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We revisit a deterministic model for studying the dynamics of allelopathy. The model is formulated in terms of a non-homogeneous linear system of differential equations whose forcing or source term is a piecewise constant function (square wave). To account for the inherent uncertainties present in this natural phenomenon, we reformulate the model as a system of random differential equations where all model parameters and the initial condition are assumed to be random variables, while the forcing term is a stochastic process. Taking extensive advantage of the so-called Random Variable Transformation (RVT) method, we obtain the solution of the randomized model by providing explicit expressions of the first probability density function of the solution under very general assumptions on the model data. We also determine the joint probability density function of the non-trivial equilibrium point, which is a random vector. If the source term is a time-dependent stochastic process, the RVT method might not be applicable since no explicit solution of the model is available. We then show an alternative approach to overcome this drawback by applying the Liouville–Gibbs partial differential equation. All the theoretical findings are illustrated through several examples, including the application of the randomized model to real-world data on alkaloid contents from leaching thornapple seed. [ABSTRACT FROM AUTHOR]

Current video generation models usually convert signals indicating appearance and motion received from inputs (e.g., image and text) or latent spaces (e.g., noise vectors) into consecutive frames, fulfilling a stochastic generation process for the uncertainty introduced by latent code sampling. However, this generation pattern lacks deterministic constraints for both appearance and motion, leading to uncontrollable and undesirable outcomes. To this end, we propose a new task called Text-driven Video Prediction (TVP). Taking the first frame and text caption as inputs, this task aims to synthesize the following frames. Specifically, appearance and motion components are provided by the image and caption separately. The key to addressing the TVP task depends on fully exploring the underlying motion information in text descriptions, thus facilitating plausible video generation. In fact, this task is intrinsically a cause-and-effect problem, as the text content directly influences the motion changes of frames. To investigate the capability of text in causal inference for progressive motion information, our TVP framework contains a Text Inference Module (TIM), producing step-wise embeddings to regulate motion inference for subsequent frames. In particular, a refinement mechanism incorporating global motion semantics guarantees coherent generation. Extensive experiments are conducted on Something-Something V2 and Single Moving MNIST datasets. Experimental results demonstrate that our model achieves better results over other baselines, verifying the effectiveness of the proposed framework. [ABSTRACT FROM AUTHOR]

This paper gives a new property for stochastic processes, called square-mean μ - pseudo-S-asymptotically Bloch-type periodicity. We show how this property is preserved under some operations, such as composition and convolution, for stochastic processes. Our main results extend the classical results on S-asymptotically Bloch-type periodic functions. We also apply our results to some problems involving semilinear stochastic integrodifferential equations in abstract spaces [ABSTRACT FROM AUTHOR]

This study proposes a novel velocity divergence‐generalized adaptive probability density evolution method (VD‐GAPDEM) for calculating the probability density function of the stochastic response process of stochastic structures under stochastic dynamic loads. First, based on the principle of probability conservation, the velocity divergence‐generalized adaptive probability density evolution equation (VD‐GAPDEE) is derived for a stochastic system that can effectively consider the shape and location changes of the joint transitional probability density of representative points (RPs) in the stochastic response process. Second, a novel VD‐GAPDEM is proposed to solve the VD‐GAPDEE directly using the point selection technique based on the generalized F discrepancy and the second‐order Runge–Kutta method with a smoothing kernel method (Runge–Kutta‐SKFAM). Furthermore, the differences and connections between VD‐GAPDEM and the existing probability density evolution method are analyzed. Additionally, the high computational efficiency and accuracy of the proposed VD‐GAPDEM are demonstrated through three typical examples of stochastic response analysis, involving stochastic systems subjected to stochastic dynamic loads. [ABSTRACT FROM AUTHOR]

For a 24/7 database system, backups should be implemented right after a large volume of data has been updated, putting their backup windows in non-busy states with user's convenience.From this viewpoint, this paper studies periodic and random incremental backup policies, in which, incremental backup is implemented right after data update and full backup is performed at periodic times KT , or at a number N of data updates, respectively. We firstly describe the stochastic processes of data update and database failure, and then model the expected cost rates for data backup and data restoration.Respective K ∗ , N ∗ , K f ∗ , and N f ∗ are obtained to minimize their expected cost rates in analytical ways, respectively. Finally, numerical examples are given to illustrate the optimum policies. [ABSTRACT FROM AUTHOR]

