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In nowadays, the chief attention of the researcher is to study how the reliability analysis of manufacturing industrial systems by using the stochastic process. This topic tells us, how the manufacturing industries perform over time with the help of mathematical models which include randomness and uncertainty. Through stochastic processes we examine the reliability of these systems, technologists can recognize possible failure points and develop tactics to improve overall performance and effectiveness. The reliability of a manufacturing industrial system can be examined through a stochastic process, which permits for the estimate of failure rates and maintenance agendas. This analysis can lead to more well-organized and cost-effective procedure of the system. In this study, the researcher analysed the possibility plan for reliability through many distributions such as the normal distribution, gamma distribution, weibull distribution, and exponential distribution. The result of the study was prepared using Minitab software. The result of the study shows that the normal distribution of reliability fits best in comparison to the gamma, weibull, and exponential distributions. [ABSTRACT FROM AUTHOR]

In recent years, the focus has shifted towards leveraging physics-based modelling and data-driven analysis to predict drilling incidents and anomalies in real time, with the goal of reducing non-productive periods. However, much of this attention has directed at specific drilling operations like drilling and tripping, leaving other vital processes, such as wellbore conditioning, comparatively overlooked. The primary objective of this study is to employ data-driven techniques for predicting the dynamic state of the wellbore by utilising sensor data, operating parameters, and surface measurements. Accurate predictions are pivotal for automating these processes, promising significant savings in both redundant time and associated costs, ultimately elevating operational efficiency. In this research, the surface drilling parameters such as flowrate, rotation speed, block position, and drill string length are incorporated with the surface measurements such as hookload, pressure, and torque during wellbore conditioning operation to predict further surface sensor measurements. Different parameter settings are evaluated to find the best approach. Six supervised learning algorithms are used to select the best prediction method. The findings reveal that considering all surface parameters and measurements yields the most accurate predictions. Among various single and multi-target regression methods, including deep learning approaches, the Gaussian process and random forest models exhibit the lowest prediction errors. By reliably predicting and understanding wellbore behaviour, this research paves the way for more efficient and autonomous drilling operations in the future, bridging a critical gap in the industry's automation capabilities. [ABSTRACT FROM AUTHOR]

Bayesian optimization (BO) is a sequential optimization strategy that is increasingly employed in a wide range of areas such as materials design. In real-world applications, acquiring high-fidelity (HF) data through physical experiments or HF simulations is the major cost component of BO. To alleviate this bottleneck, multi-fidelity (MF) methods are used to forgo the sole reliance on the expensive HF data and reduce the sampling costs by querying inexpensive low-fidelity (LF) sources whose data are correlated with HF samples. However, existing multi-fidelity BO (MFBO) methods operate under the following two assumptions that rarely hold in practical applications: (1) LF sources provide data that are well correlated with the HF data on a global scale, and (2) a single random process can model the noise in the MF data. These assumptions dramatically reduce the performance of MFBO when LF sources are only locally correlated with the HF source or when the noise variance varies across the data sources. In this paper, we view these two limitations and uncertainty sources and address them by building an emulator that more accurately quantifies uncertainties. Specifically, our emulator (1) learns a separate noise model for each data source, and (2) leverages strictly proper scoring rules in regularizing itself. We illustrate the performance of our method through analytical examples and engineering problems in materials design. The comparative studies indicate that our MFBO method outperforms existing technologies, provides interpretable results, and can leverage LF sources which are only locally correlated with the HF source. [ABSTRACT FROM AUTHOR]

The core principle shared by most theories and models of succession is that, following a major disturbance, plant–environment feedback dynamics drive a directional change in the plant community. The most commonly studied feedback loops are those in which the regrowth of the plant community causes changes to the abiotic (e.g. soil nutrients) or biotic (e.g. dispersers) environment, which differentially affect species availability or performance. This, in turn, leads to shifts in the species composition of the plant community. However, there are many other PE feedback loops that potentially drive succession, each of which can be considered a model of succession. While plant–environment feedback loops in principle generate predictable successional trajectories, succession is generally observed to be highly variable. Factors contributing to this variability are the stochastic processes involved in feedback dynamics, such as individual mortality and seed dispersal, and extrinsic causes of succession, which are not affected by changes in the plant community but do affect species performance or availability. Both can lead to variation in the identity of dominant species within communities. This, in turn, leads to further contingencies if these species differ in their effect on their environment (priority effects). Predictability and variability are thus intrinsically linked features of ecological succession. We present a new conceptual framework of ecological succession that integrates the propositions discussed above. This framework defines seven general causes: landscape context, disturbance and land‐use, biotic factors, abiotic factors, species availability, species performance, and the plant community. When involved in a feedback loop, these general causes drive succession and when not, they are extrinsic causes that create variability in successional trajectories and dynamics. The proposed framework provides a guide for linking these general causes into causal pathways that represent specific models of succession. Our framework represents a systematic approach to identifying the main feedback processes and causes of variation at different successional stages. It can be used for systematic comparisons among study sites and along environmental gradients, to conceptualise studies, and to guide the formulation of research questions and design of field studies. Mapping an extensive field study onto our conceptual framework revealed that the pathways representing the study's empirical outcomes and conceptual model had important differences, underlining the need to move beyond the conceptual models that currently dominate in specific fields and to find ways to examine the importance of and interactions among alternative causal pathways of succession. To further this aim, we argue for integrating long‐term studies across environmental and anthropogenic gradients, combined with controlled experiments and dynamic modelling. [ABSTRACT FROM AUTHOR]

The study of orbital resonances in the dynamics of asteroids and major planets is important from the point of view of solving the asteroid hazard problem. In the course of such studies, there is often a need to analyze a large number of time series of resonant (critical) arguments, since to complete the picture it is necessary to consider not only the main argument, but also the entire multiplet. To work with multiplets, we developed an algorithm and program for classifying the behavior of the resonant argument, which were applied to the study of the dynamics of resonant objects with small perihelion distances. The paper presents the results of constructing and analyzing resonance multiplets for 13 such asteroids. The study showed that in order to identify the features of the resonant interaction of the studied asteroids with planets, in most cases it is enough to consider the behavior of the main critical argument. The use of a program to automate the process of classifying the behavior of arguments significantly reduced the time spent and the likelihood of random errors in the process of processing the received data. [ABSTRACT FROM AUTHOR]

