BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Claremont Center for the Mathematical Sciences - ECPv6.17.3.1//NONSGML v1.0//EN CALSCALE:GREGORIAN METHOD:PUBLISH X-ORIGINAL-URL:https://colleges.claremont.edu/ccms X-WR-CALDESC:Events for Claremont Center for the Mathematical Sciences REFRESH-INTERVAL;VALUE=DURATION:PT1H X-Robots-Tag:noindex X-PUBLISHED-TTL:PT1H BEGIN:VTIMEZONE TZID:America/Los_Angeles BEGIN:DAYLIGHT TZOFFSETFROM:-0800 TZOFFSETTO:-0700 TZNAME:PDT DTSTART:20210314T100000 END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:-0700 TZOFFSETTO:-0800 TZNAME:PST DTSTART:20211107T090000 END:STANDARD BEGIN:DAYLIGHT TZOFFSETFROM:-0800 TZOFFSETTO:-0700 TZNAME:PDT DTSTART:20220313T100000 END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:-0700 TZOFFSETTO:-0800 TZNAME:PST DTSTART:20221106T090000 END:STANDARD BEGIN:DAYLIGHT TZOFFSETFROM:-0800 TZOFFSETTO:-0700 TZNAME:PDT DTSTART:20230312T100000 END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:-0700 TZOFFSETTO:-0800 TZNAME:PST DTSTART:20231105T090000 END:STANDARD BEGIN:DAYLIGHT TZOFFSETFROM:-0800 TZOFFSETTO:-0700 TZNAME:PDT DTSTART:20240310T100000 END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:-0700 TZOFFSETTO:-0800 TZNAME:PST DTSTART:20241103T090000 END:STANDARD BEGIN:DAYLIGHT TZOFFSETFROM:-0800 TZOFFSETTO:-0700 TZNAME:PDT DTSTART:20250309T100000 END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:-0700 TZOFFSETTO:-0800 TZNAME:PST DTSTART:20251102T090000 END:STANDARD END:VTIMEZONE BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20240505T080000 DTEND;TZID=America/Los_Angeles:20240505T170000 DTSTAMP:20240505T202338Z CREATED:20240505T202338Z LAST-MODIFIED:20240505T202338Z UID:10002140-1714896000-1714928400@colleges.claremont.edu SUMMARY:Prof. Sigifredo Herrón (Universidad Nacional de Colombia-Medellín) DESCRIPTION: URL:https://colleges.claremont.edu/ccms/event/prof-sigifredo-herron-universidad-nacional-de-colombia-medellin/ LOCATION:This event is virtual. Zoom link: https://pomonacollege.zoom.us/my/radzoom\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20240429T161500 DTEND;TZID=America/Los_Angeles:20240429T173000 DTSTAMP:20240421T181945Z CREATED:20240421T181945Z LAST-MODIFIED:20240421T181945Z UID:10001926-1714407300-1714411800@colleges.claremont.edu SUMMARY:Emer Lopera Arias (HMC) DESCRIPTION:Title: The fractional p-Laplacian operator. Motivation for its definition and related boundary value problems \nAbstract: \nLast decades\, nonlocal operators\, as the fractional Laplacian\, have gained to much attention due to its applications to several physical Phenomena. In this talk we aim to motivate the definition of the fractional laplacian operator through a simple but quite illustrative example related to Long jump random walks. then\, we will present a generalization to the fractional p-laplacian operator\, p>1\, and we will show a new result concerning the existence of solutions for a boundary value problem with this operator. URL:https://colleges.claremont.edu/ccms/event/emer-lopera-arias-hmc/ LOCATION:Emmy Noether Room\, Estella 1021\, Pomona College\,\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20240422T161500 DTEND;TZID=America/Los_Angeles:20240422T173000 DTSTAMP:20240421T181538Z CREATED:20240421T181538Z LAST-MODIFIED:20240421T181538Z UID:10001924-1713802500-1713807000@colleges.claremont.edu SUMMARY:İrma Hacınlıyan (Istanbul Technical University) DESCRIPTION:Title: On Nonlinear Schrödinger Type Equations: Wave Modulation and Mathematical Analysis \nAbstract: The nonlinear Schrödinger (NLS) equation describes the evolution of slowly varying packets of quasi-monochromatic waves in weakly nonlinear dispersive media. The NLS equation with soliton solutions is one of the significant and widely pursued research areas on the nonlinear wave motions. Sub-studies on such evolution equations include derivations of those equations; finding exact solutions and developing methods for these; studies of the analytic and geometric structure of the equations as integrable systems; singularities and collapses of solutions; analyzing modulation equations by dynamical systems methods; and related subjects. In this talk\, nonlinear modulation of waves propagating in a generalized elastic solid according to different physical scenarios will be discussed. Properties of the solutions of NLS-type equations that are derived using the reductive perturbation method will be examined by mathematical analysis methods. URL:https://colleges.claremont.edu/ccms/event/irma-hacinliyan-istanbul-technical-university/ LOCATION:Emmy Noether Room\, Estella 1021\, Pomona College\,\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20240401T161500 DTEND;TZID=America/Los_Angeles:20240401T171500 DTSTAMP:20240330T172834Z CREATED:20240330T172834Z LAST-MODIFIED:20240330T172834Z UID:10001918-1711988100-1711991700@colleges.claremont.edu SUMMARY:Chiu-Yen Kao (Claremont McKenna College) DESCRIPTION:Title: Geometric Optimization Involving Partial Differential Equations and Its Applications \nSpeaker: Professor Chiu-Yen Kao\, Claremont McKenna College\, Claremont\, CA USA \nAbstract: Optimal geometric design for energy functionals\, which depends on solutions to partial differential equations\, provides a vast number of interesting and challenging mathematical problems. One of the famous problems is that L. Rayleigh conjectured that the disk should minimize the fundamental frequency of vibration (the square root of the first