Operator Calculus on Graphs: Theory and Applications in Computer Science
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Singapore
World Scientific
2012
|
| Subjects: | |
| Online Access: | FAW01 FAW02 Volltext |
| Item Description: | 11. Partition-Dependent Stochastic Measures Print version record |
| Physical Description: | 1 online resource (428 pages) |
| ISBN: | 1280669063 1848168764 1848168772 9781280669064 9781848168763 9781848168770 |
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| 500 | |a 11. Partition-Dependent Stochastic Measures | ||
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| 505 | 8 | |a Preface; Acknowledgments; Contents; Combinatorial Algebras and Their Properties; 1. Introduction; 1.1 Notational Preliminaries; 2. Combinatorial Algebra; 2.1 Six Group and Semigroup Algebras; 2.1.1 The group of blades Bp, q; 2.1.1.1 Involutions; 2.1.1.2 The n-dimensional hypercube Qn; 2.1.2 The abelian blade group Bp, q sym; 2.1.3 The null blade semigroup; 2.1.4 The abelian null blade semigroup sym; 2.1.5 The semigroup of idempotent blades idem; 2.1.6 The path semigroup n; 2.1.7 Summary; 2.1.7.1 Algebras I-IV; 2.1.7.2 Algebra V; 2.1.7.3 Algebra VI; 2.2 Clifford and Grassmann Algebras | |
| 505 | 8 | |a 2.2.1 Grassmann (exterior) algebras2.2.2 Clifford algebras; 2.2.3 Operator calculus on Clifford algebras; 2.3 The Symmetric Clifford Algebra sym; 2.4 The Idempotent-Generated Algebra idem; 2.5 The n-Particle Zeon Algebra nil; 2.6 Generalized Zeon Algebras; 3. Norm Inequalities on Clifford Algebras; 3.1 Norms on C p; q; 3.2 Generating Functions; 3.3 Clifford Matrices and the Clifford-Frobenius Norm; 3.4 Powers of Clifford Matrices; Combinatorics and Graph Theory; 4. Specialized Adjacency Matrices; 4.1 Essential Graph Theory; 4.2 Clifford Adjacency Matrices; 4.3 Nilpotent Adjacency Matrices | |
| 505 | 8 | |a 4.3.1 Euler circuits4.3.2 Conditional branching; 4.3.3 Time-homogeneous random walks on finite graphs; 5. Random Graphs; 5.1 Preliminaries; 5.2 Cycles in Random Graphs; 5.3 Convergence of Moments; 6. Graph Theory and Quantum Probability; 6.1 Concepts; 6.1.1 Operators as random variables; 6.1.2 Operators as adjacency matrices; 6.2 From Graphs to Quantum Random Variables; 6.2.1 Nilpotent adjacency operators in infinite spaces; 6.2.2 Decomposition of nilpotent adjacency operators; 6.3 Connected Components in Graph Processes; 6.3.1 Algebraic preliminaries; 6.3.2 Connected components | |
| 505 | 8 | |a 6.3.2.1 (k, d)-components6.3.3 Second quantization of graph processes; 7. Geometric Graph Processes; 7.1 Preliminaries; 7.2 Dynamic Graph Processes; 7.2.1 Vertex degrees in Gn; 7.2.2 Energy and Laplacian energy of geometric graphs; 7.2.3 Convergence conditions and a limit theorem; 7.3 Time-Homogeneous Walks on Random Geometric Graphs; Probability on Algebraic Structures; 8. Time-Homogeneous Random Walks; 8.1 sym and Random Walks on Hypercubes; 8.2 Multiplicative Walks on C p, q; 8.2.1 Walks on directed hypercubes; 8.2.2 Random walks on directed hypercubes with loops | |
| 505 | 8 | |a 8.2.3 Properties of multiplicative walks8.3 Induced Additive Walks on C p, q; 8.3.1 Variance of N; 8.3.2 Variance of; 8.3.3 Central limit theorems; 9. Dynamic Walks in Clifford Algebras; 9.1 Preliminaries; 9.2 Expectation; 9.3 Limit Theorems; 9.3.1 Conditions for convergence; 9.3.2 Induced additive walks; 9.3.3 Central limit theorem; 10. Iterated Stochastic Integrals; 10.1 Preliminaries; 10.2 Stochastic Integrals in; 10.3 Graph-Theoretic Iterated Stochastic Integrals; 10.3.1 Functions on partitions; 10.3.2 The Clifford evolution matrix; 10.3.3 Orthogonal polynomials | |
