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.

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 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.

On Perturbation Bounds for the Joint Stationary Distribution of Multivariate Markov Chain Models

2013 ◽  
Vol 3 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Wen Li ◽  
Lin Jiang ◽  
Wai-Ki Ching ◽  
Lu-Bin Cui
Keyword(s):  
Markov Chain ◽  
Stationary Distribution ◽  
Categorical Data ◽  
Markov Chain Model ◽  
Chain Model ◽  
Perturbation Bounds ◽  
Markov Chain Models ◽  
Joint Stationary Distribution ◽  
Distribution Vector ◽  
The Stability

AbstractMultivariate Markov chain models have previously been proposed in for studying dependent multiple categorical data sequences. For a given multivariate Markov chain model, an important problem is to study its joint stationary distribution. In this paper, we use two techniques to present some perturbation bounds for the joint stationary distribution vector of a multivariate Markov chain with s categorical sequences. Numerical examples demonstrate the stability of the model and the effectiveness of our perturbation bounds.

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.

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