Critical population and error threshold on the sharp peak landscape for a Moran model / / Raphaël Cerf |
Autore | Cerf Raphaël |
Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2014 |
Descrizione fisica | 1 online resource (87 p.) |
Disciplina | 547/.7 |
Collana | Memoirs of the American Mathematical Society |
Soggetto topico |
Molecular dynamics - Mathematical models
Macromolecules - Mathematical models Chromosome replication - Mathematical models |
Soggetto genere / forma | Electronic books. |
ISBN | 1-4704-1964-5 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | ""Cover""; ""Title page""; ""Chapter 1. Introduction""; ""Chapter 2. The Model""; ""Chapter 3. Main Results""; ""Chapter 4. Coupling""; ""Chapter 5. Normalized Model""; ""Chapter 6. Lumping""; ""6.1. Distance process""; ""6.2. Occupancy process""; ""6.3. Invariant probability measures""; ""Chapter 7. Monotonicity""; ""7.1. Coupling of the lumped processes""; ""7.2. Monotonicity of the model""; ""Chapter 8. Stochastic Bounds""; ""8.1. Lower and upper processes""; ""8.2. Dynamics of the bounding processes""; ""8.3. A renewal argument""; ""8.4. Bounds on "" |
Record Nr. | UNINA-9910478914503321 |
Cerf Raphaël
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Providence, Rhode Island : , : American Mathematical Society, , 2014 | ||
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Lo trovi qui: Univ. Federico II | ||
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Critical population and error threshold on the sharp peak landscape for a Moran model / / Raphaël Cerf |
Autore | Cerf Raphaël |
Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2014 |
Descrizione fisica | 1 online resource (87 p.) |
Disciplina | 547/.7 |
Collana | Memoirs of the American Mathematical Society |
Soggetto topico |
Molecular dynamics - Mathematical models
Macromolecules - Mathematical models Chromosome replication - Mathematical models |
ISBN | 1-4704-1964-5 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | ""Cover""; ""Title page""; ""Chapter 1. Introduction""; ""Chapter 2. The Model""; ""Chapter 3. Main Results""; ""Chapter 4. Coupling""; ""Chapter 5. Normalized Model""; ""Chapter 6. Lumping""; ""6.1. Distance process""; ""6.2. Occupancy process""; ""6.3. Invariant probability measures""; ""Chapter 7. Monotonicity""; ""7.1. Coupling of the lumped processes""; ""7.2. Monotonicity of the model""; ""Chapter 8. Stochastic Bounds""; ""8.1. Lower and upper processes""; ""8.2. Dynamics of the bounding processes""; ""8.3. A renewal argument""; ""8.4. Bounds on "" |
Record Nr. | UNINA-9910797018203321 |
Cerf Raphaël
![]() |
||
Providence, Rhode Island : , : American Mathematical Society, , 2014 | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
|
Critical population and error threshold on the sharp peak landscape for a Moran model / / Raphaël Cerf |
Autore | Cerf Raphaël |
Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2014 |
Descrizione fisica | 1 online resource (87 p.) |
Disciplina | 547/.7 |
Collana | Memoirs of the American Mathematical Society |
Soggetto topico |
Molecular dynamics - Mathematical models
Macromolecules - Mathematical models Chromosome replication - Mathematical models |
