Description |
1 online resource (402 pages) |
Series |
Studies in Systems, Decision and Control ; v. 304 |
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Studies in systems, decision and control ; v. 304.
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Contents |
Intro -- Preface -- Acknowledgements -- Contents -- List of Contributors -- I Dynamics -- A Continuation Approach to Computing Phase Resetting Curves -- 1 Introduction -- 2 Basic Setting and Definitions -- 3 Algorithm for Computing a Phase Resetting Curve -- 3.1 Continuation Set-Up for Rotated Representation of -- 3.2 Continuation Set-Up for the Phase Reset -- 4 Illustration of the Method with a Model Example -- 4.1 Computing the PTC -- 4.2 Loss of Invertibility -- 5 Phase Resetting in the FitzHugh-Nagumo Model -- 6 Phase Resetting in a Seven-Dimensional Sinoatrial Node Model -- 7 Conclusions |
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10 Evolving Towards Homeostasis -- 11 Input-Output Maps with Two Inputs -- 11.1 Catastrophe Theory Classification -- 11.2 Normal Forms and Plateaus -- 11.3 The Hyperbolic Umbilic -- 12 Gene Regulatory Networks and Housekeeping Genes -- 12.1 Gene Regulatory Networks and Homeostasis -- 12.2 Basic Structural Elements of GRNs -- 12.3 The Gene Regulatory Network for PGA2 -- References -- The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems -- 1 Introduction -- 2 Infinite Dimensional Embedding Techniques -- 3 The Core Dynamical System -- 4 Computation of Embedded Invariant Sets |
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4.1 A Subdivision Scheme for the Approximation of Embedded Attractors -- 4.2 A Continuation Technique for the Approximation of Embedded Unstable Manifolds -- 5 Numerical Realization of the CDS -- 5.1 Delay Differential Equations -- 5.2 Partial Differential Equations -- 6 Numerical Results -- 6.1 The Mackey-Glass Equation -- 6.2 The Kuramoto-Sivashinsky Equation -- 7 Conclusion -- References -- Set-Oriented and Finite-Element Study of Coherent Behavior in Rayleigh-Bénard Convection -- 1 Introduction -- 2 Nonautonomous Dynamics, Transfer Operators and Transport -- 3 Set-Oriented Numerical Framework |
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3.1 Approximation of Transfer Operator -- 3.2 Extracting Finite-Time Coherent Sets -- 3.3 Set-Oriented Computation of FTE -- 4 Finite-Element Framework -- 4.1 Disentangling Multiple Features with SEBA -- 5 Application to Rayleigh-Bénard Convection -- 5.1 2D System -- 5.2 3D System -- 6 Conclusion and Outlook -- References -- Singular Value Decomposition of Operators on Reproducing Kernel Hilbert Spaces -- 1 Introduction -- 2 Preliminaries -- 3 Decompositions of RKHS Operators -- 3.1 RKHS -- 3.2 RKHS Operators -- 3.3 Basis Orthonormalization and Kernel QR Decomposition |
Summary |
This book presents a collection of papers on recent advances in problems concerning dynamics, optimal control and optimization. In many chapters, computational techniques play a central role. Set-oriented techniques feature prominently throughout the book, yielding state-of-the-art algorithms for computing general invariant sets, constructing globally optimal controllers and solving multi-objective optimization problems |
Bibliography |
References-Input-Output Networks, Singularity Theory, and Homeostasis-1 Introduction-2 Thermoregulation: A Motivation for Homeostasis-3 Biochemical Input-Output Networks-3.1 Feedforward Excitation-3.2 Product Inhibition-3.3 Substrate Inhibition-3.4 Negative Feedback Loop-4 Infinitesimal Homeostasis-5 Input-Output Networks-6 Core Networks-7 Types of Infinitesimal Homeostasis-8 Low Degree Homeostasis Types-9 Singularity Theory of Input-Output Functions-9.1 Chair Points for Blocks of Degree 1 and 2-9.2 Elementary Catastrophe Theory and Homeostasis |
Notes |
3.4 Eigendecomposition via Auxiliary Problem |
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Includes author index |
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Print version record |
Subject |
Dynamics.
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Mathematical optimization.
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Automatic control engineering.
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Computer science.
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Mathematical theory of computation.
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Applied mathematics.
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Maths for engineers.
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Technology & Engineering -- Automation.
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Computers -- Computer Science.
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Science -- Quantum Theory.
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Mathematics -- Applied.
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Technology & Engineering -- Engineering (General)
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Dynamics
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Mathematical optimization
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Genre/Form |
Electronic books
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Festschriften
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Festschriften.
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Form |
Electronic book
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Author |
Junge, Oliver
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Schütze, Oliver (Computer scientist)
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Froyland, Gary.
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Ober-Blöbaum, Sina
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Padberg-Gehle, Kathrin
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ISBN |
9783030512644 |
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3030512649 |
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