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The Resource Discrete and continuous models in the theory of networks, Fatihcan M. Atay, Pavel B. Kurasov, Delio Mugnolo, editors

Discrete and continuous models in the theory of networks, Fatihcan M. Atay, Pavel B. Kurasov, Delio Mugnolo, editors

Contributor
Summary
This book contains contributions from the participants of the research group hosted by the ZiF - Center for Interdisciplinary Research at the University of Bielefeld during the period 2013-2017 as well as from the conclusive conference organized at Bielefeld in December 2017. The contributions consist of original research papers: they mirror the scientific developments fostered by this research program or the state-of-the-art results presented during the conclusive conference. The volume covers current research in the areas of operator theory and dynamical systems on networks and their applications, indicating possible future directions. The book will be interesting to researchers focusing on the mathematical theory of networks; it is unique as, for the first time, continuous network models - a subject that has been blooming in the last twenty years - are studied alongside more classical and discrete ones. Thus, instead of two different worlds often growing independently without much intercommunication, a new path is set, breaking with the tradition. The fruitful and beneficial exchange of ideas and results of both communities is reflected in this book
Language
eng
Work
Publication
Extent
1 online resource
Contents
  • Intro -- Preface -- Contents -- Stability Matters for Reaction-Diffusion-Equations on Metric Graphs Under the Anti-Kirchhoff Vertex Condition -- 1 Metric Graphs -- 2 Stationary Solutions -- 3 Stability -- 4 Nonlinearities Vanishing at 0 -- 5 Constant Nonlinearities -- 6 Odd Nonlinearities -- 7 Loops -- References -- Many-Particle Quantum Graphs: A Review -- 1 Introduction -- 2 Preliminaries -- 2.1 One-Particle Quantum Graphs -- 2.2 Many-Particle Kinematics -- 3 Singular Pair Interactions -- 3.1 Vertex-Induced Singular Interactions -- 3.2 Contact Interactions
  • 3.3 A Lieb-Liniger Model on Graphs -- 4 Bose-Einstein Condensation -- 4.1 Free Bosons -- 4.2 Interacting Bosons -- 5 Exactly Solvable Many-Particle Quantum Graphs -- 6 Many-Particle Models on a Quantum Wire -- 6.1 The Model Without Hard-Wall Binding Potential -- 6.2 The Model with a Hard-Wall Binding Potential -- 6.3 Random Singular Pair Interactions -- 6.4 The Condensation of Electron Pairs in a Quantum Wire -- 6.5 The Impact of Surface Defects on a Condensate of Electrons -- References -- Deterministic and Stochastic Mean-Field SIRS Models on Heterogeneous Networks -- 1 Introduction
  • 2 The Deterministic Model -- 3 The Critical Threshold -- 3.1 Computing the Meta-Stable State -- 3.2 The Heterogeneous Case -- 4 Simulations for the Deterministic Heterogeneous Case -- 5 Stochastic SIRS Model -- 6 Conclusion -- References -- Kreĭn Formula and Convergence of Hamiltonians with Scaled Potentials in Dimension One -- 1 Introduction -- 2 Main Result -- 3 Kreĭn resolvent Formula -- 3.1 Operators in the Outer Space -- 3.2 Operators in the Inner Space -- 3.3 Operator in the Full Space -- 4 Limit of R(z) -- 4.1 Limiting Hamiltonian: Generic Case -- 4.2 Limiting Hamiltonian: Non-generic Case
  • 4 The Asymptotic Expansion of the Regularized Trace of the Heat Kernel -- Appendix 1: Notations -- Appendix 2: Integral Identities for the K0-Macdonald Function -- 2.1 A Converse Watson Lemma -- References -- Modeling Dynamic Coupling in Social Interactions -- 1 Introduction -- 2 Coupling and Information Exchange -- 3 Dynamic Exchanges and Coupling in Sensorimotor Synchronisation -- 4 Quantifying Interactive Coupling -- 5 Applying Dynamic Timecourse Models to Sensorimotor Synchronisation Data -- 5.1 Nature of the Partner -- 5.2 Nature of the Information Being Exchanged
Isbn
9783030440978
Instance
Label
Discrete and continuous models in the theory of networks
Title
Discrete and continuous models in the theory of networks
Statement of responsibility
Fatihcan M. Atay, Pavel B. Kurasov, Delio Mugnolo, editors
