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The multi-task allocation has become the key to be solved urgently in applying a coal gangue sorting robot system (CGSRS) in raw coal with high throughput. This paper constructs a multi-task allocation framework of CGSRS for time-varying raw coal flow (TVRCF), including task decomposition, task allocation, and collaborative strategy. Establish the TVRCF decomposition model using the tumbling time window method to obtain the gangue model. A multi-task allocation model based on M/M/s queuing model with impatient customers is proposed because arrival time, granularity, and spatial position of the gangue model are uncertain. By introducing trajectory function and designing benefit function, to solve environment states of sorting area. Creating an iterative mechanism for environment states based on the infinite Markov process, using service time and arrival time interval. An adaptive weights rule based on the greedy algorithm (GAW) is proposed to improve the benefit of multi-task allocation. Simulating 18 groups of TVRCF with 9 productivity. Experimental results show that the proposed framework suits the multi-task allocation of CGSRS to TVRCF. The GAW rule always ensures the optimal sorting rate, the near-optimal task completion success rate, and the manipulator utilization rate. In addition, the stability of the GAW rule is best. [ABSTRACT FROM AUTHOR]

Background: Extended illness-death models (a specific class of multistate models) are a useful tool to analyse situations like hospital-acquired infections, ventilation-associated pneumonia, and transfers between hospitals. The main components of these models are hazard rates and transition probabilities. Calculation of different measures and their interpretation can be challenging due to their complexity. Methods: By assuming time-constant hazards, the complexity of these models becomes manageable and closed mathematical forms for transition probabilities can be derived. Using these forms, we created a tool in R to visualize transition probabilities via stacked probability plots. Results: In this article, we present this tool and give some insights into its theoretical background. Using published examples, we give guidelines on how this tool can be used. Our goal is to provide an instrument that helps obtain a deeper understanding of a complex multistate setting. Conclusion: While multistate models (in particular extended illness-death models), can be highly complex, this tool can be used in studies to both understand assumptions, which have been made during planning and as a first step in analysing complex data structures. An online version of this tool can be found at https://eidm.imbi.uni-freiburg.de/. [ABSTRACT FROM AUTHOR]

We consider finite graphical n-person games with perfect information that have no Nash equilibria in pure stationary strategies. Solving these games in stationary mixed strategies, we introduce probability distributions in all non-terminal positions. The corresponding probability distributions on the set of plays can be defined in two different ways called the Markov and a-priori realizations. The former one guarantees existence of a uniform best response for each player in every situation. Nevertheless, Nash equilibrium may fail to exist even in stationary mixed strategies. The classical Nash's theorem is not applicable, because in this case limit distributions and expected payoffs may be discontinuous. Although a-priori realizations do not share many nice properties of the Markov ones (for example, the existence of uniform best responses) but in return, Nash's theorem is applicable. We illustrate both realizations in details by two examples with 2 and 3 players. We also survey some general results related to Nash-solvability, in pure and mixed stationary strategies, of stochastic n-person games with perfect information and n-person graphical games among them. [ABSTRACT FROM AUTHOR]

Accepted by: M. Zied Babai In the medical service system, when the number of expert seats is in short supply, it is difficult to make full use of hospital resources by the traditional queuing method. Without changing the existing resources, an overflow model with triage in a Markov queuing system is established by overflowing a part of patients in the expert queue into the general queue under a certain condition to allocate reasonably the capacity of each outpatient. The numerical simulation using ProModel, a simulation software, shows that the average queue length, waiting time and other service indices are better than the traditional models. [ABSTRACT FROM AUTHOR]

The mission success probability (MSP) is a critical indicator for phased mission systems (PMSs). In the modern aerospace industry, redundancy techniques, including component/phase redundancy, are commonly seen to increase the MSP of the whole system. These component/phase redundancies make the reliability analysis more complex. Meanwhile, one or more components are required for normal working for different subsystems, called the K/N structure. In this article, a Markov‐process method is proposed for PMS with K/N subsystems and different redundancy strategies. Then, a universal system optimization model is proposed to optimize system structure and redundancy strategies for all subsystems at the same time. Then, an improved genetic algorithm (GA) is used to resolve the optimization problem. At last, a propulsion system is used as an engineering case, showing the proposed binary decision diagram‐based method. [ABSTRACT FROM AUTHOR]

Lyme disease is the most common vector-borne disease in the United States impacting the Northeast and Midwest at the highest rates. Recently, it has become established in southeastern and south-central regions of Canada. In these regions, Lyme disease is caused by Borrelia burgdorferi, which is transmitted to humans by an infected Ixodes scapularis tick. Understanding the parasite-host interaction is critical as the white-footed mouse is one of the most competent reservoir for B. burgdorferi. The cycle of infection is driven by tick larvae feeding on infected mice that molt into infected nymphs and then transmit the disease to another susceptible host such as mice or humans. Lyme disease in humans is generally caused by the bite of an infected nymph. The main aim of this investigation is to study how diapause delays and demographic and seasonal variability in tick births, deaths, and feedings impact the infection dynamics of the tick-mouse cycle. We model tick-mouse dynamics with fixed diapause delays and more realistic Erlang distributed delays through delay and ordinary differential equations (ODEs). To account for demographic and seasonal variability, the ODEs are generalized to a continuous-time Markov chain (CTMC). The basic reproduction number and parameter sensitivity analysis are computed for the ODEs. The CTMC is used to investigate the probability of Lyme disease emergence when ticks and mice are introduced, a few of which are infected. The probability of disease emergence is highly dependent on the time and the infected species introduced. Infected mice introduced during the summer season result in the highest probability of disease emergence. [ABSTRACT FROM AUTHOR]

