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The transport of molecules through biological and synthetic nanopores is governed by multiple stochastic processes that lead to noisy, fluctuating currents. Disentangling the characteristics of different noise-generating mechanisms is central to better understanding molecular transport at a fundamental level but is extremely challenging in molecular systems due to their complexity and relative experimental inaccessibility. Here, we construct a colloidal model microfluidic system for the experimental measurement of particle currents, where the governing physical properties are directly controllable and particle dynamics directly observable, unlike in the molecular case. Currents of hard spheres fluctuate due to the random arrival times of particles into the channel and the distribution of particle speeds within the channel, which results in characteristic scalings in the power spectral density. We rationalize these scalings by quantitatively comparing to a model for shot noise with a finite transit time, extended to include the distribution of particle speeds. Particle velocity distributions sensitively reflect the confining geometry, and we interpret and model these in terms of the underlying fluid flow profiles. Finally, we explore the extent to which details of these distributions govern the form of the resulting power spectral density, thereby establishing concrete links between the power spectral density and underlying mechanisms for this experimental system. This paves the way for establishing a more systematic understanding of the links between characteristics of transport fluctuations and underlying molecular mechanisms in driven systems such as nanopores. [ABSTRACT FROM AUTHOR]

We consider a stochastic capacitated lot sizing problem with in-line rework. Both defective and defect-free products can be the result of an imperfect production process in real-world production systems. However, the proportion of defective items in a production lot is subject to uncertainty. For economic and environmental reasons, the possibility to rework defective products appears reasonable since these products usually have considerable value. In this paper, a nonlinear model formulation for integrated lot sizing and rework planning is proposed. We use a sample average approach to approximate the generic nonlinear model formulation. To cope with the randomness of the proportion of defective products, we apply a flexible planning approach that allows the adjustment of production and rework quantities. We conduct extensive numerical investigations to evaluate the performance of the proposed planning approach. [ABSTRACT FROM AUTHOR]

Generic open quantum systems are notoriously difficult to simulate unless one looks at specific regimes. In contrast, classical dissipative systems can often be effectively described by stochastic processes, which are generally less computationally expensive. Here, we use the paradigmatic case of a dissipative quantum oscillator to give a pedagogic introduction to the modeling of open quantum systems using quasiclassical methods, i.e., classical stochastic methods that use a "quantum" noise spectrum to capture the influence of the environment on the system. Such quasiclassical methods have the potential to offer insights into the impact of the quantum nature of the environment on the dynamics of the system of interest while still being computationally tractable. [ABSTRACT FROM AUTHOR]

Spontaneous gas-bubble nucleation in weak gas–liquid solutions has been a challenging topic in theory, experimentation, and computer simulations. In analogy with recent advances in crystallization and droplet formation studies, the diffusive-shielding stabilization and thermodynamic irreversibility of bulk nanobubble (bNB) mechanisms are revisited and deployed to characterize nucleation processes in a stochastic framework of computer experiments using the large-scale atomic/molecular massively parallel simulator code. Theoretical bases, assumptions, and limitations underlying the irreversibility hypothesis of bNBs, and their computational counterparts, are extensively described and illustrated. In essence, it is established that the irreversibility hypothesis can be numerically investigated by converging the system volume (due to the finiteness of interatomic forces) and the initial dissolved-gas concentration in the solution (due to the single-bNB limitation). Helium nucleation in liquid Pb17Li alloy is selected as a representative case study, where it exhibits typical characteristics of noble-gas/liquid-metal systems. The proposed framework lays down the bases on which the stability of gas-bNBs in weak and supersaturated gas–liquid solutions can be inferred and explained from a novel perspective. In essence, it stochastically marches toward a unique irreversible state along out-of-equilibrium nucleation/growth trajectories. Moreover, it does not attempt to characterize the interface or any interface-related properties, neither theoretically nor computationally. It was concluded that bNBs of a few tens of He-atoms are irreversible when dissolved-He concentrations in the weak gas–liquid solution are at least ∼50 and ∼105 mol m−3 at 600 and 1000 K (and ∼ 80 MPa), respectively, whereas classical molecular dynamics -estimated solubilities are at least two orders of magnitude smaller. [ABSTRACT FROM AUTHOR]

We consider a single-machine scheduling problem with due-date assignment and stochastic processing times, where only the mean and support (i.e. an interval bounded with lower and upper values) of processing times are known to the decision maker. The objective is to jointly determine a scheduling policy and a set of due dates for all jobs, so as to minimise the total expected individually weighted costs of earliness, tardiness and due-date assignment. By identifying an upper bound with the robust optimisation approach and a lower bound, and using a linear function of them to approximate the studied objective function, we establish an approximated problem. Then, a branch-and-bound algorithm is proposed to find an optimal solution for the approximated problem. Finally, a series of computational experiments are conducted to examine the performance of problem approximation and two developed heuristic algorithms. HIGHLIGHTS Study due-date assignment scheduling problem with stochastic processing times. Apply the mean and support (interval data) to model stochastic processing times. Use a linear function of identified lower and upper bounds to make an approximation. Derive optimal due-date assignment and develop branch-and-bound algorithms. Evaluate the efficiency of branch-and-bound algorithm and heuristic algorithms. [ABSTRACT FROM AUTHOR]

The aim of this study is to suggest a novel approach for estimating the intramolecular mobility of a charge carrier that migrates within a polymer chain and is involved in a pair reaction with a particle located on the same chain. The approach is based on the effect of an external electric field on the migration rate and, consequently, the kinetics of the reaction. As a first step, this problem is considered a stochastic one-step process with absorbing and reflecting boundaries, and an analytical solution is obtained in the case that the second reactant is immobile. With the use of computer simulations of stochastic migration, the effect of the mobility of both reactants and the influence of the Coulomb interaction between them are considered. It is found that the ratio of the pair reaction rates with and without an external field is relatively little dependent on these factors and that the analytical expressions derived can be applied to estimate the relative mobility of recombining particles with accuracy better than a factor of two in many realistic situations. [ABSTRACT FROM AUTHOR]

Generative Adversarial Networks (GANs) have shown immense potential in fields such as text and image generation. Only very recently attempts to exploit GANs to statistical-mechanics models have been reported. Here we quantitatively test this approach by applying it to a prototypical stochastic process on a lattice. By suitably adding noise to the original data we succeed in bringing both the Generator and the Discriminator loss functions close to their ideal value. Importantly, the discreteness of the model is retained despite the noise. As typical for adversarial approaches, oscillations around the convergence limit persist also at large epochs. This undermines model selection and the quality of the generated trajectories. We demonstrate that a simple multi-model procedure where stochastic trajectories are advanced at each step upon randomly selecting a Generator leads to a remarkable increase in accuracy. This is illustrated by quantitative analysis of both the predicted equilibrium probability distribution and of the escape-time distribution. Based on the reported findings, we believe that GANs are a promising tool to tackle complex statistical dynamics by machine learning techniques. [ABSTRACT FROM AUTHOR]

