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检索条件"任意字段=Abel Symposium on Computation and Combinatorics in Dynamics, Stochastics and Control"

共 6 条记录，以下是1-10 订阅

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Universality in Numerical computation with Random Data: Case Studies, Analytical Results and Some Speculations

Universality in Numerical Computation with Random Data: Case...

引用

abel symposium on computation and combinatorics in dynamics, stochastics and control

作者： Deift, Percy Trogdon, Thomas NYU Courant Inst New York NY 10012 USA Univ Calif Irvine Irvine CA USA

We discuss various universality aspects of numerical computations using standard algorithms. These aspects include empirical observations and rigorous results. We also make various speculations about computation in a ... 详细信息

ISBN: (纸本)9783030015930;9783030015923

关键词： Artificial intelligence

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The Clebsch Representation in Optimal control and Low Rank Integrable Systems

The Clebsch Representation in Optimal Control and Low Rank I...

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abel symposium on computation and combinatorics in dynamics, stochastics and control

作者： Bloch, Anthony M. Gay-Balmaz, Francois Ratiu, Tudor S. Univ Michigan Dept Math Ann Arbor MI 48109 USA Ecole Normale Super CNRS LMD IPSL Paris France Shanghai Jiao Tong Univ Sch Math Shanghai Peoples R China Univ Geneva Sect Math Geneva Switzerland Ecole Polytech Fed Lausanne Lausanne Switzerland

ISBN: (纸本)9783030015930;9783030015923

Certain kinematic optimal control problems (the Clebsch problems) and their connection to classical integrable systems are considered. In particular, the rigid body problem and its rank 2k counterparts, the geodesic flows on Stiefel manifolds and their connection with the work of Moser, flows on symmetric matrices, and the Toda flows are studied.

关键词： Optimal control systems

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Infinite Dimensional Rough dynamics

Infinite Dimensional Rough Dynamics

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abel symposium on computation and combinatorics in dynamics, stochastics and control

作者： Gubinelli, Massimiliano IAM Bonn Germany Hausdorff Ctr Math Bonn Germany

ISBN: (纸本)9783030015930;9783030015923

We review recent results about the analysis of controlled or stochastic differential systems via local expansions in the time variable. This point of view has its origin in Lyons' theory of rough paths and has been vastly generalised in Hairer's theory of regularity structures. Here our concern is to understand this local expansions when they feature genuinely infinite dimensional objects like distributions in the space variable. Our analysis starts reviewing the simple situation of linear controlled rough equations in finite dimensions, then we introduce unbounded operators in such linear equations by looking at linear rough transport equations. Loss of derivatives in the estimates requires the introduction of new ideas, specific to this infinite dimensional setting. Subsequently we discuss how the analysis can be extended to systems which are not intrinsically rough but for which local expansion allows to highlight other phenomena: in our case, regularisation by noise in linear transport. Finally we comment about other application of these ideas to fully-nonlinear conservations laws and other PDEs.

关键词： Stochastic systems

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The Faa di Bruno Hopf Algebra for Multivariable Feedback Recursions in the Center Problem for Higher Order abel Equations

The Faa di Bruno Hopf Algebra for Multivariable Feedback Rec...

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abel symposium on computation and combinatorics in dynamics, stochastics and control

作者： Ebrahimi-Fard, Kurusch Gray, W. Steven Norwegian Univ Sci & Technol Trondheim Norway Old Dominion Univ Norfolk VA 23529 USA

ISBN: (纸本)9783030015930;9783030015923

Poincare's center problem asks for conditions under which a planar polynomial system of ordinary differential equations has a center. It is well understood that the abel equation naturally describes the problem in a convenient coordinate system. In 1990, Devlin described an algebraic approach for constructing sufficient conditions for a center using a linear recursion for the generating series of the solution to the abel equation. Subsequent work by the authors linked this recursion to feedback structures in control theory and combinatorial Hopf algebras, but only for the lowest degree case. The present work introduces what turns out to be the nontrivial multivariable generalization of this connection between the center problem, feedback control, and combinatorial Hopf algebras. Once the picture is completed, it is possible to provide generalizations of some known identities involving the abel generating series. A linear recursion for the antipode of this new Hopf algebra is also developed using coderivations. Finally, the results are used to further explore what is called the composition condition for the center problem.

关键词： Algebra

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The abel symposium, 2016

The Abel Symposium, 2016

引用

The abel symposium, 2016

ISBN: (纸本)9783030015923

The proceedings contain 25 papers. The special focus in this conference is on abel symposium. The topics include: The Faà di Bruno Hopf Algebra for Multivariable Feedback Recursions in the Center Problem for Higher Order abel Equations;continuous-time autoregressive moving-average processes in hilbert space;pre- and post-lie algebras: The algebro-geometric view;Extension of the product of a post-lie algebra and application to the SISO feedback transformation group;infinite dimensional rough dynamics;Heavy tailed random matrices: How they differ from the GOE, and open problems;An analyst’s take on the BPHZ theorem;parabolic anderson model with rough dependence in space;perturbation of conservation laws and averaging on manifolds;free probability, random matrices, and representations of non-commutative rational functions;stochastic functional differential equations and sensitivity to their initial path;a review on comodule-bialgebras;renormalization: A quasi-shuffle approach;hopf algebra techniques to handle dynamical systems and numerical integrators;quantitative limit theorems for local functionals of arithmetic random waves;combinatorics on words and the theory of markoff;an algebraic approach to integration of geometric rough paths;grassmannian flows and applications to nonlinear partial differential equations;gog and magog triangles;the clebsch representation in optimal control and low rank integrable systems;the geometry of characters of hopf algebras;Shape analysis on homogeneous spaces: A generalised SRVT framework;universality in numerical computation with random data: Case Studies, Analytical Results and Some Speculations;BSDEs with default jump.

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computation and combinatorics in dynamics, stochastics and control 1

引用

丛书名： abel Symposia

1000年

作者： Elena Celledoni Kurusch Ebrahimi-Fard Giulia Di Nunno Hans Zanna Munthe-Kaas

The abel Symposia volume at hand contains a collection of high-quality articles written by the world’s leading experts, and addressing all mathematicians interested in advances in deterministic and stochastic dynamic... 详细信息

ISBN: (数字)9783030015930

ISBN: (纸本)9783030015923

关键词： computational Mathematics and Numerical Analysis Ordinary Differential Equations Approximations and Expansions Systems Theory, control Group Theory and Generalizations

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