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This paper proposes an efficient method for quantifying the stratigraphic uncertainties and modeling the geological formations based on boreholes. Two Markov chains are used to describe the soil transitions along different directions, and the transition probability matrices (TPMs) of the Markov chains are analytically expressed by copulas. This copula expression is efficient since it can represent a large TPM by a few unknown parameters. Due to the analytical expression of the TPMs, the likelihood function of the Markov chain model is given in an explicit form. The estimation of the TPMs is then re-casted as a multi-objective constrained optimization problem that aims to maximize the likelihoods of two independent Markov chains subject to a set of parameter constraints. Unlike the method which determines the TPMs by counting the number of transitions between soil types, the proposed method is more statistically sound. Moreover, a random path sampling method is presented to avoid the directional effect problem in simulations. The soil type at a location is inferred from its nearest known neighbors along the cardinal directions. A general form of the conditional probability, based on Pickard's theorem and Bayes rule, is presented for the soil type generation. The proposed stratigraphic characterization and simulation method is applied to real borehole data collected from a construction site in Wuhan, China. It is illustrated that the proposed method is accurate in prediction and does not show an inclination during simulation. [ABSTRACT FROM AUTHOR]

Objective. Severe radiation-induced lymphopenia occurs in 40% of patients treated for primary brain tumors and is an independent risk factor of poor survival outcomes. We developed an in-silico framework that estimates the radiation doses received by lymphocytes during volumetric modulated arc therapy brain irradiation. Approach. We implemented a simulation consisting of two interconnected compartmental models describing the slow recirculation of lymphocytes between lymphoid organs ( M 1 ) and the bloodstream ( M 2 ). We used dosimetry data from 33 patients treated with chemo-radiation for glioblastoma to compare three cases of the model, corresponding to different physical and biological scenarios: (H1) lymphocytes circulation only in the bloodstream i.e. circulation in M 2 only; (H2) lymphocytes recirculation between lymphoid organs i.e. circulation in M 1 and M 2 interconnected; (H3) lymphocytes recirculation between lymphoid organs and deep-learning computed out-of-field (OOF) dose to head and neck (H&N) lymphoid structures. A sensitivity analysis of the model's parameters was also performed. Main results. For H1, H2 and H3 cases respectively, the irradiated fraction of lymphocytes was 99.8 ± 0.7%, 40.4 ± 10.2% et 97.6 ± 2.5%, and the average dose to irradiated pool was 309.9 ± 74.7 mGy, 52.6 ± 21.1 mGy and 265.6 ± 48.5 mGy. The recirculation process considered in the H2 case implied that irradiated lymphocytes were irradiated in the field only 1.58 ± 0.91 times on average after treatment. The OOF irradiation of H&N lymphoid structures considered in H3 was an important contribution to lymphocytes dose. In all cases, the estimated doses are low compared with lymphocytes radiosensitivity, and other mechanisms could explain high prevalence of RIL in patients with brain tumors. Significance. Our framework is the first to take into account OOF doses and recirculation in lymphocyte dose assessment during brain irradiation. Our results demonstrate the need to clarify the indirect effects of irradiation on lymphopenia, in order to potentiate the combination of radio-immunotherapy or the abscopal effect. [ABSTRACT FROM AUTHOR]

When we observe a stationary time series with observations missing at periodic time points, we can still estimate its marginal distribution well, but the dependence structure of the time series may not be recoverable at all, or the usual estimators may have much larger variance than in the fully observed case. We show how non‐parametric estimators can often be improved by adding unbiased estimators. We focus on a simple setting, first‐order Markov chains on a finite state space, and an observation pattern in which a fixed number of consecutive observations is followed by an observation gap of fixed length, say workdays and weekends. The new estimators perform astonishingly well in some cases, as illustrated with simulations. The approach extends to continuous state space and to higher‐order Markov chains. [ABSTRACT FROM AUTHOR]

This study employs the diffusion process to construct Markov chains for analyzing the common two-inertia systems used in industry. Two-inertia systems are prevalent in commonly used equipment, where the load is influenced by the coupling of external force and the drive shaft, leading to variations in the associated output states. Traditionally, the control of such systems is often guided by empirical rules. This paper examines the equilibrium distribution and convergence rate of the two-inertia system and develops a predictive model for its long-term operation. We explore the qualitative behavior of the load end at discrete time intervals. Our findings are applicable not only in control engineering, but also provide insights for small-scale models incorporating dual-system variables. [ABSTRACT FROM AUTHOR]

Unmanned aerial vehicle (UAV) swarms serve as a dynamic platform for diverse missions, including communication relays, search and rescue operations, and environmental monitoring. The success of these operations crucially depends on the resilience of their electrical support systems, especially in terms of battery management. This paper examines the reliability of electrical support for UAV swarms engaged in missions that require prioritization into high and low categories. The paper proposes a dynamic resource allocation strategy that permits the flexible reassignment of drones across different-priority tasks, ensuring continuous operation while optimizing resource use. By leveraging the Markov chain theory, an analytical model for the evaluation of the resilience of the battery management system under different operational scenarios was developed. The paper quantitatively assesses the impact of different operational strategies and battery management approaches on the overall system resilience and mission efficacy. This approach aims to ensure uninterrupted service delivery for critical tasks while optimizing the overall utilization of available electrical resources. Through modeling and analytical evaluations, the paper quantifies the impact of various parameters and operating strategies on overall system resilience and mission availability, considering the utilization strategies of batteries and their reliability and maintenance metrics. The developed models and strategies can inform the development of robust battery management protocols, resource allocation algorithms, and mission planning frameworks, ultimately enhancing the operational availability and effectiveness of UAV swarms in critical special missions. [ABSTRACT FROM AUTHOR]

This study considers an application of the first-order Grey Markov Model to foresee the values of Italian power generation in relation to the available energy sources. The model is used to fit data from the Italian energy system from 2000 to 2022. The integration of Markovian error introduces a random element to the model, which is able now to capture inherent uncertainties and misalignments between the Grey Model predictions and the real data. This application provides valuable insights for strategic planning in the energy sector and future developments. The results show good accuracy of the predictions, which could provide powerful information for the effective implementation of energy policies concerning the evolution of energy demand in the country. Results show an improvement in the performance of more than 50% in terms of Root Mean Squared Error (RMSE) when the Markov chain is integrated in the analysis. Despite advancements, Italy's 2032 energy mix will still significantly rely on fossil fuels, emphasizing the need for sustained efforts beyond 2032 to enhance sustainability. [ABSTRACT FROM AUTHOR]