A study of earthquake seismicity is undertaken over the areas of Central and South America, the tectonics of which are of great interest. The whole territory is divided into 10 seismic zones based on some seismotectonic characteristics, as in previously published studies. The earthquakes used in the present study are extracted from the catalogs of the International Seismological Center, cover the period of 1900–2021, and are restricted to shallow depths (≤60 km) and a magnitude M ≥ 4.5 . Fore- and aftershocks are removed according to Reasenberg's technique. The paper confines itself to the evaluation of earthquake occurrence probabilities in the seismic zones covering parts of Central and South America, and we implement the hidden Markov model (HMM) and apply the EM algorithm. [ABSTRACT FROM AUTHOR]

In this work, we develop two stable estimators for solving linear functional regression problems. It is well known that such a problem is an ill-posed stochastic inverse problem. Hence, a special interest has to be devoted to the stability issue in the design of an estimator for solving such a problem. Our proposed estimators are based on combining a stable least-squares technique and a random projection of the slope function β 0 (·) ∈ L 2 (J) , where J is a compact interval. Moreover, these estimators have the advantage of having a fairly good convergence rate with reasonable computational load, since the involved random projections are generally performed over a fairly small dimensional subspace of L 2 (J). More precisely, the first estimator is given as a least-squares solution of a regularized minimization problem over a finite dimensional subspace of L 2 (J). In particular, we give an upper bound for the empirical risk error as well as the convergence rate of this estimator. The second proposed stable LFR estimator is based on combining the least-squares technique with a dyadic decomposition of the i.i.d. samples of the stochastic process, associated with the LFR model. In particular, we provide an L 2 -risk error of this second LFR estimator. Finally, we provide some numerical simulations on synthetic as well as on real data that illustrate the results of this work. These results indicate that our proposed estimators are competitive with some existing and popular LFR estimators. [ABSTRACT FROM AUTHOR]

Abstract Background Sanniang Bay (SNB) and Dafeng River (DFR), located in the northern Beibu Gulf, is well-known as one of the eight habitats for humpback dolphins in China. This region is representative of typical estuarine and bay ecosystems and produce complex hydrodynamic seawater conditions. Moreover, anthropogenic pressure, such as eutrophication and large-scale infrastructure projects, have caused ongoing habitat deterioration and loss. It is urgent to know the phytoplankton community and their relationships with environmental factors in this region. Results In this study, we assessed the diversity and assembly mechanisms of phytoplankton communities, as well as their relationship with the physicochemical characteristics of seawater in SNB and DFR region using 18 S rDNA metabarcoding analysis. The results showed that seasonal changes markedly impacted the alpha diversity of the phytoplankton community. From March to July, with the average temperature increasing from 25.2℃ to 28.1℃,the Shannon or Species Richness were negatively correlated with temperature. During hot season (in Sep, average temperature 32.1℃), phytoplankton diversity was negatively correlated with nutrients (NH4 +, NO3 −, PO4 3−, TN). Additionally, during the rainy season, the Bray-Curtis similarity of the phytoplankton community was significantly lower than during the dry season. In March, the distance among the sampling sites was most strongly and positively correlated with the Bray-Curtis dissimilarity. Stochastic processes, specifically dispersal limitation and ecological drift, are the primary drivers of community assembly, while deterministic assembly processes (mainly heterogeneous selection) contribute a relatively minor portion (

