scholarly journals A probabilistic algorithm for finding the rate matrix of a block-GI/M/1 Markov chain

2004 ◽  
Vol 45 (4) ◽  
pp. 457-475 ◽  
Author(s):  
Emma Hunt
Keyword(s):  
Markov Chain ◽  
Probabilistic Algorithm ◽  
Rate Matrix ◽  
Chain Recurrence

AbstractAn efficient probabilistic algorithm is presented for the determination of the rate matrix of a block-GI/M/1 Markov chain. Recurrence of the chain is not assumed.

scholarly journals Ramaswami's duality and probabilistic algorithms for determining the rate matrix for a structured GI/M/1 Markov chain

2005 ◽  
Vol 46 (4) ◽  
pp. 485-493
Author(s):  
Emma Hunt
Keyword(s):  
Markov Chain ◽  
Fundamental Matrix ◽  
Efficient Algorithms ◽  
Death Process ◽  
Birth And Death Process ◽  
Probabilistic Algorithms ◽  
Rate Matrix

AbstractWe show that Algorithm H* for the determination of the rate matrix of a block-GI/M/1 Markov chain is related by duality to Algorithm H for the determination of the fundamental matrix of a block-M/G/1 Markov chain. Duality is used to generate some efficient algorithms for finding the rate matrix in a quasi-birth-and-death process.

Test on the Structure of Biological Sequences via Chaos Game Representation

2005 ◽  
Vol 4 (1) ◽  
Author(s):  
Peggy Cénac
Keyword(s):  
Markov Chain ◽  
Statistical Tests ◽  
Biological Sequences ◽  
Chaos Game Representation ◽  
New Family ◽  
Chaos Game ◽  
Tests For Independence ◽  
Game Representation

In this paper biological sequences are modelled by stationary ergodic sequences. A new family of statistical tests to characterize the randomness of the inputs is proposed and analyzed. Tests for independence and for the determination of the appropriate order of a Markov chain are constructed with the Chaos Game Representation (CGR), and applied to several genomes.

Exact and ordinary lumpability in finite Markov chains

1994 ◽  
Vol 31 (1) ◽  
pp. 59-75 ◽  
Author(s):  
Peter Buchholz
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Exact Determination ◽  
Finite Markov Chains

Exact and ordinary lumpability in finite Markov chains is considered. Both concepts naturally define an aggregation of the Markov chain yielding an aggregated chain that allows the exact determination of several stationary and transient results for the original chain. We show which quantities can be determined without an error from the aggregated process and describe methods to calculate bounds on the remaining results. Furthermore, the concept of lumpability is extended to near lumpability yielding approximative aggregation.

scholarly journals Planets and Stellar Activity: Hide and Seek in the CoRoT-7 system

2013 ◽  
Vol 8 (S299) ◽  
pp. 237-240
Author(s):  
R. D. Haywood ◽  
A. C. Cameron ◽  
D. Queloz ◽  
S. C. C. Barros ◽  
M. Deleuil ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Precise Determination ◽  
Photometric Data ◽  
Stellar Activity ◽  
Level Of Activity ◽  
Reliable Detection ◽  
Harmonic Decomposition ◽  
High Level

AbstractSince the discovery of the transiting Super-Earth CoRoT-7b, several investigations have been made of the number and precise masses of planets present in the system, but they all yield different results, owing to the star's high level of activity. Radial velocity (RV) variations induced by stellar activity therefore need to be modelled and removed to allow a reliable detection of all planets in the system. We re-observed CoRoT-7 in January 2012 with both HARPS and the CoRoT satellite, so that we now have the benefit of simultaneous RV and photometric data. We fitted the off-transit variations in the CoRoT lightcurve using a harmonic decomposition similar to that implemented in Queloz et al. (2009). This fit was then used to model the stellar RV contribution, according to the methods described by Aigrain et al. (2011). This model was incorporated into a Monte Carlo Markov Chain in order to make a precise determination of the orbits of CoRoT-7b and CoRoT-7c. We also assess the evidence for the presence of one or two additional planetary companions.

scholarly journals Risk Management of Pension Fund: A Model for Salary Evolution

2019 ◽  
Vol 7 (3) ◽  
pp. 44 ◽  
Author(s):  
Guglielmo D'Amico ◽  
Ada Lika ◽  
Filippo Petroni
Keyword(s):  
Risk Management ◽  
Markov Chain ◽  
Pension Fund ◽  
Balance Sheet ◽  
Pension Scheme ◽  
Large Dataset ◽  
Almost All