Phylogenetic Trees are critical in human genome research for investigating human evolution and identifying disease-associated genetic markers. New high-throughput genome sequencing technologies raise an urgent need to develop statistical methods that can construct phylogenetic trees from long genome sequences with quick computation speeds, while considering various biological complexities. Though an ancestral mixture model has been proposed [Chen SC, Lindsay BG. Building mixture trees from binary sequence data. Biometrika. 2006;93(4):843–860. doi: 10.1093/biomet/93.4.843] to this end by allowing genetic mutations over generations, another essential evolution factor, genetic recombination, is missed. Therefore, in this paper, we develop a novel genetic recombination model for tree construction and propose to use Markov chain composite likelihood (MCCL) to make model estimation computationally feasible. To further reduce computation complexity, a hierarchical estimator is constructed to estimate unknown ancestral distributions through MCCL. Simulation studies and real data example show that our proposed methods perform well and fast, so have the potential for implementation in long sequence genome data. [ABSTRACT FROM AUTHOR]

Metaheuristic algorithms are increasingly used for feature selection (FS) problems due to their robustness and searchability. This study presents a unique optimization technique called fuzzy bluefin trevally optimizer (BTO). BTO draws its inspiration from bluefin’s cooperative nature and sudden ambush behavior. The trevally will jump out of the water and attack its food in the air or even snag it off the water when it is sufficiently close to it. This study uses mathematical modeling to create an optimization algorithm to replicate dynamic patterns and behaviors. Since parameters play a critical role in optimization, we use the fuzzy concept for dynamic parameter adaptation in fuzzy BTO. By introducing the idea of signature and demonstrating that fuzzy BTO converges to the global optimal point, the mathematical basis for the proposed algorithm is provided. The convergence of fuzzy BTO is proved using the Markov chain property. On benchmark functions (BF), the effectiveness of the suggested strategies is evaluated and compared with other metaheuristic algorithms. Then the proposed algorithms are applied to a fuzzy FS problem. Then they are compared with traditional and recent metaheuristic algorithms on the UCI machine learning repository datasets. Finally, the statistical significance is examined using the Kruskal–Wallis test (KWT). [ABSTRACT FROM AUTHOR]

The historic evolution of global primary energy consumption (GPEC) mix, comprising of fossil (liquid petroleum, gaseous and coal fuels) and non-fossil (nuclear, hydro and other renewables) energy sources while highlighting the impact of the novel corona virus 2019 pandemic outbreak, has been examined through this study. GPEC data of 2005–2021 has been taken from the annually published reports by British Petroleum. The equilibrium state, a property of the classical predictive modeling based on Markov chain, is employed as an investigative tool. The pandemic outbreak has proved to be a blessing in disguise for global energy sector through, at least temporarily, reducing the burden on environment in terms of reducing demand for fossil energy sources. Some significant long term impacts of the pandemic occurred in second and third years (2021 and 2022) after its outbreak in 2019 rather than in first year (2020) like the penetration of other energy sources along with hydro and renewable ones in GPEC. Novelty of this research lies within the application of the equilibrium state feature of compositional Markov chain based prediction upon GPEC mix. The analysis into the past trends suggests the advancement towards a better global energy future comprising of cleaner fossil resources (mainly natural gas), along with nuclear, hydro and renewable ones in the long run. [ABSTRACT FROM AUTHOR]

In the United States, regions (such as states or counties) are frequently divided into districts for the purpose of electing representatives. How the districts are drawn can have a profound effect on who is elected, and drawing the districts to give an advantage to a certain group is known as gerrymandering. It can be surprisingly difficult to detect when gerrymandering is occurring, but one algorithmic method is to compare a current districting plan to a large number of randomly sampled plans to see whether it is an outlier. Recombination Markov chains are often used to do this random sampling: randomly choose two districts, consider their union, and split this union up in a new way. This approach works well in practice and has been widely used, including in litigation, but the theory behind it remains underdeveloped. For example, it is not known if recombination Markov chains are irreducible, that is, if recombination moves suffice to move from any districting plan to any other. Irreducibility of recombination Markov chains can be formulated as a graph problem: for a planar graph G , is the space of all partitions of G into k connected subgraphs (k districts) connected by recombination moves? While the answer is yes when districts can be as small as one vertex, this is not realistic in real-world settings where districts must have approximately balanced populations. Here we fix district sizes to be k 1 ± 1 vertices, k 2 ± 1 vertices, ... for fixed k 1 , k 2 , ... , a more realistic setting. We prove for arbitrarily large triangular regions in the triangular lattice, when there are three simply connected districts, recombination Markov chains are irreducible. This is the first proof of irreducibility under tight district size constraints for recombination Markov chains beyond small or trivial examples. The triangular lattice is the most natural setting in which to first consider such a question, as graphs representing states/regions are frequently triangulated. The proof uses a sweep-line argument, and there is hope it will generalize to more districts, triangulations satisfying mild additional conditions, and other redistricting Markov chains. [ABSTRACT FROM AUTHOR]

To accurately predict bridge performance degradation, the inherent data randomness and the subtle perturbations leading to state transitions were considered. A combined prediction method for the bridge performance degradation based on the D-S theory and the Markov chain, and the performance degradation rate concept, were proposed. In this model, the exponential smoothing (ES) methodology was employed as the basis for generating new sequences of predictive data. It was continuously optimized through the utilization of the Markov chains and the Dempster-Shafer (D-S) evidence theory. The combined prediction of bridge performance degradation was achieved. The application results from practical engineering show that, the performance degradation rate serves as an intuitive indicator of the speed at which the bridge performance degrades. Subsequently, the combined model demonstrates an average relative error of 1.54%, improves by 1.11%, 0.88%, and 2.8% in accuracy, respectively in comparison with other models of the regression, the grey system, and the fuzzy weighted Markov chain. Additionally, the calculated posterior difference ratio is 0.242, well below the established threshold of 0.35. In terms of stability, the standard deviation of the model is 9.021, reduces by 3.978, 3.405 and 7.500, respectively compared with those of the other 3 models. The coefficient of variation is 0.109, indicating a significant reduction in comparison to those of the other models. The combined prediction model, with verified accuracy and stability, establishes a theoretical foundation for prediction and maintenance of in-service bridg- es' structural performance degradation. [ABSTRACT FROM AUTHOR]