Abstract We use a statistical model to discuss nonequilibrium fragmentation phenomena taking place in the stochastic dynamics of the log sector in log gravity. From the canonical Gibbs model, a combinatorial analysis reveals an important aspect of the n-particle evolution previously shown to generate a collection of random partitions according to the Ewens distribution realized in a disconnected double Hurwitz number in genus zero. By treating each possible partition as a member of an ensemble of fragmentations, and ensemble averaging over all partitions with the Hurwitz number as a special case of the Gibbs distribution, a resulting distribution of cluster sizes appears to fall as a power of the size of the cluster. Dynamical systems that exhibit a distribution of sizes giving rise to a scale-invariant power-law behavior at a critical point possess an important property called self-organized criticality. As a corollary, the log sector of log gravity is a self-organized critical system at the critical point μl = 1. A similarity between self-organized critical systems, spin glass models and the dynamics of the log sector which exhibits aging behavior reminiscent of glassy systems is pointed out by means of the Pòlya distribution, also known to classify various models of (randomly fragmented) disordered systems, and by presenting the cluster distribution in the log sector of log gravity as a distinguished member of this probability distribution. We bring arguments from a probabilistic perspective to discuss the disorder in log gravity, largely anticipated through the conjectured AdS3/LCFT2 correspondence.

Abstract 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 We formulate a geometric measurement theory of dynamical classical systems possessing both continuous and discrete degrees of freedom. The approach is covariant with respect to choices of clocks and naturally incorporates laboratories. The latter are embedded symplectic submanifolds of an odd-dimensional symplectic structure. When suitably defined, symplectic geometry in odd dimensions is exactly the structure needed for covariance. A fundamentally probabilistic viewpoint allows classical supergeometries to describe discrete dynamics. We solve the problem of how to construct probabilistic measures on supermanifolds given a (possibly odd dimensional) supersymplectic structure. This relies on a superanalog of the Hodge star for differential forms and a description of probabilities by convex cones. We also show how stochastic processes such as Markov chains can be described by supergeometry.

Abstract Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang (KPZ) scaling in late-time correlators and autocorrelators of certain interacting many-body systems, such as Heisenberg spin chains, has been reported. Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis. We focus on the Heisenberg time scale, which approximately corresponds to the ramp–plateau transition for the Krylov complexity in systems with a large but finite number degrees of freedom. Two frameworks are under consideration: i) the system with growing Lanczos coefficients and an artificial cut-off, and ii) the system with the finite Hilbert space. In both cases via numerical analysis, we observe the transition from Gaussian to KPZ-like scaling, or equivalently, the diffusion-superdiffusion transition at the critical Euclidean time t E ∗ $$ {t}_E^{\ast } $$ = c cr K, for the Krylov chain of finite length K, and c cr = O(1). In particular, we find a scaling ~ K 1/3 for fluctuations in the one-point correlation function and a dynamical scaling ~ K −2/3 associated with the return probability (Loschmidt echo) corresponding to autocorrelators in physical space. In the first case, the transition is of the 3rd order and can be considered as an example of dynamical quantum phase transition (DQPT), while in the second, it is a crossover. For case ii), utilizing the relationship between the spectrum of tridiagonal matrices at the spectral edge and the spectrum of the stochastic Airy operator, we demonstrate analytically the origin of the KPZ scaling for the particular Krylov chain using the results of the probability theory. We argue that there is interesting outcome of our study for the double scaling limit of matrix models. For the case of topological gravity, the white noise term of order O (1/N) is identified, which should be taken into account in the controversial issue of ensemble averaging in 2D/1D holography.

