On dams with Markovian inputs

1973 ◽  
Vol 10 (2) ◽  
pp. 317-329 ◽  
Author(s):  
A. G. Pakes
Keyword(s):  
Markov Chain ◽  
Generating Functions ◽  
Transition Probabilities ◽  
Heavy Traffic ◽  
General Situation ◽  
Input Process ◽  
Heavy Traffic Limit ◽  
Special Cases ◽  
The Matrix ◽  
Special Case

Some recent work on discrete time dam models has been concerned with special cases in which the input process is a Markov chain whose transition probabilities, pij, are given by where A(·) and B(·) are probability generating functions (p.g.f.'s). In this paper we obtain some results for the general situation. The convergence norm of the matrix [pijxj] is found and the results are used to obtain the p.g.f. of the first emptiness time. Distributions of the dam content are obtained and conditions are found for the existence of their limits. The p.g.f. of this distribution is so complicated that its identification in any special case is extremely difficult, or even impossible. Thus useful approximations are needed; we obtain a ‘heavy traffic’ limit theorem which suggests that under certain circumstances the limiting distribution can be approximated by an exponential distribution.

On dams with Markovian inputs

1973 ◽  
Vol 10 (02) ◽  
pp. 317-329 ◽  
Author(s):  
A. G. Pakes
Keyword(s):  
Markov Chain ◽  
Generating Functions ◽  
Transition Probabilities ◽  
Heavy Traffic ◽  
General Situation ◽  
Input Process ◽  
Heavy Traffic Limit ◽  
Special Cases ◽  
The Matrix ◽  
Special Case

Some recent work on discrete time dam models has been concerned with special cases in which the input process is a Markov chain whose transition probabilities, p ij , are given by where A(·) and B(·) are probability generating functions (p.g.f.'s). In this paper we obtain some results for the general situation. The convergence norm of the matrix [p ij xj] is found and the results are used to obtain the p.g.f. of the first emptiness time. Distributions of the dam content are obtained and conditions are found for the existence of their limits. The p.g.f. of this distribution is so complicated that its identification in any special case is extremely difficult, or even impossible. Thus useful approximations are needed; we obtain a ‘heavy traffic’ limit theorem which suggests that under certain circumstances the limiting distribution can be approximated by an exponential distribution.

Some exact results for dams with Markovian inputs

1976 ◽  
Vol 13 (02) ◽  
pp. 329-337
Author(s):  
Pyke Tin ◽  
R. M. Phatarfod
Keyword(s):  
Probability Distribution ◽  
Stationary Distribution ◽  
Special Form ◽  
Geometric Distribution ◽  
Transition Probabilities ◽  
Exact Results ◽  
Input Process ◽  
Largest Eigenvalue ◽  
The Matrix ◽  
Finite Dam

In the theory of dams with Markovian inputs explicit results are not usually obtained, as the theory depends very heavily on the largest eigenvalue of the matrix (pijzj ) where p ij are the transition probabilities of the input process. In this paper we show that explicit results can be obtained if one considers an input process of a special form. The probability distribution of the time to first emptiness is obtained for both the finite and the infinite dam, as well as the stationary distribution of the dam content for the finite dam. Explicit results are given for the case where the stationary distribution of the input process has a geometric distribution.

A Markov chain associated with the minimal quasi-stationary distribution of birth–death chains

1995 ◽  
Vol 32 (01) ◽  
pp. 25-38
Author(s):  
Servet Martínez ◽  
Maria Eulália Vares
Keyword(s):  
Markov Chain ◽  
Stationary Distribution ◽  
Conditional Distribution ◽  
Transition Probabilities ◽  
The Matrix ◽  
Quasi Stationary Distribution ◽  
Birth Death

We show that if the limiting conditional distribution for an absorbed birth–death chain exists, then the chain conditioned to non-absorption converges to a Markov chain with transition probabilities given by the matrix associated with the minimal quasi-stationary distribution.

Some exact results for dams with Markovian inputs

1976 ◽  
Vol 13 (2) ◽  
pp. 329-337 ◽  
Author(s):  
Pyke Tin ◽  
R. M. Phatarfod
Keyword(s):  
Probability Distribution ◽  
Stationary Distribution ◽  
Special Form ◽  
Geometric Distribution ◽  
Transition Probabilities ◽  
Exact Results ◽  
Input Process ◽  
Largest Eigenvalue ◽  
The Matrix ◽  
Finite Dam

In the theory of dams with Markovian inputs explicit results are not usually obtained, as the theory depends very heavily on the largest eigenvalue of the matrix (pijzj) where pij are the transition probabilities of the input process. In this paper we show that explicit results can be obtained if one considers an input process of a special form. The probability distribution of the time to first emptiness is obtained for both the finite and the infinite dam, as well as the stationary distribution of the dam content for the finite dam. Explicit results are given for the case where the stationary distribution of the input process has a geometric distribution.