In the past few years, significant advancements in microscopic imaging technology have led to the production of numerous high-resolution images capturing brain neurons at the micrometer scale. The reconstructed structure of neurons from neuronal images can serve as a valuable reference for research in brain diseases and neuroscience. Currently, there lacks an accurate and efficient method for neuron reconstruction. Manual reconstruction remains the primary approach, offering high accuracy but requiring significant time investment. While some automatic reconstruction methods are faster, they often sacrifice accuracy and cannot be directly relied upon. Therefore, the primary goal of this paper is to develop a neuron reconstruction tool that is both efficient and accurate. The tool aids users in reconstructing complete neurons by calculating the confidence of branches during the reconstruction process. The method models the neuron reconstruction as multiple Markov chains, and calculates the confidence of the connections between branches by simulating the reconstruction artifacts in the results. Users iteratively modify low-confidence branches to ensure precise and efficient neuron reconstruction. Experiments on both the publicly accessible BigNeuron dataset and a self-created Whole-Brain dataset demonstrate that the tool achieves high accuracy similar to manual reconstruction, while significantly reducing reconstruction time. [ABSTRACT FROM AUTHOR]

Predicting vehicle mobility is crucial in domains such as ride-hailing, where the balance between offer and demand is paramount. Since city road networks can be easily represented as graphs, recent works have exploited graph neural networks (GNNs) to produce more accurate predictions on real traffic data. However, a better understanding of the characteristics and limitations of this approach is needed. In this work, we compare several GNN aggregated mobility prediction schemes to a selection of other approaches in a very restricted and controlled simulation scenario. The city graph employed represents roads as directed edges and road intersections as nodes. Individual vehicle mobility is modeled as transitions between nodes in the graph. A time series of aggregated mobility is computed by counting vehicles in each node at any given time. Three main approaches are employed to construct the aggregated mobility predictors. First, the behavior of the moving individuals is assumed to follow a Markov chain (MC) model whose transition matrix is inferred via a least squares estimation procedure; the recurrent application of this MC provides the aggregated mobility prediction values. Second, a multilayer perceptron (MLP) is trained so that—given the node occupation at a given time—it can recursively provide predictions for the next values of the time series. Third, we train a GNN (according to the city graph) with the time series data via a supervised learning formulation that computes—through an embedding construction for each node in the graph—the aggregated mobility predictions. Some mobility patterns are simulated in the city to generate different time series for testing purposes. The proposed schemes are comparatively assessed compared to different baseline prediction procedures. The comparison illustrates several limitations of the GNN approaches in the selected scenario and uncovers future lines of investigation. [ABSTRACT FROM AUTHOR]

In a Hidden Markov model (HMM), from hidden states, the model generates emissions that are visible. Generally, the problems to be solved by such models, are based on such emissions that are considered as observed data. In this work, we propose to study the case where some emissions are missing in a given emission sequence using different techniques, in particular a split technique which reduces the computational cost. Mainly we resolve the fundamental problems of an HMM with a lack of observations. The algorithms obtained following this approach are successfully tested through numerical examples. [ABSTRACT FROM AUTHOR]

A new highly nonlinear hybrid stochastic neural network with variable time delays is formulated, which is usually found to be unstable. In addition, the network coefficients considered in this article grow polynomially rather than linearly as we always considered before. Since original system is unstable, the purpose of this article is to construct a variable-delay feedback control function to make the augmented system stable. Then, four results on the stabilisation of the controlled system are given separately. At last, an example is provided to display the feasibility of theoretical results. [ABSTRACT FROM AUTHOR]

Summary: Rapid intelligent transportation systems (ITS) innovations need a reliable MAC protocol to enable massive nonsafety message delivery and high‐priority safety broadcasts. The significant rise in spectrum need is regulated by collaboration in cognitive vehicular networks (CVNs). For QoS improvement, a reliable cooperative MAC for CVNs (CCVN‐MAC) is presented in this study. CCVN allows vehicles to collaborate and share channel status information, allowing for proactive channel switching in case of a legacy user (LU) appearance. To enable transmission mode selection, additional control signals are included. Using the suggested cooperative makeup technique, the helper nodes resend failed transmission. A Markov chain represents the protocol, and NS‐2 is used to evaluate it for several performance characteristics. Compared with conventional MAC techniques, the proposed protocol depicts improved performance, including depreciation of 70% in average latency and an increment of 42.4% in throughput. [ABSTRACT FROM AUTHOR]

By a scheme of a musical canon, we mean the time and pitch displacement of each entering voice. When the time displacements are unequal, achieving consonant sonorities is especially challenging. Using a first-species theoretical model, we quantify the flexibility of schemes that Renaissance composers used or could have used. We craft an algorithm to compute this flexibility value precisely (finding in the process that it is an algebraic integer). We find that Palestrina consistently selected some of the most flexible schemes, more so than his predecessors, but that he by no means exhausted all feasible schemes. To add support to the model, we present two new compositions within the limits of the style utilizing unexplored canonic schemes. In the Online Supplement, we provide MIDI realizations of the musical examples and Sage code used in the numerical computations. [ABSTRACT FROM AUTHOR]

Epidemics pose a serious threat to public health, and effective disease control measures are essential. To address this challenge, we propose a novel stochastic Susceptible Vaccinees Infected Recovered (SVIR) epidemic model that incorporates temporary immunities, media coverage, and three types of noises: white noise, telegraph noise, and L é$$ \overset{\acute }{e} $$vy noise. Our model is more realistic than traditional epidemic models, as it accounts for the random fluctuations in disease transmission and the impact of media coverage on public behavior. We use Lyapunov functions and stopping times to prove the existence of a global positive solution to our model. We also derive sufficient conditions for the extinction and persistence of the infection. Furthermore, we develop a numerical scheme to validate our theoretical findings and to analyze the influence of various parameters on the model's dynamics. Our model can be used to guide policymakers in developing and implementing effective disease control measures. [ABSTRACT FROM AUTHOR]