| 505 | 8 | |a This pioneering book presents a study of the interrelationships among operator calculus, graph theory, and quantum probability in a unified manner, with significant emphasis on symbolic computations and an eye toward applications in computer science. Presented in this book are new methods, built on the algebraic framework of Clifford algebras, for tackling important real world problems related, but not limited to, wireless communications, neural networks, electrical circuits, transportation, and the world wide web. Examples are put forward in Mathematica throughout the book, together with pack | |
| 650 | 4 | |a Clifford algebras | |
| 650 | 4 | |a Combinatorial analysis | |
| 650 | 4 | |a Operator theory | |
| 650 | 4 | |a Mathematics | |
| 650 | 7 | |a MATHEMATICS / Calculus |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS / Mathematical Analysis |2 bisacsh | |
| 650 | 4 | |a Informatik | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Calculus, Operational | |
| 650 | 4 | |a Graph theory | |
| 650 | 4 | |a Quantum statistics | |
| 650 | 4 | |a Computer science | |
| 700 | 1 | |a Staples, G. Stacey |e Sonstige |4 oth | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |a Schott, Rene |t Operator Calculus on Graphs : Theory and Applications in Computer Science |
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Record in the Search Index
| _version_ | 1804175390475812864 |
|---|---|
| any_adam_object | |
| author | Schott, Rene |
| author_facet | Schott, Rene |
| author_role | aut |
| author_sort | Schott, Rene |
| author_variant | r s rs |
| building | Verbundindex |
| bvnumber | BV043032858 |
| collection | ZDB-4-EBA |
| contents | Preface; Acknowledgments; Contents; Combinatorial Algebras and Their Properties; 1. Introduction; 1.1 Notational Preliminaries; 2. Combinatorial Algebra; 2.1 Six Group and Semigroup Algebras; 2.1.1 The group of blades Bp, q; 2.1.1.1 Involutions; 2.1.1.2 The n-dimensional hypercube Qn; 2.1.2 The abelian blade group Bp, q sym; 2.1.3 The null blade semigroup; 2.1.4 The abelian null blade semigroup sym; 2.1.5 The semigroup of idempotent blades idem; 2.1.6 The path semigroup n; 2.1.7 Summary; 2.1.7.1 Algebras I-IV; 2.1.7.2 Algebra V; 2.1.7.3 Algebra VI; 2.2 Clifford and Grassmann Algebras 2.2.1 Grassmann (exterior) algebras2.2.2 Clifford algebras; 2.2.3 Operator calculus on Clifford algebras; 2.3 The Symmetric Clifford Algebra sym; 2.4 The Idempotent-Generated Algebra idem; 2.5 The n-Particle Zeon Algebra nil; 2.6 Generalized Zeon Algebras; 3. Norm Inequalities on Clifford Algebras; 3.1 Norms on C p; q; 3.2 Generating Functions; 3.3 Clifford Matrices and the Clifford-Frobenius Norm; 3.4 Powers of Clifford Matrices; Combinatorics and Graph Theory; 4. Specialized Adjacency Matrices; 4.1 Essential Graph Theory; 4.2 Clifford Adjacency Matrices; 4.3 Nilpotent Adjacency Matrices 4.3.1 Euler circuits4.3.2 Conditional branching; 4.3.3 Time-homogeneous random walks on finite graphs; 5. Random Graphs; 5.1 Preliminaries; 5.2 Cycles in Random Graphs; 5.3 Convergence of Moments; 6. Graph Theory and Quantum Probability; 6.1 Concepts; 6.1.1 Operators as random variables; 6.1.2 Operators as adjacency matrices; 6.2 From Graphs to Quantum Random Variables; 6.2.1 Nilpotent adjacency operators in infinite spaces; 6.2.2 Decomposition of nilpotent adjacency operators; 6.3 Connected Components in Graph Processes; 6.3.1 Algebraic preliminaries; 6.3.2 Connected components 6.3.2.1 (k, d)-components6.3.3 Second quantization of graph processes; 7. Geometric Graph Processes; 7.1 Preliminaries; 7.2 Dynamic Graph Processes; 7.2.1 Vertex degrees in Gn; 7.2.2 Energy and Laplacian energy of geometric graphs; 7.2.3 Convergence conditions and a limit theorem; 7.3 Time-Homogeneous Walks on Random Geometric Graphs; Probability on Algebraic Structures; 8. Time-Homogeneous Random Walks; 8.1 sym and Random Walks on Hypercubes; 8.2 Multiplicative Walks on C p, q; 8.2.1 Walks on directed hypercubes; 8.2.2 Random walks on