The Resource An introduction to random currents and their applications, Vincenzo Capasso
An introduction to random currents and their applications, Vincenzo Capasso
Resource Information
The item An introduction to random currents and their applications, Vincenzo Capasso represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item An introduction to random currents and their applications, Vincenzo Capasso represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.
This item is available to borrow from 1 library branch.
 Summary
 This book introduces random currents by presenting underlying mathematical methods necessary for applications. The theory of currents is an advanced topic in geometric measure theory that extends distribution to linear functionals within the space of differential forms of any order. Methods to extend random distributions to random currents are introduced and analyzed in this book. Beginning with an overview of mathematical aspects of the theory of currents, this book moves on to examine applications in medicine, material science, and image analysis. Applied researchers will find the practical modern mathematical methods along with the detailed appendix useful to stimulate new applications and research.
 Language
 eng
 Extent
 1 online resource.
 Contents

 Intro; Foreword; Preface; Contents; 1 Introduction and Motivations; 2 Differential Forms; 2.1 Spaces of Functions; 2.1.1 Differential; 2.2 Differential mForms; 2.2.1 Operations on Differential Forms; 2.2.1.1 Sum of Differential Forms; 2.2.1.2 Exterior Product of Differential Forms; 2.2.1.3 Inner Multiplication of a Form by a Vector Field; 2.2.2 Pullback of a Form; 2.2.3 Differentiation of Forms; 2.2.3.1 Lie Derivative of a Differential Form in the Direction of a Vector Field; 2.3 Line Integrals of Differential Forms; 2.4 Surface Integrals of mForms; 2.4.1 Stokes Theorem
 3 Currents: The Deterministic Case3.1 The Space D(U) and Its Topology; 3.2 0Currents: Distributions; 3.3 mCurrents; 3.3.1 Operations on Currents; 3.3.1.1 Exterior Multiplication of a Current with a Vector Field; 3.3.1.2 Exterior Multiplication of a Current with a Form; 3.3.1.3 Expansion of a Current; 3.3.1.4 Cartesian Product of Currents; 3.3.2 Boundary, and Lie Derivative of a Current; 3.3.3 PushForward of a Current; 3.3.4 Currents Associated with Oriented Surfaces; 4 Currents: The Stochastic Case; 4.1 Random Radon Measures; 4.2 Random Radon Measures Associated with Random Closed Sets
 4.2.1 Absolutely Continuous (in Mean) Random Sets4.3 Random Currents; 5 Applications; 5.1 TumorDriven Angiogenesis; 5.1.1 The Capillary Network; 5.1.1.1 Branching; 5.1.1.2 Anastomosis; 5.1.1.3 Mean Field Equation; 5.2 Crystal Dislocations; 5.2.1 Ensemble Averaging; 5.3 Gaussian Currents in Statistical Shape Analysis; 5.3.1 Shapes as Currents; 5.3.2 The Space of Currents on a RKHS; 5.3.2.1 The Isometric Mapping; 5.3.3 Finite Dimensional Approximation of Shapes; 5.3.4 Random Currents on Hilbert Spaces; 5.3.5 Gaussian Currents; 5.3.5.1 Statistics for Gaussian Shape Models
 B.2.2 Gaussian ProcessesB.2.3 Processes with Independent Increments; B.2.4 Markov Processes; B.2.5 Brownian Motion and the Wiener Process; B.2.6 Marked Counting Processes; B.3 The Itô Integral; B.3.1 Itô Integrals of Multidimensional Wiener Processes; B.3.2 The Stochastic Differential; B.4 Multidimensional Stochastic Differentials; B.5 Stochastic Differential Equations; C Vector Calculus; C.1 mVectors; C.2 mCovectors; C.2.1 Duality Pairing; C.2.2 Inner Product; C.2.3 Operations on Covectors; D Regular Surfaces; D.1 Tangent Plane, Normal Vectors, Oriented Surfaces
 Isbn
 9783319945767
 Label
 An introduction to random currents and their applications
 Title
 An introduction to random currents and their applications
 Statement of responsibility
 Vincenzo Capasso
 Language
 eng
 Summary
 This book introduces random currents by presenting underlying mathematical methods necessary for applications. The theory of currents is an advanced topic in geometric measure theory that extends distribution to linear functionals within the space of differential forms of any order. Methods to extend random distributions to random currents are introduced and analyzed in this book. Beginning with an overview of mathematical aspects of the theory of currents, this book moves on to examine applications in medicine, material science, and image analysis. Applied researchers will find the practical modern mathematical methods along with the detailed appendix useful to stimulate new applications and research.
 Cataloging source
 N$T
 http://library.link/vocab/creatorDate
 1945
 http://library.link/vocab/creatorName
 Capasso, Vincenzo
 Dewey number
 519.2
 Index
 index present
 LC call number
 QA274
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 SpringerBriefs in mathematics,
 http://library.link/vocab/subjectName
 Stochastic processes
 Label
 An introduction to random currents and their applications, Vincenzo Capasso
 Antecedent source
 unknown
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 Intro; Foreword; Preface; Contents; 1 Introduction and Motivations; 2 Differential Forms; 2.1 Spaces of Functions; 2.1.1 Differential; 2.2 Differential mForms; 2.2.1 Operations on Differential Forms; 2.2.1.1 Sum of Differential Forms; 2.2.1.2 Exterior Product of Differential Forms; 2.2.1.3 Inner Multiplication of a Form by a Vector Field; 2.2.2 Pullback of a Form; 2.2.3 Differentiation of Forms; 2.2.3.1 Lie Derivative of a Differential Form in the Direction of a Vector Field; 2.3 Line Integrals of Differential Forms; 2.4 Surface Integrals of mForms; 2.4.1 Stokes Theorem
 3 Currents: The Deterministic Case3.1 The Space D(U) and Its Topology; 3.2 0Currents: Distributions; 3.3 mCurrents; 3.3.1 Operations on Currents; 3.3.1.1 Exterior Multiplication of a Current with a Vector Field; 3.3.1.2 Exterior Multiplication of a Current with a Form; 3.3.1.3 Expansion of a Current; 3.3.1.4 Cartesian Product of Currents; 3.3.2 Boundary, and Lie Derivative of a Current; 3.3.3 PushForward of a Current; 3.3.4 Currents Associated with Oriented Surfaces; 4 Currents: The Stochastic Case; 4.1 Random Radon Measures; 4.2 Random Radon Measures Associated with Random Closed Sets
 4.2.1 Absolutely Continuous (in Mean) Random Sets4.3 Random Currents; 5 Applications; 5.1 TumorDriven Angiogenesis; 5.1.1 The Capillary Network; 5.1.1.1 Branching; 5.1.1.2 Anastomosis; 5.1.1.3 Mean Field Equation; 5.2 Crystal Dislocations; 5.2.1 Ensemble Averaging; 5.3 Gaussian Currents in Statistical Shape Analysis; 5.3.1 Shapes as Currents; 5.3.2 The Space of Currents on a RKHS; 5.3.2.1 The Isometric Mapping; 5.3.3 Finite Dimensional Approximation of Shapes; 5.3.4 Random Currents on Hilbert Spaces; 5.3.5 Gaussian Currents; 5.3.5.1 Statistics for Gaussian Shape Models
 B.2.2 Gaussian ProcessesB.2.3 Processes with Independent Increments; B.2.4 Markov Processes; B.2.5 Brownian Motion and the Wiener Process; B.2.6 Marked Counting Processes; B.3 The Itô Integral; B.3.1 Itô Integrals of Multidimensional Wiener Processes; B.3.2 The Stochastic Differential; B.4 Multidimensional Stochastic Differentials; B.5 Stochastic Differential Equations; C Vector Calculus; C.1 mVectors; C.2 mCovectors; C.2.1 Duality Pairing; C.2.2 Inner Product; C.2.3 Operations on Covectors; D Regular Surfaces; D.1 Tangent Plane, Normal Vectors, Oriented Surfaces
 Dimensions
 unknown
 Extent
 1 online resource.
 File format
 unknown
 Form of item
 online
 Isbn
 9783319945767
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number