Laplace-Dirichlet eigenvalue) among all shapes of equal area\, more than a century ago. In this talk\, we will share our recent findings related to geometric optimization for eigenvalue problems. Our approach involves the development of various computational methods to optimize Steklov eigenvalues and Laplace-Beltrami eigenvalues. Additionally\, we explore applications of these methods. URL:https://colleges.claremont.edu/ccms/event/chiu-yen-kao-claremont-mckenna-college/ LOCATION:Emmy Noether Room\, Estella 1021\, Pomona College\,\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20240325T161500 DTEND;TZID=America/Los_Angeles:20240325T171500 DTSTAMP:20240330T173059Z CREATED:20240330T173049Z LAST-MODIFIED:20240330T173059Z UID:10001920-1711383300-1711386900@colleges.claremont.edu SUMMARY:Ami Radunskaya (Pomona College) DESCRIPTION:Title:  Can a function tell us how immune cells kill? \nSpeaker: Prof. Ami Radunskaya (Pomona College\, Claremont CA) \nAbstract: The immune system is able to fight cancer by mustering and training an army of effector “killer” cells.  Mathematical models of tumor-immune interactions must describe the proliferation\, recruiting and killing rates of immune cells.  Earlier work surprisingly showed that the functions describing the kill rates distinguish between two types of immune cells.  The mechanisms behind these differences have been a mystery\, however.  In an attempt to unravel this mystery\, we have created a cell-based fixed-lattice model that simulates immune cell and tumor cell interaction involving tumor recognition and two killing mechanisms.  These mechanisms play a big role in the effectiveness of many cancer immunotherapies. Results from model simulations\, along with theories developed by ecologists\, can help to illuminate which mechanisms are at work in different conditions. URL:https://colleges.claremont.edu/ccms/event/ami-radunskaya-pomona-collegeo/ LOCATION:Emmy Noether Room\, Estella 1021\, Pomona College\,\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20240318T161500 DTEND;TZID=America/Los_Angeles:20240318T171500 DTSTAMP:20240330T174651Z CREATED:20240313T230255Z LAST-MODIFIED:20240330T174651Z UID:10001916-1710778500-1710782100@colleges.claremont.edu SUMMARY:Sigifredo Herron (UNAL) DESCRIPTION: URL:https://colleges.claremont.edu/ccms/event/fernando-a-gallego-unal/ LOCATION:This event is virtual. Zoom link: https://pomonacollege.zoom.us/my/radzoom\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20240304T161500 DTEND;TZID=America/Los_Angeles:20240304T171500 DTSTAMP:20240228T002704Z CREATED:20240228T002704Z LAST-MODIFIED:20240228T002704Z UID:10001914-1709568900-1709572500@colleges.claremont.edu SUMMARY:Gabe Chandler (Pomona College) DESCRIPTION:Title: Graphical Anomaly Detection for High Dimensional and Object Data \nAbstract: Anomaly detection is an important task in data analysis\, though an agreed upon definition of what constitutes an outlier does not exist.  Accordingly\, a graphical tool that can highlight interesting observations in a data set that the scientist can then investigate with domain specific knowledge would be of value.  The depth quantile function (DQF)\, a recently introduced feature map that takes data of arbitrary dimension to a function of a single variable while encoding certain geometric information\, will provide such a tool.  After introducing the DQF\, we will discuss adaptations that make it particularly suited to the problem of anomaly detection\, particularly the case where the non-anomalous data is living on a lower dimensional manifold in the data space.  The DQF is also kernelizable\, allowing applications to non-Euclidean data\, as will be demonstrated via several examples. URL:https://colleges.claremont.edu/ccms/event/gabe-chandler-pomona-college/ LOCATION:Emmy Noether Room\, Estella 1021\, Pomona College\,\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20240226T161500 DTEND;TZID=America/Los_Angeles:20240226T171500 DTSTAMP:20240220T224116Z CREATED:20240220T215244Z LAST-MODIFIED:20240220T224116Z UID:10001910-1708964100-1708967700@colleges.claremont.edu SUMMARY:Javier Gonzalez Anaya (Harvey Mudd College) DESCRIPTION:This is the continuation of the semester’s joint seminar with the Universidad Nacional de Colombia-Manizales. \nTitle: Enumerating linearity regions of max-pooling layers in convolutional neural networks \nAbstract: Convolutional neural networks (CNN’s) are central tools in the application of machine learning to text\, audio and image processing. Their success stems from the ability of these networks to identify key features in complex datasets at a relatively low computational cost. Max-pooling layers (MPL’s) are key components of CNN’s that reduce the number of parameters used by the network while making it more robust to small changes in the input data. From a mathematical point of view\, MPLs are piecewise-linear functions\, and their number of linearity regions can be interpreted as a measure of complexity of the layer. In this talk I will explain how we can use combinatorial techniques to count these linearity regions\, and survey our current results in the area. URL:https://colleges.claremont.edu/ccms/event/javier-gonzalez-anaya-harvey-mudd-college/ LOCATION:Emmy Noether Room\, Estella 1021\, Pomona College\,\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20240219T161500 DTEND;TZID=America/Los_Angeles:20240219T171500 DTSTAMP:20240220T215909Z CREATED:20240220T215909Z