Order Markov Chain Research Articles

SpeciateIT and vSpeciateDB: novel, fast, and accurate per sequence 16S rRNA gene taxonomic classification of vaginal microbiota

BackgroundClustering of sequences into operational taxonomic units (OTUs) and denoising methods are a mainstream stopgap to taxonomically classifying large numbers of 16S rRNA gene sequences. Environment-specific reference databases generally yield optimal taxonomic assignment.ResultsWe developed SpeciateIT, a novel taxonomic classification tool which rapidly and accurately classifies individual amplicon sequences (https://github.com/Ravel-Laboratory/speciateIT). We also present vSpeciateDB, a custom reference database for the taxonomic classification of 16S rRNA gene amplicon sequences from vaginal microbiota. We show that SpeciateIT requires minimal computational resources relative to other algorithms and, when combined with vSpeciateDB, affords accurate species level classification in an environment-specific manner.ConclusionsHerein, two resources with new and practical importance are described. The novel classification algorithm, SpeciateIT, is based on 7th order Markov chain models and allows for fast and accurate per-sequence taxonomic assignments (as little as 10 min for 107 sequences). vSpeciateDB, a meticulously tailored reference database, stands as a vital and pragmatic contribution. Its significance lies in the superiority of this environment-specific database to provide more species-resolution over its universal counterparts.

Information flow and catalytic dyad in SARS-CoV2 main protease Mpro enzyme using embedded discrete Markov chains and centrality measures

Abstract In this work, we use a network representation of the globular crystalline structure of a given protein as a graph structure with N nodes and E edges in order to analyze quantitatively the flow information and to identify key sites within the globular structure. Each node nj represents a $ C_{\alpha}^{i}$ carbon of the main backbone whereas the node’s degree ki is a measure of its physical interactions. In order to identify biologically relevant and active nodes, we compute local per residue closeness $ C_{c}(i)$, betweenness $ C_{b}(i)$ and eigenvector centralities $ C_{e}(i)$. Further analysis is done by embedding a stochastic dynamic discrete Markov chain in order to evaluate the dynamics of a set of normal random walkers (NRW’s) within the network. From this, we compute the mean first passage time matrix M and the stationary occupation probability vector ψi for each node. These two measures provide very useful information on the dynamical process embed within the $ C_{\alpha}$ network. We apply this to SARS-CoV2 Mpro main protease which is a key enzyme in the virus replication cycle. In particular, we focus our attention to the properties of the catalytic dyad integrated by His41-Cys145 in Mpro main protease since this active site has been under intense scrutiny as a pharmaceutical target. In addition, our results show the existence of additional relevant aminoacids that might play a fundamental role on signal propagation and allosteric pathways in SARS-CoV main proteases.

Forecasting Non-Metal and Rock Mineral (MBLB) Tax Revenue Using the Fuzzy Time Series Markov Chain Method in East Lombok Regency

Indonesia is one of the countries that is included in a developing countries. Therefore, the Indonesian Goverment is trying to carry out various developments in various regions. Regional development is one of the Indonesian government’s ways of achieving national goals. In carrying out regional development, of course funds are needed as the main source to support the achievement of national development. The main source of funds obtained by the Government comes from Regional Oroginal Income. One source of Regional Oroginal Income is tax. There are various types of taxes managed by the government in East Lombok Regency. One of them is the Non-Metal Minerals and Rocks, which is a tax on the extraction of non-metallic minerals and rock Tax, which is a tax on the extraction of of non-metallic minerals and rocks from natural sources within or on the surface of the earth for use. This Non-Metal and Rock Mineral tax provides quite large revenues for East Lombok district regional taxes. Non-Metal and Rock Mineral tax income is often not constant, meaning that there is an increases and there is a decreases in the amount of income. For this reason, it is necessary to forecast Non-Metal and Rock Mineral tax revenue to predict income in the future. The method used in this study is the FTS Markov Chain order 1 and order 2. Based on the MAPE indicator, the results of forecasting using the FTS Markov Chain method of order 1 amounted to Rp. 1.117.069.497 with an accuracy of 48,55% with a just good forecasting classification. While the results of forecasting using the FTS Markov Chain method of order 2 amounted to Rp.1.761.652.173 with an accuracy of 39,12% with a just good forecasting classification. If seen from the MAPE value obtained, the forecasting results using the 2nd order FTS Markov Chain are more accurate than using the 1st order Markov Chain FTS method.

