Coverart for item
The Resource An introduction to random currents and their applications, Vincenzo Capasso

An introduction to random currents and their applications, Vincenzo Capasso

Label
An introduction to random currents and their applications
Title
An introduction to random currents and their applications
Statement of responsibility
Vincenzo Capasso
Creator
Author
Subject
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.
Member of
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
Instantiates
Publication
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 m-Forms; 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 m-Forms; 2.4.1 Stokes Theorem
  • 3 Currents: The Deterministic Case3.1 The Space D(U) and Its Topology; 3.2 0-Currents: Distributions; 3.3 m-Currents; 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 Push-Forward 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 Tumor-Driven 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 m-Vectors; C.2 m-Covectors; 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
Publication
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 m-Forms; 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 m-Forms; 2.4.1 Stokes Theorem
  • 3 Currents: The Deterministic Case3.1 The Space D(U) and Its Topology; 3.2 0-Currents: Distributions; 3.3 m-Currents; 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 Push-Forward 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 Tumor-Driven 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 m-Vectors; C.2 m-Covectors; 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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