LAST-MODIFIED:20240220T215909Z UID:10001912-1708359300-1708362900@colleges.claremont.edu SUMMARY:Cristian Lopez Morales (UNAL) DESCRIPTION:Join us for the first talk in the joint seminar with CCMS Applied Math and the Universidad Nacional de Colombia \nTitle \nSerre Conjecture. Geometric interpretation of the Quillen-Suslin Theorem. \nAbstract: \nThe Quillen-Suslin theorem asserts that over the polynomial ring with coefficients in a field K[x_1\,…\,x_n]\, every projective module is free. Despite the algebraic nature of the objects involved in this theorem and its proof\, this is a problem motivated by geometry. \n\nOriginally\, this problem was proposed by the French mathematician Jean-Pierre Serre as one of his famous conjectures. In this talk\, we will discuss the original formulation of Serre’s conjecture (the Quillen-Suslin theorem)\, along with the necessary concepts to translate the geometric statement into the algebraic one. URL:https://colleges.claremont.edu/ccms/event/cristian-lopez-morales-unal/ LOCATION:Emmy Noether Room\, Estella 1021\, Pomona College\,\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20240212T161500 DTEND;TZID=America/Los_Angeles:20240212T171500 DTSTAMP:20240207T150322Z CREATED:20240207T150322Z LAST-MODIFIED:20240207T150322Z UID:10001908-1707754500-1707758100@colleges.claremont.edu SUMMARY:Dagan Karp (Harvey Mudd College) DESCRIPTION:Title: Tropical Linear Series\n\nAbstract: In this talk I’ll attempt to give a friendly and example-driven introduction to the theory of linear series on tropical curves. While in some respects mirroring the classical study of linear series\, in the tropical setting there are many surprises and even basic questions remain open. This work is joint with Chang Chih-Wei\, Hernan Iriarte\, David Jensen\, Sam Payne\, and Jidong Wang. URL:https://colleges.claremont.edu/ccms/event/dagan-karp-harvey-mudd-college/ LOCATION:Estella 1021 (Emmy Noether Room)\, Pomona College\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20240129T041500 DTEND;TZID=America/Los_Angeles:20240129T171500 DTSTAMP:20240125T032138Z CREATED:20240125T032110Z LAST-MODIFIED:20240125T032138Z UID:10002139-1706501700-1706548500@colleges.claremont.edu SUMMARY:Applied Math Seminar: Adolfo Rumbos (Pomona College) DESCRIPTION:Title: Existence and multiplicity of solutions for a cooperative elliptic system using Morse theory \nThis is joint work with Leandro Recova (Cal Poly Pomona) \nAbstract URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-adolfo-rumbos-pomona-collegeo/ LOCATION:Emmy Noether Room\, Estella 1021\, Pomona College\,\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20231113T041500 DTEND;TZID=America/Los_Angeles:20231113T171500 DTSTAMP:20231110T160645Z CREATED:20230912T154722Z LAST-MODIFIED:20231110T160645Z UID:10002118-1699848900-1699895700@colleges.claremont.edu SUMMARY:Applied Math Seminar: Adam Yassine (Pomona College) DESCRIPTION:Title: On the Composition of Classical Mechanical Systems \nAbstract: Compositionality is a basic principle for understanding the physical world. The underlying idea is to study a system by studying the ways in which the components of the system compose to form the system. Category theory is an area in mathematics that is particularly well-suited for studying questions about compositionality. This talk will outline a way to use category theory to study classical mechanical systems from a compositional perspective. URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-adam-yassine-pomona-college/ LOCATION:Estella 1021 (Emmy Noether Room)\, Pomona College\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20231106T161500 DTEND;TZID=America/Los_Angeles:20231106T171500 DTSTAMP:20230912T155411Z CREATED:20230912T155411Z LAST-MODIFIED:20230912T155411Z UID:10002119-1699287300-1699290900@colleges.claremont.edu SUMMARY:Applied Math Seminar: Claremont Colleges Course Previews for Spring 2024 DESCRIPTION:During this student-centered Applied Math Seminar\, there will be discussion and presentations about upcoming courses offered in applied mathematics\, to help students make their enrollment choices for Spring 2024 and beyond. URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-claremont-colleges-course-previews-for-spring-2024/ LOCATION:Estella 1021 (Emmy Noether Room)\, Pomona College\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20231030T161500 DTEND;TZID=America/Los_Angeles:20231030T173000 DTSTAMP:20231023T034142Z CREATED:20231019T153510Z LAST-MODIFIED:20231023T034142Z UID:10002138-1698682500-1698687000@colleges.claremont.edu SUMMARY:Applied Math Seminar: Jeremy Brandman (DCS corporation) DESCRIPTION:Title \nControl algorithms for unmanned underwater vehicles: new approaches based on Hamilton-Jacobi equations and reinforcement learning. \nAbstract \nUnmanned underwater vehicles (UUVs) are defined by their ability to operate without direct human intervention.  As a result\, UUVs are valuable for surveillance tasks\, especially in the presence of hazardous environmental conditions. Specific applications of UUVs include seafloor mapping\, mine detection\, and oil pipeline inspection. \nIn this talk\, we propose new algorithms for two aspects of UUV control: path planning and vehicle guidance.  