain classical nonlinear equations, such as nonlinear Schroedinger, Korteweg de Vries and wave equations, with random initial data. I will explain the motivation for this setting, describe some of the results obtained by using probabilistic methods for dispersive nonlinear equations, and finish by describing some recent and ongoing work by myself and collaborators on the subject. Bio: I graduated from McGill University in Montreal in 2009 with a BSc in Mathematics. I obtained my PhD in Mathematics in 2014 under Michael Aizenman at Princeton, where I worked on random matrices and percolation models. This was followed by a three-year postdoctoral position at Harvard's (then) new Center for Mathematical Sciences and Applications in H.T. Yau's group. I joined the faculty at Cornell in August, 2017.http://www.cam.cornell.edu/news/colloquium.cfm?event=18259
http://www.cam.cornell.edu/news/colloquium.cfm?event=18259
Fri, 02 Mar 2018 15:30:00 -0500