Markovian Method Research Articles

Markovian Approach for Exploring Competitive Diseases with Heterogeneity-Evidence from COVID-19 and Influenza in China.

Due to the complex interactions between multiple infectious diseases, the spreading of diseases in human bodies can vary when people are exposed to multiple sources of infection at the same time. Typically, there is heterogeneity in individuals' responses to diseases, and the transmission routes of different diseases also vary. Therefore, this paper proposes an SIS disease spreading model with individual heterogeneity and transmission route heterogeneity under the simultaneous action of two competitive infectious diseases. We derive the theoretical epidemic spreading threshold using quenched mean-field theory and perform numerical analysis under the Markovian method. Numerical results confirm the reliability of the theoretical threshold and show the inhibitory effect of the proportion of fully competitive individuals on epidemic spreading. The results also show that the diversity of disease transmission routes promotes disease spreading, and this effect gradually weakens when the epidemic spreading rate is high enough. Finally, we find a negative correlation between the theoretical spreading threshold and the average degree of the network. We demonstrate the practical application of the model by comparing simulation outputs to temporal trends of two competitive infectious diseases, COVID-19 and seasonal influenza in China.

A fast Markovian method for modeling channel noise in neurons

Channel noise results from rapid transitions of protein channels from closed to open state and is generally considered as the most dominant source of electrical noise causing membrane-potential fluctuations even in the absence of synaptic inputs. The simulation of a realistic channel noise remains a source of possible error. Although the Markovian method is considered as the golden standard for appropriate description of channel noise, its computation time increasing exponentially with the number of channels, it is poorly suitable to simulate realistic features. We describe here a novel algorithm at discrete time unit for simulating ion channel noise based on Markov chains (MC). Although this new algorithm refers to a Monte-Carlo process, it only needs few random numbers whatever the number of channels involved. Our fast MC (FMC) model does not exhibit the drawbacks due to approximations based on stochastic differential equations and the values of spike jitter are comparable to those obtained with the true Markovian method. In fact, we show here, that these drawbacks can be highlighted in the approximation based on stochastic differential equation methods even for a high number of channels (standard deviation of the 5th spike is about two-fold larger than that of MCF or true Markovian method for 5000 sodium channels). The FMC model appears therefore as the most accurate method to simulate channel noise with a fast execution time that does not depend on the channel number.

System reliability-redundancy optimization with cold-standby strategy by fitness-distance balance stochastic fractal search algorithm

Reliability-redundancy allocation problem (RRAP) is an interesting subject in the field of reliability engineering that attracted attention of many researchers. RRAP tries to maximize the system reliability while creating a tradeoff between the component reliability and level of redundancy for each subsystem. Early studies in the cold-standby strategy used the lower bound formula to estimate the system reliability. But in this paper, a newly introduced Markovian process-based approach is applied for calculating the exact reliability values of cold-standby systems with the imperfect switching system. A newly developed evolutionary algorithm called fitness-distance balance stochastic fractal search is adjusted for solving the RRAP as an NP-hard optimization model, and the obtained results are compared with other counterparts by using numerical examples on three well-known benchmark problems. Finally, to justify the performance of the applied Markovian method in practical viewpoint, a pump system with non-identical components in a chemical plant is analysed as a real-world case study.

On the safety assessment of an automatic train operation system

The paper examines the automatic train operation system as part of the locomotive control and protection system, the remote supervision centre’s means for control of onboard and trackside machine vision facilities. The focus is on the dependence of the system’s safety and dependability on the dependability characteristics of its components and adverse weather effects. The criteria of a system’s wrong-side and right-side failures were defined, the graph models were constructed of the safety and dependability states of an automatic train operation system. The Markovian graph method of calculating the safety and dependability of complex systems was substantiated. That allowed defining such key safety indicators of an automatic train operation system as the mean time to wrong-side failure, probability of wrong-side failure, wrong-side failure rate. The study established that the safety of an automatic train operation system primarily depends on the dependability of machine vision facilities. The growth of the system’s wrong-side failure rate is limited to half the failure rate of machine vision facilities. It was also established that the dependability of an automatic train operation system is defined by the failure rate of a locomotive control and protection system and the failure rate of machine vision facilities. The conducted analysis allows concluding that in order to achieve an acceptable level of safety of an automatic train operation system, efforts should focus on machine vision redundancy, ensuring the SIL4 functional safety of on-board and trackside machine vision facilities, as well as regular comparison of the outputs of on-board and trackside machine vision facilities, redundant output comparison, integration of the outputs in motion. Additionally, adverse weather effects are to be countered by improving the efficiency of machine learning of the machine vision software.

