Markovian Methods Research Articles

HSMM multi-observations for prognostics and health management

An efficient maintenance policy allows for determining the current state of a system (diagnosis phase) and its future state (prognosis phase). We show in this paper that Markovian methods allow for obtaining many efficient indicators for the expert. To characterize the quality and robustness of these methods, we compared the Hidden Semi-Markov Model (HSMM) with the Hidden Markov Model (HMM). Several learning and decoding methods were included in the competition. A real case study was used as a particularly interesting working tool. The Remaining Useful Life (RUL) has also been included in this work.

Inferring the demographic history of Japanese eel (Anguilla japonica) from genomic data: Insights for conservation and fisheries management

Abstract Assessing the status or population size of species is a key task for wildlife conservation and the sustainable management of harvested species. In particular, assessing historical changes in population size provides an evolutionary perspective on current population dynamics. Japanese eel (Anguilla japonica) is an endangered yet commercially important catadromous fish species. This article assesses the demographic history of Japanese eel using the pairwise and multiple sequentially Markovian coalescent methods. The analyses indicate a reduction in effective population size Ne from 38,000 to 10,000 individuals between 4 and 1 Mya, followed by an increase to 80,000 individuals between 1 Mya and 22–30 kya. Approximately 22–30 kya there is evidence for a reduction in Ne to approximately 60,000 individuals. These events may be related to changes in environmental conditions, especially around the last glacial maximum (19–33 kya). The results of this study suggest that Japanese eel has experienced at least two population bottlenecks, interspersed by a period of population growth. The overall level of genetic diversity is relatively low, although there is no evidence for inbreeding. Data from this study will be used to help model the extinction risk of Japanese eel.

Model Reduction Captures Stochastic Gamma Oscillations on Low-Dimensional Manifolds.

Gamma frequency oscillations (25–140 Hz), observed in the neural activities within many brain regions, have long been regarded as a physiological basis underlying many brain functions, such as memory and attention. Among numerous theoretical and computational modeling studies, gamma oscillations have been found in biologically realistic spiking network models of the primary visual cortex. However, due to its high dimensionality and strong non-linearity, it is generally difficult to perform detailed theoretical analysis of the emergent gamma dynamics. Here we propose a suite of Markovian model reduction methods with varying levels of complexity and apply it to spiking network models exhibiting heterogeneous dynamical regimes, ranging from nearly homogeneous firing to strong synchrony in the gamma band. The reduced models not only successfully reproduce gamma oscillations in the full model, but also exhibit the same dynamical features as we vary parameters. Most remarkably, the invariant measure of the coarse-grained Markov process reveals a two-dimensional surface in state space upon which the gamma dynamics mainly resides. Our results suggest that the statistical features of gamma oscillations strongly depend on the subthreshold neuronal distributions. Because of the generality of the Markovian assumptions, our dimensional reduction methods offer a powerful toolbox for theoretical examinations of other complex cortical spatio-temporal behaviors observed in both neurophysiological experiments and numerical simulations.

A practical introduction to sequentially Markovian coalescent methods for estimating demographic history from genomic data.

A common goal of population genomics and molecular ecology is to reconstruct the demographic history of a species of interest. A pair of powerful tools based on the sequentially Markovian coalescent have been developed to infer past population sizes using genome sequences. These methods are most useful when sequences are available for only a limited number of genomes and when the aim is to study ancient demographic events. The results of these analyses can be difficult to interpret accurately, because doing so requires some understanding of their theoretical basis and of their sensitivity to confounding factors. In this practical review, we explain some of the key concepts underpinning the pairwise and multiple sequentially Markovian coalescent methods (PSMC and MSMC, respectively). We relate these concepts to the use and interpretation of these methods, and we explain how the choice of different parameter values by the user can affect the accuracy and precision of the inferences. Based on our survey of 100 PSMC studies and 30 MSMC studies, we describe how the two methods are used in practice. Readers of this article will become familiar with the principles, practice, and interpretation of the sequentially Markovian coalescent for inferring demographic history.

