Stationary distributions under mutation-selection balance: structure and properties

1996 ◽  
Vol 28 (1) ◽  
pp. 227-251 ◽  
Author(s):  
Reinhard Bürger ◽  
Immanuel M. Bomze
Keyword(s):  
Existence And Uniqueness ◽  
Probability Distributions ◽  
Semigroup Theory ◽  
Complete Characterization ◽  
Stationary Distributions ◽  
Borel Measures ◽  
Classical Models ◽  
Balance Structure

A general model for the evolution of the frequency distribution of types in a population under mutation and selection is derived and investigated. The approach is sufficiently general to subsume classical models with a finite number of alleles, as well as models with a continuum of possible alleles as used in quantitative genetics. The dynamics of the corresponding probability distributions is governed by an integro-differential equation in the Banach space of Borel measures on a locally compact space. Existence and uniqueness of the solutions of the initial value problem is proved using basic semigroup theory. A complete characterization of the structure of stationary distributions is presented. Then, existence and uniqueness of stationary distributions is proved under mild conditions by applying operator theoretic generalizations of Perron–Frobenius theory. For an extension of Kingman's original house-of-cards model, a classification of possible stationary distributions is obtained.

Stationary distributions under mutation-selection balance: structure and properties

1996 ◽  
Vol 28 (01) ◽  
pp. 227-251 ◽  
Author(s):  
Reinhard Bürger ◽  
Immanuel M. Bomze
Keyword(s):  
Existence And Uniqueness ◽  
Probability Distributions ◽  
Semigroup Theory ◽  
Complete Characterization ◽  
Stationary Distributions ◽  
Borel Measures ◽  
Classical Models ◽  
Balance Structure

A general model for the evolution of the frequency distribution of types in a population under mutation and selection is derived and investigated. The approach is sufficiently general to subsume classical models with a finite number of alleles, as well as models with a continuum of possible alleles as used in quantitative genetics. The dynamics of the corresponding probability distributions is governed by an integro-differential equation in the Banach space of Borel measures on a locally compact space. Existence and uniqueness of the solutions of the initial value problem is proved using basic semigroup theory. A complete characterization of the structure of stationary distributions is presented. Then, existence and uniqueness of stationary distributions is proved under mild conditions by applying operator theoretic generalizations of Perron–Frobenius theory. For an extension of Kingman's original house-of-cards model, a classification of possible stationary distributions is obtained.

scholarly journals The Underlying Order Induced by Orthogonality and the Quantum Speed Limit

2021 ◽  
Vol 3 (3) ◽  
pp. 376-388
Author(s):  
Francisco J. Sevilla ◽  
Andrea Valdés-Hernández ◽  
Alan J. Barrios
Keyword(s):  
Energy Spectrum ◽  
Energy Distribution ◽  
Finite Time ◽  
Complete Characterization ◽  
Comprehensive Analysis ◽  
Orthogonality Condition ◽  
Speed Limit ◽  
Physical Quantities

We perform a comprehensive analysis of the set of parameters {ri} that provide the energy distribution of pure qutrits that evolve towards a distinguishable state at a finite time τ, when evolving under an arbitrary and time-independent Hamiltonian. The orthogonality condition is exactly solved, revealing a non-trivial interrelation between τ and the energy spectrum and allowing the classification of {ri} into families organized in a 2-simplex, δ2. Furthermore, the states determined by {ri} are likewise analyzed according to their quantum-speed limit. Namely, we construct a map that distinguishes those ris in δ2 correspondent to states whose orthogonality time is limited by the Mandelstam–Tamm bound from those restricted by the Margolus–Levitin one. Our results offer a complete characterization of the physical quantities that become relevant in both the preparation and study of the dynamics of three-level states evolving towards orthogonality.

Kenoplumbomicrolite, (Pb,□)2Ta2O6[□,(OH),O], a new mineral from Ploskaya, Kola Peninsula, Russia

2018 ◽  
Vol 82 (5) ◽  
pp. 1049-1055 ◽  
Author(s):  
Daniel Atencio ◽  
Marcelo B. Andrade ◽  
Luca Bindi ◽  
Paola Bonazzi ◽  
Matteo Zoppi ◽  
...  
Keyword(s):  
Kola Peninsula ◽  
Northern Region ◽  
Complete Characterization ◽  
New Mineral ◽  
X Ray Diffraction ◽  
International Mineralogical Association ◽  
Cell Parameters ◽  
Mohs Hardness