directed hypercubes with loops 8.2.3 Properties of multiplicative walks8.3 Induced Additive Walks on C p, q; 8.3.1 Variance of N; 8.3.2 Variance of; 8.3.3 Central limit theorems; 9. Dynamic Walks in Clifford Algebras; 9.1 Preliminaries; 9.2 Expectation; 9.3 Limit Theorems; 9.3.1 Conditions for convergence; 9.3.2 Induced additive walks; 9.3.3 Central limit theorem; 10. Iterated Stochastic Integrals; 10.1 Preliminaries; 10.2 Stochastic Integrals in; 10.3 Graph-Theoretic Iterated Stochastic Integrals; 10.3.1 Functions on partitions; 10.3.2 The Clifford evolution matrix; 10.3.3 Orthogonal polynomials This pioneering book presents a study of the interrelationships among operator calculus, graph theory, and quantum probability in a unified manner, with significant emphasis on symbolic computations and an eye toward applications in computer science. Presented in this book are new methods, built on the algebraic framework of Clifford algebras, for tackling important real world problems related, but not limited to, wireless communications, neural networks, electrical circuits, transportation, and the world wide web. Examples are put forward in Mathematica throughout the book, together with pack |
| ctrlnum | (OCoLC)794328387 (DE-599)BVBBV043032858 |
| dewey-full | 515 515.72 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 515.72 |
| dewey-search | 515 515.72 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043032858 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:15:32Z |
| institution | BVB |
| isbn | 1280669063 1848168764 1848168772 9781280669064 9781848168763 9781848168770 |
| language | English |
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| oclc_num | 794328387 |
| open_access_boolean | |
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| owner_facet | DE-1046 DE-1047 |
| physical | 1 online resource (428 pages) |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Schott, Rene Verfasser aut Operator Calculus on Graphs Theory and Applications in Computer Science Singapore World Scientific 2012 1 online resource (428 pages) txt rdacontent c rdamedia cr rdacarrier 11. Partition-Dependent Stochastic Measures Print version record Preface; Acknowledgments; Contents; Combinatorial Algebras and Their Properties; 1. Introduction; 1.1 Notational Preliminaries; 2. Combinatorial Algebra; 2.1 Six Group and Semigroup Algebras; 2.1.1 The group of blades Bp, q; 2.1.1.1 Involutions; 2.1.1.2 The n-dimensional hypercube Qn; 2.1.2 The abelian blade group Bp, q sym; 2.1.3 The null blade semigroup; 2.1.4 The abelian null blade semigroup sym; 2.1.5 The semigroup of idempotent blades idem; 2.1.6 The path semigroup n; 2.1.7 Summary; 2.1.7.1 Algebras I-IV; 2.1.7.2 Algebra V; 2.1.7.3 Algebra VI; 2.2 Clifford and Grassmann Algebras 2.2.1 Grassmann (exterior) algebras2.2.2 Clifford algebras; 2.2.3 Operator calculus on Clifford algebras; 2.3 The Symmetric Clifford Algebra sym; 2.4 The Idempotent-Generated Algebra idem; 2.5 The n-Particle Zeon Algebra nil; 2.6 Generalized Zeon Algebras; 3. Norm Inequalities on Clifford Algebras; 3.1 Norms on C p; q; 3.2 Generating Functions; 3.3 Clifford Matrices and the Clifford-Frobenius Norm; 3.4 Powers of Clifford Matrices; Combinatorics and Graph Theory; 4. Specialized Adjacency Matrices; 4.1 Essential Graph Theory; 4.2 Clifford Adjacency Matrices; 4.3 Nilpotent Adjacency Matrices 4.3.1 Euler circuits4.3.2 Conditional branching; 4.3.3 Time-homogeneous random walks on finite graphs; 5. Random Graphs; 5.1 Preliminaries; 5.2 Cycles in Random Graphs; 5.3 Convergence of Moments; 6. Graph Theory and Quantum Probability; 6.1 Concepts; 6.1.1 Operators as random variables; 6.1.2 Operators as adjacency matrices; 6.2 From Graphs to Quantum Random Variables; 6.2.1 Nilpotent adjacency operators in infinite spaces; 6.2.2 Decomposition