In this paper, we propose a semi-Markov chain to model the salary levels of participants ina pension scheme. The aim of the models is to understand the evolution in time of the salary of activeworkers in order to implement it in the construction of the actuarial technical balance sheet. It isworth mentioning that the level of the contributions in a pension scheme is directly proportional tothe incomes of the active workers; in almost all cases, it is a percentage of the worker’s incomes. As aconsequence, an adequate modeling of the salary evolution is essential for the determination of thecontributions paid to the fund and thus for the determination of the fund’s sustainability, especiallycurrently, when all jobs and salaries are subject to changes due to digitalization, ICT, innovation, etc.The model is applied to a large dataset of a real compulsory Italian pension scheme of the first pillar.The semi-Markovian hypothesis is tested, and the advantages with respect to Markov chain modelsare assessed.

scholarly journals Determination of gold, palladium and copper by flame atomic absorption spectrometry after preconcentration on silica gel modified with 3-(2-aminoethylamino)propyl group

2005 ◽  
Vol 3 (2) ◽  
pp. 252-262 ◽  
Author(s):  
Mustafa Imamoglu ◽  
Ali Aydin ◽  
Mustafa Dundar
Keyword(s):  
Silica Gel ◽  
Volume Flow Rate ◽  
Absorption Spectrometry ◽  
Rate Matrix ◽  
Modified Silica ◽  
Modified Silica Gel ◽  
Flame Atomic Absorption ◽  
Ft Ir ◽  
Preconcentration Method

AbstractA preconcentration method of gold, palladium and copper based on the sorption of Au (III), Pd (II) and Cu (II) ions on a column packed with 3-(2-aminoethylamino)propyl bonded silica gel is described. The modified silica gel was synthesized and characterized by FT-IR and C, H, N elemental analysis. At column preconcentration, the effects of parameters such as pH, volume, flow rate, matrix constituents of solutions and type of eluent on preconcentration of gold, palladium and copper were studied. The recoveries of Au (III), Pd (II) and Cu (II) were 98.93±0.51, 98.81±0.36 and 99.21±0.42 % at 95 % confidence level, respectively. The detection limits (δ) of the elements were 0.032, 0.016 and 0.012 μg ml−1, respectively. The preconcentration method was applied for determination of gold and palladium in certified reference material SARM 7B and copper in river and synthetic seawater by FAAS. Gold, palladium and copper were determined with relative error lower than 10 %.

scholarly journals Steady-State Analysis of Genetic Regulatory Networks Modelled by Probabilistic Boolean Networks

2003 ◽  
Vol 4 (6) ◽  
pp. 601-608 ◽  
Author(s):  
Ilya Shmulevich ◽  
Ilya Gluhovsky ◽  
Ronaldo F. Hashimoto ◽  
Edward R. Dougherty ◽  
Wei Zhang
Keyword(s):  
Markov Chain ◽  
Steady State ◽  
Markov Chains ◽  
Regulatory Networks ◽  
Boolean Networks ◽  
Genetic Regulatory Networks ◽  
Long Run ◽  
Probabilistic Boolean Networks

Probabilistic Boolean networks (PBNs) have recently been introduced as a promising class of models of genetic regulatory networks. The dynamic behaviour of PBNs can be analysed in the context of Markov chains. A key goal is the determination of the steady-state (long-run) behaviour of a PBN by analysing the corresponding Markov chain. This allows one to compute the long-term influence of a gene on another gene or determine the long-term joint probabilistic behaviour of a few selected genes. Because matrix-based methods quickly become prohibitive for large sizes of networks, we propose the use of Monte Carlo methods. However, the rate of convergence to the stationary distribution becomes a central issue. We discuss several approaches for determining the number of iterations necessary to achieve convergence of the Markov chain corresponding to a PBN. Using a recently introduced method based on the theory of two-state Markov chains, we illustrate the approach on a sub-network designed from human glioma gene expression data and determine the joint steadystate probabilities for several groups of genes.

A Bayesian Approach to Simulated Annealing

1989 ◽  
Vol 3 (4) ◽  
pp. 453-475 ◽  
Author(s):  
P.J.M. Van Laarhoven ◽  
C.G.E. Boender ◽  
E.H.L. Aarts ◽  
A. H. G. Rinnooy Kan
Keyword(s):  
Markov Chain ◽  
Simulated Annealing ◽  
Probability Distribution ◽  
Posterior Distribution ◽  
Prior Distribution ◽  
Numerical Experiments ◽  
Optimization Problems ◽  
Probabilistic Algorithm ◽  
Unknown Parameters ◽  
Combinatorial Optimization Problems

Simulated annealing is a probabilistic algorithm for approximately solving large combinatorial optimization problems. The algorithm can mathematically be described as the generation of a series of Markov chains, in which each Markov chain can be viewed as the outcome of a random experiment with unknown parameters (the probability of sampling a cost function value). Assuming a probability distribution on the values of the unknown parameters (the prior distribution) and given the sequence of configurations resulting from the generation of a Markov chain, we use Bayes's theorem to derive the posterior distribution on the values of the parameters. Numerical experiments are described which show that the posterior distribution can be used to predict accurately the behavior of the algorithm corresponding to the next Markov chain. This information is also used to derive optimal rules for choosing some of the parameters governing the convergence of the algorithm.

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