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DynamIC Seminars (Complete List)

Name Title Date Time Room
Erik Bollt (Clarkson University)Geometry and Good Dictionaries for Koopman Analysis of Dynamical Systems Abstract: In the spirit of optimal approximation and reduced order modelling the goal of DMD methods and variants is to describe the dynamical evolution as a linear evolution in an appropriately transformed lower rank space, as best as possible. That Koopman eigenfunctions follow a linear PDE that is solvable by the method of characteristics yields several interesting relationships between geometric and algebraic properties. We focus on contrasting cardinality, algebraic multiplicity and other geometric aspects with the introduction of an equivalence class, “primary eigenfunctions,” for those eigenfunctions with identical sets of level sets. We present a construction that leads to functions on the data surface that yield optimal Koopman eigenfunction DMD, (oKEEDMD). We will also describe that disparate systems can be “matched” transformed by a diffeomorphism constructed via eigenfunctions from each system, a reinterpretation of integrability, computationally stated by our “matching extended dynamic mode decomposition (EDMD)” (EDMD-M). Tuesday, 9 March 2021 1:00pm Online
Yoshito Hirata (University of Tsukuba)Unified time series analysis for nonlinear deterministic/stochastic systems Abstract: Distinguishing deterministic systems from stochastic systems has been discussed for a long time. But, such analysis had been qualitative or contrasting nonlinear deterministic systems with linear stochastic systems. Thus, we could not identify nonlinear stochastic systems with some hypothesis tests. Here, we propose to use permutations or recurrence plots for distinguishing stochastic systems from deterministic systems with a hypothesis test. Therefore, permutations and recurrence plots can be used also for analyzing a time series generated from nonlinear stochastic systems. Tuesday, 16 March 2021 1:00pm Online
Christoph Kawan (University of Munich)Control of chaos with minimal information transferAbstract: Networked control systems violate standard assumptions of classical control theory. One of the many challenges in their analysis and design concerns information constraints present in the communication between sensors, controllers and actuators. A fundamental question in this field is thus concerned with the smallest rate of information flowing from the sensors to the controller, above which a given control task can be solved. In this talk, we address this question in the context of set-stabilization for nonlinear systems. To obtain exact results, we impose the assumption of uniform hyperbolicity on the sets under consideration, which provides us with powerful tools such as shadowing and hyperbolic volume estimates. As we can then see, the minimal information rate is closely related to quantities extensively studied in smooth dynamical systems: escape rates, topological pressure, measure-theoretic entropy and Lyapunov exponents. Tuesday, 23 March 2021 1:00pm Online
Woojin Kim (Duke University)The Persistent Topology of Dynamic DataAbstract: This talk introduces a method for characterizing the dynamics of time-evolving data within the framework of topological data analysis (TDA), specifically through the lens of persistent homology. Popular instances of time-evolving data include flocking or swarming behaviors in animals, and social networks in the human sphere. A natural mathematical model for such collective behaviors is that of a dynamic metric space. In this talk I will describe how to extend the well-known Vietoris-Rips filtration for metric spaces to the setting of dynamic metric spaces. Also, we extend a celebrated stability theorem on persistent homology for metric spaces to multiparameter persistent homology for dynamic metric spaces. In order to address this stability property, we extend the notion of Gromov-Hausdorff distance between metric spaces to dynamic metric spaces. This talk will not require any prior knowledge of TDA. This talk is based on joint work with Facundo Memoli and Nate Clause. Tuesday, 23 March 2021 2:15 pm Online

DynamIC Workshops and Mini-Courses (Complete List)

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Short-term DynamIC Visitors (Complete List)

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