The advent of the Internet of Things brought a new age of interconnected device functionality, ranging from personal devices and smart houses to industrial control systems. However, increased security risks have emerged in its wake, in particular self-replicating malware that exploits weak device security. Studies modeling malware epidemics aim to predict malware behavior in essential ways, usually assuming a number of simplifications, but they invariably simplify the single most important subdynamics of malware: random propagation. In our previous work, we derived and presented the first exact mathematical model of random propagation, defined as the subdynamics of propagation of a malware model. The propagation dynamics were derived for the SIS model in discrete form. In this work, we generalize the methodology of derivation and extend it to any Markov chain model of malware based on random propagation. We also propose a second method of derivation based on modifying the simplest form of the model and adjusting it for more complex models. We validated the two methodologies on three malware models, using simulations to confirm the exactness of the propagation dynamics. Stochastic errors of less than 0.2% were found in all simulations. In comparison, the standard nonlinear model of propagation (present in ∼95% of studies) has an average error of 5% and a maximum of 9.88% against simulations. Moreover, our model has a low mathematical trade-off of only two additional operations, being a proper substitute to the standard literature model whenever the dynamical equations are solved numerically. [ABSTRACT FROM AUTHOR]

The iron and steel industry significantly contributes to global energy use and greenhouse gas emissions. The rising deployment of volatile renewables and the resultant need for flexibility, coupled with specific challenges in electric steelmaking (e.g., operation optimization, optimized power purchasing, effective grid capacity monitoring), require accurate energy consumption and demand forecasts for electric steel mills to align with the energy transition. This study investigates diverse approaches to forecast the energy consumption and demand of an electric arc furnace—one of the largest consumers on the grid—considering various forecast horizons and objectives with limited knowledge on process parameters. The results are evaluated for accuracy, robustness, and costs. Two grid connection capacity monitoring approaches—a one-step and a multi-step Long Short-Term Memory neural network—are assessed for intra-hour energy demand forecasts. The one-step approach effectively models energy demand, while the multi-step approach encounters challenges in representing different operational phases of the furnace. By employing a combined statistic–stochastic model integrating a Seasonal Auto-Regressive Moving Average model and Markov chains, the study extends the forecast horizon for optimized day-ahead electricity procurement. However, the accuracy decreases as the forecast horizon lengthens. Nevertheless, the day-ahead forecast provides substantial benefits, including reduced energy balancing needs and potential cost savings. [ABSTRACT FROM AUTHOR]

In the quality management system, skip-lot sampling is a prominent beneficial sampling plan concerning the economic aspect since it requires minimum expenses for inspection. This study attempts to propose an innovative sampling plan by assimilating the concept of a resampling scheme in a two-level skip-lot sampling plan of type 3, that is, SkSP-2L.3, and the resultant plan is designated as SkSP-2L.3-R with a single sampling plan as the reference plan. Using Markov chain formulation, the performance measures are derived. The designing methodology is provided to determine the plan parameters of the SkSP-2L.3-R plan to minimize the average sample number by using two points on the operating characteristic curve approach. Tables are constructed to select the plan parameters under binomial distribution and Poisson distribution by considering various combinations of producer and consumer quality levels along with respective producer and consumer risks. An illustrative example is provided to depict the execution of the proposed SkSP-2L.3-R plan. The comparative study substantiates that the proposed SkSP-2L.3-R plan with a single sampling plan as the reference plan has outstanding performance than some other existing plans under binomial and Poisson distributions. [ABSTRACT FROM AUTHOR]

The problem of stabilizing an unstable highly nonlinear hybrid neutral stochastic functional differential equation with infinite delay (HNSFDEwID) is addressed in this article. The objective of this study is to propose a discrete‐time feedback control (DTFC) approach for stabilizing the original system. Sufficient conditions are derived for the existence and uniqueness of the system's solution, as well as its boundedness, prerequisites for studying the system's dynamic behavior. Four distinct criteria for stabilizing the controlled system are provided, including H∞$$ {H}_{\infty } $$ stabilization, asymptotic stabilization, exponential stabilization, and almost surely exponentially stabilization. Additionally, the upper limit of the time interval for discrete observations is calculated based on these criteria. Finally, the proposed theory is validated through an illustrative example. [ABSTRACT FROM AUTHOR]

Understanding the historical and projected changes in land use and land cover (LULC) in Djelfa city is crucial for sustainable land management, considering both natural and human influences. This study employs Landsat images from the Google Earth Engine and the support vector machine (SVM) technique for LULC classification in 1990, 2005, and 2020, achieving over 90% accuracy and kappa coefficients above 88%. The Land Change Modeler (LCM) was used for detecting changes and predicting future LULC patterns, with Markov Chain (MC) and Multi Layer Perceptron (MLP) techniques applied for 2035 projections, showing an average accuracy of 83.96%. Key findings indicate a substantial urban expansion in Djelfa city, from 924.09 hectares in 1990 to 2742.30 hectares in 2020, with a projected increase leading to 1.6% of nonurban areas transitioning to urban by 2035. There has been significant growth in steppe areas, while forested, agricultural, and barren lands have seen annual declines. Projections suggest continued degradation of bare land and a slight reduction in steppe areas by 2035. These insights underscore the need for reinforced policies and measures to enhance land management practices within the region to cater to its evolving landscape and promote sustainable development. [ABSTRACT FROM AUTHOR]

The traditional rule-based energy management strategy for plug-in hybrid vehicles has issues, such as difficulty in online correction and limited online optimization capabilities. In addition, the global optimization energy management strategy cannot be applied online or in real-time. Considering the above difficulties, this study proposes a real-time optimization energy management strategy based on the Markov chain for driving condition prediction and online optimization with the minimum principle. To verify the proposed control strategy, the plug-in hybrid vehicle dynamics model, driving condition prediction model, and online optimization control model were first established. The initial value of the battery state of charge was set to 0.4 under the UDDS (Urban Dynamometer Driving Schedule) standard cycle. The simulation results showed that the comprehensive fuel consumption cost was 1.66 yuan, which was 8.28% better than the energy economy of the traditional rule-based energy management strategy. At the same time, a complete vehicle test was also conducted based on a sample vehicle test platform. The experimental results indicated that the energy management strategy proposed herein exhibits better fuel economy compared to that exhibited by the traditional rule-based energy management strategy. Simulations and experiments have verified the effectiveness of the proposed control strategy in this study. [ABSTRACT FROM AUTHOR]