Path planning identifies a vehicle trajectory\, based on anticipated environmental conditions\, that achieves desired mission objectives (e.g. obstacle avoidance\, minimization of energy consumption). Vehicle guidance responds to observed environmental conditions in order to maintain fidelity to the path selected by the path planner. \nThe first half of this talk considers a new approach to path planning based on solving Hamilton-Jacobi partial differential equations (PDE).  The starting point for this method is the observation that the vehicle’s minimum travel-time satisfies a time-independent Hamilton-Jacobi equation .  Numerical solutions to this PDE are efficiently computed using the fast sweeping method.  Our approach is validated through several examples for which optimal trajectories are derived using the calculus of variations. \nThe second half of this talk introduces a reinforcement learning framework for incorporating in situ ocean current measurements into the guidance system in an energetically optimal manner.  Scaling and symmetry considerations turn out to play an important role in the framework’s efficiency and robustness.  Numerical results demonstrate that the energetic cost of transits executed under the guidance of a trained agent approaches optimal performance. URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-jeremy-brandman/ LOCATION:Estella 1021 (Emmy Noether Room)\, Pomona College\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20231023T161500 DTEND;TZID=America/Los_Angeles:20231023T171500 DTSTAMP:20231023T033921Z CREATED:20230912T154613Z LAST-MODIFIED:20231023T033921Z UID:10002117-1698077700-1698081300@colleges.claremont.edu SUMMARY:Applied Math Seminar: Evan Rosenman (CMC) DESCRIPTION:Title:  Recalibration of Predicted Probabilities Using the “Logit Shift”: Why Does It Work\, and When Can It Be Expected to Work Well? \nAbstract: In the context of election analysis\, researchers frequently face the “recalibration problem.” That is: they must reconcile individual-level vote probabilities\, modeled prior to the election\, with vote totals observed in each precinct once the election has taken place. Making these adjustments such that the probabilities match known aggregates\, researchers can obtain better-calibrated estimates of key quantities such as vote preferences among subgroups of the electorate defined by race\, age\, and gender. \nWe provide theoretical grounding for one of the most commonly used recalibration strategies\, known colloquially as the “logit shift.” The logit shift is a heuristic adjustment\, in which a constant correction on the logit scale is found\, such that aggregated predictions match observed totals. \nWe show that the logit shift offers a fast and accurate approximation to a principled\, but computationally impractical adjustment strategy: computing the posterior probabilities\, conditional on the observed totals. After deriving analytical bounds on the quality of the approximation\, we illustrate its accuracy using Monte Carlo simulations. We also discuss scenarios in which the logit shift is less effective at recalibrating predictions: when the totals are available only for highly heterogeneous populations\, and when the original predictions correctly capture the mean of true individual probabilities\, but fail to capture the shape of their distribution. URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-evan-rosenman-cmc/ LOCATION:Estella 1021 (Emmy Noether Room)\, Pomona College\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20231009T161500 DTEND;TZID=America/Los_Angeles:20231009T171500 DTSTAMP:20231004T015412Z CREATED:20230912T154505Z LAST-MODIFIED:20231004T015412Z UID:10002116-1696868100-1696871700@colleges.claremont.edu SUMMARY:Applied Math Seminar: Dan Pirjol (Stevens Institute of Technology) DESCRIPTION:Title: The Hartman-Watson distribution: numerical evaluation and applications in mathematical finance \nAbstract: The Hartman-Watson distribution appears in several problems of applied probability and financial mathematics. Most notably\, it determines the joint distribution of the time-integral of a geometric Brownian motion and its terminal value. A classical result by Yor (1981) expresses it as a one-dimensional integral which is however difficult to evaluate numerically in the region of interest for financial applications. The talk gives an introduction to the HW distribution and presents an asymptotic expansion which can be used for an efficient numerical evaluation. Two applications from mathematical finance are discussed: Asian options pricing in the Black-Scholes model\, and option pricing in the log-normal SABR model. URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-dan-pirjol-stevens-institute-of-technology/ LOCATION:Estella 1021 (Emmy Noether Room)\, Pomona College\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20231002T161500 DTEND;TZID=America/Los_Angeles:20231002T171500 DTSTAMP:20230929T050112Z CREATED:20230912T154332Z LAST-MODIFIED:20230929T050112Z UID:10002115-1696263300-1696266900@colleges.claremont.edu SUMMARY:Applied Math Seminar: Tin Thien Phan (Los Alamos National Laboratory) DESCRIPTION:Title: Understanding SARS-CoV-2 viral rebounds with and without treatments. \nAbstract: In most instances\, the characteristics of SARS-CoV-2 mirror the patterns of an acute infection\, with viral load rapidly peaking around 5 days post-infection and subsequently clearing within 2 weeks. However\, some individuals show signs of viral recrudescence of up to 10000 viral RNA copies/mL shortly following viral remission. These instances of viral resurgence\, distinct from long COVID\, are generally resolved within