Contributor
Subject
Language
eng
Summary
This book contains contributions from the participants of the research group hosted by the ZiF - Center for Interdisciplinary Research at the University of Bielefeld during the period 2013-2017 as well as from the conclusive conference organized at Bielefeld in December 2017. The contributions consist of original research papers: they mirror the scientific developments fostered by this research program or the state-of-the-art results presented during the conclusive conference. The volume covers current research in the areas of operator theory and dynamical systems on networks and their applications, indicating possible future directions. The book will be interesting to researchers focusing on the mathematical theory of networks; it is unique as, for the first time, continuous network models - a subject that has been blooming in the last twenty years - are studied alongside more classical and discrete ones. Thus, instead of two different worlds often growing independently without much intercommunication, a new path is set, breaking with the tradition. The fruitful and beneficial exchange of ideas and results of both communities is reflected in this book
Member of
Cataloging source
YDX
Dewey number
511/.5
Index
no index present
LC call number
QA166
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
  • Atay, Fatihcan M
  • Kurasov, P
  • Mugnolo, Delio
Series statement
Operator theory, advances and applications
Series volume
281
http://library.link/vocab/subjectName
  • Graph theory
  • Mathematical analysis
  • Ergodic theory
Label
Discrete and continuous models in the theory of networks, Fatihcan M. Atay, Pavel B. Kurasov, Delio Mugnolo, editors
Instantiates
Publication
Bibliography note
References -- Ground States of the L2-Critical NLS Equation with Localized Nonlinearity on a Tadpole Graph -- 1 Introduction -- 2 Setting and Main Results -- 3 Preliminaries and Compactness -- 4 Proof of Theorem 2.1 -- References -- An Asymptotic Expansion of the Trace of the Heat Kernel of a Singular Two-particle Contact Interaction in One-dimension -- 1 Introduction -- 2 Preliminaries -- 3 The Resolvent Kernel -- 3.1 Trace Class Property of the Regularized Resolvent -- 3.2 An Asymptotic Analysis of the Trace of the Regularized Resolvent
Contents
  • Intro -- Preface -- Contents -- Stability Matters for Reaction-Diffusion-Equations on Metric Graphs Under the Anti-Kirchhoff Vertex Condition -- 1 Metric Graphs -- 2 Stationary Solutions -- 3 Stability -- 4 Nonlinearities Vanishing at 0 -- 5 Constant Nonlinearities -- 6 Odd Nonlinearities -- 7 Loops -- References -- Many-Particle Quantum Graphs: A Review -- 1 Introduction -- 2 Preliminaries -- 2.1 One-Particle Quantum Graphs -- 2.2 Many-Particle Kinematics -- 3 Singular Pair Interactions -- 3.1 Vertex-Induced Singular Interactions -- 3.2 Contact Interactions
  • 3.3 A Lieb-Liniger Model on Graphs -- 4 Bose-Einstein Condensation -- 4.1 Free Bosons -- 4.2 Interacting Bosons -- 5 Exactly Solvable Many-Particle Quantum Graphs -- 6 Many-Particle Models on a Quantum Wire -- 6.1 The Model Without Hard-Wall Binding Potential -- 6.2 The Model with a Hard-Wall Binding Potential -- 6.3 Random Singular Pair Interactions -- 6.4 The Condensation of Electron Pairs in a Quantum Wire -- 6.5 The Impact of Surface Defects on a Condensate of Electrons -- References -- Deterministic and Stochastic Mean-Field SIRS Models on Heterogeneous Networks -- 1 Introduction
  • 2 The Deterministic Model -- 3 The Critical Threshold -- 3.1 Computing the Meta-Stable State -- 3.2 The Heterogeneous Case -- 4 Simulations for the Deterministic Heterogeneous Case -- 5 Stochastic SIRS Model -- 6 Conclusion -- References -- Kreĭn Formula and Convergence of Hamiltonians with Scaled Potentials in Dimension One -- 1 Introduction -- 2 Main Result -- 3 Kreĭn resolvent Formula -- 3.1 Operators in the Outer Space -- 3.2 Operators in the Inner Space -- 3.3 Operator in the Full Space -- 4 Limit of R(z) -- 4.1 Limiting Hamiltonian: Generic Case -- 4.2 Limiting Hamiltonian: Non-generic Case
