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DTSTART;TZID=America/Los_Angeles:20210201T150000
DTEND;TZID=America/Los_Angeles:20210201T160000
DTSTAMP:20260406T001815
CREATED:20210112T175201Z
LAST-MODIFIED:20210126T180607Z
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SUMMARY:Applied math. talk: Searching for singularities in Navier-Stokes flows using variational optimization methods by Di Kang\, McMaster University\, Canada
DESCRIPTION:Abstract: In the presentation we will discuss our research program\nconcerning the search for the most singular behaviors possible in viscous\nincompressible flows. These events are characterized by extremal growth of \nvarious quantities\, such as the enstrophy\, which control the regularity of the solution. \nThey are therefore intimately related to the question of possible singularity formation \nin the 3D Navier-Stokes system\, known as the\nhydrodynamic blow-up problem. We demonstrate how new insights\nconcerning such questions can be obtained by formulating them as\nvariational PDE optimization problems which can be solved\ncomputationally using suitable discrete gradient flows. More\nspecifically\, such an optimization formulation allows one to identify\n"extreme" initial data which\, subject to certain constraints\, leads to\nthe most singular flow evolution.  In offering a systematic approach\nto finding flow solutions which may saturate known estimates\, the\nproposed paradigm provides a bridge between mathematical analysis and\nscientific computation. In particular\, it makes it possible to\ndetermine whether or not certain mathematical estimates are "sharp"\,\nin the sense that they can be realized by actual vector fields\, or if\nthese estimates may still be improved. In the presentation we will\nreview a number of results concerning 1D and 2D flows characterized by\nthe maximum possible growth of different Sobolev norms of the\nsolutions.  As regards 3D flows\, we focus on the enstrophy which is a\nwell-known indicator of the regularity of the solution. We find a family of initial \ndata with fixed enstrophy which leads to the largest possible growth of this quantity \nat some prescribed final time. Since even with such worst-case initial data the\nenstrophy remains finite\, this indicates that the 3D Navier-Stokes\nsystem reveals no tendency for singularity formation in finite time.\n\n[joint work with Dongfang Yun and Bartosz Protas]
URL:https://colleges.claremont.edu/ccms/event/applied-math-talk-searching-for-singularities-in-navier-stokes-flows-using-variational-optimization-methods-by-di-kang-mcmaster-university-canada/
LOCATION:Zoom meeting\, United States
CATEGORIES:Applied Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20210203T161500
DTEND;TZID=America/Los_Angeles:20210203T173000
DTSTAMP:20260406T001815
CREATED:20210116T020731Z
LAST-MODIFIED:20210118T155305Z
UID:2138-1612368900-1612373400@colleges.claremont.edu
SUMMARY:Prof. Heather Zinn-Brooks
DESCRIPTION:Title: Networks in social systems \nAbstract: The spread of memes and misinformation on social media\, political redistricting\, interactions in animal populations\, and the dynamics of voters during elections are among the many things that people study in the field of complex systems. All of these phenomena involve the interactions of individual parts\, which come together to produce rich\, complex collective dynamics. Obtaining a better understanding of how these interacting parts–whether they are Twitter accounts\, penguins\, or voters–respond to each other and to their environment also has potentially important implications for society. In this talk\, I will discuss how complex social systems can be modeled and analyzed from a network-theory perspective. We will investigate various network properties and highlight common themes that appear across different social networks. To gain insight into why certain properties emerge\, I will introduce several generative mathematical models of networks. Finally\, we will discuss some generalizations of networks and exciting areas of current research. \nProfessor Zinn-Brooks teaches at Harvey Mudd College.
URL:https://colleges.claremont.edu/ccms/event/prof-heather-zinn-brooks/
LOCATION:Zoom
CATEGORIES:Colloquium
ORGANIZER;CN="Andrew Bernoff":MAILTO:ajb@hmc.edu
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20210208T150000
DTEND;TZID=America/Los_Angeles:20210208T160000
DTSTAMP:20260406T001815
CREATED:20210126T021149Z
LAST-MODIFIED:20210201T225414Z
UID:2147-1612796400-1612800000@colleges.claremont.edu
SUMMARY:Applied Math. Talk: Complex Fluids in the Immersed Boundary Method: From Viscoelasticity to Blood Clots by Aaron Barrett\, Department of Mathematics\, University of Utah
DESCRIPTION:The immersed boundary method was first developed in the 1970s to model the motion of heart valves and has since been utilized to study many different biological systems. While the IB method has seen countless modifications and advancements from the perspective of fluid-structure interaction\, the use of a Newtonian fluid model remains a fundamental component of many implementations. However\, many biological fluids exhibit non-Newtonian responses to stresses\, and as such\, a Newtonian fluid model falls short to fully describe the system. In this talk\, we will discuss models of two different systems: polymeric fluids and blood clotting\, and we will address the numerical challenges associated with each system.