"Gating" is a widely observed phenomenon in biochemistry that describes the transition between the activated (or open) and deactivated (or closed) states of an ion-channel, which makes transport through that channel highly selective. In general, gating is a mechanism that imposes an additional restriction on a transport, as the process ends only when the "gate" is open and continues otherwise. When diffusion occurs in the presence of a constant bias to a gated target, i.e., to a target that switches between an open and a closed state, the dynamics essentially slow down compared to ungated drift-diffusion, resulting in an increase in the mean completion time, ⟨TG⟩ > ⟨T⟩, where T denotes the random time of transport and G indicates gating. In this work, we utilize stochastic resetting as an external protocol to counterbalance the delay due to gating. We consider a particle in the positive semi-infinite space that undergoes drift-diffusion in the presence of a stochastically gated target at the origin and is moreover subjected to rate-limiting resetting dynamics. Calculating the minimal mean completion time ⟨ T r ⋆ G ⟩ rendered by an optimal resetting rate r⋆ for this exactly solvable system, we construct a phase diagram that owns three distinct phases: (i) where resetting can make gated drift-diffusion faster even compared to the original ungated process, ⟨ T r ⋆ G ⟩ < ⟨ T ⟩ < ⟨ T G ⟩ , (ii) where resetting still expedites gated drift-diffusion but not beyond the original ungated process, ⟨ T ⟩ ≤ ⟨ T r ⋆ G ⟩ < ⟨ T G ⟩ , and (iii) where resetting fails to expedite gated drift-diffusion, ⟨ T ⟩ < ⟨ T G ⟩ ≤ ⟨ T r ⋆ G ⟩. We also highlight various non-trivial behaviors of the completion time as the resetting rate, gating parameters, and geometry of the set-up are carefully ramified. Gated drift-diffusion aptly models various stochastic processes such as chemical reactions that exclusively take place in certain activated states of the reactants. Our work predicts the conditions under which stochastic resetting can act as a useful strategy to enhance the rate of such processes without compromising their selectivity. [ABSTRACT FROM AUTHOR]

In this paper, we derive a condition-based maintenance strategy for a degradation-shock dependence system subject to two causes of failure, degradation and random shocks. We develop a reliability model for a system under warranty for failure in which we consider the dependence between the degradation process and random shocks and do a warranty cost analysis based on the suggested model. We consider a degradation-shock dependence system that is under warranty with three separate services: repair, replacement, and preventive maintenance. These are triggered when a product degradation crosses one of three predetermined degradation thresholds. We also investigate the dependence between random shocks and degradation modelled by a time-scaled covariate factor. We study the random shock considering fatal shocks that require replacement and nonfatal shocks that require only repair and the degradation caused by nonfatal shocks. The condition-based maintenance strategy for a degradation-shock dependence system is a novel approach to analysing system degradation, with a goal of optimising warranty costs; we also minimise the expected total system cost to find an optimal warranty length. We present several numeric examples and real-world applications to illustrate our proposed approach. [ABSTRACT FROM AUTHOR]

In this manuscript, we study a benchmark tracking problem when prices evolve through a Binomial model with a random environment. The agent invests a given fund's capital into different assets in a predetermined market to replicate at each stage of time a financial index or benchmark. To measure the actual deviation between the agent's wealth and the current benchmark, we apply a deviation error expressed as a total sum of quadratic functions. We also assume the agent is obligated to change her/his investment between two markets when it is mandatory. This obligation happens when the fund's wealth falls down a predetermined bankruptcy barrier. The dynamic programming method is then used to get optimal investment strategies that minimize the deviation error as well as to characterize the minimum deviation. We also apply the so-called potential function to analyze the influence of the environment on the prices. Numerical simulations are provided to illustrate our results. [ABSTRACT FROM AUTHOR]

In the field of control engineering, there has been a growing emphasis on systems with feedback loops that involve stochastic factors. Simultaneously, with the advancements in probability theory, feedback loops with stochastic processes have gained practicality due to their customizability and the potential for practical applications. Essentially, the effect of adding additive random signals in linear feedback systems can be viewed as the introduction of filtered stochastic noise. However, when random signals enter the feedback loop multiplicatively, a richer set of state behaviors emerges. This study utilizes multiplicative feedback loops to construct Markov chains and provides a probabilistic modeling approach to investigate the stability and asymptotic behavior of Markov feedback loops, offering insights for microsystems. This paper derives properties of such stochastic processes and provides corresponding theoretical proofs. The theoretical foundation of this probabilistic modeling can be applied in economics, biological variation processes, epidemic control predictions, and linear perturbation models, offering a theoretical perspective for feedback systems with uncertain triggers. [ABSTRACT FROM AUTHOR]