Time‐varying group formation tracking control problems for multi‐agent systems are investigated based on distributed multi‐sensor multi‐target filtering with intermittent observations. First, in order to estimate the states of multiple targets under the phenomenon of intermittent observations accurately, a distributed multi‐sensor multi‐target filtering algorithm is proposed based on cubature Kalman filtering. Second, a time‐varying group formation tracking protocol is designed for multi‐agent systems by using the state estimations obtained from the filtering algorithm and the neighboring interaction. The protocol enables multi‐agent systems to form time‐varying subformations and track multiple targets in the same subgroups, respectively. Third, the boundedness of the error covariance matrices is proved under the condition that the observation probability is higher than the minimum threshold. Then the estimation errors of the filtering algorithm are proved to be stochastically bounded by introducing a stochastic process. Furthermore, the boundedness of the group formation tracking errors is proved. Finally, a numerical example is used to verify the performance of the proposed algorithm and protocol. [ABSTRACT FROM AUTHOR]

This paper provides an enjoyable example through which several concepts of classical mechanics can be understood. We introduce an equation that models the motion of a cat in the presence of a person. The cat is considered as a point particle moving in a potential induced by the person. We demonstrate that this approach to the problem reproduces characteristic behaviors of these curious animals. For instance, the fact that cats do not typically come when they are called, or that they remain longer on the lap of their favorite person; even "zoomies" are reproduced (cats randomly run back and forth across the house). We use this model problem to explore topics of current research such as stochastic equations and periodically driven systems. The pedagogical value of this work and its potential use in teaching are discussed. Editor's note: Since Erwin Schrödinger, cats have become the unofficial mascots of quantum mechanics. But cats can be useful in classical mechanics too. This paper shows that typical feline behaviors, such as their preferred resting position (on your lap or, more likely, far away), ignoring calls, and purring, can actually be explained by classical mechanics. Even zoomies, those periods of time when cats are frantic, can also be modeled as a stochastic process. So, it turns out your cat might just be the perfect example for most of an undergraduate mechanics course! [ABSTRACT FROM AUTHOR]

A (4 , 5) -coloring of K n is an edge-coloring of K n where every 4-clique spans at least five colors. We show that there exist (4 , 5) -colorings of K n using 5 6 n + o (n) colors. This settles a disagreement between Erdős and Gyárfás reported in their 1997 paper. Our construction uses a randomized process which we analyze using the so-called differential equation method to establish dynamic concentration. In particular, our coloring process uses random triangle removal, a process first introduced by Bollobás and Erdős, and analyzed by Bohman, Frieze and Lubetzky. [ABSTRACT FROM AUTHOR]

Structural resistance deterioration is by nature a non-increasing stochastic process with autocorrelation on the temporal scale. The Gamma process is often used to describe the stochastic behavior of resistance deterioration. With Gamma-based deterioration models, the calculation of time-dependent reliability presents a serious challenge, and often Monte Carlo simulation is the only solution to this problem. This paper derives a closed-form solution for time-dependent reliability of aging structures, in which the resistance deterioration is described by a Gamma process and the applied load is modelled as a Gaussian process with a constant standard deviation. The accuracy of the proposed method is verified through a comparison with Monte Carlo simulation results, and its applicability is further illustrated in a time-dependent reliability analysis of an existing highway bridge whose vehicle load is modelled using weigh-in-motion (WIM) data. It is found that the measured vehicle load has a relatively small uncertainty, and the uncertainty associated with resistance deterioration is crucial to the reliability assessment because it dominates the overall uncertainty in the reliability calculation. [ABSTRACT FROM AUTHOR]

• An automatic iterative algorithm was proposed to dynamically distinguish the car-following and free-flow states of AVs and HVs. • The heterogeneous car-following behaviors of AVs and HVs were compared. • The effects of time period and vehicle type on headway distribution were explored. • The impacts of penetration rate, platoon intensity and maximum platoon size on the mixed traffic capacity were explored. This study refined the composite headway distribution model to estimate the mixed traffic capacity by utilizing extensive empirical mixed traffic data. The enhanced model integrated an automatic iterative algorithm into the stochastic process to capture the headway distributions of autonomous and human-driven vehicles in five types of car-following pair combinations. The proposed iterative algorithm automatically fitted the free-flow headway distribution and dynamically determined the threshold for distinguishing the car-following and free-flow states of autonomous and human-driven vehicles based on extensive trajectory data. Quantitative analysis was carried out to assess the impact of time period and vehicle type on the headway distributions of following vehicles in the five car-following pairs. The mixed traffic capacity was estimated using the overall composite headway distribution model, considering the effects of penetration rate, platoon intensity, and maximum platoon size of the autonomous vehicle. The findings indicated that autonomous vehicles showed more cautious and sensitive car-following behaviors compared to human-driven vehicles. Compared to the daytime, autonomous vehicles showed more cautious car-following behaviors at night. When following heavy vehicles, autonomous vehicles typically adapt conservative and stable car-following behaviors. In addition, the results also showed that the penetration rate, platoon intensity, and maximum platoon size significantly affected the capacity of mixed traffic flow. These results of this study can assist traffic management authorities in formulating rules or policies that take into consideration the growing prevalence of autonomous vehicles. [ABSTRACT FROM AUTHOR]

Identifying near‐fault pulse‐like ground motions from extensive ground motion databases holds paramount importance, as it provides a pivotal foundation for further inquiries into this specific type of ground motions, including the modeling of such stochastic processes as well as thorough analysis of their potential impact on structures and infrastructure systems. Currently, a diverse array of quantitative methods for identifying pulse‐like ground motions have emerged, all of which demonstrate good accuracy within their respective research scopes. However, due to the limitations of each individual method in identifying specific cases, these diverse approaches often yield inconsistent results for certain ground motion records, posing a significant challenge in establishing a reliable classification criterion that relies solely on a single identification method. To address this issue, the present study adopts a multifaceted approach. Instead of improving a single time‐frequency analysis‐based identification method, it carefully conducts a selection of seven baseline methods through a systematic overview of the field. By leveraging the analytic hierarchy process (AHP), a comprehensive categorization method is developed that integrates the strengths of each approach, resulting in a more robust and credible classification criterion. According to the devised category indicator, ground motions can be classified into four categories: Category A comprises definitively pulse‐like ground motions; Category B comprises apparently pulse‐like ground motions; Category C consists of probably pulse‐like ground motions; and Category D encompasses ground motions unlikely to exhibit pulse‐like characteristics. It provides a more elaborate classification beyond the binary distinction of pulse‐like and non‐pulse‐like ground motions associated with traditional onefold classification methods. For validation purposes, a basic dataset comprising near‐fault ground motion records from the NGA‐West 2 database has been utilized. To verify the comprehensive categorization method, two datasets of pulse‐like ground motion records suggested by FEMA and PEER and one dataset of ground motion records collected during the 1999 Chi‐Chi earthquake are addressed. Numerical examples illustrate the remarkable effectiveness of the proposed method in identifying near‐fault pulse‐like ground motions based on their varying degrees of pulse‐like characteristics. [ABSTRACT FROM AUTHOR]