Skolem and positivity completeness of ergodic Markov chains

We consider the following Markov Reachability decision problems that view Markov Chains as Linear Dynamical Systems: given a finite, rational Markov Chain, source and target states, and a rational threshold, does the probability of reaching the target from the source at the nth step: (i) equal the threshold for some n? (ii) cross the threshold for some n? (iii) cross the threshold for infinitely many n? These problems are respectively known to be equivalent to the Skolem, Positivity, and Ultimate Positivity problems for Linear Recurrence Sequences (LRS), number-theoretic problems whose decidability has been open for decades. We present an elementary reduction from LRS Problems to Markov Reachability Problems that improves the state of the art as follows. (a) We map LRS to ergodic (irreducible and aperiodic) Markov Chains that are ubiquitous, not least by virtue of their spectral structure, and (b) our reduction maps LRS of order k to Markov Chains of order k+1: a substantial improvement over the previous reduction that mapped LRS of order k to reducible and periodic Markov chains of order 4k+5. This contribution is significant in view of the fact that the number-theoretic hardness of verifying Linear Dynamical Systems can often be mitigated by spectral assumptions and restrictions on order.

Hindustani classical music revisited statistically: Does the order of Markov chain in the note dependence depend on the raga or the composition?

Rendering musical notes randomly does not create music. To generate music, there has to be a pattern which makes the musical notes dependent. It is therefore of interest to know whether the probability of the next note depends on the current note only or whether it depends on the note(s) prior to the current note. In other words, it is important to explore the orderof Markov chain in the musical piece. In the context of Hindustani classical music, does this order depend on the raga or the composition? The present work addresses this fascinating question and attempts to answer it through Akaike’s information criterion (AIC). It appears, interestingly, that the order of Markov chain is dependent on the raga which has a well defined melodic structure with fixed notes and a set of rules characterizing a particular mood that is conveyed by performance. As long as these rules are maintained, as in a raga bandish, the order of the Markov chain is invariant over the raga compositions.

Об абсолютной непрерывности меры Эрдeша для золотого сечения, числа трибоначчи и марковских цепей второго порядка

Рассматривается степенной ряд в фиксированной точке $\rho \in (0.5,1)$, где случайные коэффициенты принимают значения $0$, $1$ и образуют стационарный, эргодический и апериодический процесс. Мера Эрдeша - это закон распределения такого ряда. Задача об абсолютной непрерывности меры Эрдeша сводится к вопросу, когда соответствующая скрытая марковская цепь является марковской цепью Перри. Для золотого сечения и 1-марковских цепей мы получаем необходимые и достаточные условия абсолютной непрерывности меры Эрдeша и, используя марковские цепи Блекуэлла, даем новое доказательство того, что необходимые условия, найденные ранее (Теория вероятн. и ее примен., 51:1 (2006), 5-21), являются достаточными. Для числа трибоначчи и 1-марковских цепей получено новое доказательство теоремы о сингулярности меры Эрдeша. Для числа трибоначчи и 2-марковских цепей найдено только два случая абсолютной непрерывности.

On classification of states in higher order Markov chains

Classification of states in a Markov chain plays an important role for understanding various properties of the chain. In this paper, we introduce a scheme to classify states in a higher order Markov chain and establish some fundamental properties for each type of states. These results are developed using tensors, a natural tool for investigating higher order chains. They not only extend existing results on first order chains to higher order chains, but also shed light on some interesting new phenomena arising in the higher order case.

Tristochastic operations and products of quantum states

The notion of convolution of two probability vectors, corresponding to a coincidence experiment can be extended to a family of binary operations determined by (tri)stochastic tensors, to describe Markov chains of a higher order. The problem of associativity, commutativity, and the existence of neutral elements and inverses for such operations acting on classical states is analyzed. For a more general setup of multi-stochastic tensors, we present the characterization of their probability eigenvectors. Similar results are obtained for the quantum case: we analyze tristochastic channels, which induce binary operations defined in the space of quantum states. Studying coherifications of tristochastic tensors we propose a quantum analogue of the convolution of probability vectors defined for two arbitrary density matrices of the same size. Possible applications of this notion to construct schemes of error mitigation or building blocks in quantum convolutional neural networks are discussed.