To achieve the model construction and strategy selection of carbon emissions under the constraints of limited data information, this study explores the inherent laws underlying the evolution of different population models from the perspective of natural population growth, obstructive population changes constrained by environmental and other conditions, population changes considering age structure and population development in the form of partial differential equations on the basis of systematic analysis of population factors and their impact on changes in social environment and material level, then an equivalent substitution function is obtained according to the homotopy transformation idea in topology, so that the problem can be dealt with in a unified way. The results show that the extended STIRPAT model has a better fitting effect, and using Markov process to reverse adjust and correct the influencing factor which is predicted by population evolution model before yields more accurate prediction results. The idea of analyzing carbon emissions based on population changes also provides an effective method for dealing with related problems. [ABSTRACT FROM AUTHOR]

Geometries of eroding landscapes contain important information about geologic, climatic, biotic and geomorphic processes. They are also characterized by variability, which makes disentangling their origins challenging. Observations and physical models of fluvial processes, which set the pace of erosion on most continents, emphasize complexity and variability. By contrast, the spectral content of longitudinal river profiles and similarity of geometries at scales greater than approximately 100km highlight relatively simple emergent properties. A general challenge then, addressed in this manuscript, is development of a theory of landscape evolution that embraces such scale-dependent insights. We do so by incorporating randomness and probability into a theory of fluvial erosion. First, we explore the use of stochastic differential equations of the Langevin type, and the Fokker--Planck equation, for predicting migration of erosional fronts. Second, analytical approaches incorporating distributions of driving forces, critical thresholds and associated proxies are developed. Finally, a linear programming approach is introduced, that, at its core, treats evolution of longitudinal profiles as a Markovian stochastic problem. The theory is developed essentially from first principles and incorporates physics governing fluvial erosion. We explore predictions of this theory, including the natural growth of discontinuities and scale-dependent evolution, including local complexity and emergent simplicity. [ABSTRACT FROM AUTHOR]

To predict the long-term skid resistance of steel slag asphalt mixtures, accelerated wear tests were conducted using an indoor accelerated loading device on the steel slag asphalt mixtures with different aggregate types, different steel slag blends, and different temperatures. The skid resistance decay law applied to the steel slag asphalt mixture under different influencing factors was investigated. Based on the skid resistance evaluation index measured during testing, a grey residual grey model (GM)(1,1)-Markov model was established to predict skid resistance. The results showed that the incorporation of steel slag significantly improves skid resistance while helping to reduce skid attenuation loss. Skid resistance increased with the increase in steel slag incorporation. With 100% steel slag incorporation, it was optimal. In addition, the test temperature did not change the decay law of the skid resistance index. With changes in temperature, skid resistance showed a decreasing trend. The prediction accuracy of the grey residual GM(1,1)-Markov model was significantly better than that of the grey GM(1,1) model and so can be used for skid resistance prediction. The results of the study can help to determine the attenuation characteristics of skid resistance of steel slag asphalt mixtures, and provide a simple and reliable method for predicting the skid resistance of these mixtures and other pavement aggregates. At the same time, it is certain guidelines for the establishment of the prediction model of asphalt mixture skid resistance under small sample conditions. [ABSTRACT FROM AUTHOR]

The aim of the paper is to study effectiveness of the different treatments of early-stage breast cancer through analysis of a stochastic model. The early-stage breast cancer is a term used to describe breast cancer that is detected at an early stage of development, typically before it has spread to other parts of the body. Early detection of breast cancer is critical as it greatly increases the chances of successful treatment and saves lives. At early-stage breast cancer of the patient, two types of treatment namely, tamoxifen and tamoxifen combined with radiation therapy are commonly used. As it is essential to consider innovative and cost-effective strategies for early detection and treatment. Investigations through analysis of the stochastic model on early-stage breast cancer with these two types of treatments may help the stakeholders. Keeping this in view, in the present paper, a stochastic model is developed for the early-stage breast cancer considering two treatment types, namely tamoxifen and tamoxifen combined with radiation therapy. The model is analyzed by Markov process and regenerative point technique. Mean sojourn time refers to the average amount of time spent by a patient in a particular state before transitioning to another state and mean survival time refers to the average time a patient survives after diagnosis of breast cancer. Mean sojourn time and mean survival time have been calculated. Sensitivity analysis is a technique to understand how changes in input variables or parameters affect the output or outcome of a model and it helps assess the robustness, reliability, and stability of a model by quantifying the impact of variations in input factors. The paper also includes sensitivity and relative sensitivity analyses of the model which explore the impact of different parameters on the survivability of the patient. The MATLAB software has been used for numerical computing and plotting various graphs. The investigation through our analysis of the stochastic model shows that the mean survival time lessens with the rise in the rates of transition and mean survival time from the treatment, tamoxifen plus radiation is higher than the treatment, tamoxifen only. It is concluded that tamoxifen plus radiation is more effective and useful than only tamoxifen for treatment of early-stage breast cancer. [ABSTRACT FROM AUTHOR]