Let {Zn, n = 0, 1, 2, ...} be a critical branching process in a random environment, and {Sn, n = 0, 1, 2, ...} be its associated random walk. It is known that if the increments of this random walk belong (without centering) to the domain of attraction of a stable law, then there exists a regularly varying at infinity sequence a1, a2, ... such that conditional distributions P ( S n a n ≤ x | Z n > 0) , x ∈ (− ∞ , + ∞) , converge weakly to the distribution of strictly positive proper random variable. In this paper we add to this result the description of the asymptotic behavior of the probability P (Z n > 0 , S n ≤ φ (n)) , where φ (n) → ∞ for n → ∞ in such a way that φ (n) = o(an). [ABSTRACT FROM AUTHOR]

Endophytic fungi, pivotal in facilitating plant co-evolution, significantly enhance plant growth, stress resistance, and environmental adaptability. Despite their importance, the spatial distribution of stem endophytic fungi (SEF) within host plants remains poorly characterized. Here, we employed high-throughput sequencing to conduct a comparative analysis of SEF communities in Mussaenda pubescens on a regional scale. Our findings reveal that whole-SEF communities were overwhelmingly dominated by members of the phylum Ascomycota , accounting for 85.9 %, followed by Basidiomycota at 13.9 %, and that alpha diversity within the whole-SEF community of M. pubescens remains relatively consistent across sampling sites. However, significant variation was observed within conditionally abundant taxa (CAT), conditionally rare or abundant taxa (CRAT), and conditionally rare taxa (CRT). Climatic factors emerged as the primary influence on SEF community distribution, followed by spatial distance and stem chemical properties. Neutral community modeling results suggested that both stochastic and deterministic processes play a role in shaping whole-SEF communities, with deterministic processes having a stronger influence on CRT subcommunities. Furthermore, the CRT co-occurrence network exhibited a more complex structure, characterized by higher values of network betweenness and degree relative to CAT and CRAT subcommunities. These findings enhance our understanding of community assembly and ecological interactions between stem fungal endophytes, presenting opportunities for harnessing fungal resources for the benefit of humanity. [Display omitted] [ABSTRACT FROM AUTHOR]

A multivariate distribution can be described by a triangular transport map from the target distribution to a simple reference distribution. We propose Bayesian nonparametric inference on the transport map by modeling its components using Gaussian processes. This enables regularization and uncertainty quantification of the map estimation, while resulting in a closed-form and invertible posterior map. We then focus on inferring the distribution of a nonstationary spatial field from a small number of replicates. We develop specific transport-map priors that are highly flexible and are motivated by the behavior of a large class of stochastic processes. Our approach is scalable to high-dimensional distributions due to data-dependent sparsity and parallel computations. We also discuss extensions, including Dirichlet process mixtures for flexible marginals. We present numerical results to demonstrate the accuracy, scalability, and usefulness of our methods, including statistical emulation of non-Gaussian climate-model output. for this article are available online. [ABSTRACT FROM AUTHOR]

We consider the clustering of extremes for stationary regularly varying random fields over arbitrary growing index sets. We study sufficient assumptions on the index set such that the limit of the point processes of the exceedances above a high threshold exists. Under the so-called anti-clustering condition, the extremal dependence is only local. Thus the index set can have a general form compared to previous literature (Basrak and Planinić in Bernoulli 27(2):1371–1408, 2021; Stehr and Rønn-Nielsen in Extremes 24(4):753–795, 2021). However, we cannot describe the clustering of extreme values in terms of the usual spectral tail measure (Wu and Samorodnitsky in Stochastic Process Appl 130(7):4470–4492, 2020) except for hyperrectangles or index sets in the lattice case. Using the recent extension of the spectral measure for star-shaped equipped space (Segers et al. in Extremes 20:539–566, 2017), the Υ -spectral tail measure provides a natural extension that describes the clustering effect in full generality. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce a multitype branching process with random migration following the research initiated with the Galton–Watson process with migration introduced in [N. M. Yanev and K. V. Mitov, Controlled branching processes: The case of random migration, C. R. Acad. Bulgare Sci. 33 1980, 4, 473–475]. We focus our attention in what we call the critical case. Sufficient conditions are provided for the process to have unlimited growth or not. Furthermore, using suitable normalizing sequences, we study the asymptotic distribution of the process. Finally, we obtain a Feller-type diffusion approximation. [ABSTRACT FROM AUTHOR]

This research focuses on stochastic modeling of the evolution over time of biological populations through branching processes. We introduce a new class of discrete time two-sex branching processes with random mating and overlapping generations. Mating and reproduction are considered to be influenced by the numbers of females and males existing in the population. This evolution over time with generational overlap is a novel research in two-sex branching process literature. We study general probabilistic properties and establish some limiting results of biological interest. [ABSTRACT FROM AUTHOR]

Cupressus gigantea is an endangered species mainly distributed on beach land, down-slope, and middle-slope positions along the Yarlung Zangbo River on the Tibet Plateau of China, with an altitude ranging from 3000 to 3400 m. We investigated the rhizosphere and fine root microbiomes of C. gigantea at these three slope positions through metagenomic analysis. Slope positions had a greater influence on microbiome composition in the rhizosphere than that in the fine roots. Down- and middle-slope positions presented higher microbial richness indeces and community similarity, while a more complex co-occurrence network was observed in the beach land samples. Rhizosphere bacterial community assembly was determined via deterministic processes in the beach land and via stochastic processes in the down- and middle-slope positions. Archaeal and fungal community assemblies were both dominated by stochastic processes in the rhizosphere and fine roots at the three slope positions. Nitrogen (N) functional genes were more sensitive to changes in slope positions than phosphorus (N) functional genes. Soil properties explained more than 60% and 34% of the variations in the N and P functional genes and more than 30% and 10% of the variations in the microbiomes in the rhizosphere and fine roots, respectively. Variation in the microbiome was significantly driven by total nirtogen, total potassium, pH, and soil moisture in rhizosphere, and by pH and soil moisture in fine roots. Our observations suggest that the effect of slope position on the microbiomes of C. gigantea was greater for the rhizosphere than the fine roots, with down- and middle-slope positions presenting higher community similarity. [ABSTRACT FROM AUTHOR]