We consider coupled slow-fast stochastic processes, where the averaged slow motion is given by a two-dimensional Hamiltonian system with multiple critical points. On a proper time scale, the evolution of the first integral converges to a diffusion process on the corresponding Reeb graph, with certain gluing conditions specified at the interior vertices, as in the case of additive white noise perturbations of Hamiltonian systems considered by M. Freidlin and A. Wentzell. The current paper provides the first result where the motion on a graph and the corresponding gluing conditions appear due to the averaging of a slow-fast system, with a Hamiltonian structure, on a large time scale. The result allows one to consider, for instance, long-time diffusion approximation for an oscillator with a potential with more than one well. [ABSTRACT FROM AUTHOR]

The identification of a suitable transformation model and the calculation of correlation coefficients constitute essential steps in the simulation a nonstationary and non-Gaussian stochastic process. For stochastic ground motion, its nonstationary and non-Gaussian properties are well-known. In this paper, an easy-to-implement simulation method of a nonstationary and non-Gaussian stochastic process with known time-varying statistical moments is proposed. The approximate transformation model between the nonstationary and non-Gaussian stochastic process and the underlying Gaussian process, which contains the wider range of applicability and the availability of explicit expressions for determining the distribution parameters, is determined. The time-varying correlation coefficient of the underlying Gaussian process is calculated through the proposed interpolation method. Furthermore, the effectiveness of the proposed simulation method of the nonstationary and non-Gaussian stochastic ground motion is verified by numerical examples. [ABSTRACT FROM AUTHOR]

Let {Zn} be a supercritical branching process with immigration in an independent, identically distributed(i.i.d.) environment ξ. The Berry-Esseen bound for log⁡Zn has been established by Wang et al. (2021). To refine that, under the less restrictive moment conditions, we calculate the exact convergence rate in the central limit theorem for log⁡Zn under the annealed law. [ABSTRACT FROM AUTHOR]

In order to rationally characterize the nondeterministic phenomena in queueing systems, there exist two mathematical systems, one is probability theory concerned with the analysis of random phenomena and the other is uncertainty theory concerned with the analysis of uncertain phenomena. Before using the above two mathematical systems to model the real queueing systems, we often need to face such a question, are the real queueing systems random or uncertain? In order to answer this question, we collect the arriving times of passengers from online car-hailing platform in Beijing, and then analyze the collected data based on stochastic renewal process and uncertain renewal process. Finally, by comparing samples and confidence intervals of the total numbers of passengers arriving on the online car-hailing platform under two mathematical systems, we come to the conclusion that the queueing systems in the real world are uncertain rather than random. [ABSTRACT FROM AUTHOR]

We analyze the asynchronous version of the DeGroot dynamics: In a connected graph G$$ G $$ with n$$ n $$ nodes, each node has an initial opinions in [0,1]$$ \left[0,1\right] $$ and an independent Poisson clock. When a clock at a node v$$ v $$ rings, the opinion at v$$ v $$ is replaced by the average opinion of its neighbors. It is well known that the opinions converge to a consensus. We show that the expected time 피(τε) to reach ε$$ \varepsilon $$‐consensus is poly(n)$$ (n) $$ in undirected graphs and in Eulerian digraphs, but for some digraphs of bounded degree it is exponential. Our main result is that in undirected graphs and Eulerian digraphs, if the degrees are uniformly bounded and the initial opinions are i.i.d., then 피(τε)=polylog(n) for every fixed ε>0$$ \varepsilon >0 $$. We give sharp estimates for the variance of the limiting consensus opinion, which measures the ability to aggregate information ("wisdom of the crowd"). We also prove generalizations to non‐reversible Markov chains and infinite graphs. New results of independent interest on fragmentation processes and coupled random walks are crucial to our analysis. [ABSTRACT FROM AUTHOR]

Abstract It is believed that the large-scale geometric properties of two-dimensional critical percolation are described by a logarithmic conformal field theory, but it has been challenging to exhibit concrete examples of logarithmic singularities and to find an explanation and a physical interpretation, in terms of lattice observables, for their appearance. We show that certain percolation correlation functions receive independent contributions from a large number of similar connectivity events happening at different scales. Combined with scale invariance, this leads to logarithmic divergences. We study several logarithmic correlation functions for critical percolation in the bulk and in the presence of a boundary, including the four-point function of the density (spin) field. Our analysis confirms previous findings, provides new explicit calculations and explains, in terms of lattice observables, the physical mechanism that leads to the logarithmic singularities we discover. Although we adopt conformal field theory (CFT) terminology to present our results, the core of our analysis relies on probabilistic arguments and recent rigorous results on the scaling limit of critical percolation and does not assume a priori the existence of a percolation CFT. As a consequence, our results provide strong support for the validity of a CFT description of critical percolation and a step in the direction of a mathematically rigorous formulation of a logarithmic CFT of two-dimensional critical percolation.