Estimation of the failure flow of a set of passenger car doors

An estimation of the failure flows is a prerequisite for the operation of industrial products. It is based on statistical data about failures that occur within technical items in the process of their operation. In the technical product documentation, this indicator shall be featured in the “Dependability parameter estimation” section. The dependability analysis of rolling stock is still affected by the difficulty of defining the methodology for evaluating this parameter at various system levels. For the purpose of analysing a multicomponent system, a reliability block diagram should be developed, and the possible replacement (redundant) elements should be taken into consideration. Multicomponent systems are often represented through various block diagrams, where, among others, the “m-out-of-n” structure may be used referring to a system with a parallel arrangement of elements that is operable when at least m elements operate. An example of such system is a set of passenger car doors. The manufacturers and customers may have different approaches to calculating technical system dependability. First, the required dependability indicator for the entire train is defined that, in turn, defines the dependability requirements for a car. At the same time, the dependability indicator for a car is determined by the respective values of its components (subsystems, units and parts). However, the nature of the relationship between a car and its components is not always taken into account. At the same time, car manufacturers can and should define in the regulatory documentation (and later supervise in operation) the dependability indicators for a set of doors (components of a car in our case) as a single system. However, the failure criteria of a set of doors are not always defined. This paper examines the method of calculating the failure flow for a set of passenger car doors based on operational data and the failure flow of a single door. Aim. To propose a method for calculating the failure flow of a set of 6 car doors by analysing the possible reliability block diagrams with subsequent transition to transition and state graphs.Conclusions. A number of block diagrams were developed for the purpose of dependability calculation of sets of passenger car doors based on the system failure criterion. The failure flow of a set of car doors was calculated according to the developed block diagrams. It is concluded that the Markovian method of calculating the failure flow is of higher priority than the logic-and-probability approach, since it takes into account the recovery factor. A Markovian method was proposed for calculating the failure flow and recovery time of a set of car doors for the “3-out-of-4” reliability block diagram.

Option Pricing with Markov Switching

In this article, we consider a model of time-varying volatility which generalizes the classical Black-Scholes model to include regime-switching properties. Specically, the unobservable state variables for stock uctu- ations are modeled by a Markov process, and the drift and volatility pa- rameters take dierent values depending on the state of this hidden Markov process. We provide a closed-form formula for the arbitrage-free price of the European call option, when the hidden Markov process has nite number of states. Two simulation methods, the discrete diusion method and the Markovian tree method, for computing the European call option price are presented for comparison.

Kernel-based prediction of non-Markovian time series

A nonparametric method to predict non-Markovian time series of partially observed dynamics is developed. The prediction problem we consider is a supervised learning task of finding a regression function that takes a delay-embedded observable to the observable at a future time. When delay-embedding theory is applicable, the proposed regression function is a consistent estimator of the flow map induced by the delay-embedding. Furthermore, the corresponding Mori–Zwanzig equation governing the evolution of the observable simplifies to only a Markovian term, represented by the regression function. We realize this supervised learning task with a class of kernel-based linear estimators, the kernel analog forecast (KAF), which are consistent in the limit of large data. In a scenario with a high-dimensional covariate space, we employ a Markovian kernel smoothing method which is computationally cheaper than the Nyström projection method for realizing KAF. In addition to the guaranteed theoretical convergence, we numerically demonstrate the effectiveness of this approach on higher-dimensional problems where the relevant kernel features are difficult to capture with the Nyström method. Given noisy training data, we propose a nonparametric smoother as a de-noising method. Numerically, we show that the proposed smoother is more accurate than EnKF and 4Dvar in de-noising signals corrupted by independent (but not necessarily identically distributed) noise, even if the smoother is constructed using a data set corrupted by white noise. We show skillful prediction using the KAF constructed from the denoised data.

