On convergence to diffusion processes of Markov chains related to population genetics

1979 ◽  
Vol 11 (04) ◽  
pp. 673-700
Author(s):  
Norio Okada
Keyword(s):  
Population Genetics ◽  
Markov Chain ◽  
Natural Selection ◽  
Diffusion Process ◽  
Diffusion Processes ◽  
Markov Chain Model ◽  
Asymptotic Properties ◽  
Chain Model ◽  
Selection Effects ◽  
Successive Generations

A Markov chain model related to population genetics and its convergence to a diffusion process on the multi-dimensional bounded domain are treated. We discuss the case where natural selection is random and the different selection effects over successive generations are independent. Our model is a multi-allelic version of the haploid model of Karlin and Levikson. The asymptotic properties of the limiting diffusion are stated.

On convergence to diffusion processes of Markov chains related to population genetics

1979 ◽  
Vol 11 (4) ◽  
pp. 673-700 ◽  
Author(s):  
Norio Okada
Keyword(s):  
Population Genetics ◽  
Markov Chain ◽  
Natural Selection ◽  
Diffusion Process ◽  
Diffusion Processes ◽  
Markov Chain Model ◽  
Asymptotic Properties ◽  
Chain Model ◽  
Selection Effects ◽  
Successive Generations

A Markov chain model related to population genetics and its convergence to a diffusion process on the multi-dimensional bounded domain are treated. We discuss the case where natural selection is random and the different selection effects over successive generations are independent. Our model is a multi-allelic version of the haploid model of Karlin and Levikson. The asymptotic properties of the limiting diffusion are stated.

Limit diffusions of some stepping-stone models

1983 ◽  
Vol 20 (03) ◽  
pp. 460-471 ◽  
Author(s):  
Ken-Iti Sato
Keyword(s):  
Markov Chain ◽  
Natural Selection ◽  
Infinite Number ◽  
Markov Chain Model ◽  
Chain Model ◽  
Diffusion Operator ◽  
Three Stages ◽  
Stepping Stone Models ◽  
Countably Infinite ◽  
Reproduction Stage

A Markov chain model of a population consisting of a finite or countably infinite number of colonies withNparticles at each colony is considered. There aredtypes of particle and transition from thenth generation to the (n+ 1)th is made up of three stages: reproduction, migration, and sampling. Natural selection works in the reproduction stage. The limiting diffusion operator (asN→∞) for the proportion of types at colonies is found. Convergence to the diffusion is proved under certain conditions.

Limit diffusions of some stepping-stone models

1983 ◽  
Vol 20 (3) ◽  
pp. 460-471 ◽  
Author(s):  
Ken-Iti Sato
Keyword(s):  
Markov Chain ◽  
Natural Selection ◽  
Infinite Number ◽  
Markov Chain Model ◽  
Chain Model ◽  
Diffusion Operator ◽  
Three Stages ◽  
Stepping Stone Models ◽  
Countably Infinite ◽  
Reproduction Stage

A Markov chain model of a population consisting of a finite or countably infinite number of colonies with N particles at each colony is considered. There are d types of particle and transition from the nth generation to the (n + 1)th is made up of three stages: reproduction, migration, and sampling. Natural selection works in the reproduction stage. The limiting diffusion operator (as N→∞) for the proportion of types at colonies is found. Convergence to the diffusion is proved under certain conditions.

An Efficient Markov Chain Model for the Simulation of Heterogeneous Soil Structure

2004 ◽  
Vol 68 (2) ◽  
pp. 346 ◽  
Author(s):  
Keijan Wu ◽  
Naoise Nunan ◽  
John W. Crawford ◽  
Iain M. Young ◽  
Karl Ritz
Keyword(s):  
Markov Chain ◽  
Soil Structure ◽  
Markov Chain Model ◽  
Chain Model ◽  
Heterogeneous Soil

Data Mining Technique Applied To DNA Sequencing

2015 ◽  
Vol 2 (7) ◽  
pp. 18
Author(s):  
R. Jamuna
Keyword(s):  
Data Mining ◽  
Dna Methylation ◽  
Markov Chain ◽  
Human Genome ◽  
Transition Probabilities ◽  
Markov Chain Model ◽  
Effective Means ◽  
Cpg Islands ◽  
Chain Model ◽  
The Given