Abstract We study the turbulent dynamics of a relativistic (2 + 1)-dimensional fluid placed in a stochastic gravitational potential. We demonstrate that the dynamics of the fluid can be obtained using a dual holographic description realized by an asymptotically Anti-de Sitter black brane driven by a random boundary metric. Using the holographic duality we study the energy power spectrum of a fluid with an inverse energy cascade and show that it is compatible with that of a compressible fluid flow. We calculate the local energy dissipation and the local fluid velocity distribution which provide other measures of the holographic fluid turbulence.

The study of myxomycete biogeography has a long-standing history and has consistently drawn scholarly interest. Nevertheless, studies focusing specifically on the spatial and temporal distribution patterns of myxomycete diversity are relatively limited, with even fewer investigating the mechanisms driving the generation and maintenance of myxomycete diversity. Therefore, this study selected two geographically distant sampling sites within northern Chinese forests to investigate myxomycete species composition, community structure, environmental drivers, and assembly patterns under geographic barriers. We established plots in the Altai Mountains (ALE) and the Greater Khingan Mountains (GKM), gathered bark and litter, and conducted 80-day moist chamber cultures of myxomycetes. Additionally, myxomycete specimens were collected in the field simultaneously to supplement the data set. This study collected 541 myxomycete specimens belonging to 73 species from 28 genera, spanning 12 families and eight orders. The ALE and the GKM had 20 identical species, accounting for 27% of the total species. Myxomycetes from both regions exhibited abundant occurrence 18 days after cultivation, with the quantity on bark substrates notably higher than on litter. Arcyria pomiformis and Comatricha elegans were the most common species in moist chamber cultures. Mantel test outcomes revealed that environmental factors had no significant impact on myxomycete community similarity between the two areas, aligning with findings from the neutral community model analysis, indicating a predominant influence of stochastic processes on myxomycete community structure in moist chamber cultures. This study represents the first application of a quantitative framework to analyze myxomycete community assembly cultivated in moist chambers. [ABSTRACT FROM AUTHOR]

AbstractFueled in part by recent applications in neuroscience, the multivariate Hawkes process has become a popular tool for modeling the network of interactions among high-dimensional point process data. While evaluating the uncertainty of the network estimates is critical in scientific applications, existing methodological and theoretical work has primarily addressed estimation. To bridge this gap, we develop a new statistical inference procedure for high-dimensional Hawkes processes. The key ingredient for the inference procedure is a new concentration inequality on the first- and second-order statistics for integrated stochastic processes, which summarize the entire history of the process. Combining recent martingale central limit theorem with the new concentration inequality, we then characterize the convergence rate of the test statistics in a continuous time domain. Finally, to account for potential non-stationarity of the process in practice, we extend our statistical inference procedure to a flexible class of Hawkes processes with time-varying background intensities and unknown transition functions. The finite sample validity of the inferential tools is illustrated via extensive simulations and further applied to a neuron spike train dataset. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work. [ABSTRACT FROM AUTHOR]