ABSTRACTThis study presents a complete characterization of kenoplumbomicrolite, (Pb,□)2Ta2O6[□,(OH),O], occurring in an amazonite pegmatite from Ploskaya Mountain, Western Keivy Massif, Kola Peninsula, Murmanskaja Oblast, Northern Region, Russia.Kenoplumbomicrolite occurs in yellowish brown octahedral, cuboctahedral and massive crystals, up to 20 cm, has a white streak, a greasy lustre and is translucent. The Mohs hardness is ~6. Attempts to measure density (7.310–7.832 g/cm3) were affected by the ubiquitous presence of uraninite inclusions. Reflectance values were measured in air and immersed in oil. Kenoplumbocrolite is optically isotropic. The empirical formula is (Pb1.30□0.30Ca0.29Na0.08U0.03)Σ2.00(Ta0.82Nb0.62Si0.23Sn4+0.15Ti0.07Fe3+0.10Al0.01)Σ2.00O6[□0.52(OH)0.25O0.23]Σ1.00 (from the crystal used for the structural study) and (Pb1.33□0.66Mn0.01)Σ2.00(Ta0.87Nb0.72Sn4+0.18Fe3+0.11W0.08Ti0.04)Σ2.00O6[□0.80(OH)0.10O0.10]Σ1.00 (average including additional fragments). The mineral is cubic, space group Fd$\overline 3 $m. The unit-cell parameters refined from powder X-ray diffraction data are a = 10.575(2) Å and V = 1182.6(8) Å3, which are in accord with those obtained previously from a single crystal of a = 10.571(1) Å, V = 1181.3(2) Å3 and Z = 8. The mineral description and its name have been approved by the Commission on New Minerals, Nomenclature and Classification of the International Mineralogical Association (IMA2015-007a).

Quadratic-monomial generated domains from mixed signed, directed graphs

2019 ◽  
Vol 29 (02) ◽  
pp. 279-308
Author(s):  
Michael A. Burr ◽  
Drew J. Lipman
Keyword(s):  
Directed Graphs ◽  
Complete Characterization ◽  
Combinatorial Structure ◽  
Signed Directed Graph ◽  
Odd Cycle ◽  
Combinatorial Classification ◽  
Special Case ◽  
Text Condition

Determining whether an arbitrary subring [Formula: see text] of [Formula: see text] is a normal or Cohen-Macaulay domain is, in general, a nontrivial problem, even in the special case of a monomial generated domain. We provide a complete characterization of the normality, normalizations, and Serre’s [Formula: see text] condition for quadratic-monomial generated domains. For a quadratic-monomial generated domain [Formula: see text], we develop a combinatorial structure that assigns, to each quadratic monomial of the ring, an edge in a mixed signed, directed graph [Formula: see text], i.e. a graph with signed edges and directed edges. We classify the normality and the normalizations of such rings in terms of a generalization of the combinatorial odd cycle condition on [Formula: see text]. We also generalize and simplify a combinatorial classification of Serre’s [Formula: see text] condition for such rings and construct non-Cohen–Macaulay rings.

scholarly journals A Classification of Ramanujan Unitary Cayley Graphs

10.37236/478 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Andrew Droll
Keyword(s):  
Cayley Graph ◽  
Regular Graph ◽  
Adjacency Matrix ◽  
Complete Characterization ◽  
Absolute Value ◽  
Ramanujan Graph ◽  
Vertex Set ◽  
Unitary Cayley Graph

The unitary Cayley graph on $n$ vertices, $X_n$, has vertex set ${\Bbb Z}/{n\Bbb Z}$, and two vertices $a$ and $b$ are connected by an edge if and only if they differ by a multiplicative unit modulo $n$, i.e. ${\rm gcd}(a-b,n) = 1$. A $k$-regular graph $X$ is Ramanujan if and only if $\lambda(X) \leq 2\sqrt{k-1}$ where $\lambda(X)$ is the second largest absolute value of the eigenvalues of the adjacency matrix of $X$. We obtain a complete characterization of the cases in which the unitary Cayley graph $X_n$ is a Ramanujan graph.

scholarly journals Parastrophically equivalent quasigroup equations

2010 ◽  
Vol 87 (101) ◽  
pp. 39-58 ◽  
Author(s):  
Aleksandar Krapez ◽  
Dejan Zivkovic
Keyword(s):  
Functional Equations ◽  
Complete Characterization ◽  
Cubic Graphs ◽  
Quadratic Equations ◽  
Phd Thesis

Fedir M. Sokhats'kyi recently posed four problems concerning parastrophic equivalence between generalized quasigroup functional equations. Sava Krstic in his PhD thesis established a connection between generalized quadratic quasigroup functional equations and connected cubic graphs. We use this connection to solve two of Sokhats'kyi's problems, giving also complete characterization of parastrophic cancellability of quadratic equations and reducing the problem of their classification to the problem of classification of connected cubic graphs. Further, we give formulas for the number of quadratic equations with a given number of variables. Finally, we solve all equations with two variables.

scholarly journals A Complete Characterization of Projectivity for Statistical Relational Models

2020 ◽  
Author(s):  
Manfred Jaeger ◽  
Oliver Schulte
Keyword(s):  
Latent Variable ◽  
Probability Distributions ◽  
Complete Characterization ◽  
Relational Models ◽  
Lifted Inference ◽  
Relational Structures ◽  
Statistical Frequency ◽  
Exchangeable Arrays ◽  
The Given

