scholarly journals Transient Kinetic Proofreading

2021 ◽  
Author(s):  
G. Iyengar ◽  
M. Perry
Keyword(s):  
Markov Chain ◽  
Numerical Experiments ◽  
Markov Chain Model ◽  
Direct Consequence ◽  
Transient Behavior ◽  
Computational Time ◽  
Chain Model ◽  
Stochastic Version ◽  
Wide Range ◽  
Kinetic Proofreading

AbstractWe propose a 2-dimensional Markov chain model to understand and efficiently compute the transient behavior of the kinetic proofreading mechanism in a single T-cell. We show that a stochastic version of absolute ligand discrimination is a direct consequence of the finite number of receptors on the cell surface; thus, pointing to number control as being important for absolute ligand discrimination. We also develop 1-dimensional approximations for several limiting regimes that significantly decrease the computational time. We present results of numerical experiments that explore the behavior of the new model for a wide range of parameters, and its robustness to parameter errors.

Stochastic aspects of Lanchester's theory of warfare

2002 ◽  
Vol 39 (03) ◽  
pp. 455-465 ◽  
Author(s):  
J. F. C. Kingman
Keyword(s):  
Markov Chain ◽  
Time Reversal ◽  
Markov Chain Model ◽  
Chain Model ◽  
General Version ◽  
Urn Models ◽  
Final State ◽  
Stochastic Version ◽  
Powerful Technique ◽  
Remarkable Result

A Markov chain model for a battle between two opposing forces is formulated, which is a stochastic version of one studied by F. W. Lanchester. Solutions of the backward equations for the final state yield martingales and stopping identities, but a more powerful technique is a time-reversal analogue of a known method for studying urn models. A general version of a remarkable result of Williams and McIlroy (1998) is proved.

scholarly journals A New Improved Parsimonious Multivariate Markov Chain Model

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Chao Wang ◽  
Ting-Zhu Huang
Keyword(s):  
Markov Chain ◽  
Prediction Accuracy ◽  
Numerical Experiments ◽  
Markov Chain Model ◽  
Convergence Condition ◽  
Chain Model ◽  
Better Than

We present a new improved parsimonious multivariate Markov chain model. Moreover, we find a new convergence condition with a new variability to improve the prediction accuracy and minimize the scale of the convergence condition. Numerical experiments illustrate that the new improved parsimonious multivariate Markov chain model with the new convergence condition of the new variability performs better than the improved parsimonious multivariate Markov chain model in prediction.

scholarly journals A New Multivariate Markov Chain Model for Adding a New Categorical Data Sequence

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Chao Wang ◽  
Ting-Zhu Huang ◽  
Wai-Ki Ching
Keyword(s):  
Markov Chain ◽  
Categorical Data ◽  
Numerical Experiments ◽  
Markov Chain Model ◽  
Chain Model ◽  
Data Sequence ◽  
Computational Resources

We propose a new multivariate Markov chain model for adding a new categorical data sequence. The number of the parameters in the new multivariate Markov chain model is only𝒪(3s) less than𝒪((s+1)2)the number of the parameters in the former multivariate Markov chain model. Numerical experiments demonstrate the benefits of the new multivariate Markov chain model on saving computational resources.

Stochastic aspects of Lanchester's theory of warfare

2002 ◽  
Vol 39 (3) ◽  
pp. 455-465 ◽  
Author(s):  
J. F. C. Kingman
Keyword(s):  
Markov Chain ◽  
Time Reversal ◽  
Markov Chain Model ◽  
Chain Model ◽  
General Version ◽  
Urn Models ◽  
Final State ◽  
Stochastic Version ◽  
Powerful Technique ◽  
Remarkable Result

A Markov chain model for a battle between two opposing forces is formulated, which is a stochastic version of one studied by F. W. Lanchester. Solutions of the backward equations for the final state yield martingales and stopping identities, but a more powerful technique is a time-reversal analogue of a known method for studying urn models. A general version of a remarkable result of Williams and McIlroy (1998) is proved.

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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