Transient Quality Performance Evaluation of Multi-stage Flexible Manufacturing Systems

This paper aims at evaluation of the quality performance of multi-stage manufacturing system during transients. A Markovian method is constructed in order to evaluate transient propagation of quality at multi-stage manufacturing systems which have remote quality information feedback. With the derived Markovian model, analytical expressions of estimating quality metrics in transients are provided, such as settling time and dynamical quality. Case study at a factory is given to demonstrate the derived approach. The conclusions drawn illustrate the applicability of transient quality evaluation of multi-stage systems.

Toward Simulation and Risk Assessment of Weather-Related Outages

Weather and environmental factors have played significant roles in historical major outages and blackouts in interconnected power systems and should be considered in simulation and risk assessment of outages. This paper proposes a method for the risk assessment of weather-related outages. An outage rate model considering weather conditions and line conductor temperatures is proposed based on the analysis of historical outage records and weather-dependent outage mechanisms of power lines. Accordingly, an analytical form of line outage probabilities is derived. Then the risk assessment is implemented based on a Markovian tree search method. The influences of different weather and environmental factors on the outage rates are tested and analyzed on an example line segment model. The effectiveness of the risk assessment method is demonstrated on an NPCC 140-bus system model with winter and summer scenarios.

Nonlinear turbulent parallel momentum transport due to blobs

The nonlinear flux term induced by blobs is derived by using an eddy damped quasi-normal Markovian method in a three dimensional Hasegawa–Wakatani system with a strong non-adiabatic assumption. It is shown that the nonlinear flux is comparable to the quasilinear flux in the case of mixing level turbulence and can become dominant in strong turbulence regimes such as blobs. Moreover, when strong non-adiabatic or strong parallel flow shear conditions are considered, for radially elongated blobs or streamers, nonlinear residual flux can provide the opposite parallel momentum flux to the quasilinear flux and negative nonlinear diffusivity, which introduces inward momentum flux, so that rotation in the edge region is possibly reversed and momentum is convected into the core region.

Markovian Decision Modeling in Dam Projects - Niger Delta River Basin

This paper studied simulation modeling in Markovian Decision theory and its application in decision making as well as planning in water resources and environmental engineering. The research objectives deals with the multi-objective values of a River basin for its wide range of purposes such as Economic Efficiency, Regional Economic distribution, State Economic distribution, Social Well-being, and Environmental Quality control. In line with foregoing objectives, the researchers aim at achieving the following: (i) Measures the magnitude of the difference between alternative actions (ii) to present a framework for considering decision making under uncertainty. (iii) to evaluate the optimal policy or strategy or action that maximizes the expected benefit in the River Basin within the available limited resources and funds over the planning period of a course of action or alternatives. The Methodology applied involved Markovian decision model method for River basin. Data collection was based on technical literatures from books, journals, and news papers, River Basin Engineering Development, Parastatals. The analysis and presentation of results were based on simulation of Markovian Models. Furthermore, Contingency association, Chi-square, Pearson Product Moment Correlation were carried out as interaction, reliability and validity tests. However, simulating the river basin variables using Markov chain Homogeneous analysis and policy iterations resulted to a decision policy of allocating resources to the river basin objectives based on a federal government budgetary appropriation of 100 billion Naira. In conclusion the model had policy decision made as follows: Economic Efficiency [64%], Regional Economic Distribution [9%], State Economic Distribution [19%], Social Well-Being [5%] and Environmental Control [3%] [see Figure 1 and 2]. The results indicate that Markov Chain can be successfully applied in optimum policy investment decision making in multi-objective water resources management. Keywords: Investment, Optimum, Policy Decision, Dam –projects. DOI : 10.7176/CER/11-2-10 Publication date :March 31 st 2019

The Availability of Systems with Bathtub Hazard Rate Function

In our normal life we can see that the most realistic systems possess useful time governed by hazard rateof bathtub shaped. The hazard rate function, however, plays a vital role in the computation of theavailability function. The repair time, however, could be modeled as any statistical distribution. In thispaper I will investigate the nature of availability function and points of availability of systems with bathtubhazard function and exponential distribution repair time using Markovian method.

