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 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
- 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 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
- 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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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/An-introduction-to-random-currents-and-their/LXgshvPT1Co/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.liverpool.ac.uk/portal/An-introduction-to-random-currents-and-their/LXgshvPT1Co/">An introduction to random currents and their applications, Vincenzo Capasso</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.liverpool.ac.uk/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.liverpool.ac.uk/">University of Liverpool</a></span></span></span></span></div>