The paper presents a Markovian queueing model for assessing the performance of synchronisation between stations in a production system. The system at hand consists of K distinct buffers, each buffer storing an item that is needed for the next production stage. Departures are immediate when all items are present. Due to the presence of multiple buffers, there is no reasonably fast way to calculate the stationary distribution of the Markov chain. Therefore, we focused on the series expansion of the stationary distribution in terms of the arrival rate. We provide a fast algorithm for calculating these terms. Comparing our results with stochastic simulation, we show that the expansion approach converges to the simulated values for a wide range of arrival rates. [ABSTRACT FROM AUTHOR]

In clinical trials and other comparative studies, covariate balance is crucial for credible and efficient assessment of treatment effects. Covariate adaptive randomization (CAR) procedures are extensively used to reduce the likelihood of covariate imbalances occurring. In the literature, most studies have focused on balancing of discrete covariates. Applications of CAR with continuous covariates remain rare, especially when the interest goes beyond balancing only the first moment. In this article, we propose a family of CAR procedures that can balance general covariate features, such as quadratic and interaction terms. Our framework not only unifies many existing methods, but also introduces a much broader class of new and useful CAR procedures. We show that the proposed procedures have superior balancing properties; in particular, the convergence rate of imbalance vectors is O P (n ϵ) for any ϵ > 0 if all of the moments are finite for the covariate features, relative to O P (n) under complete randomization, where n is the sample size. Both the resulting convergence rate and its proof are novel. These favorable balancing properties lead to increased precision of treatment effect estimation in the presence of nonlinear covariate effects. The framework is applied to balance covariate means and covariance matrices simultaneously. Simulation and empirical studies demonstrate the excellent and robust performance of the proposed procedures. for this article are available online. [ABSTRACT FROM AUTHOR]

This study aims to contribute to the knowledge about lacking or contradictory effects of benzodiazepine on hyperaroused or aggressive behaviour in persons with intellectual disability (ID). We conducted a retrospective and natural case study in a person with mild ID and multiple adverse childhood experiences (ACE), using routine diary data consisting of 275 days including 113 consecutive days under benzodiazepine medication. The medication effects were documented as "calm / relaxed", "fretful / distressed" and "sleep / doze". Transitions between these were modelled using Markov chains. Differences in transitions were analysed using Chi-Square test for homogeneity. The results show a significantly reduced stability of mood and increased distressed behaviour under benzodiazepine. This is in line with reports about the effects of psychotropic medication in patients with ID and challenging behaviour. Besides other influences on unexpected medication effects, a possible dissociative identity disorder is discussed as an additional explanation. [ABSTRACT FROM AUTHOR]

In this paper we consider a generalization of the coupon collector problem where we assume that the set of available coupons consists of standard coupons and an additional penalty coupon, which does not belong to the collection and interferes with collecting standard coupons. Applying Markov chain approach the following problem is solved: how many coupons (on average) one has to purchase in order to complete a collection without interference or to collect n more penalty coupons than standard coupons. Also, we obtain additional results related to the distribution of the waiting time until the collection is sampled without interference or until n more penalty coupons than standard coupons is sampled. [ABSTRACT FROM AUTHOR]

When p related variables in a multivariate process need to be controlled, p1 variables are easy to measure and inexpensive, while the rest of p2 variables are difficult to measure and expensive. Therefore, controlling the whole set of p variables may be difficult and expensive. In order to reduce sampling costs of the multivariate control chart in detecting shifts in the process mean vector and the process covariance matrix of a multivariate normally distributed process, a new multivariate control chart with variable dimension (VD) is proposed, which uses two different dimensions, two different control limits and one warming limit. The VD multivariate control chart uses genetic algorithm to optimize the parameters and Markov chain model to calculate the performance measures. The performance of the proposed optimized VD chart is compared with the standard chart for which all p1 and p variables are measured. Numerical results show that the VD chart surpasses the standard chart in detecting process mean vector and the process covariance matrix, while also reducing sampling costs. [ABSTRACT FROM AUTHOR]

Context and background: In current industrialized world, extremely increase of urbanization, Agriculture land expansion and climate change have led to increase of degradation of wetland in many basins and coastal area, which result to the malfunction of its ecosystem services. However, there are few studies have been conducted to analyze how the historical degradation of wetland will continue in the future especially in most of the developing countries. Goal and objectives: The overall objective of the study intents to provide an integrated method which includes GIS, remote sensing and CA-Markov Chain modelling to analyse the influence of LULC dynamic into wetland degradation. Specifically, is to use historical land use/cover maps of 2000,2010 and 2020 to develop land use simulation model to predict the spatial degradation of wetland for three decades. Methodology: In this study will use historical land use/cover maps of 2000,2010 and 2020 to develop land use simulation model to predict the spatial degradation of wetland in Wami-Ruvu river basin for coming 30 years (2020-2050) under different scenarios using land change modeler (LCM) in Idris-TerrSet. Future land use/cover map of the study area was developed using Markov chain and artificial neural network (ANN) Analysis in LCM modeler. Results: The study found of about 1209.0753Km2 (2%), 949Km2 (1.4%), 521.33Km2 (0.78%) and 213 (0.32%) of wetland was decreasing, which was equal to 1339999, 1055066, 578584and 237199 for the year 2000, 2010, 2020 and 2050 for the individual pixel values respectively, which made a half of the total simulated wetland to have been lost that is 50% of the land in the study region. [ABSTRACT FROM AUTHOR]

In this article, we study an implementation of maximum entropy (ME) design utilizing a Markov chain. This design, which is also called the conditional Poisson sampling design, is difficult to implement. We first present a new method for calculating the weights associated with conditional Poisson sampling. Then, we study a very simple method of random exchanges of units, which allows switching from one sample to another. This exchange system defines an irreducible and aperiodic Markov chain whose ME design is the stationary distribution. The design can be implemented without enumerating all possible samples. By repeating the exchange process a large number of times, it is possible to select a sample that respects the design. The process is simple to implement, and its convergence rate has been investigated theoretically and by simulation, which led to promising results. [ABSTRACT FROM AUTHOR]