Subsampling is a practical strategy for analyzing vast survival data, which are progressively encountered across diverse research domains. While the optimal subsampling method has been applied to inferences for Cox models and parametric accelerated failure time (AFT) models, its application to semi‐parametric AFT models with rank‐based estimation have received limited attention. The challenges arise from the non‐smooth estimating function for regression coefficients and the seemingly zero contribution from censored observations in estimating functions in the commonly seen form. To address these challenges, we develop optimal subsampling probabilities for both event and censored observations by expressing the estimating functions through a well‐defined stochastic process. Meanwhile, we apply an induced smoothing procedure to the non‐smooth estimating functions. As the optimal subsampling probabilities depend on the unknown regression coefficients, we employ a two‐step procedure to obtain a feasible estimation method. An additional benefit of the method is its ability to resolve the issue of underestimation of the variance when the subsample size approaches the full sample size. We validate the performance of our estimators through a simulation study and apply the methods to analyze the survival time of lymphoma patients in the surveillance, epidemiology, and end results program. [ABSTRACT FROM AUTHOR]

Corrosion processes are often discussed as stochastic events. Here, it is shown that some of these seemingly random processes are not driven by nanoscopic fluctuations but rather by the spatial distribution of micrometer‐scale heterogeneities that trigger fast reactions associated with corrosion. Using a novel excitable reaction‐diffusion model, corrosion waves traveling over the metal surface and the associated material loss are described. This resulting nonuniform corrosion penetration, seen as a height loss in modeling, exposes buried intermetallic particles, which depending on the local electrochemical state of the surface trigger or block new waves. Informed by quantitative experimental data for the Mg–Al–Zn alloy AZ31B, wave speeds, wave widths, and average material loss are accurately captured. Morphogenic mitigation based on wave‐breaking microparticles is also simulated. While AZ31B corrosion is identified as a process driven by rare‐wave events, this study predicts several other corrosion regimes that proceed via spots or patchy patterns, opening the door for new protection, design, and prediction strategies. [ABSTRACT FROM AUTHOR]

ABSTRACT The underlying assembly processes of surface microbial communities are crucial for host plants and ecosystem functions. However, the relative importance of stochastic and deterministic processes in shaping epiphytic microbes remains poorly understood in both the phyllosphere and rhizosphere. Here, we compared the spatial variations in epiphytic microbial communities of two dominant grasses along a 1400 km transect on the Tibetan Plateau and assessed the assembly processes between the phyllosphere and rhizosphere. We found significant variations in epiphytic microbial community compositions between plant compartments and host species. Stochastic processes (drift and homogenizing dispersal) predominantly shaped microbial communities in both the phyllosphere and rhizosphere, with a greater contribution of stochastic processes in the phyllosphere. As environmental heterogeneity intensified, we found a transition from stochasticity to determinism in affecting the microbial assembly. This transition to homogeneous or variable selection depended on plant compartments and host species. Our study is among the first to compare the contribution of stochastic versus deterministic processes to epiphytic community assembly between the phyllosphere and rhizosphere on the Tibetan Plateau. These findings advance our knowledge of epiphytic microbial assembly and disentangle how host plants exploit the microbiome for improved performance and functioning in stressful alpine ecosystems. [ABSTRACT FROM AUTHOR]

Introduction: Archaeal communities play a crucial role in marine ecosystems, yet our understanding of their ecological and functional traits remains incomplete. This study focuses on northern Hangzhou Bay to fill gaps in knowledge regarding the biogeography and functionality of archaeal groups. Methods: We utilized a high-throughput sequencing dataset based on the 16S rRNA gene to characterize the archaeal community, aiming to identify biogeographic patterns and assess the influence of environmental factors on community structure. Results: The predominant phyla identified were Woesearchaeota, Thaumarchaeota, Euryarchaeota, and Crenarchaeota. Archaeal community structure in sediments showed a geographical pattern along the environmental gradient, influenced by factors such as salinity, ammonium, total phosphorus, pH, and total nitrogen content. Network analysis revealed nonrandom cooccurrence patterns, with associations changing along the salinity gradient. Additionally, this study directly proved the existence of dispersal limitation in this strongly connected marine ecological system through null model analyses. Variation in the archaeal community was attributed to both environmental constraints and stochastic processes due to dispersal limitation. Furthermore, our results revealed that the key biogeochemical functions of the archaeal community also exhibited a clear salinity gradient, the functional differences appear to be influenced by salinity, and the critical roles of archaeal diversity were highlighted. [ABSTRACT FROM AUTHOR]

This paper aims to develop a method to construct an asymmetric copula, based on which a closed form of the cumulative bivariate failure rate can be obtained. The construction method differs from existing ones. This new method can facilitate the derivation of some results such as the estimation of the expected number of occurrences for a system whose failure process is modelled by a bivariate stochastic process or the expected cost in optimisation of maintenance policies. [ABSTRACT FROM AUTHOR]

Using aquatic invertebrate assemblages for bioassessment of streams and rivers is a fast and cost-effective approach to studying the impact of environmental stressors in aquatic ecosystems. The use of aquatic invertebrates is premised on their predictable responses to environmental stressors. Assemblage structure is not, however, only influenced by environment, but also neutral processes and temporal variation. This study quantified the relative roles of the environment (niche processes), space (neutral processes) and temporal factors in structuring mayfly and blackfly assemblages at family and species levels. Asymmetric eigenvector maps in conjunction with canonical redundancy analysis and variation partitioning were used to explore the relative roles of these three factors in structuring macroinvertebrate assemblages. At a species level, flow and water temperature were more important in explaining assemblage structure than at the family level. At the family level, space was more important than temporal and environmental factors. Unexplained variation at species and family level was more than 50%. This suggests (i) caution in using family-level rapid assessments to infer the role of the environment in structuring aquatic macroinvertebrate assemblages, as neutral processes are also dominant; and (ii) that the importance of stochastic processes, such as dispersal, should not be underestimated in rapid assessments. [ABSTRACT FROM AUTHOR]