of nilpotent adjacency operators; 6.3 Connected Components in Graph Processes; 6.3.1 Algebraic preliminaries; 6.3.2 Connected components 6.3.2.1 (k, d)-components6.3.3 Second quantization of graph processes; 7. Geometric Graph Processes; 7.1 Preliminaries; 7.2 Dynamic Graph Processes; 7.2.1 Vertex degrees in Gn; 7.2.2 Energy and Laplacian energy of geometric graphs; 7.2.3 Convergence conditions and a limit theorem; 7.3 Time-Homogeneous Walks on Random Geometric Graphs; Probability on Algebraic Structures; 8. Time-Homogeneous Random Walks; 8.1 sym and Random Walks on Hypercubes; 8.2 Multiplicative Walks on C p, q; 8.2.1 Walks on directed hypercubes; 8.2.2 Random walks on directed hypercubes with loops 8.2.3 Properties of multiplicative walks8.3 Induced Additive Walks on C p, q; 8.3.1 Variance of N; 8.3.2 Variance of; 8.3.3 Central limit theorems; 9. Dynamic Walks in Clifford Algebras; 9.1 Preliminaries; 9.2 Expectation; 9.3 Limit Theorems; 9.3.1 Conditions for convergence; 9.3.2 Induced additive walks; 9.3.3 Central limit theorem; 10. Iterated Stochastic Integrals; 10.1 Preliminaries; 10.2 Stochastic Integrals in; 10.3 Graph-Theoretic Iterated Stochastic Integrals; 10.3.1 Functions on partitions; 10.3.2 The Clifford evolution matrix; 10.3.3 Orthogonal polynomials This pioneering book presents a study of the interrelationships among operator calculus, graph theory, and quantum probability in a unified manner, with significant emphasis on symbolic computations and an eye toward applications in computer science. Presented in this book are new methods, built on the algebraic framework of Clifford algebras, for tackling important real world problems related, but not limited to, wireless communications, neural networks, electrical circuits, transportation, and the world wide web. Examples are put forward in Mathematica throughout the book, together with pack Clifford algebras Combinatorial analysis Operator theory Mathematics MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Informatik Mathematik Calculus, Operational Graph theory Quantum statistics Computer science Staples, G. Stacey Sonstige oth Erscheint auch als Druck-Ausgabe Schott, Rene Operator Calculus on Graphs : Theory and Applications in Computer Science http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=457191 Aggregator Volltext |
| spellingShingle | Schott, Rene Operator Calculus on Graphs Theory and Applications in Computer Science Preface; Acknowledgments; Contents; Combinatorial Algebras and Their Properties; 1. Introduction; 1.1 Notational Preliminaries; 2. Combinatorial Algebra; 2.1 Six Group and Semigroup Algebras; 2.1.1 The group of blades Bp, q; 2.1.1.1 Involutions; 2.1.1.2 The n-dimensional hypercube Qn; 2.1.2 The abelian blade group Bp, q sym; 2.1.3 The null blade semigroup; 2.1.4 The abelian null blade semigroup sym; 2.1.5 The semigroup of idempotent blades idem; 2.1.6 The path semigroup n; 2.1.7 Summary; 2.1.7.1 Algebras I-IV; 2.1.7.2 Algebra V; 2.1.7.3 Algebra VI; 2.2 Clifford and Grassmann Algebras 2.2.1 Grassmann (exterior) algebras2.2.2 Clifford algebras; 2.2.3 Operator calculus on Clifford algebras; 2.3 The Symmetric Clifford Algebra sym; 2.4 The Idempotent-Generated Algebra idem; 2.5 The n-Particle Zeon Algebra nil; 2.6 Generalized Zeon Algebras; 3. Norm Inequalities on Clifford Algebras; 3.1 Norms on C p; q; 3.2 Generating Functions; 3.3 Clifford Matrices and the Clifford-Frobenius Norm; 3.4 Powers of Clifford Matrices; Combinatorics and Graph Theory; 4. Specialized Adjacency Matrices; 4.1 Essential Graph Theory; 4.2 Clifford Adjacency Matrices; 4.3 Nilpotent Adjacency Matrices 4.3.1 Euler circuits4.3.2 Conditional branching; 4.3.3 Time-homogeneous random walks on finite graphs; 5. Random Graphs; 5.1 Preliminaries; 5.2 Cycles in Random Graphs; 5.3 Convergence