A generative probabilistic model for relational data consists of a family of probability distributions for relational structures over domains of different sizes. In most existing statistical relational learning (SRL) frameworks, these models are not projective in the sense that the marginal of the distribution for size-n structures on induced substructures of size k<n is equal to the given distribution for size-k structures. Projectivity is very beneficial in that it directly enables lifted inference and statistically consistent learning from sub-sampled relational structures. In earlier work some simple fragments of SRL languages have been identified that represent projective models. However, no complete characterization of, and representation framework for projective models has been given. In this paper we fill this gap: exploiting representation theorems for infinite exchangeable arrays we introduce a class of directed graphical latent variable models that precisely correspond to the class of projective relational models. As a by-product we also obtain a characterization for when a given distribution over size-k structures is the statistical frequency distribution of size-k substructures in much larger size-n structures. These results shed new light onto the old open problem of how to apply Halpern et al.'s ``random worlds approach'' for probabilistic inference to general relational signatures.

On the connectedness of f-simplicial complexes

2017 ◽  
Vol 16 (01) ◽  
pp. 1750017 ◽  
Author(s):  
H. Mahmood ◽  
I. Anwar ◽  
M. A. Binyamin ◽  
S. Yasmeen
Keyword(s):  
Simplicial Complexes ◽  
Complete Characterization

In this paper, we introduce the concept of [Formula: see text]-simplicial complexes by generalizing the term of [Formula: see text]-graphs (introduced in [H. Mahmood, I. Anwar and M. K. Zafar, Construction of Cohen–Macaualy [Formula: see text]-graphs, J. Algebra Appl. 13(6) (2014) 1450012]). In particular, we discuss the problem of connectedness of pure [Formula: see text]-simplicial complexes. Moreover, we give a complete characterization of connected and disconnected [Formula: see text]-graphs and give a classification of all the disconnected [Formula: see text]-graphs.

Differentiable structures of central Cantor sets

1997 ◽  
Vol 17 (5) ◽  
pp. 1027-1042 ◽  
Author(s):  
RODRIGO BAMÓN ◽  
CARLOS G. MOREIRA ◽  
SERGIO PLAZA ◽  
JAIME VERA
Keyword(s):  
Real Line ◽  
Fractal Dimensions ◽  
Complete Characterization ◽  
Cantor Set ◽  
Cantor Sets ◽  
Local Diffeomorphisms ◽  
The Real ◽  
Global And Local

Central Cantor sets form a class of symmetric Cantor sets of the real line. Here we give a complete characterization of the $C^{k + \alpha}$ regularity of these Cantor sets. We also give a classification of central Cantor sets up to global and local diffeomorphisms. Examples of central Cantor sets with special dynamical and measure-theoretical properties are also provided. Finally, we calculate the fractal dimensions of an arbitrary central Cantor set.

Models of Functional Dependencies of Elements in Sequences for Solving Problems of Control and Management

2019 ◽  
Vol 20 (10) ◽  
pp. 579-588
Author(s):  
V. A. Tverdokhlebov
Keyword(s):  
Linear Order ◽  
Complete Characterization ◽  
Process Models ◽  
Functional Dependencies ◽  
Control Rules ◽  
Sequence Elements ◽  
Definition Of ◽  
Control And Management

In paper developed version of the basic concepts, models and methods for the formulation and solution of problems of control and diagnosing of processes in systems, tasks of constructing models of processes in which the causal relationships of events are transformed into functional dependencies between elements in sequences, problems of formalizing of process control rules, etc. For this extended classical recurrent definition of the sequences, which presents the functional elements depending on the immediately preceding to them m elements to offered Z-recurrent definition, which defines the functional relationship between sets of elements in the sequence. The orders of Z-recurrent forms have the form of a set of numbers and are convenient for accurate and complete characterization of the connections of events in processes. The tasks of control, diagnosing, constructing new models of processes, assessing the complexity of processes and rules for managing processes can be formulated and solved using numerical indicators of Z-recurrent definitions. A classification of Z-recurrent definitions of sequences and a classification of processes are constructed, an algorithm for checking the feasibility of determining a Z-recurrent form for given sequences of form is developed. The Z-recurrent definition of sequence is complemented by the Z-recurrent sequence pattern method, which includes: introducing a linear order on the base set of sequence elements, constructing an image for the sequence in the form of a sequence of executing or non-executing relationships between the elements represented by a linear order, and applying Z-recurrent definitions to the constructed image of the sequence. The problem on which the solution of the considered problems is based is the recognition of two sequences by properties, which are determined by the indicators of Z-recurrent definitions of sequences, which have the form of orders of Z-recurrent forms. Sets of orders in executing or non-executing Z-recurrent forms characterize the sequences and the analyzed sets of sequences, which allows you to set and solve problems related to system management: problems of control and diagnosing of processes in the system, problems of constructing process models, problems of formalizing and complexity estimation of control rules of processes.

Sign in / Sign up

Export Citation Format

Share Document