Understanding the Biases of Generalised Recombination: Part I

2006 ◽  
Vol 14 (4) ◽  
pp. 411-432 ◽  
Author(s):  
Riccardo Poli ◽  
Christopher R. Stephens
Keyword(s):  
Population Model ◽  
Gene Deletion ◽  
Evolution Equations ◽  
Coarse Grained ◽  
General Notion ◽  
Schema Evolution ◽  
Infinite Population ◽  
Special Cases ◽  
Model Predictions ◽  
Hierarchical Nature

This is the first part of a two-part paper where we propose, model theoretically and study a general notion of recombination for fixed-length strings, where homologous recombination, inversion, gene duplication, gene deletion, diploidy and more are just special cases. The analysis of the model reveals that the notion of schema emerges naturally from the model's equations. In Part I, after describing and characterising the notion of generalised recombination, we derive both microscopic and coarse-grained evolution equations for strings and schemata and illustrate their features with simple examples. Also, we explain the hierarchical nature of the schema evolution equations and show how the theory presented here generalises past work in evolutionary computation. In Part II, the study provides a variety of fixed points for evolution in the case where recombination is used alone, which generalise Geiringer's theorem. In addition, we numerically integrate the infinite-population schema equations for some interesting problems, where selection and recombination are used together to illustrate how these operators interact. Finally, to assess by how much genetic drift can make a system deviate from the infinite-population-model predictions we discuss the results of real GA runs for the same model problems with generalised recombination, selection and finite populations of different sizes.

Understanding the Biases of Generalised Recombination: Part II

2007 ◽  
Vol 15 (1) ◽  
pp. 95-131 ◽  
Author(s):  
Riccardo Poli ◽  
Christopher R. Stephens
Keyword(s):  
Population Model ◽  
Gene Deletion ◽  
Evolution Equations ◽  
Coarse Grained ◽  
General Notion ◽  
Schema Evolution ◽  
Infinite Population ◽  
Special Cases ◽  
Model Predictions ◽  
Hierarchical Nature

This is the second part of a two-part paper where we propose, model theoretically and study a general notion of recombination for fixed-length strings where homologous recombination, inversion, gene duplication, gene deletion, diploidy and more are just special cases. In Part I, we derived both microscopic and coarse-grained evolution equations for strings and schemata for a selecto-recombinative GA using generalised recombination, and we explained the hierarchical nature of the schema evolution equations. In this part, we provide a variety of fixed points for evolution in the case where recombination is used alone, thereby generalising Geiringer's theorem. In addition, we numerically integrate the infinite-population schema equations for some interesting problems, where selection and recombination are used together to illustrate how these operators interact. Finally, to assess by how much genetic drift can make a system deviate from the infinite-population-model predictions we discuss the results of real GA runs for the same model problems with generalised recombination, selection and finite populations of different sizes.

scholarly journals Intrinsic Discontinuities in Solutions of Evolution Equations Involving Fractional Caputo–Fabrizio and Atangana–Baleanu Operators

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2023
Author(s):  
Christopher Nicholas Angstmann ◽  
Byron Alexander Jacobs ◽  
Bruce Ian Henry ◽  
Zhuang Xu
Keyword(s):  
Initial Value Problems ◽  
Fractional Derivatives ◽  
Evolution Equations ◽  
Integral Transform ◽  
Initial Value ◽  
Intrinsic Nature ◽  
Recent Interest ◽  
Special Cases ◽  
Singular Kernels

There has been considerable recent interest in certain integral transform operators with non-singular kernels and their ability to be considered as fractional derivatives. Two such operators are the Caputo–Fabrizio operator and the Atangana–Baleanu operator. Here we present solutions to simple initial value problems involving these two operators and show that, apart from some special cases, the solutions have an intrinsic discontinuity at the origin. The intrinsic nature of the discontinuity in the solution raises concerns about using such operators in modelling. Solutions to initial value problems involving the traditional Caputo operator, which has a singularity inits kernel, do not have these intrinsic discontinuities.

scholarly journals THE IDEAL DISTRIBUTION OF FARMERS: EXPLAINING THE EURO-AMERICAN SETTLEMENT OF UTAH

2017 ◽  
Vol 83 (1) ◽  
pp. 75-90 ◽  
Author(s):  
Peter M. Yaworsky ◽  
Brian F. Codding
Keyword(s):  
Population Density ◽  
Ideal Free Distribution ◽  
Negative Relationship ◽  
Coarse Grained ◽  
Distribution Model ◽  
Test Model ◽  
Fine Grained ◽  
Fine Grain ◽  
Model Predictions ◽  
The Ideal