Integrated sensing and communication (ISAC) has been defined as one of the major usage scenarios for 6G. When sensing and communication channels coexist in ISAC scenarios, neither conventional communication nor sensing channel models are applicable. As the foundation of ISAC studies, a new channel modeling methodology is required to characterize both sensing and communication channels and their correlations. This article introduces the framework of a general ISAC channel model, which integrates a deterministic multiscattering-center (MSC) model of sensing targets to the stochastic propagation channel model. Parameterizations of the proposed channel model rely on channel measurements. This article introduces two ISAC channel measurement methodologies based on the vector network analyzer (VNA) and a novel dual-sensor measurement system. The proposed methods can be applied in future 6G ISAC channel model standardization and system evaluations. [ABSTRACT FROM AUTHOR]

Processes of random tessellations of the Euclidean space $\mathbb{R}^d$ , $d\geq 1$ , are considered that are generated by subsequent division of their cells. Such processes are characterized by the laws of the life times of the cells until their division and by the laws for the random hyperplanes that divide the cells at the end of their life times. The STIT (STable with respect to ITerations) tessellation processes are a reference model. In the present paper a generalization concerning the life time distributions is introduced, a sufficient condition for the existence of such cell division tessellation processes is provided, and a construction is described. In particular, for the case that the random dividing hyperplanes have a Mondrian distribution—which means that all cells of the tessellations are cuboids—it is shown that the intrinsic volumes, except the Euler characteristic, can be used as the parameter for the exponential life time distribution of the cells. [ABSTRACT FROM AUTHOR]

We extend the classical setting of an optimal stopping problem under full information to include problems with an unknown state. The framework allows the unknown state to influence (i) the drift of the underlying process, (ii) the payoff functions, and (iii) the distribution of the time horizon. Since the stopper is assumed to observe the underlying process and the random horizon, this is a two-source learning problem. Assigning a prior distribution for the unknown state, standard filtering theory can be employed to embed the problem in a Markovian framework with one additional state variable representing the posterior of the unknown state. We provide a convenient formulation of this Markovian problem, based on a measure change technique that decouples the underlying process from the new state variable. Moreover, we show by means of several novel examples that this reduced formulation can be used to solve problems explicitly. [ABSTRACT FROM AUTHOR]

The modeling and identification of time series data with a long memory are important in various fields. The streamflow discharge is one such example that can be reasonably described as an aggregated stochastic process of randomized affine processes where the probability measure, we call it reversion measure, for the randomization is not directly observable. Accurate identification of the reversion measure is critical because of its omnipresence in the aggregated stochastic process. However, the modeling accuracy is commonly limited by the available real‐world data. We resolve this issue by proposing the novel upper and lower bounds of a statistic of interest subject to ambiguity of the reversion measure. Here, we use the Tsallis value‐at‐risk (TsVaR) as a convex risk functional to generalize the widely used entropic value‐at‐risk (EVaR) as a sharp statistical indicator. We demonstrate that the EVaR cannot be used for evaluating key statistics, such as mean and variance, of the streamflow discharge due to the blowup of some exponential integrand. We theoretically show that the TsVaR can avoid this issue because it requires only the existence of some polynomial moment, not exponential moment. As a demonstration, we apply the semi‐implicit gradient descent method to calculate the TsVaR and corresponding Radon–Nikodym derivative for time series data of actual streamflow discharges in mountainous river environments. [ABSTRACT FROM AUTHOR]

Haptic actuators for large display panels play an important role in bridging the gap between the digital and physical world by generating interactive feedback for users. However, the generation of meaningful haptic feedback is challenging for large display panels. There are dead zones with low haptic sensations when a small number of actuators are applied. In contrast, it is important to control the traveling wave generated by the actuators in the presence of multiple actuators. In this study, we propose a particle swarm optimization (PSO)-based algorithm for the haptic localization of plates with electrostatic vibration actuators. We modeled the transverse displacement of a plate under the effect of actuators by employing the Kirchhoff-Love plate theory. In addition, starting with twenty randomly generated particles containing the actuator parameters, we searched for the optimal actuator parameters using a stochastic process to yield localization. The capability of the proposed PSO algorithm is reported and the transverse displacement has a high magnitude only in the targeted region. [ABSTRACT FROM AUTHOR]

We consider the problem of predicting values of a random process or field satisfying a linear model y (x) = θ ⊤ f (x) + ε (x) , where errors ε (x) are correlated. This is a common problem in kriging, where the case of discrete observations is standard. By focussing on the case of continuous observations, we derive expressions for the best linear unbiased predictors and their mean squared error. Our results are also applicable in the case where the derivatives of the process y are available, and either a response or one of its derivatives need to be predicted. The theoretical results are illustrated by several examples in particular for the popular Matérn 3/2 kernel. [ABSTRACT FROM AUTHOR]

Summary: This paper replicates the results of the stochastic volatility–Dirichlet process mixture (SV‐DPM) models proposed in Jensen and Maheu (2010) in both a narrow and a wide sense. By using a normal‐Wishart prior and the collapsed Gibbs sampling method, our algorithm can be applied for more general settings, and it is more efficient for sampling the Dirichlet process mixture. For the stochastic volatility component, we adopt the method in Chan (2017) to further increase the overall efficiency of our algorithm. Using the same dataset, we obtain mixed results. Some of the results have significant differences. If we use recent time period dataset, which includes the COVID‐19 pandemic period, the log market portfolio volatility seems to increase in terms of the number of clusters and size of magnitude. [ABSTRACT FROM AUTHOR]

This paper investigates tail asymptotics of stationary distributions and quasi-stationary distributions (QSDs) of continuous-time Markov chains on subsets of the non-negative integers. Based on the so-called flux-balance equation, we establish identities for stationary measures and QSDs, which we use to derive tail asymptotics. In particular, for continuous-time Markov chains with asymptotic power law transition rates, tail asymptotics for stationary distributions and QSDs are classified into three types using three easily computable parameters: (i) super-exponential distributions, (ii) exponential-tailed distributions, and (iii) sub-exponential distributions. Our approach to establish tail asymptotics of stationary distributions is different from the classical semimartingale approach, and we do not impose ergodicity or moment bound conditions. In particular, the results also hold for explosive Markov chains, for which multiple stationary distributions may exist. Furthermore, our results on tail asymptotics of QSDs seem new. We apply our results to biochemical reaction networks, a general single-cell stochastic gene expression model, an extended class of branching processes, and stochastic population processes with bursty reproduction, none of which are birth–death processes. Our approach, together with the identities, easily extends to discrete-time Markov chains. [ABSTRACT FROM AUTHOR]