four weeks post-infection and have been observed across varying treatment statuses\, vaccination statuses\, and viral strains. In this presentation\, I will review existing evidence of transient viral rebound and demonstrate that a class of dynamic models that incorporates virus-immune interaction accurately describes transient viral rebound dynamics under different treatment scenarios\, including those untreated. While these models all share a simple structure with a unique globally-asymptomatic-stable disease-free equilibrium\, the most exciting and relevant aspect hides within their transient phase and remains largely unexplored. URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-tin-thien-phan-los-alamos-national-laboratory/ LOCATION:Estella 1021 (Emmy Noether Room)\, Pomona College\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20230918T161500 DTEND;TZID=America/Los_Angeles:20230918T171500 DTSTAMP:20230912T162421Z CREATED:20230912T153609Z LAST-MODIFIED:20230912T162421Z UID:10002114-1695053700-1695057300@colleges.claremont.edu SUMMARY:Applied Math Seminar: Michael Murray (UCLA) DESCRIPTION:Title: Towards Understanding the Success of First Order Methods in Training Mildly Overparameterized Networks \nAbstract: For most problems of interest the loss landscape of a neural network is non-convex and contains a plethora of spurious critical points. Despite this first order methods such as SGD and Adam are in practice remarkably successful at finding optimal\, or at the least near optimal\, minimizers of the loss. In recent years the Neural Tangent Kernel has proven a powerful tool in explaining this phenomena and for providing guarantees for highly overparameterized networks. However\, for mildly overparameterized networks (where width scales linearithmically in the sample size) where richer feature learning can occur an explanation is lacking. In this talk I will present recent results on the loss landscape of two-layer mildly overparameterized ReLU networks. Our approach involves bounding the dimension of the sets of local and global minima using the rank of the Jacobian of the parameterization map. Using results on random binary matrices\, we show most activation patterns correspond to parameter regions with no bad differentiable local minima. Furthermore\, for one-dimensional input data\, we show most activation regions realizable by the network contain a high dimensional set of global minima and no bad local minima. We experimentally confirm these results by finding a phase transition from most regions having full rank to many regions having deficient rank depending on the amount of overparameterization. URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-michael-murray-ucla/ LOCATION:Estella 1021 (Emmy Noether Room)\, Pomona College\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20230417T161500 DTEND;TZID=America/Los_Angeles:20230417T171500 DTSTAMP:20230816T023354Z CREATED:20221207T193543Z LAST-MODIFIED:20230816T023354Z UID:10002040-1681748100-1681751700@colleges.claremont.edu SUMMARY:Applied Math Seminar: Emily de Jong (Caltech) DESCRIPTION:Title: Modeling size distributions and collisions in cloud microphysics \nAbstract:\nFeedbacks between a warming atmosphere\, emission of aerosols\, and clouds and precipitation are one of the most difficult aspects for climate models to accurately capture. While these models operate at resolutions of tens or hundreds of kilometers\, many of the physics that determine how and where clouds form or precipitate function at the micron droplet scale. This separation of scales means that most of these “microphysics” must be modeled with only a few approximate quantities and physical equations. These simplifications lead to large uncertainties about the future climate\, such as the sensitivity of global warming to human-emitted aerosols. \nThis talk presents two promising techniques for mathematically representing droplet size distributions and the microphysics that govern how droplets within the distribution evolve. The first method attempts to span a gap in complexity between a simple method of moments and expensive “bin” or spectral representations by collocating smooth basis functions over the droplet size domain. With intelligently selected basis functions\, this approach can represent the process of cloud droplets coalescing to form rain with bin-like accuracy\, but with a degree of complexity that is attainable for global simulations. Next\, we present a high-complexity high-fidelity Lagrangian approach known as the superdroplet method. This approach shows promise as a research tool to verify and train future microphysics models\, but it is currently incomplete in its purview of droplet physics. We describe a probabilistic approach to representing collisional breakup\, an often-overlooked process that can impact precipitation rates\, cloud lifetime\, and aerosol processing. URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-emily-de-jong-caltech/ LOCATION:Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Heather Zinn Brooks":MAILTO:hzinnbrooks@g.hmc.