The parking system is a vital element within intelligent transport systems, playing a pivotal role in alleviating traffic congestion and mitigating associated stress and anxiety. In response to evolving operational requirements, specialized parking systems such as autonomous valet parking (AVP) and smart parking systems (SPS) are employed based on the specific characteristics of vehicles. This research endeavor begins by introducing a loosely connected middleware designed to accommodate a variety of vehicles within a unified parking area. While the automatic parking system is designed for automated vehicles, and the manual parking system caters to manually operated vehicles, both systems lack the ability to effectively manage both automatic and manual vehicles. To address this challenge, a middleware solution is introduced, which acts as an intermediary layer between vehicles and the parking system. This middleware consists of various modules, enabling the seamless entry of all vehicle types into parking areas, regardless of classification or mode of operation. Second, it uses the Markov Chain model to determine the enhancement in the usability of the parking system after the incorporation of the middleware. Lastly, the suggested loosely coupled middleware approach is compared with tightly coupled smart parking approaches like automatic and manual systems. The matrices of assessment evaluated showed that the recommended scheme outperform its predecessors. In addition, it demonstrated remarkable achievement in terms of cost function, space availability (70%), and traffic jam reduction (56%). The advocated middleware, apart from keeping smooth traffic flow, assists in fulfilling the dire need for parking areas. [ABSTRACT FROM AUTHOR]

AbstractDue to the advancement of electronic data capturing, the amount of repeated categorical data being collected and stored has increased. This massive amount of data is complex and poses significant statistical challenges in methodology and computation. To analyze such big data, the divide and recombine method is commonly used. First, a large data set is partitioned into subsets, and each subset is analyzed separately. Then, the results are recombined in a manner that produces statistically valid output. However, available literature can only accommodate cross-sectional data. We propose a new simpler approach to analyze large, repeated categorical data using a joint modeling framework. In the proposed method, follow-up time is a natural conditioning variable that allows big data to be divided into subsets. Then, using the relationship between joint, marginal, and conditional probabilities, we can recombine the results in a statistically valid way. Several machine learning algorithms for cross-sectional data are extended for repeated outcomes to predict trajectories using the proposed framework. As an illustration, the proposed methodology is used to analyze repeatedly measured activity of daily living (ADL) data from the Health and Retirement Study (HRS), USA. We also check model performances under multiple machine learning algorithms using bootstrap simulations. [ABSTRACT FROM AUTHOR]

This paper considers the stability robustness and $ H_2 $ H2 performance robustness of continuous-time Markovian jump linear systems with uncertain transition rates. Based on the Kronecker product, the robustness problems are transformed into problems of judging whether a class of uncertain matrices can maintain nonsingularity. For the robust stability problem, the method for computing the robust upper and lower bounds of transition rates is given first and then the necessary and sufficient condition for the investigated system to maintain robust stochastic stability is given when considering interval uncertainty. For the robust $ H_2 $ H2 performance problem, the robustness bounds and sufficient and necessary conditions guaranteeing the robust $ H_2 $ H2 performance are similarly given. The robustness bounds for analysing the tolerance of continuous-time Markovian jump linear systems to parameter uncertainties can be conveniently computed by utilising the proposed results. Numerical examples illustrate that the results are less conservative than existing results. [ABSTRACT FROM AUTHOR]

Recent years have witnessed a surge in the mobile data traffic which is only expected to grow exponentially in the coming years. To cope up with this huge data demand, mobile operators have restored to a novel scheme called on-the-spot mobile data offloading wherein mobile data is offloaded onto Wi-Fi network whenever the user enters a Wi-Fi coverage area. Further reports indicate that a sizable portion of the mobile data traffic is multimedia in nature that demands good quality of service. In this context, we design and analyze a scheme to prioritize different data traffic encountered in on-the-spot mobile data offloading. Using a Markov chain model for on-the-spot mobile data offloading scheme, we derive the packet transmission delay of different traffic categories that carry different priorities. We validate out analytical results against simulation and demonstrate the effectiveness of the proposed prioritization scheme. [ABSTRACT FROM AUTHOR]

We consider the following generalization of the classical coupon collector problem. We assume that, in addition to the initial collection of standard coupons, there is one more coupon that acts as a reset button, removing all coupons from the part of the collection that has already been drawn. For the case where standard coupons have unequal probabilities of being drawn, we obtain the distribution of the waiting time until the end of the collection process. For the case where standard coupons have equal probabilities, we derive a simple formula for the expected waiting time in terms of the beta function, and discuss the asymptotic properties of this expected waiting time, when the number of standard coupons tends toward infinity. [ABSTRACT FROM AUTHOR]

Objective: The outbreak of the COVID-19 pandemic has drawn attention from all sectors of society to the level of public health services. This study aims to investigate the level of public health service supply in the four major regions of Guangdong Province, providing a basis for optimizing health resource allocation. Methods: This article uses the entropy method and panel data of 21 prefecture-level cities in Guangdong Province from 2005 to 2021 to construct the evaluation index system of public health service supply and calculate its supply index. On this basis, the standard deviation ellipse method, kernel density estimation, and Markov chain are used to analyze the spatiotemporal evolution trend of the public health service supply level in Guangdong Province. The Dagum Gini coefficient and panel regression model are further used to analyze the relative differences and the key influencing factors of difference formation. Finally, the threshold effect model is used to explore the action mechanism of the key factors. Results: Overall, the level of public health service supply in Guangdong Province is on an upward trend. Among them, polarization and gradient effects are observed in the Pearl River Delta and Eastern Guangdong regions; the balance of public health service supply in Western Guangdong and Northern Mountainous areas has improved. During the observation period, the level of public health services in Guangdong Province shifted towards a higher level with a smaller probability of leapfrogging transition, and regions with a high level of supply demonstrated a positive spillover effect. The overall difference, intra-regional difference and inter-regional difference in the level of public health service supply in Guangdong Province during the observation period showed different evolutionary trends, and spatial differences still exist. These differences are more significantly positively affected by factors such as the level of regional economic development, the degree of fiscal decentralization, and the urbanization rate. Under different economic development threshold values, the degree of fiscal decentralization and urbanization rate both have a double threshold effect on the role of public health service supply level. Conclusion: The overall level of public health service supply in Guangdong Province has improved, but spatial differences still exist. Key factors influencing these differences include the level of regional economic development, the degree of fiscal decentralization, and the urbanization rate, all of which exhibit threshold effects. It is suggested that, in view of the actual situation of each region, efforts should be made to build and maintain their own advantages, enhance the spatial linkage of public health service supply, and consider the threshold effects of key factors in order to optimize the allocation of health resources. [ABSTRACT FROM AUTHOR]

