Regular Markov Chain Research Articles

Математическая модель консенсуса в группе лояльных экспертов, построенная на основании регулярных марковских цепей

Математическая модель консенсуса в группе лояльных экспертов, построенная на основании регулярных марковских цепей

The Use of Bacterial Lysate for the Prevention of Wheezing Episodes in Preschool Children: A Cost-Utility Analysis

Although increasing recent evidence has shown the efficacy of bacterial lysate therapy for the prevention of wheezing episodes and asthma exacerbations in pediatric patients, evidence of its cost-effectiveness in preschool patients is scarce. To evaluate the cost-utility of bacterial lysate therapy as an add-on to standard care of preschool children with recurrent wheezing. To achieve the objectives of the study, we used a Markov simulation model with 3 mutually exclusive nonabsorbent states (regular Markov chain). Effectiveness parameters were obtained from a recent systematic review of the literature with meta-analyses (5 randomized controlled trials, 433 children). Cost data were obtained from hospital bills and from the national manual of drug prices in Colombia. The study was carried out from the perspective of the national health care system in Colombia. The main outcome of the model was quality-adjusted life-years. To assess the robustness of the model's results, we performed deterministic and probabilistic sensitivity analysis. Compared with standard care, bacterial lysate add-on therapy to standard care was associated with lower overall treatment costs (US $694.03 vs $830.71 average cost per patient) and the greatest gain in QALYs (0.9211 vs 0.9154 QALYs on average per patient), thus showing dominance. In Colombia, compared with standard care, bacterial lysate add-on therapy to standard care for treating preschool children with recurrent wheezing is a dominant strategy because it showed a greater gain in QALYs at lower total treatment costs.

Existence and stability of azeotropes in the terminal model of multicomponent copolymerization

AbstractA simple numerical algorithm for calculating the azeotropic composition of multicomponent copolymers (if such a composition exists) is presented. The method is based on regular Markov chains in the frame of the terminal model of irreversible chain propagation in chain‐growth copolymerization. It requires as few calculations as just solving two systems of linear equations. The stability of the azeotropic composition in a batch reactor is discussed. A numerical procedure that can distinguish between a stable and an unstable azeotropic composition is proposed. © 2021 Society of Industrial Chemistry.

Leontief Meets Markov: Sectoral Vulnerabilities Through Circular Connectivity

AbstractEconomists have been aware of the mapping between an Input-Output (I-O, hereinafter) table and the adjacency matrix of a weighted digraph for several decades (Solow, Econometrica 20(1):29–46, 1952). An I-O table may be interpreted as a network in which edges measure money flows to purchase inputs that go into production, whilst vertices represent economic industries. However, only recently the language and concepts of complex networks (Newman 2010) have been more intensively applied to the study of interindustry relations (McNerney et al. Physica A Stat Mech Appl, 392(24):6427–6441, 2013). The aim of this paper is to study sectoral vulnerabilities in I-O networks, by connecting the formal structure of a closed I-O model (Leontief, Rev Econ Stat, 19(3):109–132, 1937) to the constituent elements of an ergodic, regular Markov chain (Kemeny and Snell 1976) and its chance process specification as a random walk on a graph. We provide an economic interpretation to a local, sector-specific vulnerability index based on mean first passage times, computed by means of the Moore-Penrose inverse of the asymmetric graph Laplacian (Boley et al. Linear Algebra Appl, 435(2):224–242, 2011). Traversing from the most central to the most peripheral sector of the economy in 60 countries between 2005 and 2015, we uncover cross-country salient roles for certain industries, pervasive features of structural change and (dis)similarities between national economies, in terms of their sectoral vulnerabilities.