ISBN | 1-4704-1964-5 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | ""Cover""; ""Title page""; ""Chapter 1. Introduction""; ""Chapter 2. The Model""; ""Chapter 3. Main Results""; ""Chapter 4. Coupling""; ""Chapter 5. Normalized Model""; ""Chapter 6. Lumping""; ""6.1. Distance process""; ""6.2. Occupancy process""; ""6.3. Invariant probability measures""; ""Chapter 7. Monotonicity""; ""7.1. Coupling of the lumped processes""; ""7.2. Monotonicity of the model""; ""Chapter 8. Stochastic Bounds""; ""8.1. Lower and upper processes""; ""8.2. Dynamics of the bounding processes""; ""8.3. A renewal argument""; ""8.4. Bounds on "" |
Record Nr. | UNINA-9910810982703321 |
Cerf Raphaël
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||
Providence, Rhode Island : , : American Mathematical Society, , 2014 | ||
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Lo trovi qui: Univ. Federico II | ||
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The quasispecies equation and classical population models / / Raphaël Cerf, Joseba Dalmau |
Autore | Cerf Raphaël |
Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
Descrizione fisica | 1 online resource (236 pages) |
Disciplina | 519.2 |
Collana | Probability theory and stochastic modelling |
Soggetto topico |
Probabilities
Quasisymmetric groups Probabilitats |
Soggetto genere / forma | Llibres electrònics |
ISBN | 3-031-08663-5 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
Intro -- Foreword -- Contents -- Chapter 1 Introduction -- Part I Finite Genotype Space -- Overview of Part I -- Chapter 2 The Quasispecies Equation -- 2.1 The Equilibrium Equation -- 2.2 The Perron-Frobenius Theorem -- 2.3 Solutions -- Chapter 3 Non-Overlapping Generations -- 3.1 The Moran-Kingman Model -- 3.2 The Galton-Watson Model -- 3.3 The Wright-Fisher Model -- Chapter 4 Overlapping Generations -- 4.1 The Eigen Model -- 4.2 The Continuous Branching Model -- 4.3 The Moran Model -- Chapter 5 Probabilistic Representations -- 5.1 Stopped RandomWalk -- 5.2 Stopped Branching Process -- Part II The Sharp Peak Landscape -- Overview of Part II -- Chapter 6 Long Chain Regime -- 6.1 Genotypes and Mutations -- 6.2 Sharp Peak Fitness -- 6.3 Hamming Classes -- 6.4 Limit Equation -- Chapter 7 Error Threshold and Quasispecies -- 7.1 The Error Threshold -- 7.2 The Distribution of the Quasispecies -- Chapter 8 Probabilistic Derivation -- 8.1 Asymptotics of c* -- 8.2 Limit of the Mutant Walk Representation -- 8.3 The Poisson Random Walk -- 8.4 Formal Derivation -- Chapter 9 Summation of the Series -- 9.1 Stirling Numbers -- 9.2 Eulerian Numbers -- 9.3 Combinatorial Identities -- Chapter 10 Error Threshold in Infinite Populations -- 10.1 The Moran-Kingman Model -- 10.2 The Eigen Model -- Part III Error Threshold in Finite Populations -- Overview of Part III -- Chapter 11 Phase Transition -- 11.1 The Moran Model -- 11.2 The Wright-Fisher Model -- Chapter 12 Computer Simulations -- Chapter 13 Heuristics -- 13.1 A Simplified Process -- 13.2 A Renewal Argument -- 13.3 Persistence Time -- Chapter 14 Shape of the Critical Curve -- 14.1 Critical Curve for the Moran Model -- 14.2 Critical Curve for the Wright-Fisher Model -- Chapter 15 Framework for the Proofs -- 15.1 Candidate Limits for Moran -- 15.2 Candidate Limits for Wright-Fisher.