Motivated by applications to COVID dynamics, we describe a model of a branching process in a random environment $\{Z_n\}$ whose characteristics change when crossing upper and lower thresholds. This introduces a cyclical path behavior involving periods of increase and decrease leading to supercritical and subcritical regimes. Even though the process is not Markov, we identify subsequences at random time points $\{(\tau_j, \nu_j)\}$ —specifically the values of the process at crossing times, viz. $\{(Z_{\tau_j}, Z_{\nu_j})\}$ —along which the process retains the Markov structure. Under mild moment and regularity conditions, we establish that the subsequences possess a regenerative structure and prove that the limiting normal distributions of the growth rates of the process in supercritical and subcritical regimes decouple. For this reason, we establish limit theorems concerning the length of supercritical and subcritical regimes and the proportion of time the process spends in these regimes. As a byproduct of our analysis, we explicitly identify the limiting variances in terms of the functionals of the offspring distribution, threshold distribution, and environmental sequences. [ABSTRACT FROM AUTHOR]

Assessing drag force and Reynolds stresses in turbulent flows is crucial for evaluating the stability and longevity of hydraulic structures. Yet, this task is challenging due to the complex nature of turbulent flows. To address this, physical models are often employed. Nonetheless, this practice is associated with difficulties, especially in the case of high sampling frequency where the inherent randomness of velocity fluctuations becomes mixed with the measurement noise. This study introduces a stochastic approach, which aims to mitigate bias from measurement errors and provide a probabilistic estimate of extreme stress values. To accomplish this, a simple experimental setup with a hydraulic jump was employed to acquire long-duration velocity measurements. Subsequently, a modified first-order autoregressive model was applied through ensemble simulations, demonstrating the benefits of the stochastic approach. The analysis highlights its effectiveness in estimating the uncertainty of extreme events frequency and minimizing the bias induced by the noise in the high-magnitude velocity measurements and by the limited length of observations. These findings contribute to advancing our understanding of turbulent flow analysis and have implications for the design and assessment of hydraulic structures. [ABSTRACT FROM AUTHOR]

Expected utility theory is critical for modeling rational decision making under uncertainty, guiding economic agents as they seek to optimize outcomes. Traditional methods often require restrictive assumptions about underlying stochastic processes, limiting their applicability. This paper expands the theoretical framework by considering investment returns modeled by a stochastically ordered family of random variables under the convolution order, including Poisson, Gamma, and exponential distributions. Utilizing fractional calculus, we derive explicit, closed-form expressions for the derivatives of expected utility for various utility functions, significantly broadening the potential for analytical and computational applications. We apply these theoretical advancements to a case study involving the optimal production strategies of competitive firms, demonstrating the practical implications of our findings in economic decision making. [ABSTRACT FROM AUTHOR]

Long-term throughput, as a key performance indicator of a stochastic flow line, is affected by numerous parameters describing the features of the flow line, such as processing time and buffer size. Fast and accurate evaluation methods for a given set of values for those parameters are a prerequisite to systematically optimize such a flow line. In this paper, we consider the case of a flow line with random processing times, limited buffer capacities and so-called milkruns that supply the machines with material parts that are required to perform, e.g., assembly operations on workpieces. In such a system, shortages in the supply of material parts can limit the performance of the flow line. Up to now, there are no accurate analytical approaches to quantify the complex interactions in such milkrun-supplied flow lines for realistic problem sizes. We propose to use recurrent neural networks to determine the long-term throughput of such flow lines enabling us to evaluate production systems of flexible size. Our results show that the throughput can be determined accurately and quickly via recurrent neural networks. Furthermore, we use this new evaluation procedure as a building block to optimize this type of flow line using gradient and local search techniques. [ABSTRACT FROM AUTHOR]

Random walk is a stochastic process that moves through a network between different states according to a set of probability rules. This mechanism is crucial for understanding the importance of nodes and their similarities, and it is widely used in page ranking, information retrieval and community detection. In this study, we introduce a family of rounded fractal networks with varying topologies and conduct an analysis to investigate the scaling behaviour of the mean first-passage time (MFPT) for random walks. We present an exact analytical expression for MFPT, which is subsequently confirmed through direct numerical calculations. Furthermore, our approach for calculating this interesting quantity is based on the self-similar structure of the rounded networks, eliminating the need to compute each Laplacian spectrum. Finally, we conclude that a more efficient random walk is achieved by reducing the number of polygons and edges. Rounded fractal networks demonstrate superior efficiency in random walks at the initial state, primarily due to the minimal distances between vertices. [ABSTRACT FROM AUTHOR]

In various real-life queueing systems, part of the service can be rendered without involvement or presence of the customers themselves. In those queues, customers whose service order is still in process may leave the service station, go to ‘orbit’ for a random length of time, and then return to find out if their order has been completed. Common examples are car’s annual maintenance works, food ordering, etc. In this paper, a thorough analysis of a single-server ‘orbit while in service’ queueing model with general service time is presented. Assuming an Exponentially distributed orbit time, we derive general formulae for the distributions of (i) a customer’s total residence time in the system; (ii) a customer’s net actual residence time in the system during service (not including orbit time); (iii) the time an orbiting customer is late to return, i.e., remains in orbit after his/her service has been completed; and (iv) the total number of customers in the system. Considering the family of Gamma-distributed service times (spanning the range of distributions between the Exponential and the Deterministic), as well as the Uniform distribution, we further derive explicit formulae for the distributions of the above variables. Under linear cost assumptions, the optimal mean orbit time is numerically calculated for each of the above service-time distributions. Figures depicting the behavior of the measures as functions of the parameters are presented. [ABSTRACT FROM AUTHOR]