Study of Factors Influence on the Variability of Time for Consensus Building in Coalitions Based on Regular Markov Chains

Draft standard is approved if and only if consensus of the technical committee for standardization (TC) is ensured before its approval by the standardization body at the national, regional and international level. Previously published works of authors dedicated to the construction of a mathematical model of time to build a consensus (number of negotiations) in terms of variation in the number of TC members and their level of authoritarianism. The present study is a continuation of these works for the case of the formation of coalitions in TC. The mathematical model is constructed to ensure consensus on the work of technical standardization committees in terms of coalitions, which are overcome during the negotiation process by concessions. This paper analyzes the factors, which influence the time for consensus building in this case: the value of the assignment and an index of the effect of the coalition. It is proved that the time to build a consensus signifi-cantly depends on the value of unilateral concessions coalition and weakly depends on the size of coalitions with a fixed number of TC members. Built regression model of dependence of the average number of approvals from the value of the assignment. It was revealed that even a small concession leads to the onset of consensus, increasing the size of the as-signment results (with other factors being equal) to a sharp decline in time before the consensus. It is shown that the as-signment of a larger coalition against small coalitions takes on average more time before building a consensus. The factors influencing the variability of the number of concessions were investigated. The change in the root-mean-square deviation (RMS) of the time to build a consensus varies nonlinearly from small concessions Y=10% to large Y=75%, regardless of the ratio of the number of members between coalitions. In the simulations, at concessions Y=10% there is the largest variation among the number of consensuses in the experiments. Concession of the authoritarian leader in group reduces the number of negotiations and increases the quality of consensus. The results obtained are of practical value for all structures where the emergence of coalitions entails the impossibility of consensual decision-making and requires consideration of different ways to build a consensual solution.

Asymptotic distribution of sample Shannon entropy in the case of an underlying finite, regular Markov chain.

The inference of Shannon entropy out of sample histograms is known to be affected by systematic and random errors that depend on the finite size of the available data set. This dependence was mostly investigated in the multinomial case, in which states are visited in an independent fashion. In this paper the asymptotic behavior of the distribution of the sample Shannon entropy, also referred to as plug-in estimator, is investigated in the case of an underlying finite Markov process characterized by a regular stochastic matrix. As the size of the data set tends to infinity, the plug-in estimator is shown to become asymptotically normal, though in a way that substantially deviates from the known multinomial case. The asymptotic behavior of bias and variance of the plug-in estimator are expressed in terms of the spectrum of the stochastic matrix and of the related covariance matrix. Effects of initial conditions are also considered. By virtue of the formal similarity with Shannon entropy, the results are directly applicable to the evaluation of permutation entropy.

Detecting episodes of star formation using Bayesian model selection

ABSTRACT Bayesian model comparison frameworks can be used when fitting models to data in order to infer the appropriate model complexity in a data-driven manner. We aim to use them to detect the correct number of major episodes of star formation from the analysis of the spectral energy distributions (SEDs) of galaxies, modelled after 3D-HST galaxies at z ∼ 1. Starting from the published stellar population properties of these galaxies, we use kernel density estimates to build multivariate input parameter distributions to obtain realistic simulations. We create simulated sets of spectra of varying degrees of complexity (identified by the number of parameters), and derive SED fitting results and pieces of evidence for pairs of nested models, including the correct model as well as more simplistic ones, using the bagpipes codebase with nested sampling algorithm multinest. We then ask the question: is it true – as expected in Bayesian model comparison frameworks – that the correct model has larger evidence? Our results indicate that the ratio of pieces of evidence (the Bayes factor) is able to identify the correct underlying model in the vast majority of cases. The quality of the results improves primarily as a function of the total S/N in the SED. We also compare the Bayes factors obtained using the evidence to those obtained via the Savage–Dickey density ratio (SDDR), an analytic approximation that can be calculated using samples from regular Markov Chain Monte Carlo methods. We show that the SDDR ratio can satisfactorily replace a full evidence calculation provided that the sampling density is sufficient.

Lennon vs. McCartney

In this analysis, the chord progressions used in songs by the Beatles are modelled as Markov chains to identify potential differences between songs for which John Lennon had more influence and those for which Paul McCartney had more influence. A preliminary comparison of random samples of songs from each artist did not identify noteworthy differences between Lennon and McCartney; most pieces resulted in regular Markov chains. This analysis then focusses on two songs from the Beatles – “Norwegian Wood”, primarily written by John Lennon, and “Good Day Sunshine”, primarily written by Paul McCartney – which deviated from this pattern. Similar patterns were found between the two songs despite major differences in the chords that made up each state space. In general, however, McCartney’s song had more variety in terms of the number of chords used and the paths taken between tonic chords.