Background: Microorganisms play pivotal roles in seagrass ecosystems by facilitating material and elemental cycling as well as energy flux. However, our understanding of how seasonal factors and seagrass presence influence the assembly of bacterial communities in seagrass bed sediments is limited. Employing high-throughput sequencing techniques, this study investigates and characterizes bacterial communities in the rhizosphere of eelgrass (Zostera marina) and the bulk sediments across different seasons. The research elucidates information on the significance of seasonal variations and seagrass presence in impacting the microbial communities associated with Zostera marina. Results: The results indicate that seasonal variations have a more significant impact on the bacterial community in seagrass bed sediments than the presence of seagrass. We observed that the assembly of bacterial communities in bulk sediments primarily occurs through stochastic processes. However, the presence of seagrass leading to a transition from stochastic to deterministic processes in bacterial community assembly. This shift further impacts the complexity and stability of the bacterial co-occurrence network. Through LEfSe analysis, different candidate biomarkers were identified in the bacterial communities of rhizosphere sediments in different seasons, indicating that seagrass may possess adaptive capabilities to the environment during different stages of growth and development. Conclusions: Seasonal variations play a significant role in shaping these communities, while seagrass presence influences the assembly processes and stability of the bacterial community. These insights will provide valuable information for the ecological conservation of seagrass beds. [ABSTRACT FROM AUTHOR]

The intent of the current study is to explore convex stochastic processes within a broader context. We introduce the concept of unified stochastic processes to analyze both convex and non-convex stochastic processes simultaneously. We employ weighted quasi-mean, non-negative mapping γ , and center-radius ordering relations to establish a class of extended c r -interval-valued convex stochastic processes. This class yields a combination of innovative convex and non-convex stochastic processes. We characterize our class by illustrating its relationships with other classes as well as certain key attributes and sufficient conditions for this class of processes. Additionally, leveraging Riemann–Liouville stochastic fractional operators and our proposed class, we prove parametric fractional variants of Jensen's inequality, Hermite–Hadamard's inequality, Fejer's inequality, and product Hermite–Hadamard's like inequality. We establish an interesting relation between means by means of Hermite–Hadamard's inequality. We utilize the numerical and graphical approaches to showcase the significance and effectiveness of primary findings. Also, the proposed results are powerful tools to evaluate the bounds for stochastic Riemann–Liouville fractional operators in different scenarios for a larger space of processes. [ABSTRACT FROM AUTHOR]

A wide variety of methods have been proposed for clustering of stochastic processes. However, for clustering of periodically correlated processes (PC) it is demanding to introduce some similarity measures that take into account the inherent periodicity of these processes. The frequency-domain based methods seem more desirable to determine groups of PC processes with similar frequency characterizations. In this article, we present new similarity measures based on Hilbert-Schmidt inner product of finite Fourier transforms of PC processes. Based on simulated stochastic processes and a real gene expression dataset we illustrate the accuracy of the methods. [ABSTRACT FROM AUTHOR]

In this article, using conditional power, we extended the widely used classical Brownian motion (Bm) technique for monitoring clinical trial data to a larger class of stochastic processes fractional Brownian motion (fBm) with drift, and compare these results. We applied a Bayesian method to estimate parameters. The simulation study is presented as an example to illustrate scenarios under classical and fractional Brownian motion. We demonstrated the drift fractional Brownian motion in sequential monitoring of clinical trials and provided a formula for calculating conditional power under an alternative hypothesis for interim analysis. We investigated cases commonly used in clinical trials, with the Hurst parameter H = 0.5 and H > 0.5, respectively. Our simulation study suggests that the conditional power under the fBm assumption is generally higher than that under the Bm assumption when H > 0.5 and also matches better with our empirical results. [ABSTRACT FROM AUTHOR]

Exploring on reliability modeling and analysis on a marine equipment in a dynamic environment is a meaningful and challenging issue, because the system commonly carries out the task at sea away from land and suffers a distinct influence of environment. Thus, a reliability model of a multi‐state repairable system operating in dynamic environment is developed by introducing the background of the marine power system in this paper. The novelty of the research lies in the modeling and computing methods are relatively innovative by employing the aggregated stochastic processes, Hadamard production and matrix‐analytic method. First, the working modes of the marine power system under several different kinds of conditions are introduced. Then, the evolution of both the system states and environment are described as discrete‐time Markov chains with multiple and different transition probability matrices. The failure probability and repair probability of components are also distinct in different environments. Furthermore, some performance indexes, especially the index relevant to the environment, are derived, respectively. Finally, the conclusion is obtained by a numerical example of the marine power system, which also illustrates the validity and applicability of the proposed model. [ABSTRACT FROM AUTHOR]

The step stress accelerated degradation test (SSADT) is an effective tool for assessing the reliability of highly reliable products. However, conducting an SSADT is expensive and time consuming, and the obtained SSADT data has an impact on the accuracy of the subsequent product reliability index estimations. Consequently, devising a cost‐constrained SSADT plan that yields high‐precision reliability estimates poses a significant challenge. This paper focuses on the optimal design of SSADT for the Tweedie exponential dispersion process with random effect (TEDR), a general degradation model capable of describing product heterogeneity. Under given budget and boundary constraints, the optimal sample size, observation frequency and observation times at each stress level are obtained by minimizing the asymptotic variance of the estimated quantile life at normal operating conditions. The sensitivity and stability of the SSADT plan are also studied, and the results indicate the robustness of the optimal plan against slight parameters fluctuations. We use the expectation maximization (EM) algorithm to estimate TEDR parameters and reliability indicators under SSADT, providing a systematic method for obtaining the optimal SSADT plan under budget constraints. The proposed framework is illustrated using the case of LED chips data, showcasing its potential for practical application. [ABSTRACT FROM AUTHOR]

We study Mittag–Leffler (ML) fractional integrals involved in the solution processes of a system of coupled fractional stochastic differential equations. We introduce the ML fractional stochastic process as a ML fractional stochastic integral with respect to a standard Brownian motion. We provide some representation formulas of solution processes in terms of Mittag–Leffler fractional integrals and processes. Computable expressions of the mean functions and of the covariances of such processes are specifically given. The application in neuronal modeling is provided, and all involved functions and processes are specifically determined. Numerical evaluations are carried out and some results are shown and discussed. [ABSTRACT FROM AUTHOR]