The restricted mean time in favor (RMT‐IF) of treatment has just been added to the analytic toolbox for composite endpoints of recurrent events and death. To help practitioners design new trials based on this method, we develop tools to calculate the sample size and power. Specifically, we formulate the outcomes as a multistate Markov process with a sequence of transient states for recurrent events and an absorbing state for death. The transition intensities, in this case the instantaneous risks of another nonfatal event or death, are assumed to be time‐homogeneous but nonetheless allowed to depend on the number of past events. Using the properties of Coxian distributions, we derive the RMT‐IF effect size under the alternative hypothesis as a function of the treatment‐to‐control intensity ratios along with the baseline intensities, the latter of which can be easily estimated from historical data. We also reduce the variance of the nonparametric RMT‐IF estimator to calculable terms under a standard set‐up for censoring. Simulation studies show that the resulting formulas provide accurate approximation to the sample size and power in realistic settings. For illustration, a past cardiovascular trial with recurrent‐hospitalization and mortality outcomes is analyzed to generate the parameters needed to design a future trial. The procedures are incorporated into the rmt package along with the original methodology on the Comprehensive R Archive Network (CRAN). [ABSTRACT FROM AUTHOR]

To assess the freeze–thaw (F-T) durability of coal gangue pervious concrete (CGPC) in different F-T cycle media (water, 3.5 wt% NaCl solution), experimental studies on 36 groups of cube specimens and 6 groups of prismatic specimens were carried out, with designed porosity, F-T cycling media, and F-T failure times as variables. The changes in apparent morphology, mass, compressive behavior, relative dynamic elastic modulus, and permeability coefficient have been analyzed in detail. To predict the compressive strength after F-T cycles, a GM (1,1) model based on the grey system theory was developed and further improved into a more accurate grey residual–Markov model. The results reported that the cement slurry and coal gangue aggregates (CGAs) on the specimen surface continued to fall off as F-T cycles increased, and, finally, the weak point was fractured. Meanwhile, the decrease in compressive behavior and relative dynamic elastic modulus was gentle in the early phase of F-T cycles, and they gradually became faster in the later stage, showing a parabolic downward trend. The permeability coefficient increased gradually. When F-T failure occurred, specimen mass dropped precipitously. The F-T failure of CGPC was more likely to occur in 3.5 wt% NaCl solution, and the F-T failure times of samples were 25 times earlier than that of water. This study lays the foundation for an engineering application and provides a basis for the large-scale utilization of CGPC. [ABSTRACT FROM AUTHOR]

We introduce a class of Markov models to describe the bid–ask price dynamics in the presence of liquidity fluctuations. In a highly competitive regime, the spread evolution belongs to a class of Markov processes known as a population process with uniform catastrophes. Our mathematical analysis focuses on establishing the law of large numbers, the central limit theorem, and large deviations for this catastrophe-based model. Large deviation theory allows us to illustrate how huge deviations in the spread and prices can occur in the model. Moreover, our research highlights how these local trends and volatility are influenced by the typical values of the bid–ask spread. We calibrated the model parameters using available high-frequency data and conducted Monte Carlo numerical simulations to demonstrate its ability to reasonably replicate key phenomena in the presence of liquidity fluctuations. [ABSTRACT FROM AUTHOR]

Flow direction algorithm (FDA) is a new physics-based optimization algorithm for solving global optimization problems. Although the FDA has shown effectiveness in many areas, there has been a lack of rigorous theoretical guarantees. This paper first proves that FDA is globally convergent with probability 1 by establishing a Markov process model. Furthermore, to enhance the FDA's exploration and exploitation abilities, we propose an improved FDA algorithm (IFDA) by introducing random opposition-based learning and an adaptive neighbour generation strategy. Finally, extensive experiments and statistical tests are investigated on the classical benchmark functions, CEC 2019 benchmark function, and wireless sensor network coverage optimization problem with several state-of-the-art algorithms, demonstrating the proposed algorithm's efficiency and effectiveness. [ABSTRACT FROM AUTHOR]

Cloud infrastructure provides a real time computing environment to customers and had wide applicability in healthcare, medical facilities, business, and several other areas. Most of the health data recorded and saved on the cloud. But the cloud infrastructure is configured using several components and that makes it a complex structure. And the high value of availability and reliability is essential for satisfactory operation of such systems. So, the present study is conducted with the prominent objective of assessing the optimum availability of the cloud infrastructure. For this purpose, a novel stochastic model is proposed and optimized using dragonfly algorithm (DA) and Grey Wolf optimization (GWO) algorithms. The Markovian approach is employed to develop the Chapman-Kolmogorov differential difference equations associate with the system. It is considered that all failure and repair rates are exponentially distributed. The repairs are perfect. The numerical results are derived to highlight the importance of the study and identify the best algorithm. The system attains its optimum availability 0.9998649 at population size 120 with iteration 700 by GWO. It is revealed that grey wolf optimization algorithm performed better than the Dragonfly algorithm in assessing the availability, best fitted parametric values and execution time. [ABSTRACT FROM AUTHOR]

We consider a two-station cascade system in which waiting or externally arriving customers at station 1 move to the station 2 if the queue size of station 1 including an arriving customer itself and a customer being served is greater than a given threshold level c 1 ≥ 1 and if station 2 is empty. Assuming that external arrivals are subject to independent renewal processes satisfying certain regularity conditions and service times are i.i.d. at each station, we derive necessary and sufficient conditions for a Markov process describing this system to be positive recurrent in the sense of Harris. This result is extended to the cascade system with a general number k of stations in series. This extension requires certain traffic intensities of stations 2 , 3 , ... , k - 1 for k ≥ 3 to be defined. We finally note that the modeling assumptions on the renewal arrivals and i.i.d. service times are not essential if the notion of the stability is replaced by a certain sample path condition. This stability notion is identical with the standard stability if the whole system is described by the Markov process which is a Harris irreducible T-process. [ABSTRACT FROM AUTHOR]