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20230410T161500 DTEND;TZID=America/Los_Angeles:20230410T171500 DTSTAMP:20230816T023147Z CREATED:20230131T010146Z LAST-MODIFIED:20230816T023147Z UID:10002042-1681143300-1681146900@colleges.claremont.edu SUMMARY:Applied Math Seminar: Johannes Brust (UCSD) DESCRIPTION:Title: PLSS: A Projected Linear Systems Solver (joint work with Michael Saunders) \nAbstract:\nIteratively solving linear systems has proven to be useful for many large applications. Projection methods use sketching matrices (possibly randomized) to generate a sequence of small projected subproblems\, but even the smaller systems can be costly. We develop a method in which one column is added to the sketching matrix each iteration. By choosing the sequence of all previous residuals for a sketch\, we derive an iterative process with orthogonal residuals that leads to a simple recursive update to approximate the solution. In exact arithmetic\, our method (PLSS) converges in at most \(n\) iterations\, where \(n\) is the column rank of matrix \(A\). In experiments on large sparse systems\, PLSS compares favorably with deterministic and state-of-the-art randomized methods. URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-johannes-brust-ucsd/ LOCATION:Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Heather Zinn Brooks":MAILTO:hzinnbrooks@g.hmc.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20230403T161500 DTEND;TZID=America/Los_Angeles:20230403T171500 DTSTAMP:20230320T152627Z CREATED:20221020T204917Z LAST-MODIFIED:20230320T152627Z UID:10002038-1680538500-1680542100@colleges.claremont.edu SUMMARY:Applied Math Seminar: Ivy Xiong (USC) DESCRIPTION:Title: A common pathway to cancer: oncogenic mutations abolish p53 oscillations. \nAbstract:\nThe tumor suppressor p53 oscillates in response to DNA double-strand breaks\, a behavior that has been suggested to be essential to its anti-cancer function. Nearly all human cancers have genetic alterations in the p53 pathway; a number of these alterations have been shown to be oncogenic by experiment. These alterations include somatic mutations and copy number variations as well as germline polymorphisms. Intriguingly\, they exhibit a mixed pattern of interactions in tumors\, such as co-occurrence\, mutual exclusivity\, and paradoxically\, mutual antagonism. Using a differential equation model of p53-Mdm2 dynamics\, I employ Hopf bifurcation analysis to show that these alterations have a common mode of action\, to abolish the oscillatory competence of p53\, thereby impairing its tumor suppressive function. In this analysis\, diverse genetic alterations\, widely associated with human cancers clinically\, have a unified mechanistic explanation of their role in oncogenesis. In this talk\, I will also discuss the role of physiological oscillations in health and disease broadly. \nReferences: \nXiong\, L.\, and Garfinkel\, A. (2022). A common pathway to cancer: Oncogenic mutations abolish p53 oscillations. Progress in Biophysics and Molecular Biology. DOI: 10.1016/j.pbiomolbio.2022.06.002 \nXiong\, L.\, and Garfinkel\, A. (2023). Are physiological oscillations “physiological”? arXiv. DOI: 10.48550/arXiv.2301.08996 URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-ivy-xiong-usc/ LOCATION:Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Heather Zinn Brooks":MAILTO:hzinnbrooks@g.hmc.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20230327T161500 DTEND;TZID=America/Los_Angeles:20230327T171500 DTSTAMP:20230816T040538Z CREATED:20221026T182923Z LAST-MODIFIED:20230816T040538Z UID:10002039-1679933700-1679937300@colleges.claremont.edu SUMMARY:Applied Math Seminar: Linh Huynh (University of Utah) DESCRIPTION:Title:Inferring birth and death rates from population size time series data \nAbstract:\nModels of population dynamics are usually formulated and analyzed with net growth rates. However\, separately identifying birth and death rates is significant in various biological applications such as disambiguating (1) exploitation vs. interference competition in ecology\, (2) bacteriostatic vs. bactericidal antibiotics in clinical treatments\, and (3) enhanced-fecundity vs. reduced-mortality mechanisms in drug resistance. In each of these three contexts\, the mechanisms are different\, but could be manifest in the same mean-field population size. \nIn this talk\, I will discuss a nonparametric method that utilizes stochastic fluctuations to extract birth and death rates from population size time series data. I will demonstrate the method on logistic growth to study density dependence\, but the method can be applied to general birth-death processes and does not require a priori assumptions on the rates. I will also discuss how to implement the theory on sample data and our estimation error analysis. This is based on published work joint with Peter Thomas (Case Western Reserve University) and Jacob Scott (Cleveland Clinic) and can be found here: Inferring density-dependent population dynamics mechanisms through rate disambiguation for logistic birth-death processes. URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-linh-huynh-university-of-utah/ LOCATION:Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Heather Zinn Brooks":MAILTO:hzinnbrooks@g.hmc.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20230306T161500 DTEND;TZID=America/Los_Angeles:20230306T171500 DTSTAMP:20230208T193952Z CREATED:20230118T184527Z LAST-MODIFIED:20230208T193952Z UID:10002041-1678119300-1678122900@colleges.claremont.edu SUMMARY:Applied Math Seminar: Nataliya Vasylyeva (IAMM NAS of Ukraine) DESCRIPTION:Title: Identification of the order of semilinear subdiffusion with memory \nAbstract: See attached abstract URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-nataliya-vasylyeva-iamm-nas-of-ukraine/ LOCATION:Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Heather Zinn Brooks":MAILTO:hzinnbrooks@g.hmc.