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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]

Purpose: We compared fluctuations in treatment response after onabotulinumtoxinA and sacral neuromodulation for urgency incontinence using Markov models. Materials and Methods: We fit data from a randomized trial to Markov models to compare transitions of success/failure over 6 months between 200 U onabotulinumtoxinA and sacral neuromodulation. Objective failure was <50% reduction in urgency incontinence episodes from baseline; subjective failure "strongly disagree" to "neutral" to the Patient Global Symptom Control questionnaire. Results: Of the 357 participants (median baseline daily urgency incontinence episodes 4.7 [IQR 3.7-6.0]) 61% vs 51% and 3.2% vs 6.1% reported persistent states of objective success and failure over 6 months after onabotulinumtoxinA vs sacral neuromodulation. Participants receiving onabotulinumtoxinA vs sacral neuromodulation had lower 30-day transition probabilities from objective and subjective success to failure (10% vs 14%, ratio 0.75 [95% CI 0.55-0.95]; 14% vs 21%, ratio 0.70 [95% CI 0.51-0.89]). The 30-day transition probability from objective and subjective failure to success did not differ between onabotulinumtoxinA and sacral neuromodulation (40% vs 36%, ratio 1.11 [95% CI 0.73-1.50]; 18% vs 17%, ratio 1.14 [95% CI 0.65-1.64]). Conclusions: Over 6 months after treatment, 2 in 5 women's symptoms fluctuate. Within these initial 6 months, women receiving onabotulinumtoxinA transitioned from success to failure over 30 days less often than sacral neuromodulation. For both treatments, there was an almost 20%-40% probability over 30 days that women returned to subjective and objective success after failure. Markov models add important information to longitudinal models on how symptoms fluctuate after urgency incontinence treatment. [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]

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]

In this paper, we address the almost sure stability problem of Caputo fractional-order switched linear systems with deterministic and stochastic switching signals (DS-CFLSs). Firstly, due to the non-locality and memory of fractional-order switched systems, an inequality is proposed to solve the difficulties in the discussion of stability. Then, for DS-CFLSs, a deterministic switching strategy is predesigned, and stochastic switching signals are generated by the Markov process. After that, for the globally asymptotic stability almost surely (GAS a.s.) and exponential stability almost surely (ES a.s.) of DS-CFLSs, some sufficient conditions are proposed by using the multi-Lyapunov function and probability analysis methods. Finally, some numerical examples show that our results are effective. [ABSTRACT FROM AUTHOR]

For the successful operation of any industry or plant continuous availability of power supply is essential. Many of the large-scale plants established their power generation units. Marine power plant having two generators is also fall in this category. In this study, an effort is made to derive and optimize the availability of a marine power plant having two generators, one switch board and distribution switchboards. For this purpose, a mathematical model is proposed using Markov birth death process by considering exponentially distributed failure and repair rates of all the subsystems. The availability expression of marine power plant is derived. Metaheuristic algorithms namely dragonfly algorithm (DA), bat algorithm (BA) and whale optimization (WOA) are employed to optimize the availability of marine power plant. It is revealed that whale optimization algorithm outperforms over dragonfly algorithm (DA), and bat algorithm (BA) in optimum availability prediction and parameter estimation. The numerical values of the availability and estimated parameters are appended as numerical results. The derived results can be utilized in development of maintenance strategies of marine power plants and to carry out design modifications. [ABSTRACT FROM AUTHOR]

The objective of the study is to develop a method that enables to predict disease severity at the moment of admission to an intensive care unit and to choose appropriate respiratory support. The problem of patient classification by disease course is solved by using information about comorbid chronic states and a modified comorbidity index. To prove the applicability of the index for severe COVID-19 patients, we developed a mathematical model for disease progression. The estimated values of the model parameters showed the difference between probabilities of transition to critical states and/or lethal outcome in different groups. [ABSTRACT FROM AUTHOR]

This paper is devoted to the analysis of the finite-dimensional distributions and asymptotic behavior of extremal Markov processes connected with the Kendall convolution. In particular, we provide general formulas for the finite dimensional distributions of the random walk driven by the Kendall convolution for a large class of step size distributions. Moreover, we prove limit theorems for random walks and associated continuous-time stochastic processes. [ABSTRACT FROM AUTHOR]