In this article; a TDMA-based cognitive radio network is modeled and the call performance of secondary users in this network is analyzed for different primary and secondary user traffic parameters and for different numbers of time slots. In our model, primary users utilize Time Division Multiple Access technique as the media access control mechanism, differing from well-known classical approaches, and by means of an opportunistic approach, secondary users take advantage of time slots not used by primary users. In addition, in the proposed network model, it is assumed that primary users have higher priority in accessing the channel than secondary users and are not affected by secondary users' channel occupation. The performance of the cognitive radio network is analyzed in detail in terms of call-block and call-drop probabilities using a two-dimensional continuous Markov chain. In addition, the Monte-Carlo simulation of the proposed network model has been performed, and the obtained analytical results have been verified by the simulation results. According to the simulation results obtained, when the SU (secondary user) arrival rate is λ_s=0,07 and the number of time slot is N=4, the call block probability of SU is 0.0347, when the number of time slot is N=6, this value is improved by 95% to 0.00172 and when the number of time slot is N=8, value is improved by 99% to 0.00034. [ABSTRACT FROM AUTHOR]

Land use changes are one of the main factors in the amount of surface runoff changes in watersheds. Therefore, it is necessary to investigate it to reduce the damages (human and financial) caused by floods and to modify watershed management. The watershed of Nahre Azam is located in the north of Shiraz city and a lot of loss of life and money to the residents of Shiraz due to floods has occurred in previous years. The present research was conducted to investigate the relationship between land use change and runoff in the Nahre Azam watershed in Shiraz using the SWAT model in the period of 2004-2020. The model was calibrated using data from 2004 to 2014 and validated for 2015 to 2020. These images were classified into 6 main land uses using the supervised classification method after performing necessary preprocessing, and a land use map was prepared for 2040 using the Markov chain method. Then, the effect of the land use change in 2003 and 2040 on the amount of simulated runoff was evaluated with the recalibrated model. The calibration results of Nahre Azam watershed for the values of statistical parameters in the calibration step for the coefficient of determination, P-Facor and R-Facor are 0.77, 0.72, and 2.43, respectively, and for the validation step we obtained 0.69, 0.65, and 2.3 respectively. The analysis of the land use map showed that the main land use change in the region related to the conversion of pastures to agricultural land and urban land, which caused a decrease in pastures. Also, the results of the model simulation using the land use maps of 2003 and 2040 indicated that the amount of runoff decreased. The results revealed that if all the uncertainties are minimized, the calibrated SWAT model can produce acceptable hydrological simulation results for the user, which is useful for water resource and environmental managers and politicians as well as city managers of Shiraz. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the "Walk on Equations" (WE) Monte Carlo algorithm, a novel approach for solving linear algebraic systems. This algorithm shares similarities with the recently developed WE MC method by Ivan Dimov, Sylvain Maire, and Jean Michel Sellier. This method is particularly effective for large matrices, both real- and complex-valued, and shows significant improvements over traditional methods. Our comprehensive comparison with the Gauss–Seidel method highlights the WE algorithm's superior performance, especially in reducing relative errors within fewer iterations. We also introduce a unique dominancy number, which plays a crucial role in the algorithm's efficiency. A pivotal outcome of our research is the convergence theorem we established for the WE algorithm, demonstrating its optimized performance through a balanced iteration matrix. Furthermore, we incorporated a sequential Monte Carlo method, enhancing the algorithm's efficacy. The most-notable application of our algorithm is in solving a large system derived from a finite-element approximation in constructive mechanics, specifically for a beam structure problem. Our findings reveal that the proposed WE Monte Carlo algorithm, especially when combined with sequential MC, converges significantly faster than well-known deterministic iterative methods such as the Jacobi method. This enhanced convergence is more pronounced in larger matrices. Additionally, our comparative analysis with the preconditioned conjugate gradient (PCG) method shows that the WE MC method can outperform traditional methods for certain matrices. The introduction of a new random variable as an unbiased estimator of the solution vector and the analysis of the relative stochastic error structure further illustrate the potential of our novel algorithm in computational mathematics. [ABSTRACT FROM AUTHOR]

The Markov property is shared by several popular models for time series such as autoregressive or integer-valued autoregressive processes as well as integer-valued ARCH processes. A natural assumption which is fulfilled by corresponding parametric versions of these models is that the random variable at time t gets stochastically greater conditioned on the past, as the value of the random variable at time t - 1 increases. Then the associated family of conditional distribution functions has a certain monotonicity property which allows us to employ a nonparametric antitonic estimator. This estimator does not involve any tuning parameter which controls the degree of smoothing and is therefore easy to apply. Nevertheless, it is shown that it attains a rate of convergence which is known to be optimal in similar cases. This estimator forms the basis for a new method of bootstrapping Markov chains which inherits the properties of simplicity and consistency from the underlying estimator of the conditional distribution function. [ABSTRACT FROM AUTHOR]

It is well known that spacetime has no operational meaning beyond the Planck scale. In consequence, many high-energy theoretical physicists are seeking, and finding, new structures entirely beyond spacetime. In light of these advances, we propose that time is not fundamental. The arrow of time is an artifact of projection of a stationary dynamics, entirely beyond spacetime and quantum theory, whose entropy does not increase. [ABSTRACT FROM AUTHOR]

A two-sided sequential probability ratio test (SPRT) control chart for monitoring the mean of a normal process is proposed in this paper. Its mechanism is based on the SPRT for the mean of a normal distribution that is extended for a two-sided alternative. The exact statistical performance measures of this chart are obtained using a Markov chain approach. An approach to design the chart such that it has a specified in-control performance and the optimal out-of-control performance for detecting a mean shift of a particular size is provided. The statistical performance of this chart is numerically compared with that of various competing charts in the existing literature. It is found that the proposed chart outperforms all these charts for detecting a mean shift of any size. An example to illustrate the mechanism of the chart is provided. [ABSTRACT FROM AUTHOR]