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20230227T161500 DTEND;TZID=America/Los_Angeles:20230227T171500 DTSTAMP:20230816T040643Z CREATED:20221011T224115Z LAST-MODIFIED:20230816T040643Z UID:10002037-1677514500-1677518100@colleges.claremont.edu SUMMARY:Applied Math Seminar: Michael Perlmutter (UCLA) DESCRIPTION:Title:Geometric Scattering on Measure Spaces \nAbstract:\nGeometric Deep Learning is an emerging field of research that aims to extend the success of convolutional neural networks (CNNs) to data with non-Euclidean geometric structure. Despitebeing in its relative infancy\, this field has already found great success in many applications such as recommender systems\, computer graphics\, and traffic navigation. In order to improve our understanding of the networks used in this new field\, several works have proposed novelversions of the scattering transform\, a wavelet-based model of CNNs for graphs\, manifolds\,and more general measure spaces. In a similar spirit to the original Euclidean scattering transform\, these geometric scattering transforms provide a mathematically rigorous framework for understanding the stability and invariance of the networks used in geometric deep learning.Additionally\, they also have many interesting applications such as drug discovery\, solving combinatorial optimization problems\, and predicting patient outcomes from single-cell data. In particular\, motivated by these applications to single-cell data\, I will also discuss recent work proposing a diffusion maps style algorithm with quantitative convergence guarantees for implementing the manifold scattering transform from finitely many samples of an unknown manifold. URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-michael-perlmutter-ucla/ LOCATION:Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Heather Zinn Brooks":MAILTO:hzinnbrooks@g.hmc.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20221128T161500 DTEND;TZID=America/Los_Angeles:20221128T171500 DTSTAMP:20221122T174526Z CREATED:20220920T153253Z LAST-MODIFIED:20221122T174526Z UID:10002036-1669652100-1669655700@colleges.claremont.edu SUMMARY:Applied Math Seminar: Juergen Kritschgau (Carnegie Mellon) DESCRIPTION:Title: Using Mutual Information of Hypergraph Compressions for Clustering\n\nAbstract: Hypergraphs are often used to represent higher order observed relationships between subjects of study. In particular\, the vertices of a hypergraph could represent the basic elements of study\, and edges represent observed relationships between the vertices. Implicitly\, the assumption is that observed edges are more (or less) likely to appear between vertices that are “similar”. Therefore\, an important question in data science is whether the edges of a hypergraph can be used to recover ground truth vertex labels where two vertices receive the same label if they are similar. This is known as the clustering problem. In this talk\, we will discuss how mutual information of hypergraph compressions can be used to cluster hypergraphs\, and apply this clustering strategy to synthetic and real world data sets. URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-juergen-kritschgau-carnegie-mellon/ LOCATION:Shanahan 2407 at Harvey Mudd College\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Heather Zinn Brooks":MAILTO:hzinnbrooks@g.hmc.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20221121T161500 DTEND;TZID=America/Los_Angeles:20221121T171500 DTSTAMP:20230816T040911Z CREATED:20220905T171325Z LAST-MODIFIED:20230816T040911Z UID:10002029-1669047300-1669050900@colleges.claremont.edu SUMMARY:Applied Math Seminar: Junshan Lin (Auburn) DESCRIPTION:Title: Scattering Resonances Through Subwavelength Holes and Their Applications in Imaging and Sensing \nAbstract:\nThe so-called extraordinary optical transmission (EOT) through metallic nanoholes has triggered extensive research in modern plasmonics and their applications in bio-sensing\, imaging\, etc. This talk aims to provide quantitative mathematical theories to understand a variety of resonances that induce the EOT phenomenon and present mathematical studies for their applications in imaging and sensing. \nIn the first part of the talk\, based upon the layer potential technique\, asymptotic analysis and the homogenization theory\, I will present rigorous mathematical analysis to investigate the scattering resonances for several typical two-dimensional structures\, including Fabry-Perot resonance\, Fano resonance\, etc. In the second part of the talk\, mathematical studies for their applications in sensing and super-resolution imaging will be discussed. I will focus on the resonance frequency sensitivity analysis and how one can achieve super-resolution by using plasmonic nanohole structures. URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-junshan-lin-auburn/ LOCATION:Shanahan 2407 at Harvey Mudd College\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Heather Zinn Brooks":MAILTO:hzinnbrooks@g.hmc.