In this paper, we propose stochastic scheme models with two kinds of errors for a computer system. A highly reliable computer system needs greatly to be backed up successfully in case of computer system crashes due to hardware failures and malicious software infections. We aim to determine appropriate backup times in computer processing of constant and random tasks. For this purpose, the trade-off between backup times and data losses due to errors is considered. The total execution times until the computing processing completes are obtained, and optimal backup policies to minimize them are derived analytically. Furthermore, we take up extended models of random tasks with n sub-tasks and analyze them. [ABSTRACT FROM AUTHOR]

Fractional Brownian motion (fBm) is an experimentally-relevant, non-Markovian Gaussian stochastic process with long-ranged correlations between the increments, parametrised by the so-called Hurst exponent H ; depending on its value the process can be sub-diffusive (0 < H < 1 / 2) , diffusive (H = 1 / 2) or super-diffusive (1 / 2 < H < 1) . There exist three alternative equally often used definitions of fBm—due to Lévy and due to Mandelbrot and van Ness (MvN), which differ by the interval on which the time variable is formally defined. Respectively, the covariance functions of these fBms have different functional forms. Moreover, the MvN fBms have stationary increments, while for the Lévy fBm this is not the case. One may therefore be tempted to conclude that these are, in fact, different processes which only accidentally bear the same name. Recently determined explicit path integral representations also appear to have very different functional forms, which only reinforces the latter conclusion. Here we develop a unifying equivalent path integral representation of all three fBms in terms of Riemann–Liouville fractional integrals, which links the fBms and proves that they indeed belong to the same family. We show that the action in such a representation involves the fractional integral of the same form and order (dependent on whether H < 1 / 2 or H > 1 / 2 ) for all three cases, and differs only by the integration limits. [ABSTRACT FROM AUTHOR]

Tissue-resident memory T cells (TRM) are long-lived memory lymphocytes that persist in non-lymphoid tissues and provide the first line of defence against invading pathogens. They adapt to their environment in a tissue-specific manner, exerting effective pathogen control through a diverse T cell receptor (TCR) repertoire and the expression of proinflammatory cytokines and cytolytic proteins. More recently, several studies have indicated that TRM can egress from the tissue into the blood as so-called " ex-TRM, or circulating cells with a TRM phenotype". The numerically small ex-TRM population can re-differentiate in the circulation, giving rise to new memory and effector T cells. Following their egress, ex-TRM in the blood and secondary lymphoid organs can be identified based on their continued expression of the residency marker CD103, alongside other TRM-like features. Currently, it is unclear whether exit is a stochastic process, or is actively triggered in response to unknown factors. Also, it is not known whether a subset or all TRM are able to egress. Ex-TRM may be beneficial in health, as mobilisation of specialised TRM and their recruitment to both their site of origin as well as distant tissues results in an efficient distribution of the immune response. However, there is emerging evidence of a pathogenic role for ex-TRM, with a suggestion that they may perpetuate both local and distant tissue inflammation. Here, we review the evidence for the existence of ex-TRM and examine their potential involvement in disease pathogenesis. [ABSTRACT FROM AUTHOR]

Evolution results from the interaction of stochastic and deterministic processes that create a web of historical contingency, shaping gene content and organismal function. To understand the scope of this interaction, we examine the relative contributions of stochasticity, determinism, and contingency in shaping gene inactivation in 34 lineages of endosymbiotic bacteria, Sodalis, found in parasitic lice, Columbicola, that are independently undergoing genome degeneration. Here we show that the process of genome degeneration in this system is largely deterministic: genes involved in amino acid biosynthesis are lost while those involved in providing B-vitamins to the host are retained. In contrast, many genes encoding redundant functions, including components of the respiratory chain and DNA repair pathways, are subject to stochastic loss, yielding historical contingencies that constrain subsequent losses. Thus, while selection results in functional convergence between symbiont lineages, stochastic mutations initiate distinct evolutionary trajectories, generating diverse gene inventories that lack the functional redundancy typically found in free-living relatives. Endosymbionts often have small genomes that maintain minimal functions required to serve their hosts. This study examines cases of new endosymbiont acquisition and finds genome degeneration involves both stochastic and deterministic processes that shape gene content and organismal function. [ABSTRACT FROM AUTHOR]

The hydrographic and environmental factors along the Three Gorges Reservoir (TGR) have been significantly altered since the Three Gorges Dam (TGD) began working in 2006. Here, we collected 54 water samples, and then measured the environmental factors, followed by sequencing of the 18S rRNA gene and subsequent analysis of community assembly mechanisms. The findings indicated that the majority of environmental variables (such as AN, TP, Chl-a, CODMn, and Cu) exhibited both temporal and spatial variations due to the influences of the TGD. The distribution of different environmental factors and microeukaryotic plankton communities is influenced by the changing seasons. The community structure in TGR showed variations across three seasons, possibly due to variations in their environmental preferences, inherent dissimilarities, and seasonal succession. Furthermore, different communities exhibited a comparable distance-decay trend, suggesting that distinct taxa are likely to exhibit a similar spatial distribution. In addition, the community formation in TGR was influenced by both deterministic and stochastic factors, with the balance between them being mainly controlled by the season. Specifically, deterministic processes could explain 33.9–51.1% of community variations, while stochastic processes could contribute 23.5–32.2%. The findings of this research demonstrated that the varying ecological processes' significance relied on environmental gradients, geographical scale, and ecological conditions. This could offer a fresh outlook on comprehending the composition, assembly mechanisms, and distribution patterns of microeukaryotic plankton in reservoir ecosystems. [ABSTRACT FROM AUTHOR]

A p -adic Brownian motion is a continuous time stochastic process in a p -adic state space that has a Vladimirov operator as its infinitesimal generator. The current work shows that any such process is the scaling limit of a discrete time random walk on a discrete group. Earlier work required the exponent of the Vladimirov operator to be in (1 , ∞) , and the convergence was the weak convergence of probability measures on the Skorohod space of paths on a compact time interval. The current approach simplifies the earlier approach, allows for any positive exponent, eliminates the restriction to compact time intervals, and establishes some moment estimates for the discrete time processes that are of independent interest. [ABSTRACT FROM AUTHOR]