This work is devoted to the procedure of the construction of an abstract cyclic functional relation, which summarizes and extends the known results for a cyclically correlated random process and a cyclic (cyclically distributed) random process to the case of arbitrary cyclic functional relations. Two alternative definitions of the abstract cyclic functional relation are given, and the fundamental properties of its cyclic and phase structures are presented. The theorem on the invariance of cyclicity attributes of an abstract cyclic functional relation to shifts of its argument, and which are determined by the rhythm function of this functional relation, is formulated and proved. This theorem gives the sufficient and necessary conditions that the rhythm function of an abstract cyclic functional relation must satisfy. By specifying the range of values and attributes of the cyclicity of an abstract cyclic functional relation, the definitions of important classes of cyclic functional relations are formulated. A deductive approach to building a wide system of taxonomies of classes of deterministic, stochastic, fuzzy and interval cyclic functional relations as potential mathematical models of cyclic signals is demonstrated. A comparative analysis of an abstract cyclic functional relation with the known mathematical models of cyclic signals was carried out. The results obtained in the article significantly expand and systematize the mathematical tools of the description of cyclic signals and are the basis for the development of effective model-based technologies for processing and computer simulation of signals with a cyclic space-time structure. [ABSTRACT FROM AUTHOR]

A remarkably high growth has been observed in the uses of wireless sensor networks (WSNs), due to their momentous potential in various applications, namely the health sector, smart agriculture, safety systems, environmental monitoring, military operations, and many more. It is quite important that a WSN must have high reliability along with the least MTTF. This paper introduces a continuous-time Markov process, which is a special case of stochastic process, based on modeling of a wireless sensor network for analyzing the various reliability indices of the same. The modeling has been conducted by considering the different components, including the sensing unit, transceiver, microcontroller, power supply, standby power supply unit, and their failures/repairs, which may occur during their functioning. The study uncovered different important assessment parameters like reliability, components-wise reliability, MTTF, and sensitivity analysis. The critical components of a WSN are identified by incorporating the concept of sensitivity analysis. The outcomes emphasize that the proposed model will be ideal for understanding different reliability indices of WSNs and guiding researchers and potential users in developing a more robust wireless sensor network system. [ABSTRACT FROM AUTHOR]

This paper studies the dynamic behavior of a stochastic SEIRM model of COVID-19 with a standard incidence rate. The existence of global solutions for dynamic system models is proven by integrating stochastic process theory and the concept of stopping times, together with the contradiction method. Moreover, we construct appropriate Lyapunov functions to analyze system stability and apply Dynkin's formula and Fatou's lemma to handle stopping times and expectations of stochastic processes. Notably, the extinction study provides mathematical proof that under the given system dynamics, the total population does not grow indefinitely but tends to stabilize over time. The properties of the diffusion matrix are harnessed to guarantee the system's stationary distribution. Conclusively, numerical simulations confirm the model's extinction outcomes. [ABSTRACT FROM AUTHOR]

In order to use the high ability of the artificial neural network (ANN) in data fitting, this paper introduces an ANN in stochastic process to describe the mean function for degradation modeling. Due to the fact that the existing method cannot handle the bivariate dependent degradation conditions, a bivariate dependent degradation model based on Copula function and ANN‐supported stochastic processes is proposed. Considering the random effects caused by individual difference, it is assumed that the unknown parameters in the stochastic processes and Copula functions are randomly distributed. Based on the maximum likelihood and moment estimation methods, a related statistical inference method for ANN training and parameter estimation is developed to use the bivariate dependent degradation model. An actual fatigue crack dataset is used to demonstrate the validity of the proposed method. The obtained results show that the dependent relationship between two degradation indicators should not be neglected, and it can be efficiently handled by the proposed method. Furthermore, the proposed degradation model can provide reliability and degradation intervals with enough precision due to the fact that it considers the random effects caused by individual difference. [ABSTRACT FROM AUTHOR]

Symbionts tend to be aggregated on their hosts, such that few hosts harbor the majority of symbionts. This ubiquitous pattern can result from stochastic processes, but aggregation patterns may also depend on the type of host–symbiont interaction, along with traits that affect host exposure and susceptibility to symbionts. Untangling how aggregation patterns both within and among populations depend on stochastic processes, interaction type and host traits remains an outstanding challenge. Here, we address this challenge by using null models to compare aggregation patterns in a neutral system of Balanomorpha barnacles attached to patellid limpets and a host–parasite system of Gyrodactylus spp. monogeneans and their Trinidadian guppy Poecilia reticulata hosts. We first used a model to predict patterns of symbiont–host aggregation due to random partitioning of symbionts to hosts. This null model accurately predicted the aggregation of barnacles on limpets, but the degree of aggregation varied across 303 quadrats. Quadrats with larger limpets had less aggregated barnacles, whereas aggregation increased with variation in limpet size. Across 84 guppy populations, Gyrodactylus spp. parasites were significantly less aggregated than predicted by the null model. As in the neutral limpet–barnacle system, aggregation decreased with mean host size. Parasites were significantly less aggregated on males than females because male guppies tended to have higher prevalence and lower parasite burdens than predicted by the null model. Together, these results suggest stochastic processes can explain aggregation patterns in neutral but not parasitic systems, though in both systems host traits affect aggregation patterns. Because the distribution of symbionts on hosts can affect symbiont evolution via intraspecific interactions, and host behavior and evolution via host–symbiont interactions, identifying the drivers of aggregation enriches our understanding of host–symbiont interactions. [ABSTRACT FROM AUTHOR]

Although the classical spectral representation method (SRM) has been widely used in the generation of spatially varying ground motions, there are still challenges in efficient simulation of the non-stationary stochastic vector process in practice. The first problem is the inherent limitation and inflexibility of the deterministic time/frequency modulation function. Another difficulty is the estimation of evolutionary power spectral density (EPSD) with quite a few samples. To tackle these problems, the wavelet packet transform (WPT) algorithm is utilized to build a time-varying spectrum of seed recording which describes the energy distribution in the time-frequency domain. The time-varying spectrum is proven to preserve the time and frequency marginal property as theoretical EPSD will do for the stationary process. For the simulation of spatially varying ground motions, the auto-EPSD for all locations is directly estimated using the time-varying spectrum of seed recording rather than matching predefined EPSD models. Then the constructed spectral matrix is incorporated in SRM to simulate spatially varying non-stationary ground motions using efficient Cholesky decomposition techniques. In addition to a good match with the target coherency model, two numerical examples indicate that the generated time histories retain the physical properties of the prescribed seed recording, including waveform, temporal/spectral non-stationarity, normalized energy buildup, and significant duration. [ABSTRACT FROM AUTHOR]

Summary: This paper deals with the problem of the parameter estimation for feedback nonlinear output‐error systems. The auxiliary model‐based recursive least squares algorithm and the auxiliary model‐based stochastic gradient algorithm are derived for parameter estimation. Based on the stochastic process theory, the convergence of the proposed algorithms are proved. The simulation results indicate that the proposed algorithms can estimate the parameters of feedback nonlinear output‐error systems effectively. [ABSTRACT FROM AUTHOR]