The performance of low-voltage circuit breaker overload protection degrades slowly during service, and the service state cannot be simply described as a normal state or a fault state. To address this problem, a method is proposed to classify the operating state of low-voltage circuit breaker overload protection, taking into account the safety margin of action characteristics and a Markov-process-based operating state transfer model is established to accurately describe its actual service state. By analyzing the degradation of the overload protection performance of circuit breakers and simulating the state transfer with different operating conditions using circuit breaker reliability levels and operating time as the main variables, the change law of the service state with service time is determined. The method is not only applicable to the analysis and evaluation of circuit breakers with different reliability levels but also has guiding significance for improving the safe operation of distribution grid systems. [ABSTRACT FROM AUTHOR]

We analyzed to identify the determinants affecting the presale rate in the housing projects and verified whether there are differences in the determinants of that by regimes. We found that the effects of determinants, such as the ratio of the new apartments' sales price to existing apartments' prices, educational environment, the number of unsold houses, and the interest rate of a mortgage on the initial presale rate, could have been different depending on which regime the housing market belongs to. This suggests that the government in Korea and Asian countries should consider the differentiation in effects of the determinants depending on the regime when the government tries to make housing policies. [ABSTRACT FROM AUTHOR]

Scintillation detectors find wide application in detection of ionizing radiation. To prevent lateral loss of scintillation photons out of the scintillator volume, it is a regular practice in radiation detectors to cover the scintillator surfaces with some kind of reflective material. Typical choices of reflective materials are diffused reflectors such as PTFE sheets/tapes and specular reflectors like Aluminium coatings. The study proposes structured probabilistic modelling of purely diffused and specular reflection mechanisms for an ideal scintillator in the shape of a regular cube, for which conditional probabilities associated with individual reflection events have been obtained through Monte Carlo simulations and compiled in the form of a look-up table (LUT). This work presents a novel approach of modelling specular and diffused reflection processes as stochastic Markov processes and compares between their respective collection efficiencies on the basis of their respective governing principles. The study also involves computation of probabilities for all reflection scenarios and aggregation of individual reflection event probabilities and volumetric photon loss probabilities as a function of the photon-ray path-length in scintillator bulk, for determination of total photon collection efficiencies. The study also proposes generalizations in the ideal model to make it suitable for modelling real-world scintillators with arbitrary shapes and surface conditions. It suggests a possible means of volumetric discretization of arbitrarily shaped scintillators into voxels in the shape of regular cubes, for which photon transport probabilities can be computed by referring to data available in the form of the LUTs. [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]

Compatibility is a decisive and necessary factor which impacts the successfulness and correctness of establishing connections among services. Reliable service parameter predictions on compatibility may not only provide assurance on fulfilling workflow, but also reduce the risk of unexpected wasting on time and expenses. Recent research on service's parameter prediction focus on two aspects: Collaborative Filtering and Matrix Factorization. Both of them faces challenges from data-sparse problem, lack of solid mathematical support, and weakness on tracking dynamic services. In this paper, we propose Link-ability, a parameter to reveal the compatibility of a service. Firstly, we propose an architecture called Topology-Retrievable Service Oriented Architecture (TSOA), which is capable of collecting successful invocation records from service requesters and generate the whole topology of the service pool in a specific period of time. Secondly, we bring up the Link-ability Generation Algorithm (LGA) and Markovian mathematical strategies to generate Link-ability value. The algorithm is supported by solid mathematical proof and capable of solving data-sparse problems. Both TSOA and LGA are upgraded to adapt the circumstances of services exiting the service pool (we define it as a Drop-out). Lastly, we design and conduct two series of experiment to strengthen the reliability and correctness of Link-ability. The result shows that Link-ability considers comprehensive information of the whole topology and bring 54.18% reduction in average error rate against Drop-out scenarios. [ABSTRACT FROM AUTHOR]

The Tweedie distribution is a useful tool to model zero-inflated non-negative continuous data. However, the Tweedie dispersion relationship (DR) is not general enough to cover some important forms such as quadratic dispersion, and an easy and fast-to-implement Tweedie AR(1) model (first-order autoregressive model) needs to be developed for spatio-temporal modelling. In this research we extend the Tweedie distribution to accommodate flexible DRs, and propose a Tweedie Markov process (TMP) with the AR(1) autocorrelation structure. This TMP is simple to implement and requires only the Tweedie probability density function. Simulation studies and real data analysis are conducted to validate our new approach. [ABSTRACT FROM AUTHOR]