We consider a long-run impulse control problem for a generic Markov process with a multiplicative reward functional. We construct a solution to the associated Bellman equation and provide a verification result. The argument is based on the probabilistic properties of the underlying process combined with the Krein-Rutman theorem applied to the specific non-linear operator. Also, it utilises the approximation of the problem in the bounded domain and with the help of the dyadic time-grid. [ABSTRACT FROM AUTHOR]

Due to the high sensitivity in applying electronic and mechanical equipment in functional systems, creating conditions to increase a system's reliability is always critical for system designers. In most of the studies in the reliability area, it is assumed that the failure rates of the system's components are constant but considering time-dependent failure rates for the components is more realistic and draws the models near to real conditions. This paper presents a framework to use Markov process to obtain the system's reliability under some assumptions. In this regard, we worked on a load-sharing system with identical time-dependent failure rate components and used Markov process to calculate the system reliability. First, we define the requirements for using Markov process, and it is shown that it is possible to use it to calculate the considered system's reliability. Then, a formula is presented to calculate the reliability of the considered system using the Markov process through solving the Chapman Kolmogorov equation, when the components' life has Weibull Distribution. Next, we validate the results of the presented formula using the simulation technique. Finally, we compare the computational time of the proposed model for solving large-size problems with the simulation technique. The results show the superiority of the proposed model in terms of computational time. [ABSTRACT FROM AUTHOR]

The fuel injection system heavily relies on the high-pressure fuel pump, which plays a critical role in its overall performance. The fuel pump plunger is subjected to high levels of stress and experiences irregular lubrication during dynamic loads, causing premature wear. In the industrial sector, laser surface micro-texturing has been utilized to reduce friction and enhance anti-wear properties, and its positive impact has been supported by both theoretical and experimental evidence. This article presents a method for determining the hydromechanical characteristics of plunger pairs under conditions of hydrodynamic friction. The microgeometry of friction surfaces was taken into account through the cavitation effect of the lubricating fluid, described by the modified Reynolds equation. Software was developed according to the proposed method. The developed software can be used to analyze the contacting surfaces of plunger pairs and evaluate their tribotechnical characteristics based on the microgeometry parameters of the friction surfaces. The article also discusses the impact of the microgeometry parameters on the quality criteria of the hydromechanical characteristics of the plunger pairs. Computational examples are given for the analysis of contacting surfaces of plunger pairs separated by a lubrication layer. The technical characteristics are evaluated depending on the parameters of the microgeometry of the roughness of the friction surfaces. The influence of the microgeometry parameters on the quality criteria of the hydromechanical characteristics of the plunger pairs is presented. [ABSTRACT FROM AUTHOR]

In this paper, motivated by considerations of server utilization and energy consumption in cloud computing, we investigate a homogeneous queueing system with a threshold-based workload control scheme. In this system, a virtual machine will be turned off when there are no tasks in its buffer upon the completion of a service by the machine, and turned on when the number of tasks in its buffer reaches a pre-set threshold value. Due to complexity of this system, we propose approximations to system performance measures by mean field limits. An iterative algorithm is suggested for the solution to the mean field limit equations. In addition, numerical and simulation results are presented to justify the proposed approximation method and to provide a numerical analysis on the impact of the system performances by system parameters, which suggests that the proposed system saves about (1 − λ μ) × 100 % of the energy consumption compared to the ordinary supermarket models. [ABSTRACT FROM AUTHOR]

In this paper, state space of a time-homogeneous Markov process is split into several ordered subspaces. Then, there are three kinds of transitions between states—transitions from a higher-order subspace to a lower-order subspace, transitions within the same subspace, and transitions from a lower-order subspace to a higher-order subspace. Considering time interval omission problem and first passage time considered, we define some related counting processes for the Markov process and discuss their associated probabilities, expectations and generating functions by using Laplace transform. The main results are presented in matrix forms. The relationships among counting processes and their special cases are also discussed briefly. Some simple numerical examples are presented to illustrate the established results. These results will be useful in different problems arising in reliability, economics and social science fields. [ABSTRACT FROM AUTHOR]

In this paper, the design of a dynamic output feedback controller for a networked control system with dual-channel data packet loss and special discrete-time delay is studied, in which the data packet loss is described by the Markov process. In order to effectively alleviate the problem of network congestion, a quantizer was added to the sensor-to-controller channel. The transition probabilities of the Markov process are uncertain, but they exist in the convex sets of known convex polyhedron types. The mode-dependent Lyapunov function was constructed, and a sufficient condition was given to make the closed-loop system stochastically stable and satisfy the performance index. The parameters of the controller were solved by the linear matrix inequality method. Finally, an example of aircraft shows the validity of the proposed approach. A numerical example is compared with other literature, showing the superiority of the proposed approach. [ABSTRACT FROM AUTHOR]

A distance stochastic modelwas constructed for the S-type picking strategy to address the picking efficiency problem resulting from increased order volume in the warehouse and to explore the relationship between the number of pickers and warehouse area for rational scheduling. The congestion problem arising from the picking strategy was studied, along with the congestion rate problem of the two-person picking system previously studied by other researchers. A state transfer matrix and a smooth distribution function were constructed for the three-person picking system using a Markov process. Finally, simulation was used to evaluate the congestion rate of the multi-person picking system. The influence of the number relationship between the picking surface and the pickers on the congestion rate was derived by comparing the two-person and three-person picking systems and the distance models under the two picking strategies. This provides a basis for effectively responding to emergency logistics demand and reasonably controlling the congestion rate of the e-commerce picking operation chain. [ABSTRACT FROM AUTHOR]