Analysis of Program Representations Based on Abstract Syntax Trees and Higher-Order Markov Chains for Source Code Classification Task

In this paper we consider the research and development of classifiers that are trained to predict the task solved by source code. Possible applications of such task detection algorithms include method name prediction, hardware–software partitioning, programming standard violation detection, and semantic code duplication search. We provide the comparative analysis of modern approaches to source code transformation into vector-based representations that extend the variety of classification and clustering algorithms that can be used for intelligent source code analysis. These approaches include word2vec, code2vec, first-order and second-order Markov chains constructed from abstract syntax trees (AST), histograms of assembly language instruction opcodes, and histograms of AST node types. The vectors obtained with the forementioned approaches are then used to train such classification algorithms as k-nearest neighbor (KNN), support vector machine (SVM), random forest (RF), and multilayer perceptron (MLP). The obtained results show that the use of program vectors based on first-order AST-based Markov chains with an RF-based classifier leads to the highest accuracy, precision, recall, and F1 score. Increasing the order of Markov chains considerably increases the dimensionality of a vector, without any improvements in classifier quality, so we assume that first-order Markov chains are best suitable for real world applications. Additionally, the experimental study shows that first-order AST-based Markov chains are least sensitive to the used classification algorithm.

First passage times in portfolio optimization: A novel nonparametric approach

This paper introduces a portfolio optimization procedure that aims to minimize the intra-horizon (IH) risk subject to a minimum expected time to achieve a target cumulative return. To estimate the first passage probabilities and the expected time a novel nonparametric method and a new Markov chain order determination approach are developed. The optimization framework proposed allows us to include novel path-dependent measures of risk and return in the asset allocation problem. An empirical application to S&P 100 companies, a risk-free asset and stock indices is provided. Our empirical results suggest that the proposed framework exhibits more consistency between in-sample and out-of-sample performance than the mean-variance model and an alternative optimization problem that minimizes the MaxVaR measure of Boudoukh et al. (2004). Overall, the portfolio optimization approach we introduce results in higher out-of-sample annualized returns for relatively low levels of IH risk.

A Long-term Prediction of Covid-19 by Building a Transition Probability Matrix

The outbreak of the covid-19 pandemic caused a devastating scenario in the human lives for a long period of time. Since the outbreak of the pandemic, many researchers have published papers on the prediction of covid-19 using machine learning techniques, artificial intelligence, statistical techniques such as regression analysis, Markov chain models etc. In this paper a transition probability matrix is introduced by building a first order Markov chain. This first order Markov chain is built by generating sequences from the data. Later with the help of Chapman Kolmogorov theorem and ergodic theorem, higher order transition probabilities and limiting probabilities are obtained.

A multi-dimensional non-homogeneous Markov chain of order K to jointly study multi-pollutant exceedances

In this work we consider a multivariate non-homogeneous Markov chain of order K ge 0 to study the occurrences of exceedances of environmental thresholds. In the model, d ge 1 pollutants may be observed and, according to their respective environmental thresholds, a pollutant’s concentration measurement may be considered an exceedance or not. The parameters of the model are the order of the chain, and its initial and transition distributions. These parameters are estimated under the Bayesian point of view with the maximum a posteriori and leave-one-out cross validation methods used to estimate the order. In the case of the initial and transition probabilities, the estimation is made through samples generated using their respective posterior distributions. Once these parameters are obtained, we may estimate the probability of having no, one or more pollutants exceeding the associated environmental thresholds. This is made using the Markov property as well as a recurrence formula. Results are applied to the case where d = 2 which will correspond to ozone and particulate matter with diameter smaller than 10 microns (PM_{10}) measurements obtained from the Mexico City monitoring network.

A new preconditioned AOR method for solving multi-linear systems

In this paper, a new preconditioned AOR method for solving the multi-linear systems with -tensor is presented. The convergence of the new method and the corresponding comparison for the spectral radius of preconditioned iterative tensors are given. Numerical examples demonstrate that the new method is feasible and effective. As an application, we also show the efficiency of our preconditioner for solving higher order Markov chains.

A Number of look-back runs until a stopping time for higher order Markov chain

A Number of look-back runs until a stopping time for higher order Markov chain

Second Order Markov Chains with Finite Vectors Known Stationary

Second Order Markov Chains with Finite Vectors Known Stationary

Ever-reaching probabilities and mean first passage times of higher order ergodic Markov chains

Within a tensor framework, the notions of ergodicity, ever-reaching probabilities, and mean first passage times of Markov chains have recently been extended to higher order Markov chains. In this paper, we establish the relations between ergodicity of a higher order Markov chain and its ever-reaching probabilities and mean first passage times. In particular, we demonstrate the key role ergodicity plays in the existence and uniqueness of the mean first passage times. We exploit the structure of the tensor equation governing the mean first passage times and propose a block iterative algorithm and a block direct algorithm for computing these quantities. We show that ergodicity guarantees the convergence of the block iterative algorithm. Some illustrative numerical results comparing these algorithms with a brute-force direct method are also given.