Reverse mortgage is one of the products (perhaps the main one) that is good to obtain additional income by using the habitual residence as collateral. The main objective of this paper is to analyse the effects that reverse mortgage contracting has on household finances over the lifetime of a family according to the socioeconomic group to which it belongs in Spain. Four indicators are employed to measure the immediate and long-term effects. We use a stochastic model with a double source of randomness, survival and entry into dependency, and apply it to the three socioeconomic groups obtained with cluster methodology from the 2017 Spanish Household Financial Survey data. We conclude that the effects are very different depending on the group: regarding only the effects of hiring a reverse mortgage on the income of the family, widowed women aged between 81 and 85 years, with low income and expenses as well as little net wealth, and a habitual residence that represents half of her net wealth (Cluster 1) are the most benefited; considering that the highest impact indicators are on the probability of illiquidity and on the value of lack of liquidity, the use of reverse mortgages benefits more the families in Cluster 3 (high income and expenses and really high net wealth, head of household aged between 76 and 80 years) and less the families in Cluster 2 (medium income, net wealth and expenses, head of household aged between 65 and 75 years). First published online 17 April 2024

In this paper, we address the almost sure stability problem of Caputo fractional-order switched linear systems with deterministic and stochastic switching signals (DS-CFLSs). Firstly, due to the non-locality and memory of fractional-order switched systems, an inequality is proposed to solve the difficulties in the discussion of stability. Then, for DS-CFLSs, a deterministic switching strategy is predesigned, and stochastic switching signals are generated by the Markov process. After that, for the globally asymptotic stability almost surely (GAS a.s.) and exponential stability almost surely (ES a.s.) of DS-CFLSs, some sufficient conditions are proposed by using the multi-Lyapunov function and probability analysis methods. Finally, some numerical examples show that our results are effective.

After over three years of COVID-19, it has become clear that infectious diseases are difficult to eradicate, and humans remain vulnerable under their influence in a long period. The presence of presymptomatic and asymptomatic patients is a significant obstacle to preventing and eliminating infectious diseases. However, the long-term transmission of infectious diseases involving asymptomatic patients still remains unclear. To address this issue, this paper develops a novel Markov process for infectious diseases with asymptomatic patients by means of a continuous-time level-dependent quasi-birth-and-death (QBD) process. The model accurately captures the transmission of infectious diseases by specifying several key parameters (or factors). To analyze the role of asymptomatic and symptomatic patients in the infectious disease transmission process, a simple sufficient condition for the stability of the Markov process of infectious diseases is derived using the mean drift technique. Then, the stationary probability vector of the QBD process is obtained by using RG-factorizations. A method of using the stationary probability vector is provided to obtain important performance measures of the model. Finally, some numerical experiments are presented to demonstrate the model's feasibility through analyzing COVID-19 as an example. The impact of key parameters on the system performance evaluation and the infectious disease transmission process are analyzed. The methodology and results of this paper can provide theoretical and technical support for the scientific control of the long-term transmission of infectious diseases, and we believe that they can serve as a foundation for developing more general models of infectious disease transmission.

To address the issues in reliability bench tests for drive motor system of electric vehicle, particularly low correlation between reliability test conditions and real-world user driving scenarios, as well as non-equivalence in damage effects, a method for constructing reliability test cycles based on user driving models is proposed. Firstly, driving scenarios are analyzed and actual driving characteristics of users are identified by utilizing big data from real-world driving. Secondly, K-means clustering analysis is conducted to establish typical operating conditions, from which segments with unit damage intensity ranging from the 95th percentile to the 99th percentile are selected into an alternative library. Finally, reliability test cycles are constructed through a genetic algorithm and Markov process. The results of damage analysis show that the operating conditions constructed for reliability test maintain the typical driving characteristics of users and demonstrate a good acceleration test effect. When the motor product is continuously loaded on the test bench for 1625.7h and 1302.1h respectively, the shafting and gear train are considered achieving the users' damage expectation, equivalent to a whole life cycle of 300,000 km.