CpG islands (CGIs) play a vital role in genome analysis as genomic markers.  Identification of the CpG pair has contributed not only to the prediction of promoters but also to the understanding of the epigenetic causes of cancer. In the human genome [1] wherever the dinucleotides CG occurs the C nucleotide (cytosine) undergoes chemical modifications. There is a relatively high probability of this modification that mutates C into a T. For biologically important reasons the mutation modification process is suppressed in short stretches of the genome, such as ‘start’ regions. In these regions [2] predominant CpG dinucleotides are found than elsewhere. Such regions are called CpG islands. DNA methylation is an effective means by which gene expression is silenced. In normal cells, DNA methylation functions to prevent the expression of imprinted and inactive X chromosome genes. In cancerous cells, DNA methylation inactivates tumor-suppressor genes, as well as DNA repair genes, can disrupt cell-cycle regulation. The most current methods for identifying CGIs suffered from various limitations and involved a lot of human interventions. This paper gives an easy searching technique with data mining of Markov Chain in genes. Markov chain model has been applied to study the probability of occurrence of C-G pair in the given   gene sequence. Maximum Likelihood estimators for the transition probabilities for each model and analgously for the  model has been developed and log odds ratio that is calculated estimates the presence or absence of CpG is lands in the given gene which brings in many  facts for the cancer detection in human genome.

Evaluating basketball player’s rotation line-ups performance via statistical markov chain modelling

2021 ◽  
pp. 174795412110090
Author(s):  
Pavlos Kolias ◽  
Nikolaos Stavropoulos ◽  
Alexandra Papadopoulou ◽  
Theodoros Kostakidis
Keyword(s):  
Markov Chain ◽  
Markov Chain Model ◽  
Specific Rotation ◽  
Multiple Regression Model ◽  
Chain Model ◽  
Know How ◽  
Basketball Game ◽  
Long Run ◽  
Rotation Line ◽  
Rating Category

Coaches in basketball often need to know how specific rotation line-ups perform in either offense or defense and choose the most efficient formation, according to their specific needs. In this research, a sample of 1131 ball possession phases of Greek Basket League was utilized, in order to estimate the offensive and defensive performance of each formation. Offensive and defensive ratings for each formation were calculated as a function of points scored or received, respectively, over possessions, where possessions were estimated using a multiple regression model. Furthermore, a Markov chain model was implemented to estimate the probabilities of the associated formation’s performance in the long run. The model could allow us to distinguish between overperforming and underperforming formations and revealed the probabilities over the evolution of the game, for each formation to be in a specific rating category. The results indicated that the most dominant formation, in terms of offense, is Point Guard-Point Guard-Small Forward-Power Forward-Center, while defensively schema Point Guard-Shooting Guard-Small Forward-Center-Center had the highest rating. Such results provide information, which could operate as a supplementary tool for the coach’s decisions, related to which rotation line-up patterns are mostly suitable during a basketball game.

An improved grey Markov chain model with ANN error correction and its application in gross domestic product forecasting

2021 ◽  
pp. 1-11
Author(s):  
Yuan Zou ◽  
Daoli Yang ◽  
Yuchen Pan
Keyword(s):  
Neural Network ◽  
Markov Chain ◽  
Gross Domestic Product ◽  
Error Correction ◽  
Historical Data ◽  
Markov Chain Model ◽  
Back Propagation ◽  
The United States ◽  
Domestic Product ◽  
Chain Model

Gross domestic product (GDP) is the most widely-used tool for measuring the overall situation of a country’s economic activity within a specified period of time. A more accurate forecasting of GDP based on standardized procedures with known samples available is conducive to guide decision making of government, enterprises and individuals. This study devotes to enhance the accuracy regarding GDP forecasting with given sample of historical data. To achieve this purpose, the study incorporates artificial neural network (ANN) into grey Markov chain model to modify the residual error, thus develops a novel hybrid model called grey Markov chain with ANN error correction (abbreviated as GMCM_ANN), which assembles the advantages of three components to fit nonlinear forecasting with limited sample sizes. The new model has been tested by adopting the historical data, which includes the original GDP data of the United States, Japan, China and India from 2000 to 2019, and also provides predications on four countries’ GDP up to 2022. Four models including autoregressive integrated moving average model, back-propagation neural network, the traditional GM(1,1) and grey Markov chain model are as benchmarks for comparison of the predicted accuracy and application scope. The obtained results are satisfactory and indicate superior forecasting performance of the proposed approach in terms of accuracy and universality.

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