The optimal designing of the hybrid energy system (HES) is a challenging task due to the multiple objectives and various uncertainties. Especially for HES, primarily powered by solar energy, the reference solar radiation data directly impact the result of the optimization design. To incorporate the stochastic characteristics of solar radiation into the sizing process, a data-driven stochastic modeling method for solar radiation is proposed. The method involves two layers of stochastic processes that capture the intraday variation and daily evolution of solar radiation. First, the clearness index (CI) is introduced to describe the radiation intensity at different times. Then, the daily clearness state (DCS) is proposed, based on the statistical indicators of the intraday CI. The Markov model is used to describe the stochastic evolutionary characteristics between different DCSs. The probabilistic distribution of the CI under different DCS is obtained based on the diffusion kernel density estimation (DKDE), which is used for the stochastic generation of the CI at various times of the day. Finally, the radiation profile required for the optimal design is obtained by the stochastic generation of the DCS sequences and the intraday clearness index under corresponding states. A case study of an off-grid solar-powered HES is provided to illustrate this methodology. [ABSTRACT FROM AUTHOR]

The paper treats the modeling of stationary multivariate stochastic processes via frequency domain, and extends the notion of generalized autocovariance function, given by Proietti and Luati (2015) for univariate time series, to the multivariate setting. The generalized autocovariance matrices are defined for stationary multivariate stochastic processes as the Fourier transform of the power transformation of the spectral density matrix. Then we prove the consistency and derive the asymptotic distribution of frequency domain non-parametric estimators of the generalized autocovariance matrices, based on the power transformation of the periodogram matrix. Generalized autocovariance matrices are used to construct white noise hypothesis testing, to discriminate stochastic processes, and to introduce a generalized Yule–Walker estimator for the spectrum. A so-called λ–squared distance between two multivariate stochastic processes is also defined by using their generalized autocovariance matrices, and it serves for clustering time series and estimation by feature matching. Another use is in discriminant analysis. [ABSTRACT FROM AUTHOR]

A very important class of models widely used nowadays to describe and predict, at least in stochastic terms, the behavior of many-particle systems (where the word "particle" is not meant in the purely mechanical sense: particles can be cells of a living tissue, or cars in a traffic flow, or even members of an animal or human population) is the Kinetic Theory for Active Particles, i.e., a scheme of possible generalizations and re-interpretations of the Boltzmann equation. Now, though in the literature on the subject this point is systematically disregarded, this scheme is based on Markov Chains, which are special stochastic processes with important properties they share with many natural processes. This circumstance is here carefully discussed not only to suggest the different ways in which Markov Chains can intervene in equations describing the stochastic behavior of any many-particle system, but also, as a preliminary methodological step, to point out the way in which the notion of a Markov Chain can be suitably generalized to this aim. As a final result of the discussion, we find how to develop new very plausible and likely ways to take into account possible effects of the external world on a non-isolated many-particle system, with particular attention paid to socio-economic problems. [ABSTRACT FROM AUTHOR]

The focus of this paper is to examine the dynamic factor of the suburban railway by utilizing the random vibration approach. Breaking through the previous methods of relying on huge amounts of measured data, herein, the dynamic factor essentially results from two major parts: the dynamic effect caused by moving train loads and that generated by track irregularity, which has clear physical significance. As the internal excitation of the vehicle–bridge system, track irregularity has strong randomness. Based on the dimension reduction method, the spatial domain power spectral density (PSD) of the track irregularity is transformed into the time-domain PSD. Therefore, the randomness of the random process is reduced by exploiting the constraint form of a random function, and then, the typical samples of the track irregularity considering randomness are constructed. Using the vehicle–bridge coupled vibration model, the standard deviation of the dynamic factor is evaluated accounting for the random track irregularity and 99.7% guarantee rate. Finally, the impact coefficient of the track irregularity on the bridge is methodically obtained. The sensitivity of the standard deviation of the dynamic factor to vehicle speed and bridge frequency is analyzed. The given solution methodology can fully take into account the randomness of the track irregularity. Thereby, it provides the dynamic factor formulas as a reference for the dynamic performance evaluation of suburban railway bridges and possible revision of current design specifications. [ABSTRACT FROM AUTHOR]

Kuroshio intrusion (KI) is a key process that transports water from the western Pacific Ocean to the northern South China Sea (nSCS), where KI-induced surface water mixing often causes variations in microbial assemblages. Yet, how interannual KIs affect the biogeography of diazotrophs and associated environmental factors remains poorly characterized. Here, by quantifying the degree of KIs in 2 consecutive years, coupled with monitoring the diversity and distribution of nitrogenase-encoding nifH phylotypes with quantitative PCR and high-throughput sequencing, we show that changes in the diazotrophic community structure in the nSCS are highly correlated with KI-induced variations in a range of physicochemical parameters. Specifically, the filamentous cyanobacteria in the genus Trichodesmium were more abundant at stations strongly affected by KI and thereby with a deeper mixed layer and higher surface salinity and temperature; the unicellular N 2 -fixing cyanobacteria in group B (UCYN-B) were more abundant at stations least affected by KI and correlated with nutrient availability, whereas UCYN-C and the γ -proteobacteria were prevalent at stations moderately affected by KI. The neutral community model further demonstrated that dominant diazotrophic subcommunities were significantly affected by environmental factors in 2017 when KI was stronger compared to 2018 when KI retreated. Our analyses provide insightful evidence for the role of KI in shaping the diazotrophic community structure primarily as a stochastic process, implying a potential region-scale redistribution of diazotrophs and nitrogen budget, given that KIs are projected to intensify in a future warming ocean. [ABSTRACT FROM AUTHOR]

The basic functioning of the central nervous system is based on the opening and closing of ionic channels in the membranes of neurons. The behavior of ionic channels is considered to be a random process with an exponential probability distribution function. The central limit theorem implies that the mean of the sum of random variables generates a distribution in which the new variable tends to be normally distributed. The theorem implicitly implies that randomness can be embedded in a certain probability distribution but does not disappear. The present report will explore the possible implications for the functioning of nervous system and behavior of the constituent neural randomness. The possible functionality of "noise" to increase the exploratory space of nervous and behavioral systems will be considered. [ABSTRACT FROM AUTHOR]

