Critical Population And Error Threshold On The Sharp Peak Landscape For A Moran Model
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Critical Population And Error Threshold On The Sharp Peak Landscape For A Moran Model
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Author : Raphaël Cerf
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-12-20
Critical Population And Error Threshold On The Sharp Peak Landscape For A Moran Model written by Raphaël Cerf and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-20 with Mathematics categories.
The goal of this work is to propose a finite population counterpart to Eigen's model, which incorporates stochastic effects. The author considers a Moran model describing the evolution of a population of size of chromosomes of length over an alphabet of cardinality . The mutation probability per locus is . He deals only with the sharp peak landscape: the replication rate is for the master sequence and for the other sequences. He studies the equilibrium distribution of the process in the regime where
The Quasispecies Equation And Classical Population Models
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Author : Raphaël Cerf
language : en
Publisher: Springer Nature
Release Date : 2022-07-30
The Quasispecies Equation And Classical Population Models written by Raphaël Cerf and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-30 with Mathematics categories.
This monograph studies a series of mathematical models of the evolution of a population under mutation and selection. Its starting point is the quasispecies equation, a general non-linear equation which describes the mutation-selection equilibrium in Manfred Eigen’s famous quasispecies model. A detailed analysis of this equation is given under the assumptions of finite genotype space, sharp peak landscape, and class-dependent fitness landscapes. Different probabilistic representation formulae are derived for its solution, involving classical combinatorial quantities like Stirling and Euler numbers. It is shown how quasispecies and error threshold phenomena emerge in finite population models, and full mathematical proofs are provided in the case of the Wright–Fisher model. Along the way, exact formulas are obtained for the quasispecies distribution in the long chain regime, on the sharp peak landscape and on class-dependent fitness landscapes. Finally, several other classical population models are analyzed, with a focus on their dynamical behavior and their links to the quasispecies equation. This book will be of interest to mathematicians and theoretical ecologists/biologists working with finite population models.
Critical Population And Error Threshold On The Sharp Peak Landscape For A Moran Model
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Author : Raphaël Cerf
language : en
Publisher:
Release Date : 2014
Critical Population And Error Threshold On The Sharp Peak Landscape For A Moran Model written by Raphaël Cerf and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Chromosome replication categories.
On The Differential Structure Of Metric Measure Spaces And Applications
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Author : Nicola Gigli
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-06-26
On The Differential Structure Of Metric Measure Spaces And Applications written by Nicola Gigli and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-26 with Mathematics categories.
The main goals of this paper are: (i) To develop an abstract differential calculus on metric measure spaces by investigating the duality relations between differentials and gradients of Sobolev functions. This will be achieved without calling into play any sort of analysis in charts, our assumptions being: the metric space is complete and separable and the measure is Radon and non-negative. (ii) To employ these notions of calculus to provide, via integration by parts, a general definition of distributional Laplacian, thus giving a meaning to an expression like , where is a function and is a measure. (iii) To show that on spaces with Ricci curvature bounded from below and dimension bounded from above, the Laplacian of the distance function is always a measure and that this measure has the standard sharp comparison properties. This result requires an additional assumption on the space, which reduces to strict convexity of the norm in the case of smooth Finsler structures and is always satisfied on spaces with linear Laplacian, a situation which is analyzed in detail.
Deformation Quantization For Actions Of Kahlerian Lie Groups
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Author : Pierre Bieliavsky
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-06-26
Deformation Quantization For Actions Of Kahlerian Lie Groups written by Pierre Bieliavsky and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-26 with Mathematics categories.
Let B be a Lie group admitting a left-invariant negatively curved Kählerian structure. Consider a strongly continuous action of B on a Fréchet algebra . Denote by the associated Fréchet algebra of smooth vectors for this action. In the Abelian case BR and isometric, Marc Rieffel proved that Weyl's operator symbol composition formula (the so called Moyal product) yields a deformation through Fréchet algebra structures R on . When is a -algebra, every deformed Fréchet algebra admits a compatible pre- -structure, hence yielding a deformation theory at the level of -algebras too. In this memoir, the authors prove both analogous statements for general negatively curved Kählerian groups. The construction relies on the one hand on combining a non-Abelian version of oscillatory integral on tempered Lie groups with geom,etrical objects coming from invariant WKB-quantization of solvable symplectic symmetric spaces, and, on the second hand, in establishing a non-Abelian version of the Calderón-Vaillancourt Theorem. In particular, the authors give an oscillating kernel formula for WKB-star products on symplectic symmetric spaces that fiber over an exponential Lie group.