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20221114T161500 DTEND;TZID=America/Los_Angeles:20221114T171500 DTSTAMP:20221101T152658Z CREATED:20220919T154642Z LAST-MODIFIED:20221101T152658Z UID:10002035-1668442500-1668446100@colleges.claremont.edu SUMMARY:Applied Math Seminar: Jahrul Alum (Memorial University of Newfoundland) DESCRIPTION:Title: Data-driven large eddy simulation of atmospheric turbulence \nAbstract: Over the last few years\, machine learning has been critical in science and engineering and emerged as a data-driven turbulence model. However\, machine learning depends on training data from previous experiments on turbulent flows. Typically\, training data capture only a fraction of the active scales of turbulence. Despite decades of research\, the best turbulence theory has yet to emerge\, which limits the training of supervised machine learning models. Reinforcement learning is one way to alleviate these challenges. A reinforcement learning model interacts directly with the dynamical system itself. In this talk\, I will use the Burgers equation to illustrate data-driven learning of dynamical systems. Then\, I use simulations of a NACA airfoil and a wind farm to outline the reinforcement learning framework. Finally\, the talk presents a proof of concept for optimizing large eddy simulation through reinforcement learning. URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-jahrul-alum-memorial-university-of-newfoundland/ LOCATION:Shanahan 2407 at Harvey Mudd College\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Heather Zinn Brooks":MAILTO:hzinnbrooks@g.hmc.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20221107T161500 DTEND;TZID=America/Los_Angeles:20221107T171500 DTSTAMP:20230816T041034Z CREATED:20220913T161358Z LAST-MODIFIED:20230816T041034Z UID:10002034-1667837700-1667841300@colleges.claremont.edu SUMMARY:Applied Math Seminar: Angel Chavez (Pomona) DESCRIPTION:Title: Randomized Sums of Graph Spectra \nAbstract:\nThe adjacency matrix of an Erdős-Rényi-Gilbert graph is a random symmetric matrix whose entries are Bernoulli random variables. These entries\, modulo the constraints imposed by symmetry\, are independent. We aim to understand the asymptotic behavior of randomized sums of the spectra and singular spectra of these matrices. In particular\, we establish several central-limit type theorems for these randomized sums of eigenvalues and singular values. URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-angel-chavez-pomona/ LOCATION:Shanahan 2407 at Harvey Mudd College\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Heather Zinn Brooks":MAILTO:hzinnbrooks@g.hmc.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20221031T161500 DTEND;TZID=America/Los_Angeles:20221031T171500 DTSTAMP:20221026T145641Z CREATED:20220909T224518Z LAST-MODIFIED:20221026T145641Z UID:10002031-1667232900-1667236500@colleges.claremont.edu SUMMARY:Applied Math Seminar: Anna Nelson (Duke) DESCRIPTION:Title: Mathematical modeling of polymerization processes in physiology\n\nAbstract: Polymerization\, or aggregation\, is essential for many physiological systems. For example\, the emergence of a fibrin polymer mesh during the formation of a blood clot is required for a stable clot and long-term\, sustained intracellular transport in neurons rely on persistent yet dynamic polymers that comprise the microtubule cytoskeleton. In the first part of the talk\, I will discuss a kinetic polymerization model that represents the formation of a fibrin polymer mesh with interactions with its precursor molecule\, fibrinogen. With this model\, we investigate how fibrin-fibrinogen interactions can impact gel structure (such as concentration of branch points) and gel time. In the second part\, I will introduce a stochastic mathematical model of individual microtubule growth and catastrophe in the dendrite of a neuron. Using parameters informed by experimental data\, we explore what mechanisms could control the equilibrium microtubule length and validate these mechanisms using fluorescence microscopy data.  \n\n  URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-anna-nelson-duke/ LOCATION:Shanahan 2407 at Harvey Mudd College\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Heather Zinn Brooks":MAILTO:hzinnbrooks@g.hmc.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20221024T161500 DTEND;TZID=America/Los_Angeles:20221024T171500 DTSTAMP:20220929T220052Z CREATED:20220929T220052Z LAST-MODIFIED:20220929T220052Z UID:10002028-1666628100-1666631700@colleges.claremont.edu SUMMARY:Applied Math Seminar: Susan Friedlander (USC) DESCRIPTION:Title: Kolmogorov\, Onsager and a Dyadic Model for Turbulence \nAbstract: We will briefly review Kolmogorov’s ( 41) theory of homogeneous turbulence\nand Onsager’s ( 49 ) conjecture that in 3-dimensional turbulent flows energy\ndissipation might exist even in the limit of vanishing viscosity. \nAlthough over the past 70 years there is a vast body of literature related to this subject\,\nat present there is no rigorous mathematical proof that the solutions to the Navier-Stokes\nequations yield Kolmogorov’s laws. For this reason various models have been introduced\nthat are more tractable but capture some of the essential features of the Navier-Stokes\nequations themselves. We will discuss one such dyadic model for turbulent energy cascades.\nWe will describe how results can be used to prove this dyadic model is consistent with\nKolmogorov’s theory and Onsager’s conjecture. \nAspects of the work are joint with Alexey Cheskidov\, Nathan Glatt-Holtz\, Roman Shvydkoy\, and Vlad Vicol. URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-susan-friedlander-usc/ LOCATION:Shanahan 2407 at Harvey Mudd College\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Heather Zinn Brooks":MAILTO:hzinnbrooks@g.hmc.edu END:VEVENT END:VCALENDAR