Different Markov chains modulate visual stimuli processing in a Go-Go experiment in 2D, 3D, and augmented reality.

The introduction of Augmented Reality (AR) has attracted several developments, although the people's experience of AR has not been clearly studied or contrasted with the human experience in 2D and 3D environments. Here, the directional task was applied in 2D, 3D, and AR using simplified stimulus in video games to determine whether there is a difference in human answer reaction time prediction using context stimulus. Testing of the directional task adapted was also done. Research question: Are the main differences between 2D, 3D, and AR able to be predicted using Markov chains? Methods: A computer was fitted with a digital acquisition card in order to record, test and validate the reaction time (RT) of participants attached to the arranged RT for the theory of Markov chain probability. A Markov chain analysis was performed on the participants' data. Subsequently, the way certain factors influenced participants RT amongst the three tasks time on the accuracy of the participants was sought in the three tasks (environments) were statistically tested using ANOVA. Results: Markov chains of order 1 and 2 successfully reproduced the average reaction time by participants in 3D and AR tasks, having only 2D tasks with the variance predicted with the current state. Moreover, a clear explanation of delayed RT in every environment was done. Mood and coffee did not show significant differences in RTs on a simplified videogame. Gender differences were found in 3D, where endogenous directional goals are in 3D, but no gender differences appeared in AR where exogenous AR buttons can explain the larger RT that compensate for the gender difference. Our results suggest that unconscious preparation of selective choices is not restricted to current motor preparation. Instead, decisions in different environments and gender evolve from the dynamics of preceding cognitive activity can fit and improve neurocomputational models.

An improved estimator of Shannon entropy with applications to systems with memory

We investigate the memory properties of discrete sequences built upon a finite number of states. We find that the block entropy can reliably determine the memory for systems modeled as Markov chains of arbitrary finite order. Further, we provide an entropy estimator that remarkably gives accurate results when correlations are present. To illustrate our findings, we calculate the memory of daily precipitation series at different locations. Our results are in agreement with existing methods being at the same time valid in the undersampled regime and independent of model selection.

Direction and Export Performance of Coffee in India

The present study was conducted in the Department of Economics and Sociology, College of Basic Sciences and Humanities, Punjab Agricultural University, Punjab, India to examine growth performance and share of coffee in agricultural export from 2000-01 to 2016–17. The data on quantity of coffee exports from 2005-06 to 2016-17 were collected and used to examine the direction of trade and changing pattern of coffee exports with the use of first order Markov chain analysis. The top six major destinations in each type of coffee were selected for the analysis. The share of coffee in agricultural export earnings was nearly 4% in 2000-01 and decreased to 2% in 2016–17 which is a matter of great concern. The results of Markov Chain Analysis revealed that the major destinations for Indian coffee were Italy, Germany, Belgium, USA, Turkey and Slovenia. Kuwait was the most stable destination for plantation coffee exports, while in case of Arabica cherry Belgium, for Robusta parchment Italy, Germany and Spain for Robusta cherry and for Instant coffee Turkey and Russian federation were the most stable destinations. The climatic events and supply shocks remain the real threat to the development of a balanced market and sustainable conditions for the Indian coffee economy. The Government of India is expected to announce an interest subsidy scheme for exporters in order to boost coffee exports and explore new markets.

Information entropy and temperature of binary Markov chains.

We propose two different approaches for introducing the information temperature of binary Nth-order Markov chains. The first approach is based on a comparison of Markov sequences with equilibrium Ising chains at given temperatures. The second approach uses probabilities of finite-length subsequences of symbols occurring, which determine their entropies. The derivative of the entropy with respect to the energy gives the information temperature measured on the scale of introduced energy. For the case of a nearest-neighbor spin-symbol interaction, both approaches give similar results. However, the method based on the correspondence of the N-step Markov and Ising chains appears to be very cumbersome for N>3. We also introduce the information temperature for the weakly correlated one-parametric Markov chains and present results for the stepwise and power memory functions. An application of the developed method to obtain the information temperature of some literary texts is given.