Hyperbolic Groupoids And Duality
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Author : Volodymyr Nekrashevych
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-08-21
Hyperbolic Groupoids And Duality written by Volodymyr Nekrashevych and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-21 with Mathematics categories.
The author introduces a notion of hyperbolic groupoids, generalizing the notion of a Gromov hyperbolic group. Examples of hyperbolic groupoids include actions of Gromov hyperbolic groups on their boundaries, pseudogroups generated by expanding self-coverings, natural pseudogroups acting on leaves of stable (or unstable) foliation of an Anosov diffeomorphism, etc. The author describes a duality theory for hyperbolic groupoids. He shows that for every hyperbolic groupoid G there is a naturally defined dual groupoid G⊤ acting on the Gromov boundary of a Cayley graph of G. The groupoid G⊤ is also hyperbolic and such that (G⊤)⊤ is equivalent to G. Several classes of examples of hyperbolic groupoids and their applications are discussed.
Geometric Complexity Theory Iv Nonstandard Quantum Group For The Kronecker Problem
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Author : Jonah Blasiak
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-04-09
Geometric Complexity Theory Iv Nonstandard Quantum Group For The Kronecker Problem written by Jonah Blasiak and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-09 with Mathematics categories.
The Kronecker coefficient is the multiplicity of the -irreducible in the restriction of the -irreducible via the natural map , where are -vector spaces and . A fundamental open problem in algebraic combinatorics is to find a positive combinatorial formula for these coefficients. The authors construct two quantum objects for this problem, which they call the nonstandard quantum group and nonstandard Hecke algebra. They show that the nonstandard quantum group has a compact real form and its representations are completely reducible, that the nonstandard Hecke algebra is semisimple, and that they satisfy an analog of quantum Schur-Weyl duality.
Multiple Hilbert Transforms Associated With Polynomials
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Author : Joonil Kim
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-08-21
Multiple Hilbert Transforms Associated With Polynomials written by Joonil Kim and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-21 with Mathematics categories.
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Poincare Einstein Holography For Forms Via Conformal Geometry In The Bulk
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Author : A. Rod Gover
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-04-09
Poincare Einstein Holography For Forms Via Conformal Geometry In The Bulk written by A. Rod Gover and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-09 with Mathematics categories.
The authors study higher form Proca equations on Einstein manifolds with boundary data along conformal infinity. They solve these Laplace-type boundary problems formally, and to all orders, by constructing an operator which projects arbitrary forms to solutions. They also develop a product formula for solving these asymptotic problems in general. The central tools of their approach are (i) the conformal geometry of differential forms and the associated exterior tractor calculus, and (ii) a generalised notion of scale which encodes the connection between the underlying geometry and its boundary. The latter also controls the breaking of conformal invariance in a very strict way by coupling conformally invariant equations to the scale tractor associated with the generalised scale.
Level One Algebraic Cusp Forms Of Classical Groups Of Small Rank
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Author : Gaëtan Chenevier
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-08-21
Level One Algebraic Cusp Forms Of Classical Groups Of Small Rank written by Gaëtan Chenevier and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-21 with Mathematics categories.
The authors determine the number of level 1, polarized, algebraic regular, cuspidal automorphic representations of GLn over Q of any given infinitesimal character, for essentially all n≤8. For this, they compute the dimensions of spaces of level 1 automorphic forms for certain semisimple Z-forms of the compact groups SO7, SO8, SO9 (and G2) and determine Arthur's endoscopic partition of these spaces in all cases. They also give applications to the 121 even lattices of rank 25 and determinant 2 found by Borcherds, to level one self-dual automorphic representations of GLn with trivial infinitesimal character, and to vector valued Siegel modular forms of genus 3. A part of the authors' results are conditional to certain expected results in the theory of twisted endoscopy.