URL:https://colleges.claremont.edu/ccms/event/applied-math-talk-by-aaron-barrett-department-of-mathematics-university-of-utah/
LOCATION:CA
CATEGORIES:Applied Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20210210T161500
DTEND;TZID=America/Los_Angeles:20210210T171500
DTSTAMP:20260406T001815
CREATED:20210116T020409Z
LAST-MODIFIED:20210116T020409Z
UID:2136-1612973700-1612977300@colleges.claremont.edu
SUMMARY:Prof. Henry Schellhorn
DESCRIPTION:Title: No-arbitrage pricing in a market for position on a multilane freeway\, with an application to lane changing \nAbstract: We introduce a trading mechanism allowing cars to change position in a multilane congested freeway by doing peer-to-peer transactions. For the car initiating the operation\, or incoming car\, the goal can be to increase speed\, to have less speed variability\, to join a platoon\, or to join an exit lane that is slower but full. We focus in this paper on the maneuver where the incoming car changes lanes by asking an adjacent car on a busy target lane (to the left or right) to slow down\, but we also consider the case where the incoming car asks the car in front of it to change lanes\, so that the incoming car takes its position but stays on the same lane. In both cases\, the incoming car pays a transaction fee.\nWe solve the microscopic problem of determining these transaction fees by (i) embedding the problem in a macroscopic model and (ii) determining lane prices by the no arbitrage condition. This no-arbitrage condition states that no future trajectory will always be better than all others in terms of both speed and money exchanged to change lanes.  The terms “always better” has to be understood in a probabilistic sense: we analyze a stochastic model\, in order to include uncertainty in both the speed model and the driver decision. We highlight the advantages of no-arbitrage theory over a traditional expected utility maximization approach. First\, no-arbitrage pricing does not require any individual data\, whether on the driver’s risk-aversion\, preference of speed over money or increased safety\, or final destination. Second\, the macroscopic model that we use considers endogeneously the global impact of any individual priced transaction\, as opposed to local models that require extraneous assumptions on the road conditions after the transaction.\nWe implemented a simple case of our lane change model. After simulating it extensively\, we implemented it in real-time\, with 2 cars trading position on a freeway using macroscopic speed information to determine the transaction fee. \nProf. Schellhorn is Professor of Mathematics and Academic Director of the Financial Engineering Program at Claremont Graduate University.
URL:https://colleges.claremont.edu/ccms/event/prof-henry-schellhorn/
LOCATION:Zoom
CATEGORIES:Colloquium
ORGANIZER;CN="Andrew Bernoff":MAILTO:ajb@hmc.edu
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20210215T150000
DTEND;TZID=America/Los_Angeles:20210215T160000
DTSTAMP:20260406T001815
CREATED:20210114T013414Z
LAST-MODIFIED:20210127T210557Z
UID:2120-1613401200-1613404800@colleges.claremont.edu
SUMMARY:Applied Math. Talk:  Modeling and Simulation of Ultrasound-mediated Drug Delivery to the Brain  by Peter Hinow\, University of Wisconsin\, Milwaukee
DESCRIPTION:We use a mathematical model to describe the delivery of a drug to a specific region of the brain. The drug is carried by liposomes that can release their cargo by application of focused ultrasound. Thereupon\, the drug is absorbed through the endothelial cells that line the brain capillaries and form the physiologically important blood-brain barrier. We present a compartmental model of a capillary that is able to capture the complex binding and transport processes the drug undergoes in the blood plasma and at the blood-brain barrier. We apply this model to the delivery of L-dopa\, (used to treat Parkinson’s disease) and doxorubicin (an anticancer agent). The goal is to optimize the delivery of drug while at the same time minimizing possible side effects of the ultrasound. In a second project\, we present a mathematical model for drug delivery through capillary networks with increasingly complex topologies with the goal to understand the scaling behavior of model predictions on a coarse-to-fine sequence of grids.