This paper proposes a robust guaranteed-cost controller for a half-vehicle active suspension system (HVASS) where the controller is subject to stochastic gain fluctuations. This randomly occurring uncertainty is a result of the imperfect implementation of the controller as well as the aging of the components. In this approach, the state-feedback controller is represented via multiple gains orchestrated by a Markovian process, and then an optimal multi-mode design approach with H2 norm constraints is considered to ensure system's asymptotic stability with a prescribed disturbance attenuation level. This design is based on Lyapunov theory and the controller is realized via a set of linear matrix inequalities. Compared to the existing works, the design is more reliable for practical HVASSs and is directly reducible to systems with perfectly implemented controllers. Simulation results and comparisons demonstrate the applicability and potentials of the proposed method. [ABSTRACT FROM AUTHOR]

In the same context as in the seminal paper [P. Cheridito, Bernoulli, 7 (2001), pp. 913-934], we are concerned with the semimartingale property of the sum of some Gaussian martingale and an independent fractional Brownian motion with Hurst parameter H = (0, 1). At the same time, we emphasize that the Markov property is lost even if the martingale owns it. [ABSTRACT FROM AUTHOR]

There is continuing pressure to improve the cost effectiveness of quality control (QC) for clinical laboratory testing. Risk-based approaches are promising but recent research has uncovered problems in some common methods. There is a need for improvements in risk-based methods for quality control. We provide an overview of a dynamic model for assay behavior. We demonstrate the practical application of the model using simulation and compare the performance of simple Shewhart QC monitoring against Westgard rules. We also demonstrate the utility of trade-off curves for analysis of QC performance. Westgard rules outperform simple Shewhart control over a narrow range of the trade-off curve of false-positive and false negative risk. The risk trade-off can be visualized in terms of risk, risk vs. cost, or in terms of cost. Risk trade-off curves can be "smoothed" by log transformation. Dynamic risk-models may provide advantages relative to static models for risk-based QC analysis. [ABSTRACT FROM AUTHOR]

A multi‐state weighted K‐out‐of‐n system is of great importance in system engineering due to its generalized nature. In earlier studies, usually all the components of the multi‐state weighted K‐out‐of‐n system were considered to be in a steady state though we can encounter engineering systems where the components of this type of system can be dynamic in nature, that is, the states of components change over time. To deal with this situation, in the current study an algorithm, based on Lz${L}_z$‐transform is presented to determine the reliability indices of multi‐state weighted K‐out‐of‐n system in dynamic setup. The components of the system are assumed to follow Markov process and are repaired only when they are completely failed. In this proposed study reliability, availability, instantaneous mean expected performance, and performance deficiency are obtained for the considered system. Finally, a case study of the power system of warship is considered to apply and validate the proposed approach. [ABSTRACT FROM AUTHOR]

Optimal designs minimize the number of experimental runs (samples) needed to accurately estimate model parameters, resulting in algorithms that, for instance, efficiently minimize parameter estimate variance. Governed by knowledge of past observations, adaptive approaches adjust sampling constraints online as model parameter estimates are refined, continually maximizing expected information gained or variance reduced. We apply adaptive Bayesian inference to estimate transition rates of Markov chains, a common class of models for stochastic processes in nature. Unlike most previous studies, our sequential Bayesian optimal design is updated with each observation and can be simply extended beyond two-state models to birth–death processes and multistate models. By iteratively finding the best time to obtain each sample, our adaptive algorithm maximally reduces variance, resulting in lower overall error in ground truth parameter estimates across a wide range of Markov chain parameterizations and conformations. [ABSTRACT FROM AUTHOR]

We study the Dyson–Ornstein–Uhlenbeck diffusion process, an evolving gas of interacting particles. Its invariant law is the beta Hermite ensemble of random matrix theory, a non-product log-concave distribution. We explore the convergence to equilibrium of this process for various distances or divergences, including total variation, relative entropy, and transportation cost. When the number of particles is sent to infinity, we show that a cutoff phenomenon occurs: the distance to equilibrium vanishes abruptly at a critical time. A remarkable feature is that this critical time is independent of the parameter beta that controls the strength of the interaction, in particular the result is identical in the non-interacting case, which is nothing but the Ornstein–Uhlenbeck process. We also provide a complete analysis of the non-interacting case that reveals some new phenomena. Our work relies among other ingredients on convexity and functional inequalities, exact solvability, exact Gaussian formulas, coupling arguments, stochastic calculus, variational formulas and contraction properties. This work leads, beyond the specific process that we study, to questions on the high-dimensional analysis of heat kernels of curved diffusions. [ABSTRACT FROM AUTHOR]

Our object of study is the asymptotic growth of heaviest paths in a charged (weighted with signed weights) complete directed acyclic graph. Edge charges are i.i.d. random variables with common distribution F supported on [-∞; 1] with essential supremum equal to 1 (a charge of -∞ is understood as the absence of an edge). The asymptotic growth rate is a constant that we denote by C(F). Even in the simplest case where F = pδ1 + (1 - p)δ-∞, corresponding to the longest path in the Barak-Erdos random graph, there is no closed-form expression for this function, but good bounds do exist. In this paper we construct a Markovian particle system that we call "Max Growth System" (MGS), and show how it is related to the charged random graph. The MGS is a generalization of the Infinite Bin Model that has been the object of study of a number of papers. We then identify a random functional of the process that admits a stationary version and whose expectation equals the unknown constant C(F). Furthermore, we construct an effective perfect simulation algorithm for this functional which produces samples from the random functional. [ABSTRACT FROM AUTHOR]

A variational formula for the asymptotic variance of general Markov processes is obtained. As application, we get an upper bound of the mean exit time of reversible Markov processes, and some comparison theorems between the reversible and non-reversible diffusion processes. [ABSTRACT FROM AUTHOR]

