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DTSTART;TZID=America/Chicago:20251010T140000
DTEND;TZID=America/Chicago:20251010T153000
DTSTAMP:20260417T203627
CREATED:20251006T192316Z
LAST-MODIFIED:20251006T192316Z
UID:10016250-1760104800-1760110200@uwm.edu
SUMMARY:Colloquium: Dr. Dexuan Xie
DESCRIPTION:Recent Advances in Nonlocal Dielectric Continuum Models for Predicting Protein and Ion Channel Electrostatics\nDr. Dexuan Xie\nProfessor\nUniversity of Wisconsin-Milwaukee \nThe calculation of electrostatics for proteins and ion channels is a fundamental challenge in structural biology\, computational biochemistry\, biophysics\, and mathematical biology. Traditional dielectric continuum models\, such as the Poisson–Boltzmann equation and its variants\, are widely used for this calculation. However\, their prediction accuracy often deteriorates near highly charged biomolecular surfaces because they neglect the polarization correlations of water molecules. To address these limitations\, a nonlocal dielectric continuum modeling approach was introduced roughly four decades ago. Over the past decade\, this approach has seen substantial theoretical and computational advances\, largely driven by our group’s work under support from the National Science Foundation. \nIn this seminar\, I will present our nonlocal dielectric theory and report our recent progress in developing nonlocal dielectric continuum models and finite element solvers for proteins and ion channels. I will also compare the predictions of our novel nonlocal models with those of the traditional local models and present numerical results demonstrating the efficiency of our solvers and the high performance of our software package. This work is a collaboration with my students\, Liam Jemison and Matthew Stahl. It has been partially supported by the National Science Foundation under award DMS-2153376 and by the Simons Foundation under research award 711776.
URL:/math/event/colloquium-dr-dexuan-xie/
LOCATION:EMS Building\, E495\, 3200 N Cramer St\, Milwaukee\, WI\, United States
CATEGORIES:Colloquia
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DTSTART;TZID=America/Chicago:20251024T140000
DTEND;TZID=America/Chicago:20251024T150000
DTSTAMP:20260417T203627
CREATED:20251013T164539Z
LAST-MODIFIED:20251013T164539Z
UID:10016251-1761314400-1761318000@uwm.edu
SUMMARY:Colloquium: Prof. Greg Ongie
DESCRIPTION:A Function Space View of Neural Networks\nProf. Greg Ongie\nAssistant Professor\nMarquette University \nMany mathematical analyses of deep learning focus on how neural network (NN) parameters evolve during training. A complementary perspective is to view NN training as fitting a function belonging to a function space implicitly defined by the architecture and training procedure. In particular\, when parameter norms are explicitly or implicitly constrained\, NNs exhibit a bias toward functions with low “representation cost\,” defined as the minimal parameter norm required to realize the function with a given NN architecture. This talk surveys recent results that characterize representation cost of shallow NN architectures in terms of Banach space norms\, and through non-linear notions of function rank for deeper NN architectures. Finally\, we discuss how bias towards low representation cost functions helps to explain generalization in various applications.
URL:/math/event/colloquium-prof-greg-ongie/
LOCATION:EMS Building\, E495\, 3200 N Cramer St\, Milwaukee\, WI\, United States
CATEGORIES:Colloquia
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DTSTART;TZID=America/Chicago:20251031T140000
DTEND;TZID=America/Chicago:20251031T150000
DTSTAMP:20260417T203627
CREATED:20251013T164833Z
LAST-MODIFIED:20251013T164833Z
UID:10016252-1761919200-1761922800@uwm.edu
SUMMARY:Colloquium: Dr. Daniel Noelck
DESCRIPTION:Exponential Stability Of The Discrete Stochastic Filter Via Non-degeneracy Andanalytic Stability Of The Signal\nDr. Daniel Noelck\nSenior Research Associate\nIllinois Institute of Technology \nThe stability of discrete time filters has been an active field of research\, particularly when applied to numerical filter approximation schemes. Most results in the field are obtained on a compact signal space\, but there is no reason to believe the results should not carry over to non-compact spaces. In this talk\, we will introduce the discrete time filtering problem\, discuss some well known results on compact spaces\, and the difficulties of expanding those results to non-compact spaces\, and then introduce recent results for stability on those non-compact spaces. Finally\, we will discuss the future work available in the continuous time setting.
URL:/math/event/colloquium-dr-daniel-noelck/
LOCATION:EMS Building\, E495\, 3200 N Cramer St\, Milwaukee\, WI\, United States
CATEGORIES:Colloquia
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