Reynolds number effect on the velocity derivative flatness factor

This paper investigates the effect of a finite Reynolds number (FRN) on the flatness factor ($F$) of the velocity derivative in decaying homogeneous isotropic turbulence by applying the eddy damped quasi-normal Markovian (EDQNM) method to calculate all terms in an analytic expression for $F$ (Djenidi et al., Phys. Fluids, vol. 29 (5), 2017b, 051702). These terms and hence $F$ become constant when the Taylor microscale Reynolds number, $Re_{\unicode[STIX]{x1D706}}$ exceeds approximately $10^{4}$. For smaller values of $Re_{\unicode[STIX]{x1D706}}$, $F$, like the skewness $-S$, increases with $Re_{\unicode[STIX]{x1D706}}$; this behaviour is in quantitative agreement with experimental and direct numerical simulation data. These results indicate that one must first ensure that $Re_{\unicode[STIX]{x1D706}}$ is large enough for the FRN effect to be negligibly small before the hypotheses of Kolmogorov (Dokl. Akad. Nauk SSSR, vol. 30, 1941a, pp. 301–305; Dokl. Akad. Nauk SSSR, vol. 32, 1941b, pp. 16–18; J. Fluid Mech., vol. 13, 1962, pp. 82–85) can be assessed unambiguously. An obvious implication is that results from experiments and direct numerical simulations for which $Re_{\unicode[STIX]{x1D706}}$ is well below $10^{4}$ may not be immune from the FRN effect. Another implication is that a power-law increase of $F$ with respect to $Re_{\unicode[STIX]{x1D706}}$, as suggested by the Kolmogorov 1962 theory, is not tenable when $Re_{\unicode[STIX]{x1D706}}$ is large enough.

Ranking journals using social choice theory methods: A novel approach in bibliometrics

Abstract We use data on economic, management and political science journals to produce quantitative estimates of (in)consistency of the evaluations based on six popular bibliometric indicators (impact factor, 5-year impact factor, immediacy index, article influence score, SNIP and SJR). We advocate a new approach to the aggregation of journal rankings. Since the rank aggregation is a multicriteria decision problem, ranking methods from social choice theory may solve it. We apply either a direct ranking method based on the majority rule (the Copeland rule, the Markovian method) or a sorting procedure based on a tournament solution, such as the uncovered set and the minimal externally stable set. We demonstrate that the aggregate rankings reduce the number of contradictions and represent the set of the single-indicator-based rankings better than any of the six rankings themselves.

Availability optimisation of pre-heat exchanger system with random repair and failure rates using PSO

The main objective of this study is to carry out performance analysis and availability maximisation with randomly selected failure and repair rates (FRR) of a Pre-Heat Exchanger (PHE) system of a brewery plant using the particle swarm algorithm. The behavioural analysis of each system is carried out by Markovian method and the schematic diagram of the PHE system represents various components and their connectivity (series/parallel/hybrid) whereas the transition diagram explores various possibilities and combinations of working states of the components i.e. full capacity working (FCW), reduced capacity working (RCW) and failed state (FS). The mathematical equations are formulated using the transition diagrams in order to carry out steady state availability (SSA) and transient state availability (TSA) analysis. The prediction of failure and repair rate to attain maximum availability of a system is done by using Particle Swarm Optimisation (PSO) technique. These results are beneficial for plant personnel by steering of failure and repair rates to achieve maximum availability.

Availability optimisation of pre-heat exchanger system with random repair and failure rates using PSO

The main objective of this study is to carry out performance analysis and availability maximisation with randomly selected failure and repair rates (FRR) of a Pre-Heat Exchanger (PHE) system of a brewery plant using the particle swarm algorithm. The behavioural analysis of each system is carried out by Markovian method and the schematic diagram of the PHE system represents various components and their connectivity (series/parallel/hybrid) whereas the transition diagram explores various possibilities and combinations of working states of the components i.e. full capacity working (FCW), reduced capacity working (RCW) and failed state (FS). The mathematical equations are formulated using the transition diagrams in order to carry out steady state availability (SSA) and transient state availability (TSA) analysis. The prediction of failure and repair rate to attain maximum availability of a system is done by using Particle Swarm Optimisation (PSO) technique. These results are beneficial for plant personnel by steering of failure and repair rates to achieve maximum availability.