Plant communities are complex systems shaped by a combination of deterministic and stochastic ecological processes. Bryophytes are an essential component of plant diversity in natural ecosystems, yet our understanding of their community ecology needs to catch up to that of other organisms. The unique geological history, alpine climatic conditions, and high habitat heterogeneity of Tibet provide suitable areas for bryophytes to survive in the alpine regions. Therefore, field surveys were conducted across 184 plots in forest, thicket, and herbaceous vegetation of Tibet to investigate the role of deterministic processes such as biological interactions and abiotic effects, along with stochastic processes, in shaping the distribution of bryophyte assemblages. We employed various analytical methods, including mixed effects models, partial least squares path modeling, null model analysis, and neutral community models. The study showed that bryophyte richness was highest in forests. Bryophyte assemblages showed greater segregation in forest and thicket environments compared to herbaceous vegetation. As the influence of stochastic processes increased, that of deterministic processes decreased from forests through thickets to herbaceous vegetation. Deterministic processes were the main driving forces for the bryophyte assemblage pattern. Soil properties and climatic factors, particularly pH played a key role in determining bryophyte patterns in Tibet. This study has deepened our comprehension of how deterministic and stochastic ecological processes interplay and shape bryophyte distribution patterns in Tibet. [ABSTRACT FROM AUTHOR]

Mixing describes the process by which solutes evolve from an initial heterogeneous state to uniformity under the stirring action of a fluid flow. Fluid stretching forms thin scalar lamellae that coalesce due to molecular diffusion. Owing to the linearity of the advection–diffusion equation, coalescence can be envisioned as an aggregation process. Here, we demonstrate that in smooth two-dimensional chaotic flows, mixing obeys a correlated aggregation process, where the spatial distribution of the number of lamellae in aggregates is highly correlated with their elongation, and is set by the fractal properties of the advected material lines. We show that the presence of correlations makes mixing less efficient than a completely random aggregation process because lamellae with similar elongations and scalar levels tend to remain isolated from each other. We show that correlated aggregation is uniquely determined by a single exponent that quantifies the effective number of random aggregation events. These findings expand aggregation theories to a larger class of systems, which have relevance to various fundamental and applied mixing problems. [ABSTRACT FROM AUTHOR]

Turning is one of the most important material removal processes in manufacturing, where the proper understanding of the process is crucial for the quality of the final product. In this study, the stochastic cutting force is utilized to enhance the existing 1-degree-of-freedom turning model. A stochastic model is adopted to address the stochastic resonance phenomenon occurring near stability boundaries. Additionally, a novel simplified stochastic model is introduced with additive noise only. The comparison of the two models reveals that, with the recommended noise intensity of 0.1 to 1%, there is no significant difference in the stability charts and mean square characteristics between the two models. As a result, the time-consuming numerical methods can be bypassed, as the simplified model offers a computationally more efficient analytical approach to compute variance based on power spectral density (PSD). By combining techniques such as D-separation to determine stability boundaries and the PSD-based variance calculation, it only takes a minute instead of hours to construct a heatmap using the introduced simplified stochastic turning model that clearly outlines dangerous stochastic resonance regions inside the stable domain. [ABSTRACT FROM AUTHOR]

Continuous time Bayesian networks (CTBNs) represent a class of stochastic processes, which can be used to model complex phenomena, for instance, they can describe interactions occurring in living processes, social science models or medicine. The literature on this topic is usually focused on a case when a dependence structure of a system is known and we are to determine conditional transition intensities (parameters of a network). In the paper, we study a structure learning problem, which is a more challenging task and the existing research on this topic is limited. The approach, which we propose, is based on a penalized likelihood method. We prove that our algorithm, under mild regularity conditions, recognizes a dependence structure of a graph with high probability. We also investigate properties of the procedure in numerical studies. [ABSTRACT FROM AUTHOR]

In the analysis of clustered failure time data, Cox frailty models have been extensively studied by incorporating frailty with a prespecified distribution to address potential correlation of data within clusters. In this paper, we propose a frailty proportional mean residual life regression model to analyze such data. A novel conditional quasi‐likelihood inference procedure is developed, utilizing a stochastic process and the inverse probability of censoring weighting (IPCW) to form estimating equations for regression parameters. Our proposal employs conditional inference based on a penalized quasi‐likelihood to address within‐cluster correlation without need to specify the frailty distribution, bringing the method closer to what suffices for real‐world applications. By adopting the Buckley–James estimator in the IPCW, the method further allows for dependent censoring. We establish asymptotic properties of the proposed estimator and evaluate its finite sample performance via simulation studies. An application to the data from a multi‐institutional breast cancer study is presented for illustration. [ABSTRACT FROM AUTHOR]