Background: Deciphering the assembly rules of microbial communities is vital for a mechanistic understanding of the general principles driving microbiome structures and functions. In this study, a null modeling-based framework was implemented to infer the assembly rules of bacterial community in oat silages harvested in southern China starting from the grain-filling stage through to full ripening. Results: Most silages displayed "inferior" or "very inferior" fermentation quality. The fermentation qualities of silages tended to further decrease with the delay of harvest. Lactobacillus, Pediococcus, unclassified_f_Enterobacteriaceae, and Hafnia–Obesumbacterium constituted the predominated genera in silages. Delaying harvest increased the proportions of Hafnia–Obesumbacterium. Null model analysis revealed that stochastic processes were the primary contributor to the assembly of rare subcommunity during silage fermentation. The succession of abundant subcommunity was controlled both by stochastic and deterministic processes. Deterministic processes, more specifically, heterogeneous selection, were more prominent in the assembly of abundant bacteria in silages with the delay of harvest. Linear regression analysis indicated the important roles of DM, WSC and pH in the assembly of abundant subcommunity. Conclusion: This study, from the ecological perspectives, revealed the ecological processes controlling the bacterial community assembly in silage, providing new insights into the mechanisms underlying the construction of silage bacterial community. [ABSTRACT FROM AUTHOR]

We study a correspondence between gravitational shockwave geometry and its fluid description near a Rindler horizon in Minkowski spacetime. Utilizing the Petrov classification that describes algebraic symmetries for Lorentzian spaces, we establish an explicit mapping between a potential fluid and the shockwave metric perturbation, where the Einstein equation for the shockwave geometry is equivalent to the incompressibility condition of the fluid, augmented by a shockwave source. Then we consider an Ansatz of a stochastic quantum source for the potential fluid, which has the physical interpretation of shockwaves created by vacuum energy fluctuations. Under such circumstance, the Einstein equation, or equivalently, the incompressibility condition for the fluid, becomes a stochastic differential equation. By smearing the quantum source on a stretched horizon in a Lorentz invariant manner with a Planckian width (similarly to the membrane paradigm), we integrate fluctuations near the Rindler horizon to find an accumulated effect of the variance in the round-trip time of a photon traversing the horizon of a causal diamond. [ABSTRACT FROM AUTHOR]

In this work, we establish a direct connection between generative diffusion models (DMs) and stochastic quantization (SQ). The DM is realized by approximating the reversal of a stochastic process dictated by the Langevin equation, generating samples from a prior distribution to effectively mimic the target distribution. Using numerical simulations, we demonstrate that the DM can serve as a global sampler for generating quantum lattice field configurations in two-dimensional ϕ4 theory. We demonstrate that DMs can notably reduce autocorrelation times in the Markov chain, especially in the critical region where standard Markov Chain Monte-Carlo (MCMC) algorithms experience critical slowing down. The findings can potentially inspire further advancements in lattice field theory simulations, in particular in cases where it is expensive to generate large ensembles. [ABSTRACT FROM AUTHOR]

Despite the importance of wood-inhabiting fungi on nutrient cycling and ecosystem functions, their ecology, especially related to their community assembly, is still highly unexplored. In this study, we analyzed the wood-inhabiting fungal richness, community composition, and phylogenetics using PacBio sequencing. Opposite to what has been expected that deterministic processes especially environmental filtering through wood-physicochemical properties controls the community assembly of wood-inhabiting fungal communities, here we showed that both deterministic and stochastic processes can highly contribute to the community assembly processes of wood-inhabiting fungi in this tropical forest. We demonstrated that the dynamics of stochastic and deterministic processes varied with wood decomposition stages. The initial stage was mainly governed by a deterministic process (homogenous selection), whereas the early and later decomposition stages were governed by the stochastic processes (ecological drift). Deterministic processes were highly contributed by wood physicochemical properties (especially macronutrients and hemicellulose) rather than soil physicochemical factors. We elucidated that fine-scale fungal-fungal interactions, especially the network topology, modularity, and keystone taxa of wood-inhabiting fungal communities, strongly differed in an initial and decomposing deadwood. This current study contributes to a better understanding of the ecological processes of wood-inhabiting fungi in tropical regions where the knowledge of wood-inhabiting fungi is highly limited. [ABSTRACT FROM AUTHOR]

Context. The variety and complexity of long duration gamma-ray burst (LGRB) light curves (LCs) encode a wealth of information about the way LGRB engines release their energy following the collapse of the progenitor massive star. Thus far, attempts to characterise GRB LCs have focused on a number of properties, such as the minimum variability timescale and power density spectra (both ensemble average and individual), or considering different definitions of variability. In parallel, a characterisation as a stochastic process has been pursued by studying the distributions of waiting times, peak flux, and fluence of individual peaks that can be identified within GRB time profiles. However, an important question remains as to whether the diversity of GRB profiles can be described in terms of a common stochastic process. Aims. Here, we address this issue by extracting and modelling, for the first time, the distribution of the number of peaks within a GRB profile. Methods. We analysed four different GRB catalogues: CGRO/BATSE, Swift/BAT, BeppoSAX/GRBM, and Insight-HXMT. The statistically significant peaks were identified by means of well tested and calibrated algorithm MEPSA and further selected by applying a set of thresholds on the signal-to-noise ratio. We then extracted the corresponding distributions of number of peaks per GRB. Results. Among the different models considered (power-law, simple or stretched exponential), we find that only a mixture of two exponentials was able to model all the observed distributions. This suggests the existence of two distinct behaviours: (i) an average number of 2.1 ± 0.1 peaks per GRB ("peak-poor"), accounting for about 80% of the observed population of GRBs; and (ii) an average number of 8.3 ± 1.0 peaks per GRB ("peak-rich"), accounting for the remaining 20% of the observed population. Conclusions. We associate the class of peak-rich GRBs with the presence of sub-second variability, which appears to be surprisingly absent among peak-poor GRBs. The two classes could result from two distinct regimes in which the inner engines of GRBs release their energy or otherwise dissipate that energy as gamma rays. [ABSTRACT FROM AUTHOR]