Part IV Proof for Wright-Fisher -- Overview of Part IV -- Chapter 16 Strategy of the Proof -- 16.1 Main Ideas -- 16.2 Invariant Probability Measure -- 16.3 Upper Bounds -- Chapter 17 The Non-Neutral Phase M -- 17.1 Large Deviations Principle -- 17.2 Perturbed Dynamical System -- 17.3 Time away from the Fixed Points -- 17.4 Reaching the Quasispecies -- 17.5 Escape from the Quasispecies -- Chapter 18 Mutation Dynamics -- 18.1 Binary Process of Differences -- 18.2 Hamming Class Dynamics -- 18.3 Time away from the Equilibrium -- 18.4 Reaching the Equilibrium -- 18.5 Escape from the Equilibrium -- Chapter 19 The Neutral Phase N -- 19.1 Ancestral Lines -- 19.2 Monotonicity and Correlations -- 19.3 Time away from the Disorder -- 19.4 Reaching the Disorder -- 19.5 Escape from the Disorder -- Chapter 20 Synthesis -- 20.1 The Quasispecies Regime -- 20.2 The Disordered Regime -- Part V Class-Dependent Fitness Landscapes -- Overview of Part V -- Chapter 21 Generalized Quasispecies Distributions -- 21.1 Class-Dependent Fitness Landscapes -- 21.2 Up-Down Coefficients -- 21.3 Re-Expansion -- Chapter 22 Error Threshold -- 22.1 Eventually Constant Fitness Functions -- 22.2 Error Threshold -- 22.3 Further Solutions -- Chapter 23 Probabilistic Representation -- 23.1 Asymptotics of Perron-Frobenius -- 23.2 Mutant Walk Representation -- 23.3 Computation of the Limit -- 23.4 Rearranging the Sums -- Chapter 24 Probabilistic Interpretations -- 24.1 Poisson Random Walk -- 24.2 The Branching Poisson Walk -- Chapter 25 Infinite Population Models -- 25.1 The Moran-Kingman Model -- 25.2 The Eigen Model -- Part VI A Glimpse at the Dynamics -- Overview of Part VI -- Chapter 26 Deterministic Level -- 26.1 The Moran-Kingman Model -- 26.2 The Eigen Model -- Chapter 27 From Finite to Infinite Population -- 27.1 From Moran's to Eigen's Model. 27.2 From Wright-Fisher's to Moran-Kingman's Model -- Chapter 28 Class-Dependent Landscapes -- 28.1 Moran Model -- 28.2 The Wright-Fisher Model -- Appendix A Markov Chains and classical results -- A.1 Monotonicity -- A.2 Construction of Markov Processes -- A.3 Lumping -- A.4 The FKG Inequality -- A.5 Hoeffding's Inequality -- References -- Index. |
Record Nr. | UNISA-996483153803316 |
Cerf Raphaël
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Cham, Switzerland : , : Springer, , [2022] | ||
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Lo trovi qui: Univ. di Salerno | ||
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The quasispecies equation and classical population models / / Raphaël Cerf, Joseba Dalmau |
Autore | Cerf Raphaël |
Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
Descrizione fisica | 1 online resource (236 pages) |
Disciplina | 519.2 |
Collana | Probability theory and stochastic modelling |
Soggetto topico |
Probabilities
Quasisymmetric groups Probabilitats |
Soggetto genere / forma | Llibres electrònics |
ISBN | 3-031-08663-5 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
Intro -- Foreword -- Contents -- Chapter 1 Introduction -- Part I Finite Genotype Space -- Overview of Part I -- Chapter 2 The Quasispecies Equation -- 2.1 The Equilibrium Equation -- 2.2 The Perron-Frobenius Theorem -- 2.3 Solutions -- Chapter 3 Non-Overlapping Generations -- 3.1 The Moran-Kingman Model -- 3.2 The Galton-Watson Model -- 3.3 The Wright-Fisher Model -- Chapter 4 Overlapping Generations -- 4.1 The Eigen Model -- 4.2 The Continuous Branching Model -- 4.3 The Moran Model -- Chapter 5 Probabilistic Representations -- 5.1 Stopped RandomWalk -- 5.2 Stopped Branching Process -- Part II The Sharp Peak Landscape -- Overview of Part II -- Chapter 6 Long Chain Regime -- 6.1 Genotypes and Mutations -- 6.2 Sharp Peak Fitness -- 6.3 Hamming Classes -- 6.4 Limit Equation -- Chapter 7 Error Threshold and Quasispecies -- 7.1 The Error Threshold -- 7.2 The Distribution of the Quasispecies -- Chapter 8 Probabilistic Derivation -- 8.1 Asymptotics of c* -- 8.2 Limit of the Mutant Walk Representation -- 8.3 The Poisson Random Walk -- 8.4 Formal Derivation -- Chapter 9 Summation of the Series -- 9.1 Stirling Numbers -- 9.2 Eulerian Numbers -- 9.3 Combinatorial Identities -- Chapter 10 Error Threshold in Infinite Populations -- 10.1 The Moran-Kingman Model -- 10.2 The Eigen Model -- Part III Error Threshold in Finite Populations -- Overview of Part III -- Chapter 11 Phase Transition -- 11.1 The Moran Model -- 11.2 The Wright-Fisher Model -- Chapter 12 Computer Simulations -- Chapter 13 Heuristics -- 13.1 A Simplified Process -- 13.2 A Renewal Argument -- 13.3 Persistence Time -- Chapter 14 Shape of the Critical Curve -- 14.1 Critical Curve for the Moran Model -- 14.2 Critical Curve for the Wright-Fisher Model -- Chapter 15 Framework for the Proofs -- 15.1 Candidate Limits for Moran -- 15.2 Candidate Limits for Wright-Fisher.