Explaining how and why populations settle a new landscape is central to many questions in American archaeology. Recent advances in settlement research have adopted predictions from the Ideal Free Distribution model (IFD). While tests of IFD predictions to date rely either on archaeologically derived coarse-grained diachronic data or ethnographically derived fine-grained synchronic data, here we provide the first test using historically derived data that is both fine-grained and diachronic. Fine-grain diachronic data allow us to test model predictions at a temporal scale in line with human settlement decisions and to validate proxies for application in archaeological contexts. To test model predictions pertaining to the relationship between population density and habitat quality, we use data from the historical settlement of Utah. The results demonstrate a negative relationship between population density and the quality of habitats occupied. These results are consistent with IFD predictions, suggesting that Euro-American settlement of Utah resulted from individuals attempting to maximize individual returns via agricultural productivity. Our results provide a quantitative and testable explanation for population dispersion over time and explain the spatial distribution of population density today. The results support predictions derived from a general theory of behavior, providing an explanatory framework for colonization events worldwide.

scholarly journals Generalizations of 3-Sasakian manifolds and skew torsion

2020 ◽  
Vol 20 (3) ◽  
pp. 331-374 ◽  
Author(s):  
Ilka Agricola ◽  
Giulia Dileo
Keyword(s):  
Ricci Curvature ◽  
General Notion ◽  
Heisenberg Groups ◽  
Canonical Connection ◽  
Contact Metric Manifolds ◽  
Special Cases ◽  
Commutator Function ◽  
Killing Function ◽  
Generalized Killing Spinors ◽  
Sasaki Manifolds

AbstractIn the first part, we define and investigate new classes of almost 3-contact metric manifolds, with two guiding ideas in mind: first, what geometric objects are best suited for capturing the key properties of almost 3-contact metric manifolds, and second, the new classes should admit ‘good’ metric connections with skew torsion. In particular, we introduce the Reeb commutator function and the Reeb Killing function, we define the new classes of canonical almost 3-contact metric manifolds and of 3-(α, δ)-Sasaki manifolds (including as special cases 3-Sasaki manifolds, quaternionic Heisenberg groups, and many others) and prove that the latter are hypernormal, thus generalizing a seminal result of Kashiwada. We study their behaviour under a new class of deformations, called 𝓗-homothetic deformations, and prove that they admit an underlying quaternionic contact structure, from which we deduce the Ricci curvature. For example, a 3-(α, δ)-Sasaki manifold is Einstein either if α = δ (the 3-α-Sasaki case) or if δ = (2n + 3)α, where dim M = 4n + 3.In the second part we find these adapted connections. We start with a very general notion of φ-compatible connections, where φ denotes any element of the associated sphere of almost contact structures, and make them unique by a certain extra condition, thus yielding the notion of canonical connection (they exist exactly on canonical manifolds, hence the name). For 3-(α, δ)-Sasaki manifolds, we compute the torsion of this connection explicitly and we prove that it is parallel, we describe the holonomy, the ∇-Ricci curvature, and we show that the metric cone is a HKT-manifold. In dimension 7, we construct a cocalibrated G2-structure inducing the canonical connection and we prove the existence of four generalized Killing spinors.

scholarly journals Mixed self and random mating at two loci

1973 ◽  
Vol 21 (3) ◽  
pp. 247-262 ◽  
Author(s):  
B. S. Weir ◽  
C. Clark Cockerham
Keyword(s):  
Mating System ◽  
Arbitrary Number ◽  
Random Mating ◽  
Constant Amount ◽  
Infinite Population ◽  
Special Cases

SUMMARYAn infinite population practising a constant amount of selfing and random mating is studied. The effects of the mating system on two linked loci with an arbitrary number of neutral alleles are determined. Expressions are obtained for the two-locus descent measure, and hence genotypic frequencies and disequilibria functions, in any generation. The nature of the equilibrium population is deduced. The special cases of pure selfing or pure random mating and completely linked or completely unlinked loci are considered separately.

Constitutive Modeling of Polymer Films From Viscoelasticity to Viscoplasticity

1998 ◽  
Vol 120 (2) ◽  
pp. 145-149 ◽  
Author(s):  
Z. Qian ◽  
M. Lu ◽  
S. Liu
Keyword(s):  
Polymer Films ◽  
Constitutive Modeling ◽  
Evolution Equations ◽  
Small Deformation ◽  
Back Stress ◽  
Deformation Mechanisms ◽  
Master Curves ◽  
Model Predictions ◽  
Polycarbonate Film ◽  
Good Agreement

A unified constitutive model for polymer films is proposed with viscoelastic characterization at small deformation and viscoplastic characterization at large deformation based on molecular chain deformation mechanisms. The evolution equations and the temperature dependence of drag stress and back stress are established from molecular network theories in this paper. The material constants are then determined by master curves and a consistent procedure. A good agreement between the experimental data of polycarbonate film tests and model predictions is achieved.