Particularities of the Recent Evolution of Higher Education in Romania. Analysis and Forecasts

Abstract Objective: The purpose of this article is to present a brief analysis of the Romanian higher education system from the perspective of basic indicators, as well as the use of Markovian techniques for studying the evolution of the schooling process. Methodology: The descriptive statistical analysis was mainly used to visualize and synthesize the information extracted from the data on the Romanian higher education system. Markovian methods were used to study and predict the evolution of the schooling process. Findings: The rapid dynamics of the number of students in Romania in the last two decades has been accompanied by a series of structural changes, of which the most important are: a) constantly increasing the degree of feminisation of student achievements and b) increasing the relative importance of economic studies, legal studies and other social sciences, while reducing the relative importance of technical sciences and of medical-pharmaceutical studies within university specialties. Also, the distribution of the graduates’ specializations correlated to a very small extent with the requirements of economic and social activity. It can be said that the development of tertiary education in Romania was stimulated mainly by the action of factors of social and cultural nature and only at second level by the demand for qualified personnel generated by the productive apparatus. Value Added: This study highlights the current state of Romanian higher education. The fact that the evolution of tertiary education has been “explosive” over the past two decades makes some econometric methods, involving the use of stationary data or which have a high degree of complexity, more difficult to use. In this context, the use of Markovian modelling methods for studying and forecasting the evolution of the schooling process can contribute to improving access to and participation in higher education. Recommendations: In the current conjucture, when trying to increase the insertion of graduates into the labour market, it is natural for decision-makers to use various estimation methods and techniques that allow them to correlate university study programs with the needs of the labour market and at the same time provide them with scientific support for their prognosis.

Algorithm of calculation and forecasting of functional safety indicators of railway power supply systems

Acknowledgement: the authors express their personal gratitude to Prof. Igor B. Shubinsky, Doctor of Engineering, for his recommendations regarding the choice of the theoretical background that provided the foundation for the practical research, as well as hisadvice and valuable observations that contributed to this paper.Abstract. Aim. Uninterrupted transportation process is ensured by the highly dependable and safe power supply system of railway transport. In addition, the railway power supply system provides power to external consumers. A risk-oriented approach to railway transportation management requires an infrastructure risk management and safety system. The main purpose of risk management in this area is to improve the dependability and safety of railway infrastructure facilities [1, 2]. Additionally, given the growing numbers of intelligent information systems, as well as automated railway transportation management systems, the task of ensuring functional safety becomes very important. In most cases this problem is solved by introducing redundancy that is understood as an exceeding complexity of the system structure compared to the minimal values required for the performance of the specified task [3]. The simplest way of ensuring redundancy is by creating backup capabilities, particularly standby duplication within the system of functional units and components. In order to evaluate the safety of the railway transportation power supply systems it is required to calculate the functional safety indicators of their components and system as a whole taking into account the factor of redundancy. This approach will enable the optimal redundancy architectures and ensure compliance with the assigned level of general system safety. That requires taking into consideration the complex structure of the evaluated facilities: presence of diagnostics systems, right-side failures, wrong-side failures, as well as their random nature. The paper aims to develop an applied algorithm of calculation and prediction of functional safety indicators using the example of railway power supply systems that can be used in both manual and automated calculation.Methods. The power supply system evaluated for functional safety indicators is, from the functional point of view, a sequence of function implementations, while the failures of its components are random and some of them cause hazardous events. In this case, system analysis commonly involves Markovian and semi-Markovian methods, as well as graph methods. The advantage of these methods consists in the capability to evaluate the functional safety indicators of complex systems that go into many states, which is also typical for railway power supply systems.Result. This paper examines the application of graph semiMarkovian methods for calculation of stationary and non-stationary functional safety indicators for components of power supply systems taking into account redundancy and right-side failures. This algorithm allows calculating safety indicators using the example of power supply systems and includes a set of incremental actions aimed at constructing the state graph, calculation of the initial and intermediate graph factors. An example is provided of calculation of the functional safety indicators of a graph of a traction substation power transformer.