This study is motivated by industries in which products can be partially prepared and stored before demand occurs, while demand is stock-dependent. We study a multi-server system in which the servers utilise their idle time to produce and store 'preliminary services' (PSs) in order to reduce customers' sojourn time and, as a result, stimulating demand by creating the anticipation of a shorter sojourn time. In order to facilitate closed-form solutions, we analyse a Markovian queueing-inventory model and apply matrix geometric (MG) methods. In contrast to most applications in which the rate matrix R of the MG analysis is calculated numerically, our analysis enables derivation of explicit solutions for the entries of R and discovers their relation to Catalan numbers, allowing a rapid solution for large systems. Consequently, the system's stability condition is readily obtained and shown to be identical to that of a regular M/M/s queue. Two models are developed: one for non-perishable PSs, the other for perishable ones. An economic analysis is provided for two case studies: a bike store and a pizza store. We observe that the reward has low sensitivity to deviation from the optimal PSs capacity and high sensitivity to deviation from the optimal promotional level. [ABSTRACT FROM AUTHOR]

In this work, a two-level control system is used to minimize the total active power losses of an active distribution system connected to the external grid and composed of a wind turbine, two photovoltaic power sources, and two batteries. At the first control level, a model-based predictive control (MPC) is run, using non-homogeneous Markov reward models for wind power prediction and homogeneous Markov reward models for photovoltaic power. At the second level, an algorithm is run for optimal management of voltage control assets, such as voltage regulating transformers, to minimize losses. Different scenarios have been considered, highlighting the advantages of using an MPC framework. This results in an optimization process that can be influenced by different time horizons depending on whether or not the MPC is applied. The predictions allow considering a long-horizon stepwise optimization process that leads to an increasing number of variables along with the decrease of total active power losses. When the MPC is not applied, a short-horizon analysis is performed with a decrease in both the number of variables and the quality of the results. Different cases are considered in which the nominal power of a photovoltaic unit and the battery capacity are modified.

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]

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]

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]

Subject to intense high-energy particle irradiation, various effects manifest within a material. Specifically, when high-energy particles collide with lattice atoms in a crystal material, a sequence of interactions is set in motion, initiating irradiation effects. Using GaAs solar cells as an example, this study investigates how potential barriers in different directions of atoms in sphalerite structures affect atomic displacement and establishes a probability model for lattice atomic displacement under proton irradiation. By combining Markov chains, changes in displacement threshold energy with different crystal orientations are described, and a damage model for cascading collision relationships that cause irradiation effects is established. Finally, the new model is compared to classical models, and differences in defects caused by proton impacts at several energies on GaAs crystals are simulated. [ABSTRACT FROM AUTHOR]

We propose a refined dynamic programming model based on a hidden Markov chain formulation and a nonlinear filtering technique to calculate the optimal debt ratio for public and private sectors for different scenarios. We then conduct the empirical analysis of the U.S. markets in real estate and equities during 1991.Q1 and 2020.Q1, comparing them with the theoretical results. It indicates that U.S. households and governments spent more than they can afford. While households reduced their debt ratio during times of economic distress, the public sector hiked its debt ratio to stimulate the economy. The policy effect took a long time to accumulate, and the outcome was lower than expected to revitalize the economy in time. [ABSTRACT FROM AUTHOR]

Image forgery detection is a challenging issue because fake images can be prepared accurately using precise editing tools. In this paper, a robust image forensics technique based on a multi-direction threshold (MDT) is proposed to detect median filtering. In the proposed method, an optimal thresholded array is derived from difference arrays in multiple directions. The Markov process is applied to fetch the joint probability statistics of neighboring pixels on optimally thresholded difference arrays. The proposed optimal MDT utilizes both first and second-order difference arrays for additional information that leads to a more comprehensive feature set. As a result, the proposed technique achieves 93.40%, 90.59%, and 85.76% detection accuracy on JPEG compressed images of size 64 × 64 pixels with quality factors 70, 50, and 30, correspondingly. The non-filtered and median filtered images are classified using LDA and SVM classifiers. The superiority of the proposed technique is analyzed through exhaustive experimental analysis on centrally cropped and zero-padded median filtered images. [ABSTRACT FROM AUTHOR]

Copyright of China Mechanical Engineering is the property of Editorial Board of China Mechanical Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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]

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]

Hidden Markov chains are widely applied statistical models of stochastic processes, from fundamental physics and chemistry to finance, health, and artificial intelligence. The hidden Markov processes they generate are notoriously complicated, however, even if the chain is finite state: no finite expression for their Shannon entropy rate exists, as the set of their predictive features is generically infinite. As such, to date one cannot make general statements about how random they are nor how structured. Here, we address the first part of this challenge by showing how to efficiently and accurately calculate their entropy rates. We also show how this method gives the minimal set of infinite predictive features. A sequel addresses the challenge’s second part on structure.