The optimization of boiler soot blowing strategy and repair plan is investigated based on Hamilton–Jacobi–Bellman (HJB) equation in this paper. From the perspective of soot, we build a Markov process with three modes to describe the boiler running process. For the sake of applying HJB equation, a cost function is constructed according to the built Markov model, and HJB equation is derived by using optimality principle. The optimal soot blowing strategy and repair plan can be obtained by solving HJB equation. Particularly, the properties of value function, which are regarded as the optimality conditions, can ensure the existence and uniqueness of HJB equation solution. On this basis, Kushner method is used to overcome the difficulty of obtaining analytical solution of HJB equation. Moreover, numerical simulations are performed to verify the effectiveness of the proposed method and analyse the robustness of the obtained soot blowing strategy and repair plan when the system parameters vary. [ABSTRACT FROM AUTHOR]

In this study, we consider different poverty indexes in a dynamic framework where individuals change their rate of income randomly in time. The primary objective of this paper is to assess the accuracy of the approximation of the indexes that can be obtained by applying the strong law of large numbers to an economic system composed of an infinite number of agents. The main result is a multivariate central limit theorem for dynamic poverty measures, which is obtained applying the theory of U-statistics. We also show how to get the confidence sets for the considered dynamic indexes, which show the appropriateness of the model. An application to the Italian income data from 1998 to 2012 confirms the effectiveness of the considered approach and the possibility to determine the evolution of poverty and inequality in real economies. [ABSTRACT FROM AUTHOR]

We consider the motion of a symmetric gyroscope under the action of gravity and random influences that form a sequence of discrete events (the system parameters "jump" into some random values in the phase space at some random moments). To study the dynamic system, we construct a probabilistic model described by a Markov process that, in turn, is a solution of a differential equation with random parameters. Next, we consider the asymptotic situation where a discrete events becomes rarer, tending to vanish at infinity. This is ensured by replacing the transition function of the Markov process with a function that depends on a small parameter. After that, the behavior of the system as the parameter tends to zero and time tends to infinity is studied. [ABSTRACT FROM AUTHOR]

Abstract In this paper, random environment and random time delay are introduced into general nonlinear autoregressive models to improve the applicability of these models. The introduction of random environment makes nonlinear autoregressive models more flexible and more widely used. Random time delay is a new way for models to be applied in new fields. In order to analyze the properties of the proposed new model, we construct a new stochastic process and prove that it is an irreducible and aperiodic time-homogeneous Markov chain. The nonrecurrence of the proposed new type of models is considered, and some sufficient conditions for nonrecurrence are investigated. [ABSTRACT FROM AUTHOR]

This article shows that the change of rough surfaces in the way of their contact interaction can be analyzed using the theory of Markov's processes. In the framework of existing models, this problem cannot be solved. In this article, the idea of reducing to Markov's model is shown on a simple discrete scheme, which is then generalized. The approach was applied to the analysis of the friction process, to the fatigue failure mode, in which the surface element changes after multiple contacts, possibly many millions. The Kolmogorov-Feller's equations for the model of this regime were presented and the model of the influence of lubrication is offered. A calculated example of estimating the evolution of surfaces separated by a lubricant layer is given. Additionally, the technical characteristics as functions of the friction path and the load were evaluated. [ABSTRACT FROM AUTHOR]

In view of the time series update of airport runway health status detection data, the Markov chain of stochastic process theory was adopted. Considering the influence of aircraft traffic load, age, and pavement structure surface-layer thickness on the performance deterioration process of airport runways, the method of survival analysis was used. The parameter model of survival analysis was used to establish the duration function model of the four condition states of the airport runway PCI (pavement condition index). The Markov transition matrix for the performance prediction of airport runways was constructed. In order to evaluate the ability of the Markov transition matrix method to predict the trend of deterioration for PCI of the airport runway under different conditions of aircraft traffic volume and thickness of the runway pavement surface, a data set was constructed with the actual inspection data of the airport runway, and the corresponding samples were selected for analysis. The results showed that a Markov transition matrix for airport runway performance prediction, constructed based on survival analysis theory, can combine discontinuous inspection data or monitoring data with Weibull function survival curves. The method proposed in this paper can quantitatively predict the remaining service life of airport runways and provide support for cost-effective decisions about airport pavement maintenance and rehabilitation. [ABSTRACT FROM AUTHOR]

In this survey we provide an overview of recent advances on scalable load balancing schemes which provide favorable delay performance and yet require minimal implementation overhead. The basic load balancing scenario involves a single dispatcher where tasks arrive that must immediately be forwarded to one of N single-server queues. The join-the-shortestqueue (JSQ) policy yields vanishing delays as N grows large, as in a centralized queuing arrangement, but involves a prohibitive communication burden. In contrast, JSQ(d) schemes that assign an incoming task to a server with the shortest queue among d servers selected uniformly at random require little communication, but lead to constant delays. In order to examine this fundamental trade-off between delay performance and implementation overhead, we discuss a body of recent research on JSQ(d(N)) schemes in which the diversity parameter d(N) depends on N and investigate the growth rate of d(N) required to match the optimal JSQ performance on fluid and diffusion scales. Stochastic coupling techniques and scaling limits play an instrumental role in establishing this asymptotic optimality. We demonstrate how this methodology carries over to infinite-server settings, finite buffers, multiple dispatchers, servers arranged on graph topologies, and token-based load balancing schemes such as join-the-idle-queue (JIQ), thus providing a broad overview of the main trends in the field. [ABSTRACT FROM AUTHOR]