Demography and its effects on genomic variation in crop domestication.

Over two thousand plant species have been modified morphologically through cultivation and human use. Here, we review three aspects of crop domestication that are currently undergoing marked revisions, due to analytical advancements and their application to whole genome resequencing (WGS) data. We begin by discussing the duration and demographic history of domestication. There has been debate as to whether domestication occurred quickly or slowly. The latter is tentatively supported both by fossil data and application of WGS data to sequentially Markovian coalescent methods that infer the history of effective population size. This history suggests the possibility of extended human impacts on domesticated lineages prior to their purposeful cultivation. We also make the point that demographic history matters, because it shapes patterns and levels of extant genetic diversity. We illustrate this point by discussing the evolutionary processes that contribute to the empirical observation that most crops examined to date have more putatively deleterious alleles than their wild relatives. These deleterious alleles may contribute to genetic load within crops and may be fitting targets for crop improvement. Finally, the same demographic factors are likely to shape the spectrum of structural variants (SVs) within crops. SVs are known to underlie many of the phenotypic changes associated with domestication and crop improvement, but we currently lack sufficient knowledge about the mechanisms that create SVs, their rates of origin, their population frequencies and their phenotypic effects.

Comparison of Single Genome and Allele Frequency Data Reveals Discordant Demographic Histories.

Inference of demographic history from genetic data is a primary goal of population genetics of model and nonmodel organisms. Whole genome-based approaches such as the pairwise/multiple sequentially Markovian coalescent methods use genomic data from one to four individuals to infer the demographic history of an entire population, while site frequency spectrum (SFS)-based methods use the distribution of allele frequencies in a sample to reconstruct the same historical events. Although both methods are extensively used in empirical studies and perform well on data simulated under simple models, there have been only limited comparisons of them in more complex and realistic settings. Here we use published demographic models based on data from three human populations (Yoruba, descendants of northwest-Europeans, and Han Chinese) as an empirical test case to study the behavior of both inference procedures. We find that several of the demographic histories inferred by the whole genome-based methods do not predict the genome-wide distribution of heterozygosity, nor do they predict the empirical SFS. However, using simulated data, we also find that the whole genome methods can reconstruct the complex demographic models inferred by SFS-based methods, suggesting that the discordant patterns of genetic variation are not attributable to a lack of statistical power, but may reflect unmodeled complexities in the underlying demography. More generally, our findings indicate that demographic inference from a small number of genomes, routine in genomic studies of nonmodel organisms, should be interpreted cautiously, as these models cannot recapitulate other summaries of the data.

Flow-Graph and Markovian Methods for Cyber Security Analysis

A flow-graph depicts the interrelationships among cyber security and security threats/incidents (i.e., internal, external, and accidental). Using a flow-graph, the manner in which security threats may affect systems can be investigated. This paper reports analytical approaches to analyze time to security threats and probability of security threat occurrence. Considering embedded threat detection functions in a safe-guard unit, the proposed approaches use the flow-graph concept, and Markovian method to calculate time to security threat occurrence and its probability. The threat detection functions are featured by incident detection and recovery mechanisms. The results of this study can be used by all parties (public and private sector organizations, service providers, IT, and insurance companies) to better deal with cyber security issues with respect to utilizing technology, investment, and insurance. An illustrative example is demonstrated to present the application of the approach.

Uniform sampling of steady states in metabolic networks: heterogeneous scales and rounding.