Теоретическое моделирование достижения консенсуса в условиях коалиций на основе регулярных марковских цепей

Теоретическое моделирование достижения консенсуса в условиях коалиций на основе регулярных марковских цепей

Local distributions of the 1D dilute Ising model

The local distributions of the one-dimensional dilute annealed Ising model with charged impurities are studied. Explicit expressions are obtained for the pair distribution functions and correlation lengths, and their low-temperature asymptotic behavior is explored depending on the concentration of impurities. For a more detailed consideration of the ordering processes, we study local distributions. Based on the Markov property of the dilute Ising chain, we obtain an explicit expression for the probability of any finite sequence and find a geometric probability distribution for the lengths of sequences consisting of repeating blocks. An analysis of distributions shows that the critical behavior of the spin correlation length is defined by ferromagnetic or antiferromagnetic sequences, while the critical behavior of the impurity correlation length is defined by the sequences of impurities or by the charge-ordered sequences. For the dilute Ising chain, there are no other repeating sequences whose mean length diverges at zero temperature. While both the spin correlation and the impurity correlation lengths can diverge only at zero temperature, the ordering processes result in a maximum of the specific heat at finite temperature defined by the maximum rate of change of the impurity-spin pairs concentration. A simple approximate equation is found for this temperature. We show that the non-ordered dilute Ising chains correspond to the regular Markov chains, while various orderings generate the irregular Markov chains of different types.

Taiwan depository receipts forecasting along a novel regular Markov chain model

ABSTRACT This paper introduces a novel regular Markov chain model to forecast price trends in Taiwan Depository Receipts (TDRs), secondary listed companies in Taiwan. No studies of TDRs have used such a model. This research establishes a regular Markov chain model that identifies three levels: Rising more than average, rising less than average, and falling. The purpose of the proposed model is to integrate three levels of the rising quality with TDR’s settlement price on one trading day and the preceding day simultaneously. Thus, the methodology of this study is to introduce a 3*3-state regular Markov chain model, to use formulas to establish a Markov chain probability matrix, and to give a graphical representation for the proposed regular Markov chain model. The numerical result shows that, through a regular Markov chain model, the forecasting outcomes can provide investors with useful information, such as the long-term price of TDRs or whether or not the distribution of the states for the price of the TDRs will stabilize over time.

A Forgetting Property of Reciprocal Chains

Reciprocal chains (RC) are a class of discrete-index, finite-state stochastic processes with a generalized Markov nearest-neighbour property. All Markov chains (MC) are RC but not conversely. It is well known that a sufficiently regular MC “forgets” its initial distribution in a geometric manner. This article addresses the issues of forgetting for RC. Using the properties of inhomogeneous products of nonnegative matrices, this article establishes that a RC forget its endpoint distributions in a more complicated manner. In particular, this article shows that the forgetting function for the initial conditions is bounded by a superposition of increasing and decreasing geometric terms. Implications for modeling using RC are then discussed. The particular case of those RC that are MC with prescribed marginal distributions on the endpoints is considered. The tightness of the forgetting bounds is illustrated with numerical examples.

Control of consensus convergence in technical committees of standardization on the basis of regular Markov chains model

Model of activity of technical committee on standardization with established management from national body for standardization for the purposes of consensus convergence in less number of reconciliation steps is described. The model is based on regular Markov chains. It is shown that establishment of national body for standardization control for the purposes of reduction of reconciliation step number leads to replacement of some technical committee members.

An enhanced absorbing Markov chain model for predicting TAIEX Index Futures

ABSTRACTThis study introduces an enhanced absorbing Markov chain model for predicting Taiwan Stock Exchange Capitalization Weighted Stock Index Futures (TAIEX Futures) trends. Data were gathered from the U.S. TAIEX Futures Yahoo portal site and converted into a regular Markov chain model. A regular Markov chain enables long-term behavioral predictions to be made with regard to the probability of TAIEX Futures. This paper also demonstrates an artificial variable technique for establishing an enhanced absorbing Markov chain model for determining how long TAIEX Futures will increase before prices begin to fall. The results show that the TAIEX Futures absorbing Markov chain can warn investors about the least number of days on average that a particular TAIEX Futures that increased or decreased that day will increase before its price begins to fall.