In this paper we concern with the Fibonacci bimodal maps. We first study the topological properties of the Fibonacci bimodal maps in the context of kneading map and give an equivalent description of Fibonacci combinatorics. Then we construct a one-parameter family $ f_{\lambda} $ of countably piecewise linear Fibonacci bimodal maps depending on the parameter $ \lambda $ which are all odd functions. By a random walk argument on its induced Markov map, we will show that a phase transition occurs from Lebesgue conservative to Lebesgue dissipative behaviors.

This paper presents a more general cobweb model that incorporates the Hilfer fractional derivative in either the demand or supply function or Markov process. The main contributions of this study include deriving the analytical solution for the general model, analyzing the stability of the solution, introducing the equilibrium position using Mittag–Leffler functions, and providing detailed graphical illustrations to validate the effectiveness of the proposed model. The outcomes generalize some known results.

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]

We consider a growing population of individuals with binary opinions, namely, 0 or 1, that evolve in discrete time. The underlying interaction network is complete. At every time step, a fixed number of individuals are added to the population. The opinion of the new individuals may or may not depend on the current configuration of opinions in the population. Further, in each time step, a fixed number of individuals are chosen and they update their opinion in three possible ways: they organically switch their opinion with some probability and with some probability they adopt the majority or the minority opinion. We study the asymptotic behaviour of the fraction of individuals with either opinion and characterize conditions under which it converges to a deterministic limit. We analyze the behaviour of the limiting fraction as a function of the probability of new individuals having opinion 1 as well as with respect to the ratio of the number of people being added to the population and the number of people being chosen to update opinions. We also discuss the nature of fluctuations around the limiting fraction and study the transitions in scaling depending on the system parameters. Further, for this opinion dynamics model on a finite time horizon, we obtain optimal external influencing strategies in terms of when to influence to get the maximum expected fraction of individuals with opinion 1 at the end of the finite time horizon. [ABSTRACT FROM AUTHOR]

BACKGROUND AND OBJECTIVES: In this research, our main objective is more accurate pricing of life insurance products with a new approach of predicting mortality or survival rates. Currently, a life table is used to calculate the current value of pensions, insurance premiums, etc. Therefore, to increase the accuracy of our calculations, we are looking for a mortality prediction model for such calculations. Therefore, in this research, instead of static pricing (only using the latest life table), we used life table prediction and dynamically rated life insurance products. METHODS: In this research, a new model proposed to predict the probability of human mortality (survival) based on the Markov process, a limited state with an absorption state (death). This model measured based on the physiological age, because the physiological age of each person can be checked based on different laboratory indicators, and finally it has led to the results of the individual health index. In addition, the parameters of this model are the initial probability vector and the sub-intensity matrix of a Markov chain that changes over time. In other words, in this model, according to a possible process in the model, the initial probability vector over time selects the possible interval of the physiological age equivalent to the chronological age. FINDINGS: To show the satisfactory performance of this model, the relevant data set from the United States of America was analyzed. The predicted results with the presented model are better than Lee Carter’s model. It should be noted that the number of parameters of the model introduced in this research is much less compared to the Lee Carter model and other mortality or survival prediction models. Based on this model, a closed form for life insurance pricing relationships is obtained, which simplifies these calculations for users. CONCLUSION: The relationships obtained for pricing were investigated based on two products, 5-year term life insurance and also a 5-year term pension. The fitted results for the model used in the predictions of the probability of mortality as well as the probability of survival and pricing are very satisfactory. [ABSTRACT FROM AUTHOR]

Copyright of Automotive Engineer (1674-6546) is the property of Auto Engineering Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This research examines the reliability characteristics of a broad series–parallel system. Complex system, having elements in series and parallel configuration is considered here to compute the reliability. Due to the failure of component, the system can either breakdown or can work with reduced frequency. To analyze the effect of component failure, sensitivity of the system with respect to reliability parameters is analyzed. In this study, generally distributed and exponentially distributed repair rates are taken into consideration from failed state to the working state of the system. The mathematical model of the designed structure is developed using Markov process and supplementary variable technique. The comparative study of the system availability and its sensitivity with respect to general distribution and general as well as exponential distribution has been examined. The Gumbel–Hougaard family of copula is used to analyze the effect of both the distributions together. For a better explanation of this work, a numerical example has been provided and shown the results graphically. [ABSTRACT FROM AUTHOR]