The uniform sampling of convex polytopes is an interesting computational problem with many applications in inference from linear constraints, but the performances of sampling algorithms can be affected by ill-conditioning. This is the case of inferring the feasible steady states in models of metabolic networks, since they can show heterogeneous time scales. In this work we focus on rounding procedures based on building an ellipsoid that closely matches the sampling space, that can be used to define an efficient hit-and-run (HR) Markov Chain Monte Carlo. In this way the uniformity of the sampling of the convex space of interest is rigorously guaranteed, at odds with non markovian methods. We analyze and compare three rounding methods in order to sample the feasible steady states of metabolic networks of three models of growing size up to genomic scale. The first is based on principal component analysis (PCA), the second on linear programming (LP) and finally we employ the Lovazs ellipsoid method (LEM). Our results show that a rounding procedure dramatically improves the performances of the HR in these inference problems and suggest that a combination of LEM or LP with a subsequent PCA perform the best. We finally compare the distributions of the HR with that of two heuristics based on the Artificially Centered hit-and-run (ACHR), gpSampler and optGpSampler. They show a good agreement with the results of the HR for the small network, while on genome scale models present inconsistencies.

Risk of second primary malignancies in women with breast cancer: Results from the European prospective investigation into cancer and nutrition (EPIC).

Women with a diagnosis of breast cancer are at increased risk of second primary cancers, and the identification of risk factors for the latter may have clinical implications. We have followed-up for 11 years 10,045 women with invasive breast cancer from a European cohort, and identified 492 second primary cancers, including 140 contralateral breast cancers. Expected and observed cases and Standardized Incidence Ratios (SIR) were estimated using Aalen-Johansen Markovian methods. Information on various risk factors was obtained from detailed questionnaires and anthropometric measurements. Cox proportional hazards regression models were used to estimate the role of risk factors. Women with breast cancer had a 30% excess risk for second malignancies (95% confidence interval-CI 18-42) after excluding contralateral breast cancers. Risk was particularly elevated for colorectal cancer (SIR, 1.71, 95% CI 1.43-2.00), lymphoma (SIR 1.80, 95% CI 1.31-2.40), melanoma (2.12; 1.63-2.70), endometrium (2.18; 1.75-2.70) and kidney cancers (2.40; 1.57-3.52). Risk of second malignancies was positively associated with age at first cancer, body mass index and smoking status, while it was inversely associated with education, post-menopausal status and a history of full-term pregnancy. We describe in a large cohort of women with breast cancer a 30% excess of second primaries. Among risk factors for breast cancer, a history of full-term pregnancy was inversely associated with the risk of second primary cancer.

Markovian versus non-Markovian stochastic quantization of a complex-action model

We analyze the Markovian and non-Markovian stochastic quantization methods for a complex action quantum mechanical model analog to Maxwell–Chern–Simons electrodynamics in Weyl gauge. We show through analytical methods convergence to the correct equilibrium state for both methods. Introduction of a memory kernel generates a non-Markovian process which has the effect of slowing down oscillations that arise in the Langevin-time evolution towards equilibrium of complex-action problems. This feature of non-Markovian stochastic quantization might be beneficial in large-scale numerical simulations of complex action field theories on a lattice.

Performance Analysis of a Repairable Robot Safety System with Standby, Imperfect Coverage and Reboot Delay

The present study deals with a robot safety system composed of standby robot units and inbuilt safety unit. When the main operative unit fails, it is replaced by the standby robot unit available in the system. The concept of reboot delay is also incorporated in this study according to which the robot unit is rebooted if it is not successfully recovered. The recovery and reboot times of failed units, life time of the operative as well as standby units and the repair time are assumed be exponentially distributed. Furthermore, the repair time of partially-failed unit of total system failure is assumed to be arbitrarily distributed. The expressions for the state probabilities, availability, reliability and mean time to failure are derived with the help of Markovian and supplementary variable methods. The occurrence of standby units, imperfect coverage and reboot demonstrates the significant impact on the robot system reliability, availability and mean time to failure. A numerical illustration has been provided to validate the present model as well as to demonstrate the effects of various parameters on the performance measures of the robot safety system.