In a family of random variables, Taylor’s law or Taylor’s power law of fluctuation scaling is a variance function that gives the variance σ 2 > 0 of a random variable (rv) X with expectation μ > 0 as a power of μ : σ 2 = A μ b for finite real A > 0 , b that are the same for all rvs in the family. Equivalently, TL holds when log σ 2 = a + b log μ , a = log A , for all rvs in some set. Here we analyze the possible values of the TL exponent b in five families of infinitely divisible two-parameter distributions and show how the values of b depend on the parameters of these distributions. The five families are Tweedie–Bar-Lev–Enis, negative binomial, compound Poisson-geometric, compound geometric-Poisson (or Pólya-Aeppli), and gamma distributions. These families arise frequently in empirical data and population models, and they are limit laws of Markov processes that we exhibit in each case. [ABSTRACT FROM AUTHOR]

We study a quantum switch that distributes tripartite entangled states to sets of users. The entanglement switching process requires two steps: First, each user attempts to generate bipartite entanglement between itself and the switch, and second, the switch performs local operations and a measurement to create multipartite entanglement for a set of three users. In this work, we study a simple variant of this system, wherein the switch has infinite memory and the links that connect the users to the switch are identical. This problem formulation is of interest to several distributed quantum applications, while the technical aspects of this work result in new contributions within queueing theory. The state of the system is modeled as continuous-time Markov chain (CTMC), and performance metrics of interest (probability of an empty system, switch capacity, expectation, and variance of the number of qubit-pairs stored) are computed via the solution of a two-dimensional functional equation obtained by reducing it to a boundary value problem on a closed curve. This work is a follow-up of Nain et al. (Proc ACM Measure Anal Comput Syst(POMACS) 4, 2020) where a switch distributing entangled multipartite states to sets of users was studied, but only the switch capacity and the expected number of stored qubits were derived. [ABSTRACT FROM AUTHOR]

This paper proposes the application of generation adequacy analysis for reliability evaluation of an insulated power generation system that supplies a FPSO (Floating Production Storage and Offloading) oil and gas production platform. The frequency and duration method was adopted for generating system reliability evaluation. The historical reliability data of the floating production storage and offloading platform power system and the continuous Markov process are used to determine the generator's reliability model. The load model was also based on the platform daily peak load variation curve. The system risk indexes were obtained using Monte Carlo simulation. Two system scenarios were simulated using different failure data for one of the generators and the software PowerFactory© has been used as a tool for this simulation. For a complete generation system modeling, frequency and duration methods were developed to calculate the probabilities, frequencies and duration of the system states. Numerical results are presented and discussed to demonstrate the applicability of the proposed method. [ABSTRACT FROM AUTHOR]

Suppose X is a Markov process on the real line (or some interval). Do the distributions of its first passage times downwards (fptd) determine its law? In this paper we treat some special cases of this question. We prove that if the fptd process has the law of a subordinator, then necessarily X is a Lévy process with no negative jumps; specifying the law of the subordinator determines the law of X uniquely. We further show that, likewise, the classes of continuous-state branching processes and of self-similar processes without negative jumps are also respectively characterised by a certain structure of their fptd distributions; and each member of these classes separately is determined uniquely by the precise family of its fptd laws. The road to these results is paved by (i) the identification of Markov processes without negative jumps in terms of the nature of their fptd laws, and (ii) some general results concerning the identification of the fptd distributions for such processes. [ABSTRACT FROM AUTHOR]

This paper analyzes the effects that contracting a reverse mortgage has on the finances of families of a country or group whose members who aged 65 or older are the sole owners of the 100% of the property, regardless of the receipt of a retirement pension. For this purpose, an economic-financial model based on the life cycle model is defined, which considers a double source of randomness: mortality and dependence of family members. Long-term effects are measured using probabilistic, temporal and monetary indicators. For each country, the model must be adapted according to the legal framework for retirement and long-term care benefits and for the actuarial mortality and long-term care tables. As an illustration, this model was applied on Spanish families using data from the Spanish Survey of Household Finances 2017. The results obtained indicate that a family in Spain that meets the conditions for contracting a reverse mortgage sees, on average, an increase in its initial income and a decrease in both its probability of having liquidity problems in the future and the value of this lack of liquidity. It is also concluded that family composition influences the magnitude of these positive effects. [ABSTRACT FROM AUTHOR]

The model of the stochastic dynamics for the screening and screen-penetration processes was developed based on the Markov process to reveal the mechanism of the coal screening effect. As a partial differential equation, the model of the stochastic dynamics describes the relationship between particle position in the y direction, screening time, and particle screen-penetration probability. The obtained model for stochastic dynamics can calculate the screen-penetration probability of a specific particle size at any given time. Moreover, two coefficients, a 1 and a 2 , are defined where a 1 represents the average velocity of particles, and a 2 represents the combined effect of orderly segregation and mixing of particles in chaotic motion. These coefficients of the stochastic dynamics model were obtained by regression analysis. Additionally, the statistical analysis showed that the fitting errors were all <1. The proposed statistical dynamics model works for all particle sizes. A necessary coefficient, a 1 , was calculated based on screen-penetration coefficients k , a , and b. A large value of a 1 means a high average velocity of particles and a greater screen-penetration probability. The value of a 1 for particles smaller than 6 mm declines as the feed mass increases. Moreover, it initially decreases, followed by an increase, in response to a rising proportion of particles <6 mm. In contrast, the a 1 value for particles ranging between 6 mm and 13 mm undergoes minimal changes when subjected to variations in feed mass and the proportion of particles <6 mm. [Display omitted] • The model of the stochastic dynamics for the screen-penetration was developed. • The physical significance of the model coefficients is discussed. • The screen-penetration probability of particles can be calculated. • The accuracy of model is not affected by the feed mass and particle-size composition. [ABSTRACT FROM AUTHOR]