The integration of alternative energy sources, storage systems, and modern loads into the distribution grid is complicating its operation and maintenance. Variability in individual generation and consumption elements dynamically affects voltage profiles, which in turn undermines efficiency and power quality. This study proposes to address this dynamical variability using an online reconfiguration approach that involves opening and closing switches to modify the grid's topology and adjust voltage levels in response to load/generation variations. Other grid optimization techniques, based on reconfiguration, typically focus on static, fully instrumented grids with predictable parameters and homogeneous changes, aiming to minimize power losses but overlooking the dynamics of variable grid elements. This study proposes a testing approach that is dependent on the estimated transient status of the grid only using a limited number of measurement units and considering the individual‐stochastic variations of loads and generators. The proposed approach was tested on the IEEE 33‐bus test feeder with up to five varying distributed generators. The results confirm that the algorithm consistently finds a reconfiguration alternative that could enhance system efficiency and voltage profiles, even in the face of dynamic load/generator behavior, demonstrating its effectiveness and online adaptability for grid operation and management tasks. [ABSTRACT FROM AUTHOR]

Successional dynamics can vary because of a range of ecological and environmental factors, but our understanding of biogeographic variation in succession, and the processes contributing to community development across ecosystems, is limited. The pattern and rate of recruitment of dispersive propagules likely differs over large spatial scales and can be an important predictor of successional trajectory. Over a 20° tropical-temperate latitudinal gradient, we measured sessile invertebrates over 12 months of community development and successive 3-month recruitment windows to understand succession and how it is influenced by recruitment. Succession and recruitment patterns varied over latitude. In the tropics, fast temporal turnover, fluctuating abundances, and lack of successional progression suggest that the contribution of stochastic processes was high. As latitude increased, successional progression became more apparent, characterized by increasing species richness and community cover and a shift to more competitive taxa over time. At temperate locations, species identities were similar between older communities and recruiting assemblages; however, community composition became more variable across space over time. Such divergence suggests an important role of early colonizers and species interactions on community structure. These findings demonstrate differences in the processes contributing to community development and biodiversity patterns over latitude. Understanding such biogeographic variation in community dynamics and identifying the prevalence of different processes can provide insights into how communities assemble and persist in response to environmental variability. [ABSTRACT FROM AUTHOR]

This report characterizes forms of dialogic support that a sixth-grade teacher generated during whole-class and small-group conversations to help students develop a practice of statistical modeling. During four weeks of instruction, students constructed and revised models to account for variability and uncertainty across a variety of random processes, many of which they experienced first-hand. Data sources for the research included field notes and video recordings of classroom conversations involving the teacher. Analyses identified and characterized teacher assistance during classroom episodes in which the teacher fostered the emergence and development of fundamental aspects of statistical modeling practice. These aspects included a) establishing mappings between models of chance and the situations or processes being modeled, b) imagining outcomes as constituents of a long-run random process, c) evaluating model fit, and d) making model-based inferences. Throughout instruction, the teacher systematically helped students coordinate these distinctive aspects of modeling practice. The findings suggest how teacher practices can promote the sustained development of statistical reasoning as a dialogue between data and model, and more generally, how teacher assistance attuned to student thinking about aspects of a disciplinary practice can foster a student-centered phenomenology of that practice. [ABSTRACT FROM AUTHOR]

In this article, we establish some results on complete convergence and complete integral convergence of moving average process { X n = ∑ i = − ∞ ∞ a i Y i + n , n ≥ 1 } based on negatively dependent random variables under sub-linear expectations. We generalize corresponding conclusions obtained by Zhang and Ding, and extend convergence theorems for general function from classical probability space to the sub-linear expectation space. [ABSTRACT FROM AUTHOR]

The purpose of the present study was to examine if potentiation of mortality occurred after simultaneous administration of several Escherichia coli genotypes, each capable of inducing the E. coli peritonitis syndrome, in comparison with single genotype application. Five groups of productive specified pathogen free White Leghorn hens were housed in isolators. Groups 1–4 consisted of 32 hens each, group 5 of 10 hens. At 32 weeks of age all groups were inoculated intratracheally. Groups 1 and 2 were inoculated with a mix of four E. coli genotypes and groups 3 and 4 with a mix of four other genotypes. Groups 1 and 3 were given 1 median lethal dose (LD50) of each genotype per hen and groups 2 and 4 had a dose of 0.1 LD50 per genotype per hen; group 5 was mock inoculated. The experiment ended one week after inoculations. In Group 5, no mortality occurred and gross lesions were absent at post-mortem examination. Mortality in groups 1 and 3 was 84% and 81%, respectively; in groups 2 and 4 59% and 66%, respectively. Although mortality in groups 1 and 3 exceeded the expected 50%, this could not be due to potentiation as cluster analysis of reisolates showed that in individual hens only one genotype was found, indicating interference between E. coli genotypes. In groups all four or only two genotypes were recovered, showing that not all genotypes will induce colibacillosis in all experimental groups. Therefore, broad protection can be best assessed by challenging with various single genotypes. RESEARCH HIGHLIGHTS All four or only two E. coli genotypes were found in groups of hens given mixes of four genotypes. In contrast, only one genotype was found in individual hens. E. coli genotypes interfere with each other in hens after given as a mix. Interference is likely based on a random process. Broad protection can best be assessed by challenging with single genotypes. [ABSTRACT FROM AUTHOR]

Ground-motion models (GMMs) are fundamental for the estimation of ground shaking for probabilistic seismic hazard assessment. Because of the paucity of ground motion recordings in regions of low seismicity, stochastic approaches are often employed to generate synthetic data. In this study, we developed a GMM using a stochastic simulation approach for southwest Iberia--a zone for which seismic hazard is usually assessed using models developed for other regions. We collected geological, tectonic, and ground-motion data for offshore and inland Iberia, and calibrated several parameters for a stochastic simulation. The resulting synthetic response spectra were used to train a machine learning algorithm (artificial neural network) capable of predicting peak ground acceleration, peak ground velocity, and spectral acceleration on rock (VS30 = 760 M/S), along with the associated between-event and within-event terms. The resulting model was compared against other existing models for stable continental regions and ground-motion recordings for Portugal and Spain. The results indicate a good agreement with observations and the model can be used directly in probabilistic seismic hazard analysis for southwest Iberia. [ABSTRACT FROM AUTHOR]