Stochastic Gene Expression in Cells: A Point Process Approach

This paper investigates the stochastic fluctuations of the number of copies of a given protein in a cell. This problem has already been addressed in the past, and closed-form expressions of the mean and variance have been obtained for a simplified stochastic model of the gene expression. These results have been obtained under the assumption that the durations of all the protein production steps are exponentially distributed. In such a case, a Markovian approach (via Fokker--Planck equations) is used to derive analytic formulas of the mean and the variance of the number of proteins at equilibrium. This assumption is, however, not totally satisfactory from a modeling point of view since the distribution of the duration of some steps is more likely to be Gaussian, if not almost deterministic. In such a setting, Markovian methods can no longer be used. A finer characterization of the fluctuations of the number of proteins is therefore of primary interest to understand the general economy of the cell. In this paper, we propose a new approach, based on marked Poisson point processes, which allows us to remove the exponential assumption. This is applied in the framework of the classical three-stage models of the literature: transcription, translation, and degradation. The interest of the method is shown by recovering the classical results under the assumptions that all the durations are exponentially distributed but also by deriving new analytic formulas when some of the distributions are no longer exponential. Our results show, in particular, that the exponential assumption may, surprisingly, underestimate significantly the variance of the number of proteins when some steps are, in fact, not exponentially distributed. This counterintuitive result stresses the importance of the statistical assumptions in the protein production process. Finally, our approach can also be used to consider more detailed models of the gene expression.

Non-Markovian waiting-time distribution for quantum jumps in open systems

Simulation methods based on stochastic realizations of state vector evolutions are commonly used tools to solve open quantum system dynamics, both in the Markovian and non-Markovian regime. Here, we address the question of waiting time distribution (WTD) of quantum jumps for non-Markovian systems. We generalize Markovian quantum trajectory methods in the sense of deriving an exact analytical WTD for non-Markovian quantum dynamics and show explicitly how to construct this distribution for certain commonly used quantum optical systems.

Stochastic simulation of multiple process calculi for biology

Numerous programming languages based on process calculi have been developed for biological modelling, many of which can generate potentially unbounded numbers of molecular species and reactions. As a result, such languages cannot rely on standard reaction-based simulation methods, and are generally implemented using custom stochastic simulation algorithms. As an alternative, this paper proposes a generic abstract machine that can be instantiated to simulate a range of process calculi using a range of simulation methods. The abstract machine functions as a just-in-time compiler, which dynamically updates the set of possible reactions and chooses the next reaction in an iterative cycle. We instantiate the generic abstract machine with two Markovian simulation methods and provide encodings for four process calculi: the agent-based pi-calculus, the compartment-based bioambient calculus, the rule-based kappa calculus and the domain-specific DNA strand displacement calculus. We present a generic method for proving that the encoding of an arbitrary process calculus into the abstract machine is correct, and we use this method to prove the correctness of all four calculus encodings. Finally, we demonstrate how the generic abstract machine can be used to simulate heterogeneous models in which discrete communicating sub-models are written using different domain-specific languages and then simulated together. Our approach forms the basis of a multi-language environment for the simulation of heterogeneous biological models.

二能级系统的马尔可夫与非马尔可夫方法比较

二能级系统的马尔可夫与非马尔可夫方法比较

Stabilizing simulations of complex stochastic representations for quantum dynamical systems

Path integral representations of quantum dynamics can often be formulated as stochastic differential equations (SDEs). In a series of papers, Corney and Drummond (2004 Phys. Rev. Lett. 93 260401), Deuar and Drummond (2001 Comput. Phys. Commun. 142 442–5), Drummond and Gardnier (1980 J. Phys. A: Math. Gen. 13 2353–68), Gardiner and Zoller (2004 Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics (Springer Series in Synergetics) 3rd edn (Berlin: Springer)) and Gilchrist et al (1997 Phys. Rev. A 55 3014–32) and their collaborators have derived SDEs from coherent states representations for density matrices. Computationally, these SDEs are attractive because they seem simple to simulate. They can be quite unstable, however. In this paper, we consider some of the instabilities and propose a few remedies. Particularly, because the variances of the simulated paths typically grow exponentially, the processes become de-localized in relatively short times. Hence, the issues of boundary conditions and stable integration methods become important. We use the Bose–Einstein Hamiltonian as an example. Our results reveal that it is possible to significantly extend integration times and show the periodic structure of certain functionals.