Exact solutions for scalar field cosmology in f(R) gravity

2017 ◽  
Vol 32 (30) ◽  
pp. 1750164 ◽  
Author(s):  
S. D. Maharaj ◽  
R. Goswami ◽  
S. V. Chervon ◽  
A. V. Nikolaev
Keyword(s):  
Scalar Field ◽  
Exact Solutions ◽  
Scalar Curvature ◽  
Evolution Equations ◽  
Initial Conditions ◽  
De Sitter ◽  
Airy Functions ◽  
Special Cases ◽  
The Universe ◽  
Current Stage

We study scalar field FLRW cosmology in the content of f(R) gravity. Our consideration is restricted to the spatially flat Friedmann universe. We derived the general evolution equations of the model, and showed that the scalar field equation is automatically satisfied for any form of the f(R) function. We also derived representations for kinetic and potential energies, as well as for the acceleration in terms of the Hubble parameter and the form of the f(R) function. Next we found the exact cosmological solutions in modified gravity without specifying the f(R) function. With negligible acceleration of the scalar curvature, we found that the de Sitter inflationary solution is always attained. Also we obtained new solutions with special restrictions on the integration constants. These solutions contain oscillating, accelerating, decelerating and even contracting universes. For further investigation, we selected special cases which can be applied with early or late inflation. We also found exact solutions for the general case for the model with negligible acceleration of the scalar curvature in terms of special Airy functions. Using initial conditions which represent the universe at the present epoch, we determined the constants of integration. This allows for the comparison of the scale factor in the new solutions with that for current stage of the universe evolution in the [Formula: see text]CDM model.

scholarly journals Dynamic Memory De-allocation in Fortran 95/2003 Derived Type Calculus

2005 ◽  
Vol 13 (3) ◽  
pp. 189-203 ◽  
Author(s):  
Damian W.I. Rouson ◽  
Karla Morris ◽  
Xiaofeng Xu
Keyword(s):  
Evolution Equations ◽  
Differential Operators ◽  
Coarse Grained ◽  
State Variables ◽  
Abstract Data Types ◽  
Data Types ◽  
Levels Of Abstraction ◽  
Dynamic Memory ◽  
Abstract Data ◽  
Intermediate Results

Abstract data types developed for computational science and engineering are frequently modeled after physical objects whose state variables must satisfy governing differential equations. Generalizing the associated algebraic and differential operators to operate on the abstract data types facilitates high-level program constructs that mimic standard mathematical notation. For non-trivial expressions, multiple object instantiations must occur to hold intermediate results during the expression's evaluation. When the dimension of each object's state space is not specified at compile-time, the programmer becomes responsible for dynamically allocating and de-allocating memory for each instantiation. With the advent of allocatable components in Fortran 2003 derived types, the potential exists for these intermediate results to occupy a substantial fraction of a program's footprint in memory. This issue becomes particularly acute at the highest levels of abstraction where coarse-grained data structures predominate. This paper proposes a set of rules for de-allocating memory that has been dynamically allocated for intermediate results in derived type calculus, while distinguishing that memory from more persistent objects. The new rules are applied to the design of a polymorphic time integrator for integrating evolution equations governing dynamical systems. Associated issues of efficiency and design robustness are discussed.

Inertial effects in time-dependent motion of thin films and drops

2002 ◽  
Vol 467 ◽  
pp. 1-17 ◽  
Author(s):  
L. M. HOCKING ◽  
S. H. DAVIS
Keyword(s):  
Thin Films ◽  
Contact Angle ◽  
Contact Line ◽  
Evolution Equations ◽  
Liquid Films ◽  
Contact Angles ◽  
Terminal State ◽  
Lubrication Theory ◽  
Plate Motion ◽  
Special Cases

Capillarity is an important feature in controlling the spreading of liquid drops and in the coating of substrates by liquid films. For thin films and small contact angles, lubrication theory enables the analysis of the motion to be reduced to single evolution equations for the heights of the drops or films, provided the inertia of the liquid can be neglected. In general, the presence of inertia destroys the major simplification provided by lubrication theory, but two special cases that can be treated are identified here. In the first example, the approach of a drop to its equilibrium position is studied. For sufficiently low Reynolds numbers, the rate of approach to the terminal state and the contact angle are slightly reduced by inertia, but, above a critical Reynolds number, the approach becomes oscillatory. In the latter case there is no simple relation connecting the dynamic contact angle and contact-line speed. In the second example, the spreading drop is supported by a plate that is forced to oscillate in its own plane. For the parameter range considered, the mean spreading is unaffected by inertia, but the oscillatory motion of the contact line is reduced in magnitude as inertia increases, and the drop lags behind the plate motion. The oscillatory contact angle increases with inertia, but is not in phase with the plate oscillation.

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