[Display omitted] • 162 tunnel squeezing samples from public literature and actual engineering data were collected. • The quality of the dataset was effectively improved due to use of various data preprocessing measures. • A three-classification model with excellent performance was trained by using stacking ensemble learning. • The dynamic prediction of squeezing intensity matching the excavation is purposed by combining the Markovian geologic model. Tunnel squeezing is a deformation behavior influenced by various nonlinear factors. This not only increases the construction time and the budget but also threatens the safety of construction personnel. In this study, a novel approach to improve the accuracy of predicting squeezing intensity during the design and excavation stage is proposed. To achieve this goal, a comprehensive dataset comprising 162 tunnel squeezing samples was built from those in the published literature and from engineering practices, and a dynamic multiclass prediction method was developed that combines a stacking ensemble model and a Markovian geological model. Through data preprocessing and the implementation of the stacking ensemble algorithm, a highly accurate multiclass prediction model was trained. In the next step, appropriate predictors for the Markovian geological model, which enables dynamic prediction, were identified. This method is first applied during the tunnel design stage to obtain initial predictions of the squeezing intensity. Subsequently, the model is dynamically updated during the excavation stage by using the Markovian geological model. The results of our study demonstrate the effectiveness of the stacking ensemble model in achieving a higher level of accuracy in multiclass prediction, with an impressive accuracy rate of 90.77%. Furthermore, the dynamic prediction approach employed during the excavation stage effectively addresses the limitations caused by insufficient authenticity of the design and the survey data. The findings of this study provide reliable references for tunnel excavation methods and support measures, particularly in terms of managing squeezing intensity. [ABSTRACT FROM AUTHOR]

This paper examines the fault-tolerant control problem for discrete-time descriptor systems that are susceptible to intermittent actuator failures, nonlinear sensor data, and probability-based missing data. The discrete-time non-homogeneous Markov chain was adopted to describe the stochastic behavior of actuator faults. Moreover, Bernoulli-distributed stochastic variables with known conditional probabilities were employed to describe the practical features of random sensor non-linearity and missing data. In this study, the output signals were quantized and a dynamic output feedback controller was synthesized such that the closed-loop system was stochastically admissible and satisfied the strictly (Q , S , R) - γ -dissipative performance index. The theoretical developments are illustrated through numerical simulations of an infinite machine bus. [ABSTRACT FROM AUTHOR]

A ring oscillator is a well-known circuit used for generating random numbers, and interested readers can find many research results concerning the evaluation of the randomness with a packaged test suit. However, the authors think there is room for evaluating the unpredictability of a sequence from another viewpoint. In this paper, the authors focus on Wold's RO-based generator and propose a statistical test to numerically evaluate the randomness of the RO-based generator. The test adopts the state transition probabilities in a Markov process and is designed to check the uniformity of the probabilities based on hypothesis testing. As a result, it is found that the RO-based generator yields a biased output from the viewpoint of the transition probability if the number of ROs is small. More precisely, the transitions 01 → 01 and 11 → 11 happen frequently when the number l of ROs is less than or equal to 10. In this sense, l > 10 is recommended for use in any application, though a packaged test suit is passed. Thus, the authors believe that the proposed test contributes to evaluating the unpredictability of a sequence when used together with available statistical test suits, such as NIST SP800-22. [ABSTRACT FROM AUTHOR]

This paper focuses on the robust mean-square consensus control problem for linear multiagent systems over randomly switching signed interaction topologies. The stochastic process is governed by a time-homogeneous Markov chain with partly unknown transition rates. Sufficient conditions for a consensus in the form of linear matrix inequalities are given via distributed adaptive control based on parameter-dependent Lyapunov functions. The adaptive control protocols require only the neighbor information of the agents, and the algorithm that designs the protocols reduces the influence of the communication topology on the consensus, which can prevent undesirable interaction impacts. Moreover, the disturbance rejection problem is addressed as an extension. Finally, two simulations are utilized to illustrate the effectiveness of the algorithms. [ABSTRACT FROM AUTHOR]

Micro-grids' operations offer local reliability; in the event of faults or low voltage/frequency events on the utility side, micro-grids can disconnect from the main grid and operate autonomously while providing a continued supply of power to local customers. With the ever-increasing penetration of renewable generation, however, operations of micro-grids become increasingly complicated because of the associated fluctuations of voltages. As a result, transformer taps are adjusted frequently, thereby leading to fast degradation of expensive tap-changer transformers. In the islanding mode, the difficulties also come from the drop in voltage and frequency upon disconnecting from the main grid. To appropriately model the above, non-linear AC power flow constraints are necessary. Computationally, the discrete nature of tap-changer operations and the stochasticity caused by renewables add two layers of difficulty on top of a complicated AC-OPF problem. To resolve the above computational difficulties, the main principles of the recently developed " l 1 -proximal" Surrogate Lagrangian Relaxation are extended. Testing results based on the nine-bus system demonstrate the efficiency of the method to obtain the exact feasible solutions for micro-grid operations, thereby avoiding approximations inherent to existing methods; in particular, fast convergence of the method to feasible solutions is demonstrated. It is also demonstrated that through the optimization, the number of tap changes is drastically reduced, and the method is capable of efficiently handling networks with meshed topologies. [ABSTRACT FROM AUTHOR]