URL:https://colleges.claremont.edu/ccms/event/applied-math-talk-by-peter-hinow-university-of-wisconsin-milwaukee/
LOCATION:Zoom meeting\, United States
CATEGORIES:Applied Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20210217T161500
DTEND;TZID=America/Los_Angeles:20210217T171500
DTSTAMP:20260406T001815
CREATED:20210116T021143Z
LAST-MODIFIED:20210204T000155Z
UID:2140-1613578500-1613582100@colleges.claremont.edu
SUMMARY:Dr. Homan Igehy
DESCRIPTION:Title: Quantitative Investment and Modern Portfolio Theory \nAbstract:\nInvestment strategies come in many flavors. Quantitative strategies incorporate or fully direct investment based on mathematical models. One of the cornerstones of investment is portfolio management\, and modern portfolio theory can serve as a basis for quantitative portfolio management. In this talk\, we will discuss quantitative investing and how modern portfolio theory can be incorporated into it. We’ll take an intuitive approach toward understanding modern portfolio theory and discuss how it can (at times\, spectacularly) go wrong. \nHoman Igehy is a managing director of D. E. Shaw & Co.\, L.P. and a member of the D. E. Shaw group’s Systematic Futures trading unit.  In that capacity\, Dr. Igehy contributes to the research and development of forecast models and the technical infrastructure supporting the unit’s research efforts.  He joined the D. E. Shaw group in 2003.  Dr. Igehy received a B.S. and Ph.D.\, each in computer science\, from Stanford University.
URL:https://colleges.claremont.edu/ccms/event/dr-homan-igehy/
LOCATION:Zoom
CATEGORIES:Colloquium
ORGANIZER;CN="Andrew Bernoff":MAILTO:ajb@hmc.edu
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20210222T150000
DTEND;TZID=America/Los_Angeles:20210222T160000
DTSTAMP:20260406T001815
CREATED:20210112T175752Z
LAST-MODIFIED:20210213T053831Z
UID:2102-1614006000-1614009600@colleges.claremont.edu
SUMMARY:Applied math. talk: Heatmap centrality: a new measure to identify super-spreader nodes in scale-free networks by Christina Duron\, the University of Arizona
DESCRIPTION:Abstract: The identification of potential super-spreader nodes within a network is a critical part of the study and analysis of real-world networks. Motivated by a new interpretation of the “shortest path” between two nodes\, this talk will explore the properties of the recently proposed measure\, the heatmap centrality\, by comparing the farness of a node with the average sum of farness of its adjacent nodes in order to identify influential nodes within the network. As many real-world networks are often claimed to be scale-free\, numerical experiments based upon both simulated and real-world undirected and unweighted scale-free networks are used to illustrate the effectiveness of the new “shortest path” based measure with regards to its CPU run time and ranking of influential nodes.
URL:https://colleges.claremont.edu/ccms/event/applied-math-talk-heatmap-centrality-a-new-measure-to-identify-super-spreader-nodes-in-scale-free-networks-by-christina-duron-the-university-of-arizona/
LOCATION:Zoom meeting\, United States
CATEGORIES:Applied Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20210224T161500
DTEND;TZID=America/Los_Angeles:20210224T173000
DTSTAMP:20260406T001815
CREATED:20210116T021257Z
LAST-MODIFIED:20210209T220719Z
UID:2142-1614183300-1614187800@colleges.claremont.edu
SUMMARY:Prof. Lori Ziegelmeier
DESCRIPTION:Title:  Using Topology to Measure Shape in Data \nAbstract: Data of various kinds is being collected at an enormous rate\, and in many different forms. Often\, the data are equipped with a notion of distance that reflects similarity in some sense. Using this similarity measure\, certain topological features–e.g. the number of connected components\, loops\, and trapped volumes–can be ascertained and can provide insight into the structure of these complex data sets. In this talk\, I will introduce topology and a fundamental tool of topological data analysis\, persistent homology. Then\, we will see how these tools can be used for clustering\, with machine learning\, and to explain features in data. In particular\, we will discuss (1) using persistence to explore the relationship between country development and geography\, (2) vectorizing persistence information via a persistence image to analyze the discrete dynamical system of the linked twist map\, and (3) explore notions of minimal generators to extract geometric meaning from homological features. \nDr. Ziegelmeier is an Associate Professor at Macalester College.
URL:https://colleges.claremont.edu/ccms/event/prof-lori-ziegelmeier/
LOCATION:Zoom
CATEGORIES:Colloquium
ORGANIZER;CN="Andrew Bernoff":MAILTO:ajb@hmc.edu
END:VEVENT
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