A Practitioner's Guide to Pricing and Hedging Callable Libor Exotics in Forward Libor Models

Callable Libor exotics is a class of single-currency interest-rate contracts that are Bermuda-style exercisable into underlying contracts consisting of fixed-rate, floating-rate and option legs. Bermuda swaptions, callable inverse floaters and callable range accruals are all examples of callable Libor exotics. It is commonly agreed that these instruments are best modeled using forward Libor models. There are many problems, both technical and conceptual, that arise when applying forward Libor models to callable Libor exotics. These problems span calibration, valuation and computation of risk sensitivities. This paper, to the best of our knowledge, is the first comprehensive overview of calibration, pricing and Greeks calculation techniques for callable Libor exotics in forward Libor models. Many technical results and practical methods presented in the paper are original. Others are adaptations, generalizations and extensions of known approaches. Among the technical contributions of this paper are the recommendations for basis functions for the Longstaff-Schwartz valuation algorithm, the extension of the pathwise differentiation method to callable Libor exotics and elegant Greeks formulas that result, novel smoothing techniques for Monte-Carlo, applica- tion of Markovian approximations and PDE methods to the problem of variance reduction, and practical algorithms for obtaining vegas in forward Libor models. In addition, strategies for calibrating forward Libor models for callable Libor exotics are discussed at length.

Bootstrap Methods for Time Series

SummaryThe bootstrap is a method for estimating the distribution of an estimator or test statistic by resampling one's data or a model estimated from the data. The methods that are available for implementing the bootstrap and the accuracy of bootstrap estimates depend on whether the data are an independent random sample or a time series. This paper is concerned with the application of the bootstrap to time‐series data when one does not have a finite‐dimensional parametric model that reduces the data generation process to independent random sampling. We review the methods that have been proposed for implementing the bootstrap in this situation and discuss the accuracy of these methods relative to that of first‐order asymptotic approximations. We argue that methods for implementing the bootstrap with time‐series data are not as well understood as methods for data that are independent random samples. Although promising bootstrap methods for time series are available, there is a considerable need for further research in the application of the bootstrap to time series. We describe some of the important unsolved problems.RésuméLe bootstrap est une méthode pour estimer la distribution d'un estimateur en rééchantillonnant ses données ou un modéle estiméà partir des données. Les méthodes disponibles pour mettre en oeuvre le bootstrap et la précision des estimateurs de bootstrap dépendent de ce que les données proviennent d'un échantillon aléatoire indépendant ou d'une série temporelle. Cet article concerne l'application du bootstrap aux données des séries temporelles quand on ne dispose pas de modéle paramétrique de dimension finie qui réduise le processus de génération des données à l'échantillonnage aléatoire indépendent. Nous examinons les méthodes qui ont été proposées pour mettre en oeuvre le bootstrap dans cette situation et discutons la precision de ces méthodes comparativement à celle des approximations asymptotiques de premier ordre. Nous montrons que les méthodes pour mettre en oeuvre le bootstrap avec les données des séries temporelles ne sont pas aussi bien comprises que les méthodes pour les données des échantillons aléatoires indépendants. Bien que des méthodes de bootstrap prometteuses pour les séries temporelles soient disponibles, il y a un besoin considérable de recherche supplémental re dans leur application. Nous décrivons quelques problémes importants non résolus.