COUPLING REGULAR TESSELLATION WITH RJMCMC ALGORITHM TO SEGMENT SAR IMAGE WITH UNKNOWN NUMBER OF CLASSES

This paper presents a Synthetic Aperture Radar (SAR) image segmentation approach with unknown number of classes, which is based on regular tessellation and Reversible Jump Markov Chain Monte Carlo (RJMCMC') algorithm. First of all, an image domain is portioned into a set of blocks by regular tessellation. The image is modeled on the assumption that intensities of its pixels in each homogeneous region satisfy an identical and independent Gamma distribution. By Bayesian paradigm, the posterior distribution is obtained to build the region-based image segmentation model. Then, a RJMCMC algorithm is designed to simulate from the segmentation model to determine the number of homogeneous regions and segment the image. In order to further improve the segmentation accuracy, a refined operation is performed. To illustrate the feasibility and effectiveness of the proposed approach, two real SAR image is tested.

Applying a Markov chain for the stock pricing of a novel forecasting model

ABSTRACTIn this article, a stock-forecasting model is developed to analyze a company's stock price variation related to the Taiwanese company HTC. The main difference to previous articles is that this study uses the data of the HTC in recent ten years to build a Markov transition matrix. Instead of trying to predict the stock price variation through the traditional approach to the HTC stock problem, we integrate two types of Markov chain that are used in different ways. One is a regular Markov chain, and the other is an absorbing Markov chain. Through a regular Markov chain, we can obtain important information such as what happens in the long run or whether the distribution of the states tends to stabilize over time in an efficient way. Next, we used an artificial variable technique to create an absorbing Markov chain. Thus, we used an absorbing Markov chain to provide information about the period between the increases before arriving at the decreasing state of the HTC stock. We provide investors with information on how long the HTC stock will keep increasing before its price begins to fall, which is extremely important information to them.

On the Moment-Generating Functions of Extrema and Their Complements for Almost Semicontinuous Integer-Valued Poisson Processes on Markov Chains

For an integer-valued compound Poisson process with geometrically distributed jumps of a certain sign [these processes are called almost upper (lower) semicontinuous] defined on a finite regular Markov chain, we establish relations (without projections) for the moment-generating functions of extrema and their complements. Unlike the relations obtained earlier in terms of projections, the proposed new relations for the moment-generating functions are determined by the inversion of the perturbed matrix cumulant function. These matrix relations are expressed via the moment-generating functions for the distributions of the corresponding jumps.

Исследование времени достижения консенсуса в работе технических комитетов по стандартизации на основе регулярных марковских цепей

Исследование времени достижения консенсуса в работе технических комитетов по стандартизации на основе регулярных марковских цепей

Entropy, Age and Time Operator

The time operator and internal age are intrinsic features of entropy producing innovation processes. The innovation spaces at each stage are the eigenspaces of the time operator. The internal age is the average innovation time, analogous to lifetime computation. Time operators were originally introduced for quantum systems and highly unstable dynamical systems. Extending the time operator theory to regular Markov chains allows one to relate internal age with norm distances from equilibrium. The goal of this work is to express the evolution of internal age in terms of Lyapunov functionals constructed from entropies. We selected the Boltzmann–Gibbs–Shannon entropy and more general entropy functions, namely the Tsallis entropies and the Kaniadakis entropies. Moreover, we compare the evolution of the distance of initial distributions from equilibrium to the evolution of the Lyapunov functionals constructed from norms with the evolution of Lyapunov functionals constructed from entropies. It is remarkable that the entropy functionals evolve, violating the second law of thermodynamics, while the norm functionals evolve thermodynamically.

Time operator of Markov chains and mixing times. Applications to financial data

We extend the notion of Time Operator from Kolmogorov Dynamical Systems and Bernoulli processes to Markov processes. The general methodology is presented and illustrated in the simple case of binary processes. We present a method to compute the eigenfunctions of the Time Operator. Internal Ages are related to other characteristic times of Markov chains, namely the Kemeny time, the convergence rate and Goodman’s intrinsic time. We clarified the concept of mixing time by providing analytic formulas for two-state Markov chains. Explicit formulas for mixing times are presented for any two-state regular Markov chain. The mixing time of a Markov chain is determined also by the Time Operator of the Markov chain, within its Age computation. We illustrate these results in terms of two realistic examples: A Markov chain from US GNP data and a Markov chain from Dow Jones closing prices. We propose moreover a representation for the Kemeny constant, in terms of internal Ages.