Polyploidy, resulting from whole‐genome duplication (WGD), is ubiquitous in nature and reportedly associated with extreme environments and biological invasions. However, WGD usually comes with great costs, raising questions about the establishment chance of newly formed polyploids. The surprisingly high number of polyploid and mixed‐ploidy species observed in nature may be a consequence of their continuous emergence or may reflect stable polyploid persistence and even coexistence with the ancestral ploidy under certain circumstances. However, empirical studies on contemporary polyploid establishment often neglect the cost–benefit balances of polyploid characteristics, tradeoffs between phenotypic characteristics, intercytotype interactions, recurrent polyploid formation, and stochastic processes. Here, we advocate for considering population‐level success, combining the aforementioned factors that affect polyploid establishment and long‐term coexistence with their ancestors. We approach the paradox of polyploid establishment despite high costs from a modern coexistence theory perspective and give an overview of the diversity of mechanisms and their timing that may potentially enable stable rather than transient persistence. [ABSTRACT FROM AUTHOR]

Since late 2019 the novel coronavirus, also known as COVID-19, has caused a pandemic that persists. This paper shows how a continuous-time Markov chain model for the spread of COVID-19 can be used to explain, and justify to undergraduate students, strategies now being used in attempts to control the virus. The material in the paper is written at the level of students who are taking an introductory course on the theory and applications of stochastic processes. [ABSTRACT FROM AUTHOR]

This paper proposes criteria for establishing the asymptotic moment stability of semi-Markovian impulsive switched systems. Under some mild assumptions, we formulate an auxiliary linear time-delayed system based on the Lyapunov characterizations of the subsystems and impulses, as well as the properties of the underlying semi-Markovian impulsive switching signal. Our main result provides an upper bound on the moment, which is directly related to a solution of the aforementioned linear time-delayed system. Specifically, the semi-Markovian impulsive switched system is asymptotically moment stable if the auxiliary linear time-delayed system is asymptotically stable. In situations where the mode-dependent sojourn time distributions of the underlying impulsive switching signals are all exponential, uniform, or trigonometric, we deduce explicit formulae for the auxiliary linear time-delayed systems. To prove the main result, we compute the expected gain function, which requires formulating a generalized renewal equation. Finally, we test our stability criteria on a numerical example in different scenarios and show that our stability results are nonconservative compared to the statistically obtained average of state-norms and state-norm-squares. [ABSTRACT FROM AUTHOR]

Simulation of random fields is widely used in Earth sciences for modeling and uncertainty quantification. The spatial features of these fields may have a strong impact on the forecasts made using these fields. For instance, in flow and transport problems the connectivity of the permeability fields is a crucial aspect. Multi-Gaussian random fields are the most common tools to analyze and model continuous fields. Their spatial correlation structure is described by a covariance or variogram model. However, these types of spatial models are unable to represent highly or poorly connected structures even if a broad range of covariance models can be employed. With this type of model, the regions with values close to the mean are always well connected whereas the regions of low or high values are isolated. Substitution random functions (SRFs) belong to another broad class of random functions that are more flexible. SRFs are constructed by composing ( Z = Y ∘ T ) two stochastic processes: the directing function T (latent field) and the coding process Y (modifying the latent field in a stochastic manner). In this paper, we study the properties of SRFs obtained by combining stationary multi-Gaussian random fields for both T and Y with bounded variograms. The resulting SRFs Z are stationary, but as T has a finite variance Z is not ergodic for the mean and the covariance. This means that single realizations behave differently from each other. We propose a simple technique to control which values (low, intermediate, or high) are connected. It consists of adding a control point on the process Y to guide every single realization. The conditioning to local values is obtained using a Gibbs sampler. [ABSTRACT FROM AUTHOR]

This paper explores memory mechanisms in complex socio-technical systems, using a mobility demand model as an example case. We simplify a large-scale agent-based mobility model, formulate the corresponding stochastic process, and observe that the mobility decision process is non-Markovian. This is due to its dependence on the system's history, including social structure and local infrastructure, which evolve based on prior mobility decisions. Complementing the mobility process with two history-determined components leads to an extended mobility process that is Markovian. Although our model is a very much reduced version of the original one, it remains too complex for the application of usual analytic methods. Instead, we employ simulations to examine the functionalities of the two history-determined components. We think that the structure of the analyzed stochastic process is exemplary for many socio-technical, -economic, -ecological systems. Additionally, it exhibits analogies with the framework of extended evolution, which has previously been used to study cultural evolution. [ABSTRACT FROM AUTHOR]

The multilevel Monte Carlo (MLMC) method is highly efficient for estimating expectations of a functional of a solution to a stochastic differential equation (SDE). However, MLMC estimators may be unstable and have a poor (noncanonical) complexity in the case of low regularity of the functional. To overcome this issue, we extend our previously introduced idea of numerical smoothing in [Quant. Finance, 23 (2023), pp. 209-227], in the context of deterministic quadrature methods to the MLMC setting. The numerical smoothing technique is based on root-finding methods combined with one-dimensional numerical integration with respect to a single well-chosen variable. This study is motivated by the computation of probabilities of events, pricing options with a discontinuous payoff, and density estimation problems for dynamics where the discretization of the underlying stochastic processes is necessary. The analysis and numerical experiments reveal that the numerical smoothing significantly improves the strong convergence and, consequently, the complexity and robustness (by making the kurtosis at deep levels bounded) of the MLMC method. In particular, we show that numerical smoothing enables recovering the MLMC complexities obtained for Lipschitz functionals due to the optimal variance decay rate when using the Euler--Maruyama scheme. For the Milstein scheme, numerical smoothing recovers the canonical MLMC complexity, even for the nonsmooth integrand mentioned above. Finally, our approach efficiently estimates univariate and multivariate density functions. [ABSTRACT FROM AUTHOR]

A relativistic diffusion model with cylindrical symmetry, which propagates an initial state based on quantum chromodynamics in time toward a thermal equilibrium limit, is derived from nonequilibrium–statistical considerations: adapting an existing framework for Markovian stochastic processes representing relativistic phase‐space trajectories, a Fokker–Planck equation is obtained for the time evolution of particle‐number distribution functions with respect to transverse and longitudinal rapidity. The resulting partially‐evolved distribution functions are transformed to transverse‐momentum and pseudorapidity space, and compared with charged‐hadron data from the CERN Large Hadron Collider. [ABSTRACT FROM AUTHOR]