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Operator calculus on graphs [[electronic resource] ] : theory and applications in computer science / / René Schott, G. Stacey Staples
| Operator calculus on graphs [[electronic resource] ] : theory and applications in computer science / / René Schott, G. Stacey Staples |
| Autore | Schott René |
| Pubbl/distr/stampa | London, : Imperial College Press, 2012 |
| Descrizione fisica | 1 online resource (428 p.) |
| Disciplina |
515
515.72 |
| Altri autori (Persone) | StaplesG. Stacey |
| Soggetto topico |
Calculus
Computer science - Mathematics |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-280-66906-3
9786613645999 1-84816-877-2 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 11. Partition-Dependent Stochastic Measures |
| Record Nr. | UNINA-9910451618603321 |
Schott René
|
||
| London, : Imperial College Press, 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Operator calculus on graphs [[electronic resource] ] : theory and applications in computer science / / René Schott, G. Stacey Staples
| Operator calculus on graphs [[electronic resource] ] : theory and applications in computer science / / René Schott, G. Stacey Staples |
| Autore | Schott René |
| Pubbl/distr/stampa | London, : Imperial College Press, 2012 |
| Descrizione fisica | 1 online resource (428 p.) |
| Disciplina |
515
515.72 |
| Altri autori (Persone) | StaplesG. Stacey |
| Soggetto topico |
Calculus
Computer science - Mathematics |
| ISBN |
1-280-66906-3
9786613645999 1-84816-877-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 11. Partition-Dependent Stochastic Measures |
| Record Nr. | UNINA-9910779283803321 |
|
Schott René
|
||
| London, : Imperial College Press, 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Operator calculus on graphs [[electronic resource] ] : theory and applications in computer science / / René Schott, G. Stacey Staples
| Operator calculus on graphs [[electronic resource] ] : theory and applications in computer science / / René Schott, G. Stacey Staples |
| Autore | Schott René |
| Pubbl/distr/stampa | London, : Imperial College Press, 2012 |
| Descrizione fisica | 1 online resource (428 p.) |
| Disciplina |
515
515.72 |
| Altri autori (Persone) | StaplesG. Stacey |
| Soggetto topico |
Calculus
Computer science - Mathematics |
| ISBN |
1-280-66906-3
9786613645999 1-84816-877-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 11. Partition-Dependent Stochastic Measures |
| Record Nr. | UNINA-9910823688703321 |
|
Schott René
|
||
| London, : Imperial College Press, 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||