A new, non‐dimensional ripple reset parameter and a stochastic point process model is used to estimate the likelihood of propagating ocean waves to form ripples on sandy seabeds. The ripple reset parameter is a function only of water depth, significant wave height, and mean grain size. Ripple formation is estimated by the magnitude of an intensity function based on a time series of the ripple reset parameter. The point process model is trained with a time series of observed waves and ripple change, and is then applied to predict the probability that a ripple field with a different geometry will form within a given time interval from another time series of wave data. The model is trained and tested with four field deployments at three field sites to determine its skill in predicting the ripple formation (a) at one field site over one time period after being trained with observations from the same site over a different time period, and (b) at one field site after being trained with observations from another field site. Results show that while the model is sufficient at predicting ripple formation in both scenarios, it is sensitive to the quality and quantity of the training data. Increasing the amount of training data greatly improves model performance. Employing a stochastic model based on a simple ripple reset parameter reduces tunable model parameters and provides a prediction of the probability for ripple formation given only a water depth, grain size, and time series of wave heights. Plain Language Summary: Ripples are small, hill‐like mounds of sand that are formed by water in the ocean moving back and forth by waves. Sand ripples can cause an increase of sand movement on the seafloor, can cause ocean instrumentation to respond unexpectedly, and can bury and expose objects. Understanding when they form is important for scientists to measure and predict ocean dynamics. If the average height of the waves, the water depth, and the sand grain diameter is known, we can predict whether or not the waves will form ripples with mathematical equations. Previously, the equations to predict ripple formation required a lot of difficult to obtain ocean information. We developed an equation and model to quickly and easily predict the likelihood of ripples forming by waves in a specific size sand and water depth. Key Points: A ripple reset parameter based on wave height, water depth, and grain size is presentedA stochastic model based on the ripple reset parameter can predict the probability of ripple formationThe model accurately predicted ripple resets at three different field sites without calibration [ABSTRACT FROM AUTHOR]

We propose an extension of the model introduced by Barndorff-Nielsen and Shephard, based on stochastic processes of Ornstein–Uhlenbeck type taking values in Hilbert spaces and including the leverage effect. We compute explicitly the characteristic function of the log-return and the volatility processes. By introducing a measure change of Esscher type, we provide a relation between the dynamics described with respect to the historical and the risk-neutral measures. We discuss in detail the application of the proposed model to describe the commodity forward curve dynamics in a Heath–Jarrow–Morton framework, including the modelling of forwards with delivery period occurring in energy markets and the pricing of options. For the latter, we show that a Fourier approach can be applied in this infinite-dimensional setting, relying on the attractive property of conditional Gaussianity of our stochastic volatility model. In our analysis, we study both arithmetic and geometric models of forward prices and provide appropriate martingale conditions in order to ensure arbitrage-free dynamics. [ABSTRACT FROM AUTHOR]

This paper concerns a local volatility model in which the volatility takes two possible values, and the specific value depends on whether the underlying price is above or below a given threshold. The model is known, and a number of results have been obtained for it. In particular, option pricing formulas and a power-law behaviour of the implied volatility skew have been established in the case when the threshold is taken at the money. In this paper, we derive an alternative representation of option pricing formulas. In addition, we obtain an approximation of option prices by the corresponding Black–Scholes prices. Using this approximation streamlines obtaining the aforementioned behaviour of the skew. Our approach is based on the natural relationship of the model with skew Brownian motion and consists of the systematic use of the joint distribution of this stochastic process and some of its functionals. [ABSTRACT FROM AUTHOR]

The article proposes a sequential statistical procedure to test for the presence of level shifts affecting bounded time series, regardless of their order of integration. The article shows that bounds are relevant for the statistic that assumes that the time series are integrated of order one. In contrast, they do not affect the limiting distribution of the statistic that is defined for time series that are integrated of order zero. The article proposes a union rejection statistic for bounded processes that does not require information about the order of integration of the stochastic processes. The model specification is general enough to consider the existence of structural breaks that can affect either the level of the time series and/or the bounds that limit its evolution. Monte Carlo simulations indicate that the procedure works well in finite samples. An empirical application that focuses on the Swiss franc against the euro exchange rate evolution illustrates the usefulness of the proposal. [ABSTRACT FROM AUTHOR]

Gene transcription is a stochastic process that occurs in all organisms. Transcriptional bursting, a critical molecular dynamics mechanism, creates significant heterogeneity in mRNA and protein levels. This heterogeneity drives cellular phenotypic diversity. Currently, the lack of a comprehensive quantitative model limits the research on transcriptional bursting. This review examines various gene expression models and compares their strengths and weaknesses to guide researchers in selecting the most suitable model for their research context. We also provide a detailed summary of the key metrics related to transcriptional bursting. We compared the temporal dynamics of transcriptional bursting across species and the molecular mechanisms influencing these bursts, and highlighted the spatiotemporal patterns of gene expression differences by utilizing metrics such as burst size and burst frequency. We summarized the strategies for modeling gene expression from both biostatistical and biochemical reaction network perspectives. Single-cell sequencing data and integrated multiomics approaches drive our exploration of cutting-edge trends in transcriptional bursting mechanisms. Moreover, we examined classical methods for parameter estimation that help capture dynamic parameters in gene expression data, assessing their merits and limitations to facilitate optimal parameter estimation. Our comprehensive summary and review of the current transcriptional burst dynamics theories provide deeper insights for promoting research on the nature of cell processes, cell fate determination, and cancer diagnosis. [ABSTRACT FROM AUTHOR]

The deep‐water pipeline connector (DPC) is a key piece of equipment for the connection of multiple facilities located in different positions of the subsea production system. Establishing a DPC sealing degradation model considering the internal corrosion can provide a basis for its structural design and maintenance. Considering the characteristics of nonlinear and multiphase for the DPC degradation process, a two‐phase nonlinear Wiener process is applied to establish a DPC degradation model. It can reasonably consider the commonly encountered situation that a change point locates among the test times. DPC reliability analysis and lifetime prediction methods are constructed after a maximum likelihood method is employed to estimate the hyperparameters of the established degradation model. Finally, a subsea Christmas tree wellhead connector is taken as an example to verify the reasonability and effectiveness of the method. The results indicate that the proposed method can describe the nonlinear time‐varying properties caused by the DPC internal corrosion more accurate and reasonable than other traditional classic methods, and a more reasonable lifetime assessment result can be obtained. [ABSTRACT FROM AUTHOR]