of Moments; 6. Graph Theory and Quantum Probability; 6.1 Concepts; 6.1.1 Operators as random variables; 6.1.2 Operators as adjacency matrices; 6.2 From Graphs to Quantum Random Variables; 6.2.1 Nilpotent adjacency operators in infinite spaces; 6.2.2 Decomposition of nilpotent adjacency operators; 6.3 Connected Components in Graph Processes; 6.3.1 Algebraic preliminaries; 6.3.2 Connected components 6.3.2.1 (k, d)-components6.3.3 Second quantization of graph processes; 7. Geometric Graph Processes; 7.1 Preliminaries; 7.2 Dynamic Graph Processes; 7.2.1 Vertex degrees in Gn; 7.2.2 Energy and Laplacian energy of geometric graphs; 7.2.3 Convergence conditions and a limit theorem; 7.3 Time-Homogeneous Walks on Random Geometric Graphs; Probability on Algebraic Structures; 8. Time-Homogeneous Random Walks; 8.1 sym and Random Walks on Hypercubes; 8.2 Multiplicative Walks on C p, q; 8.2.1 Walks on directed hypercubes; 8.2.2 Random walks on directed hypercubes with loops 8.2.3 Properties of multiplicative walks8.3 Induced Additive Walks on C p, q; 8.3.1 Variance of N; 8.3.2 Variance of; 8.3.3 Central limit theorems; 9. Dynamic Walks in Clifford Algebras; 9.1 Preliminaries; 9.2 Expectation; 9.3 Limit Theorems; 9.3.1 Conditions for convergence; 9.3.2 Induced additive walks; 9.3.3 Central limit theorem; 10. Iterated Stochastic Integrals; 10.1 Preliminaries; 10.2 Stochastic Integrals in; 10.3 Graph-Theoretic Iterated Stochastic Integrals; 10.3.1 Functions on partitions; 10.3.2 The Clifford evolution matrix; 10.3.3 Orthogonal polynomials This pioneering book presents a study of the interrelationships among operator calculus, graph theory, and quantum probability in a unified manner, with significant emphasis on symbolic computations and an eye toward applications in computer science. Presented in this book are new methods, built on the algebraic framework of Clifford algebras, for tackling important real world problems related, but not limited to, wireless communications, neural networks, electrical circuits, transportation, and the world wide web. Examples are put forward in Mathematica throughout the book, together with pack Clifford algebras Combinatorial analysis Operator theory Mathematics MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Informatik Mathematik Calculus, Operational Graph theory Quantum statistics Computer science |
| title | Operator Calculus on Graphs Theory and Applications in Computer Science |
| title_auth | Operator Calculus on Graphs Theory and Applications in Computer Science |
| title_exact_search | Operator Calculus on Graphs Theory and Applications in Computer Science |
| title_full | Operator Calculus on Graphs Theory and Applications in Computer Science |
| title_fullStr | Operator Calculus on Graphs Theory and Applications in Computer Science |
| title_full_unstemmed | Operator Calculus on Graphs Theory and Applications in Computer Science |
| title_short | Operator Calculus on Graphs |
| title_sort | operator calculus on graphs theory and applications in computer science |
| title_sub | Theory and Applications in Computer Science |
| topic | Clifford algebras Combinatorial analysis Operator theory Mathematics MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Informatik Mathematik Calculus, Operational Graph theory Quantum statistics Computer science |
| topic_facet | Clifford algebras Combinatorial analysis Operator theory Mathematics MATHEMATICS / Calculus MATHEMATICS / Mathematical Analysis Informatik Mathematik Calculus, Operational Graph theory Quantum statistics Computer science |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=457191 |
| work_keys_str_mv | AT schottrene operatorcalculusongraphstheoryandapplicationsincomputerscience AT staplesgstacey operatorcalculusongraphstheoryandapplicationsincomputerscience |