r-CONSECUTIVE-k-OUT-OF-n: F SYSTEMS WITH DEPENDENT COMPONENTS

2007 ◽  
Vol 14 (04) ◽  
pp. 399-410 ◽  
Author(s):  
NAMIR GHORAF
Keyword(s):  
Markov Chain ◽  
Failure Probability ◽  
Transition Probabilities ◽  
Recursive Formula ◽  
The State ◽  
Special Case ◽  
F System

An "r-consecutive-k-out-of-n: F system" consists of n linearly ordered components. The system fails if and only if at least r non-overlapping sequences of k consecutive components fail. In this paper we examine this system in the case where the failure probability of a given component depends upon the state (good or failed) of the preceding one i.e. the states of the components form a Markov chain. First we give a recursive formula of the failure probability of such a system when the transition probabilities qi,0,qi,1 are not identical where qi,0 (respectively qi,1) is the probability that component i fails given that the preceding one fails (respectively works), for i = 1, 2, …, n. Secondly we treat a special case of the same system where qj,0 = qi,0 and qj,1 = qi,1 for j = mk + i (1 ≤ i ≤ k), and we call such a system an r-consecutive-k-out-of-n: F system with cycle (or period) k with Markov-dependent components, and in this case also we give a formula of the failure probability of the system.

Occupation times for two state Markov chains

1971 ◽  
Vol 8 (02) ◽  
pp. 381-390 ◽  
Author(s):  
P. J. Pedler
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Discrete Time ◽  
Transition Probabilities ◽  
Random Variables ◽  
Time Parameter ◽  
Conditional Probabilities ◽  
Occupation Times ◽  
The Matrix ◽  
Image Position

Consider first a Markov chain with two ergodic states E 1 and E 2, and discrete time parameter set {0, 1, 2, ···, n}. Define the random variables Z 0, Z 1, Z 2, ···, Zn by then the conditional probabilities for k = 1,2,···, n, are independent of k. Thus the matrix of transition probabilities is

Occupation times for two state Markov chains

1971 ◽  
Vol 8 (2) ◽  
pp. 381-390 ◽  
Author(s):  
P. J. Pedler
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Discrete Time ◽  
Transition Probabilities ◽  
Random Variables ◽  
Time Parameter ◽  
Conditional Probabilities ◽  
Occupation Times ◽  
The Matrix ◽  
Image Position

Consider first a Markov chain with two ergodic states E1 and E2, and discrete time parameter set {0, 1, 2, ···, n}. Define the random variables Z0, Z1, Z2, ···, Znby then the conditional probabilities for k = 1,2,···, n, are independent of k. Thus the matrix of transition probabilities is

A Markov chain associated with the minimal quasi-stationary distribution of birth–death chains

1995 ◽  
Vol 32 (1) ◽  
pp. 25-38 ◽  
Author(s):  
Servet Martínez ◽  
Maria Eulália Vares
Keyword(s):  
Markov Chain ◽  
Stationary Distribution ◽  
Conditional Distribution ◽  
Transition Probabilities ◽  
The Matrix ◽  
Quasi Stationary Distribution ◽  
Birth Death

We show that if the limiting conditional distribution for an absorbed birth–death chain exists, then the chain conditioned to non-absorption converges to a Markov chain with transition probabilities given by the matrix associated with the minimal quasi-stationary distribution.

Determination of the phase structure of polymerblends by electron microscopy

1978 ◽  
Vol 36 (1) ◽  
pp. 492-493
Author(s):  
Dr. G. Kaemof
Keyword(s):  
Screw Extruder ◽  
Electron Microscopic ◽  
Thin Sections ◽  
Single Screw Extruder ◽  
Transmission Electron ◽  
The Matrix ◽  
Twin Screw ◽  
Special Case ◽  
Microscopic Investigations

A mixture of polycarbonate (PC) and styrene-acrylonitrile-copolymer (SAN) represents a very good example for the efficiency of electron microscopic investigations concerning the determination of optimum production procedures for high grade product properties.The following parameters have been varied:components of charge (PC : SAN 50 : 50, 60 : 40, 70 : 30), kind of compounding machine (single screw extruder, twin screw extruder, discontinuous kneader), mass-temperature (lowest and highest possible temperature).The transmission electron microscopic investigations (TEM) were carried out on ultra thin sections, the PC-phase of which was selectively etched by triethylamine.The phase transition (matrix to disperse phase) does not occur - as might be expected - at a PC to SAN ratio of 50 : 50, but at a ratio of 65 : 35. Our results show that the matrix is preferably formed by the components with the lower melting viscosity (in this special case SAN), even at concentrations of less than 50 %.

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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