  • 4 The Asymptotic Expansion of the Regularized Trace of the Heat Kernel -- Appendix 1: Notations -- Appendix 2: Integral Identities for the K0-Macdonald Function -- 2.1 A Converse Watson Lemma -- References -- Modeling Dynamic Coupling in Social Interactions -- 1 Introduction -- 2 Coupling and Information Exchange -- 3 Dynamic Exchanges and Coupling in Sensorimotor Synchronisation -- 4 Quantifying Interactive Coupling -- 5 Applying Dynamic Timecourse Models to Sensorimotor Synchronisation Data -- 5.1 Nature of the Partner -- 5.2 Nature of the Information Being Exchanged
Dimensions
unknown
Extent
1 online resource
Form of item
online
Isbn
9783030440978
Other control number
  • 10.1007/978-3-030-44097-8
  • 10.1007/978-3-030-44
Specific material designation
remote
System control number
  • on1193327647
  • (OCoLC)1193327647
Label
Discrete and continuous models in the theory of networks, Fatihcan M. Atay, Pavel B. Kurasov, Delio Mugnolo, editors
Publication
Bibliography note
References -- Ground States of the L2-Critical NLS Equation with Localized Nonlinearity on a Tadpole Graph -- 1 Introduction -- 2 Setting and Main Results -- 3 Preliminaries and Compactness -- 4 Proof of Theorem 2.1 -- References -- An Asymptotic Expansion of the Trace of the Heat Kernel of a Singular Two-particle Contact Interaction in One-dimension -- 1 Introduction -- 2 Preliminaries -- 3 The Resolvent Kernel -- 3.1 Trace Class Property of the Regularized Resolvent -- 3.2 An Asymptotic Analysis of the Trace of the Regularized Resolvent
Contents
  • Intro -- Preface -- Contents -- Stability Matters for Reaction-Diffusion-Equations on Metric Graphs Under the Anti-Kirchhoff Vertex Condition -- 1 Metric Graphs -- 2 Stationary Solutions -- 3 Stability -- 4 Nonlinearities Vanishing at 0 -- 5 Constant Nonlinearities -- 6 Odd Nonlinearities -- 7 Loops -- References -- Many-Particle Quantum Graphs: A Review -- 1 Introduction -- 2 Preliminaries -- 2.1 One-Particle Quantum Graphs -- 2.2 Many-Particle Kinematics -- 3 Singular Pair Interactions -- 3.1 Vertex-Induced Singular Interactions -- 3.2 Contact Interactions
  • 3.3 A Lieb-Liniger Model on Graphs -- 4 Bose-Einstein Condensation -- 4.1 Free Bosons -- 4.2 Interacting Bosons -- 5 Exactly Solvable Many-Particle Quantum Graphs -- 6 Many-Particle Models on a Quantum Wire -- 6.1 The Model Without Hard-Wall Binding Potential -- 6.2 The Model with a Hard-Wall Binding Potential -- 6.3 Random Singular Pair Interactions -- 6.4 The Condensation of Electron Pairs in a Quantum Wire -- 6.5 The Impact of Surface Defects on a Condensate of Electrons -- References -- Deterministic and Stochastic Mean-Field SIRS Models on Heterogeneous Networks -- 1 Introduction
  • 2 The Deterministic Model -- 3 The Critical Threshold -- 3.1 Computing the Meta-Stable State -- 3.2 The Heterogeneous Case -- 4 Simulations for the Deterministic Heterogeneous Case -- 5 Stochastic SIRS Model -- 6 Conclusion -- References -- Kreĭn Formula and Convergence of Hamiltonians with Scaled Potentials in Dimension One -- 1 Introduction -- 2 Main Result -- 3 Kreĭn resolvent Formula -- 3.1 Operators in the Outer Space -- 3.2 Operators in the Inner Space -- 3.3 Operator in the Full Space -- 4 Limit of R(z) -- 4.1 Limiting Hamiltonian: Generic Case -- 4.2 Limiting Hamiltonian: Non-generic Case
  • 4 The Asymptotic Expansion of the Regularized Trace of the Heat Kernel -- Appendix 1: Notations -- Appendix 2: Integral Identities for the K0-Macdonald Function -- 2.1 A Converse Watson Lemma -- References -- Modeling Dynamic Coupling in Social Interactions -- 1 Introduction -- 2 Coupling and Information Exchange -- 3 Dynamic Exchanges and Coupling in Sensorimotor Synchronisation -- 4 Quantifying Interactive Coupling -- 5 Applying Dynamic Timecourse Models to Sensorimotor Synchronisation Data -- 5.1 Nature of the Partner -- 5.2 Nature of the Information Being Exchanged
Dimensions
unknown
Extent
1 online resource
Form of item
online
Isbn
9783030440978
Other control number
  • 10.1007/978-3-030-44097-8
  • 10.1007/978-3-030-44
Specific material designation
remote
System control number
  • on1193327647
  • (OCoLC)1193327647

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