 on1047729305
 (OCoLC)1047729305
 Label
 An introduction to random currents and their applications, Vincenzo Capasso
 Antecedent source
 unknown
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 Intro; Foreword; Preface; Contents; 1 Introduction and Motivations; 2 Differential Forms; 2.1 Spaces of Functions; 2.1.1 Differential; 2.2 Differential mForms; 2.2.1 Operations on Differential Forms; 2.2.1.1 Sum of Differential Forms; 2.2.1.2 Exterior Product of Differential Forms; 2.2.1.3 Inner Multiplication of a Form by a Vector Field; 2.2.2 Pullback of a Form; 2.2.3 Differentiation of Forms; 2.2.3.1 Lie Derivative of a Differential Form in the Direction of a Vector Field; 2.3 Line Integrals of Differential Forms; 2.4 Surface Integrals of mForms; 2.4.1 Stokes Theorem
 3 Currents: The Deterministic Case3.1 The Space D(U) and Its Topology; 3.2 0Currents: Distributions; 3.3 mCurrents; 3.3.1 Operations on Currents; 3.3.1.1 Exterior Multiplication of a Current with a Vector Field; 3.3.1.2 Exterior Multiplication of a Current with a Form; 3.3.1.3 Expansion of a Current; 3.3.1.4 Cartesian Product of Currents; 3.3.2 Boundary, and Lie Derivative of a Current; 3.3.3 PushForward of a Current; 3.3.4 Currents Associated with Oriented Surfaces; 4 Currents: The Stochastic Case; 4.1 Random Radon Measures; 4.2 Random Radon Measures Associated with Random Closed Sets
 4.2.1 Absolutely Continuous (in Mean) Random Sets4.3 Random Currents; 5 Applications; 5.1 TumorDriven Angiogenesis; 5.1.1 The Capillary Network; 5.1.1.1 Branching; 5.1.1.2 Anastomosis; 5.1.1.3 Mean Field Equation; 5.2 Crystal Dislocations; 5.2.1 Ensemble Averaging; 5.3 Gaussian Currents in Statistical Shape Analysis; 5.3.1 Shapes as Currents; 5.3.2 The Space of Currents on a RKHS; 5.3.2.1 The Isometric Mapping; 5.3.3 Finite Dimensional Approximation of Shapes; 5.3.4 Random Currents on Hilbert Spaces; 5.3.5 Gaussian Currents; 5.3.5.1 Statistics for Gaussian Shape Models
 B.2.2 Gaussian ProcessesB.2.3 Processes with Independent Increments; B.2.4 Markov Processes; B.2.5 Brownian Motion and the Wiener Process; B.2.6 Marked Counting Processes; B.3 The Itô Integral; B.3.1 Itô Integrals of Multidimensional Wiener Processes; B.3.2 The Stochastic Differential; B.4 Multidimensional Stochastic Differentials; B.5 Stochastic Differential Equations; C Vector Calculus; C.1 mVectors; C.2 mCovectors; C.2.1 Duality Pairing; C.2.2 Inner Product; C.2.3 Operations on Covectors; D Regular Surfaces; D.1 Tangent Plane, Normal Vectors, Oriented Surfaces
 Dimensions
 unknown
 Extent
 1 online resource.
 File format
 unknown
 Form of item
 online
 Isbn
 9783319945767
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number

 on1047729305
 (OCoLC)1047729305
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