Part IV Proof for Wright-Fisher -- Overview of Part IV -- Chapter 16 Strategy of the Proof -- 16.1 Main Ideas -- 16.2 Invariant Probability Measure -- 16.3 Upper Bounds -- Chapter 17 The Non-Neutral Phase M -- 17.1 Large Deviations Principle -- 17.2 Perturbed Dynamical System -- 17.3 Time away from the Fixed Points -- 17.4 Reaching the Quasispecies -- 17.5 Escape from the Quasispecies -- Chapter 18 Mutation Dynamics -- 18.1 Binary Process of Differences -- 18.2 Hamming Class Dynamics -- 18.3 Time away from the Equilibrium -- 18.4 Reaching the Equilibrium -- 18.5 Escape from the Equilibrium -- Chapter 19 The Neutral Phase N -- 19.1 Ancestral Lines -- 19.2 Monotonicity and Correlations -- 19.3 Time away from the Disorder -- 19.4 Reaching the Disorder -- 19.5 Escape from the Disorder -- Chapter 20 Synthesis -- 20.1 The Quasispecies Regime -- 20.2 The Disordered Regime -- Part V Class-Dependent Fitness Landscapes -- Overview of Part V -- Chapter 21 Generalized Quasispecies Distributions -- 21.1 Class-Dependent Fitness Landscapes -- 21.2 Up-Down Coefficients -- 21.3 Re-Expansion -- Chapter 22 Error Threshold -- 22.1 Eventually Constant Fitness Functions -- 22.2 Error Threshold -- 22.3 Further Solutions -- Chapter 23 Probabilistic Representation -- 23.1 Asymptotics of Perron-Frobenius -- 23.2 Mutant Walk Representation -- 23.3 Computation of the Limit -- 23.4 Rearranging the Sums -- Chapter 24 Probabilistic Interpretations -- 24.1 Poisson Random Walk -- 24.2 The Branching Poisson Walk -- Chapter 25 Infinite Population Models -- 25.1 The Moran-Kingman Model -- 25.2 The Eigen Model -- Part VI A Glimpse at the Dynamics -- Overview of Part VI -- Chapter 26 Deterministic Level -- 26.1 The Moran-Kingman Model -- 26.2 The Eigen Model -- Chapter 27 From Finite to Infinite Population -- 27.1 From Moran's to Eigen's Model. 27.2 From Wright-Fisher's to Moran-Kingman's Model -- Chapter 28 Class-Dependent Landscapes -- 28.1 Moran Model -- 28.2 The Wright-Fisher Model -- Appendix A Markov Chains and classical results -- A.1 Monotonicity -- A.2 Construction of Markov Processes -- A.3 Lumping -- A.4 The FKG Inequality -- A.5 Hoeffding's Inequality -- References -- Index. |
Record Nr. | UNINA-9910585971003321 |
Cerf Raphaël
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Cham, Switzerland : , : Springer, , [2022] | ||
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Lo trovi qui: Univ. Federico II | ||
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