$G$ method in action: Fast exact sampling from set of permutations of order $n$ according to Mallows model through Cayley metric

Using $G$ method, we give a fast exact (not approximate) Markovian method for sampling from $\mathbb{S}_{n}$, the set of permutations of order $n$, according to the Mallows model through Cayley metric (a model for ranked data). This method has something in common with the cyclic Gibbs sampler and something in common with the swapping method. The number of steps of our method is equal to the number of steps of swapping method, that is, $n-1$; moreover, both methods use the best probability distributions on sampling, the swapping method uses uniform probability distributions while our method uses almost uniform probability distributions (all the components of an almost uniform probability distribution are, here, identical, excepting at most one of them). But, besides sampling, we can do other things for the Mallows model through Cayley metric—we compute the normalizing constant and, by Uniqueness theorem, certain important probabilities.

Markovian approach for the analysis and prediction of weekly rainfall pattern in Makurdi, Benue State, Nigeria

A stochastic model to study weekly rainfall pattern has been presented in this paper. The Markovian method was used to predict and analyze weekly rainfall pattern of Makurdi, Benue state, Nigeria for a period of eleven years (2005-2015). After some successful iterations of the model, its stabilizes to equilibrium probabilities, revealing that in the long-run 22% of the weeks during rainy season in Makurdi, will experience no rainfall , 50% will experience low rainfall, 25% will experience moderate rainfall and 2% will experience high rainfall. The model also reveals that, a week of high rainfall cannot be followed by another week of high rainfall , a week of high rainfall cannot be followed by a week of no rainfall, and a week of moderate rainfall cannot precede a week of high rainfall. These results are important information to the residents of Markudi and environmental management scientists to plan for the uncertainty of rainfall.Keywords: Markov chain, Weekly Rainfall, Transition Probabilities, Equilibrium probabilities Probability State Vector, Makurdi.

Iterative Refinement of Possibility Distributions by Learning for Pixel-Based Classification.

This paper proposes an approach referred as: iterative refinement of possibility distributions by learning (IRPDL) for pixel-based image classification. The IRPDL approach is based on the use of possibilistic reasoning concepts exploiting expert knowledge sources as well as ground possibilistic seeds learning. The set of seeds is constructed by incrementally updating and refining the possibility distributions. Synthetic images as well as real images from the RIDER Breast MRI database are being used to evaluate the IRPDL performance. Its performance is compared with three relevant reference methods: region growing, semi-supervised fuzzy pattern matching, and Markov random fields. The IRDPL performance (in terms of recognition rate, 87.3%) is close to the Markovian method (88.8%) that is considered to be the reference in pixel-based image classification. IRPDL outperforms the other two methods, respectively, at the recognition rates of 83.9% and 84.7%. In addition, the proposed IRPDL requires fewer parameters for the mathematical representation and presents a reduced computational complexity.

Storage-Reserve Sizing With Qualified Reliability for Connected High Renewable Penetration Micro-Grid

The major challenge in high renewable penetration microgrid is the power mismatch between stochastic renewables and demand. Energy storage and reserve purchase are main techniques in reducing that. Storage sizing problem is widely investigated in literatures without reserve capacity co-optimizing. And due to innate no loss-of-load assumption, a large proportion of capacity is used to handle inessential energy deficiency with small probability. In this paper, storage-reserve sizing problem with qualified reliability is raised to integrate reserve sizing and loss-of-load probability (LOLP) index into existing storage sizing problem. Two-stage probabilistic model is established to minimize total cost with optimizing storage capacity during first-stage and reserve strategy during second-stage. Since the time-consuming Monte Carlo simulation and stage iteration are usually required in problem solving, Markovian steady-state sizing method is proposed to improve efficiency. Probability constraint is tested by mathematical quantile. And two-stage model is transformed to single-stage one attributed to analytical solution of second-stage. Meanwhile obtained relationship among storage capacity, reserve capacity, and LOLP index can help designers balance between capacity and reliability. Numerical test shows: needed capacity is significantly reduced with little sacrifice of reliability; storage–reserve combination is economical, since they are probabilistically complementary; proposed solution method is fast and accurate.