Background: Variations in community-level plant functional traits are widely used to elucidate vegetation adaptation strategies across different environmental gradients. Moreover, studying functional variation among different forest types aids in understanding the mechanisms by which environmental factors and functional strategies shift community structure. Methods: Based on five plant functional traits, including four leaf and one wood trait, for 150 woody species, we analyzed shifts in the community-weighted mean trait values across three forest types in a karst forest landscape: deciduous, mixed, and evergreen forests. We also assessed the relative contributions of stochastic processes, environmental filtering, and niche differentiation to drive community structure using a trait-based null model approach. Results: We found marked changes in functional strategy, from resource acquisition on dry, fertile soil plots in deciduous forests to resource conservation on moist, infertile soil conditions in evergreen forests. The traitbased null model showed strong evidence of environmental filtering and convergent patterns in traits across three forest types, as well as low niche differentiation in most functional traits. Some evidence of overdispersion of LDMC and LT occurred to partially support the recent theory of Scheffer and Van Nes that competition could result in a clumped pattern of species along a niche axis. Discussion: Our findings suggest a change in environmental gradient from deciduous to evergreen forest, together with a shift from acquisitive to conservative traits. Environmental filtering, stochastic processes, niche differentiation, and overdispersion mechanisms together drive community assembly in karst forest landscapes. These findings will contribute to a deeper understanding of the changes in functional traits among karst plants and their adaptive strategies, with important implications for understanding other community assemblies in subtropical forest systems. [ABSTRACT FROM AUTHOR]

Accurate forecasting of high-resolution particulate matter 2.5 (PM2.5) levels is essential for the development of public health policy. However, datasets used for this purpose often contain missing observations. This study presents a two-stage approach to handle this problem. The first stage is a multivariate spatial time series (MSTS) model, used to generate forecasts for the sampled spatial units and to impute missing observations. The MSTS model utilizes the similarities between the temporal patterns of the time series of the spatial units to impute the missing data across space. The second stage is the high-resolution prediction model, which generates predictions that cover the entire study domain. The second stage faces the big N problem giving rise to complex memory and computational problems. As a solution to the big N problem, we propose a Gaussian Markov random field (GMRF) for innovations with the Matérn covariance matrix obtained from the corresponding Gaussian field (GF) matrix by means of the stochastic partial differential equation (SPDE) method and the finite element method (FEM). For inference, we propose Bayesian statistics and integrated nested Laplace approximation (INLA) in the R-INLA package. The above approach is demonstrated using daily data collected from 13 PM2.5 monitoring stations in Jakarta Province, Indonesia, for 1 January–31 December 2022. The first stage of the model generates PM2.5 forecasts for the 13 monitoring stations for the period 1–31 January 2023, imputing missing data by means of the MSTS model. To capture temporal trends in the PM2.5 concentrations, the model applies a first-order autoregressive process and a seasonal process. The second stage involves creating a high-resolution map for the period 1–31 January 2023, for sampled and non-sampled spatiotemporal units. It uses the MSTS-generated PM2.5 predictions for the sampled spatiotemporal units and observations of the covariate's altitude, population density, and rainfall for sampled and non-samples spatiotemporal units. For the spatially correlated random effects, we apply a first-order random walk process. The validation of out-of-sample forecasts indicates a strong model fit with low mean squared error (0.001), mean absolute error (0.037), and mean absolute percentage error (0.041), and a high R² value (0.855). The analysis reveals that altitude and precipitation negatively impact PM2.5 concentrations, while population density has a positive effect. Specifically, a one-meter increase in altitude is linked to a 7.8% decrease in PM2.5, while a one-person increase in population density leads to a 7.0% rise in PM2.5. Additionally, a one-millimeter increase in rainfall corresponds to a 3.9% decrease in PM2.5. The paper makes a valuable contribution to the field of forecasting high-resolution PM2.5 levels, which is essential for providing detailed, accurate information for public health policy. The approach presents a new and innovative method for addressing the problem of missing data and high-resolution forecasting. [ABSTRACT FROM AUTHOR]

Some random processes, like a series of coin flips, can produce outcomes that seem particularly remarkable or striking. This paper explores an epistemic puzzle that arises when thinking about these outcomes and asking what, if anything, we can justifiably believe about them. The puzzle has no obvious solution, and any theory of epistemic justification will need to contend with it sooner or later. The puzzle proves especially useful for bringing out the differences between three prominent theories; the probabilist theory, the normic theory and a theory recently defended by Goodman and Salow. [ABSTRACT FROM AUTHOR]

This study explores zero-inflated count time series models used to analyze data sets with characteristics such as overdispersion, excess zeros, and autocorrelation. Specifically, we investigate the $ {\rm ZIGINAR}_{RC}(1) $ ZIGINAR RC (1) process, a first-order stationary integer-valued autoregressive model with random coefficients and a zero-inflated geometric marginal distribution. Our focus is on examining various estimation and prediction techniques for this model. We employ estimation methods, including Whittle, Taper Spectral Whittle, Maximum Empirical Likelihood, and Sieve Bootstrap estimators for parameter estimation. Additionally, we propose forecasting approaches, such as median, Bayesian, and Sieve Bootstrap methods, to predict future values of the series. We assess the performance of these methods through simulation studies and real-world data analysis, finding that all methods perform well, providing 95% highest predicted probability intervals that encompass the observed data. While Bayesian and Bootstrap methods require more time for execution, their superior predictive accuracy justifies their use in forecasting. [ABSTRACT FROM AUTHOR]

Theoretical mathematics is a key evolution factor of artificial intelligence (AI). Nowadays, representing a smart system as a mathematical model helps to analyze any system under development and supports different case studies found in real life. Additionally, the Markov chain has shown itself to be an invaluable tool for decision-making systems, natural language processing, and predictive modeling. In an Internet of Things (IoT), Machine-to-Machine (M2M) traffic necessitates new traffic models due to its unique pattern and different goals. In this context, we have two types of modeling: (1) source traffic modeling, used to design stochastic processes so that they match the behavior of physical quantities of measured data traffic (e.g., video, data, voice), and (2) aggregated traffic modeling, which refers to the process of combining multiple small packets into a single packet in order to reduce the header overhead in the network. In IoT studies, balancing the accuracy of the model while managing a large number of M2M devices is a heavy challenge for academia. One the one hand, source traffic models are more competitive than aggregated traffic models because of their dependability. However, their complexity is expected to make managing the exponential growth of M2M devices difficult. In this paper, we propose to use a Markov-Modulated Poisson Process (MMPP) framework to explore Human-to-Human (H2H) traffic and M2M heterogeneous traffic effects. As a tool for stochastic processes, we employ Markov chains to characterize the coexistence of H2H and M2M traffic. Using the traditional evolved Node B (eNodeB), our simulation results show that the network's service completion rate will suffer significantly. In the worst-case scenario, when an accumulative storm of M2M requests attempts to access the network simultaneously, the degradation reaches 8% as a completion task rate. However, using our "Coexistence of Heterogeneous traffic Analyzer and Network Architecture for Long term evolution" (CHANAL) solution, we can achieve a service completion rate of 96%. [ABSTRACT FROM AUTHOR]