With the massive ongoing efforts to mitigate climate change and reduce emission factors in the transportation sector, driving cycles (DCs) are becoming an essential tool for the testing and certification of distinct types of vehicles. Nevertheless, the open literature lacks careful comparative studies on the impact of different approaches in the development of Markov chain (MC)-based DCs, as well as DCs, developed specifically for the developing and highly congested urban areas in the Middle East and North Africa. Using a large dataset of 43 light-duty vehicles, driven over different areas in Greater Cairo, Egypt, this study aims to develop, compare, and benchmark 24 candidate MC-based DCs, against two clustering-based DCs, as well as four cycles used widely in the US and Europe. These 24 DCs differ in terms of the clustering algorithm (K-medoids and K-means), clustering parameters (different combinations of vehicle’s speed, acceleration, specific power, and percentage idling time), and definitions of microtrips (start-stop and fixed distance). The results show that the MC method outperforms random chaining of microtrips, with average relative root mean square errors (RRMSEs) of 15.8% and 23.6%, respectively. Clustering 350 m fixed distance-based microtrips using the vehicle’s speed, acceleration, and percentage idling time shows the least RRMSE of 8.207%. Defining microtrips based on fixed distance is also better than starts/stops for most vehicle types. The reference cycles (WLTP, NEDC, UDDS, and FTP-17) showed poor representativeness of the real-world data, with an average RRMSE of 76.8%. The same inferior performance of reference cycles, compared to the newly proposed ones, was also highlighted in the estimation of fuel consumption and emission factors. Hence, the proposed cycles and the reported comparative studies can be valuable tools for the assessment of emissions and fuel consumption in such developing metropolitan areas. [ABSTRACT FROM AUTHOR]

We study the inventory review policy for a healthcare facility to minimize the impact of inevitable drug shortages. Usually, healthcare facilities do not rely on a single source of supply, and alternative mechanisms are present. When the primary supplier is not available, items are produced in-house or supplied through another supplier, albeit with additional cost. Our aim in this study is to determine how optimal inventory parameters are adjusted depending on the availability of the primary supplier. We show that an approximation provides trivial results, yet fails to capture the nuances therein. Our proposed Markov chain model overcomes these issues, and numerical results illustrate the significant economic impact of inventory parameter optimization. Furthermore, we simulate uncertainty scenarios and provide sensitivity analyses concerning fixed ordering cost for the secondary supplier, shortage frequency, shortage duration, and demand rates. [ABSTRACT FROM AUTHOR]

In this paper, we have studied various types of Monte Carlo methods along with the Power method to evaluate the maximum and minimum eigenvalue of a linear system of equations. We have studied how the accuracy of the maximum eigenvalue depends on the parameters, (moves in Markova chain), (no of Markova chain), (accelerating parameter), and a parameter m (the power applied on the resolving matrix). We have applied these methods to the randomly chosen symmetric matrices. We have also made comparisons for the different matrices of different orders depending on the parameters by using the Monte Carlo methods. We are using Matlab 2020R for the calculation. [ABSTRACT FROM AUTHOR]

A generalized stochastic modification of the Colonel Blotto game, also known as the game of gladiators, is considered. In the original model, each of two players has a set of gladiators with given strengths. The battle of gladiator teams takes place through individual gladiator battles. In each fight, the probability of gladiator winning is proportional to its strength. Kaminsky et al. in 1984 had obtained a formula for the probability of winning in terms of weighted sums of exponential random variables. Here we provide an interpretation of this result from the Markov chains with continuous time point of view, and a more general statement of the problem is considered, for which a similar expression is obtained. [ABSTRACT FROM AUTHOR]

We study a graph-based generalization of the Galam opinion formation model. Consider a simple connected graph which represents a social network. Each node in the graph is colored either blue or white, which indicates a positive or negative opinion on a new product or a topic. In each discrete-time round, all nodes are assigned randomly to groups of different sizes, where the node(s) in each group form a clique in the underlying graph. All the nodes simultaneously update their color to the majority color in their group. If there is a tie, each node in the group chooses one of the two colors uniformly at random. Investigating the convergence time of the model, our experiments show that the convergence time is a logarithm function of the number of nodes for a complete graph and a quadratic function for a cycle graph. We also study the various strategies for selecting a set of seed nodes to maximize the final cascade of one of the two colors, motivated by viral marketing. We consider the algorithms where the seed nodes are selected based on the graph structure (nodes' centrality measures such as degree, betweenness, and closeness) and the individual's characteristics (activeness and stubbornness). We provide a comparison of such strategies by conducting experiments on different real-world and synthetic networks. [ABSTRACT FROM AUTHOR]

The previous stochastic hosting capacity prediction method using the Monte Carlo method for high photovoltaic (PV) penetration with a battery energy storage system (BESS) required a large number of computations to achieve the expected accuracy. The problem of high computational load must be addressed so that the electrical distribution planner can practically use the PV hosting capacity prediction in actual situations. Therefore, this study developed a Markov-chain-based PV hosting capacity prediction method for high PV penetration using BESS. The proposed method is described in detail, followed by case and validation studies. The obtained hosting capacity was 123.58 kW, which increased to 3676.4 kW after the utility-scale BESS implementation. The results demonstrate that the proposed Markov-chain-based PV hosting capacity prediction method outperforms the Monte Carlo method, which is the most popular stochastic hosting capacity method, in terms of accuracy and computational cost. [ABSTRACT FROM AUTHOR]

Determining the rules that lead to the expansion of urban areas has always been a challenging factor in urban modeling. To overcome this issue, an ANFIS model is proposed to enhance the simulation of urban growth through automatic production of transition rules. Hence, 22 ANFIS models were trained using different division methods and a Cellular Automata-based Markov Chain (CA-MC) was developed to examine their efficiencies. The results of accuracies reveal that the ANFIS accompanied by subtractive clustering (ANFIS-SC) simulating urban growth with a Kappa coefficient of 0.76 and overall accuracy of 93.41% is superior to other ANFIS and CA-MC models. [ABSTRACT FROM AUTHOR]