Microorganisms are important members of seagrass bed ecosystems and play a crucial role in maintaining the health of seagrasses and the ecological functions of the ecosystem. In this study, we systematically quantified the assembly processes of microbial communities in fragmented seagrass beds and examined their correlation with environmental factors. Concurrently, we explored the relative contributions of species replacement and richness differences to the taxonomic and functional β-diversity of microbial communities, investigated the potential interrelation between these components, and assessed the explanatory power of environmental factors. The results suggest that stochastic processes dominate community assembly. Taxonomic β-diversity differences are governed by species replacement, while for functional β-diversity, the contribution of richness differences slightly outweighs that of replacement processes. A weak but significant correlation (p < 0.05) exists between the two components of bdiversity in taxonomy and functionality, with almost no observed significant correlation with environmental factors. This implies significant differences in taxonomy, but functional convergence and redundancy within microbial communities. Environmental factors are insufficient to explain the β-diversity differences. In conclusion, the assembly of microbial communities in fragmented seagrass beds is governed by stochastic processes. The patterns of taxonomic and functional β-diversity provide new insights and evidence for a better understanding of these stochastic assembly rules. This has important implications for the conservation and management of fragmented seagrass beds. [ABSTRACT FROM AUTHOR]

AbstractLet us consider a sequence of binary (zero-one) trials. A counter registers ones but once an one is registered the mechanism is locked for a fixed number of trials following each registration. On such a sequence of a fixed length we define a random variable enumerating runs of ones of length exceeding a threshold. Exact recursive expressions are obtained for the probability mass function, generating functions and moments, as well as an exact closed formula for the mean of this random variable. A simulation algorithm is also provided for approximating values of this random variable on such a modified binary sequence. Statistical inference problems associated with the probability of ones are examined by numerical techniques and simulation. An application connected to the chance that a stochastic process remains or not in statistical control is discussed. Illustrative numerical examples exemplify further the theoretical results. [ABSTRACT FROM AUTHOR]

A network evolution with predicted tail and extremal indices of PageRank and the Max-Linear Model used as node influence indices in random graphs is considered. The tail index shows a heaviness of the distribution tail. The extremal index is a measure of clustering (or local dependence) of the stochastic process. The cluster implies a set of consecutive exceedances of the process over a sufficiently high threshold. Our recent results concerning sums and maxima of non-stationary random length sequences of regularly varying random variables are extended to random graphs. Starting with a set of connected stationary seed communities as a hot spot and ranking them with regard to their tail indices, the tail and extremal indices of new nodes that are appended to the network may be determined. This procedure allows us to predict a temporal network evolution in terms of tail and extremal indices. The extremal index determines limiting distributions of a maximum of the PageRank and the Max-Linear Model of newly attached nodes. The exposition is provided by algorithms and examples. To validate our theoretical results, our simulation and real data study concerning a linear preferential attachment as a tool for network growth are provided. [ABSTRACT FROM AUTHOR]

For the sensorless control in a low-speed range of synchronous reluctance motors (SynRMs), injecting random high-frequency (HF) square-wave-type voltages has become a widely used and technologically mature method. It can solve the noise problem of traditional injection signal methods. However, all injection signal methods will cause problems such as torque ripple, which causes speed fluctuations. This article proposes a self-regulating random model algorithm for the random injection signal method, which includes a quantity adaptive module for adding additional random processes, an evaluation module for evaluating torque deviation degree, and an updated model module that is used to receive signals from the other two modules and complete model changes and output random model elements. The main function of this algorithm is to create a model that updates to suppress the evaluation value deviation based on the evaluation situation and outputs an optimal sequence of random numbers, thereby limiting speed bias always in a small range; this can reduce unnecessary changes in the output value of the speed regulator. The feasibility and effectiveness of the proposed algorithm and control method have been demonstrated in experiments based on a 5-kW synchronous reluctance motor. [ABSTRACT FROM AUTHOR]

To ensure the efficient functioning of solar energy generation systems, it is crucial to have dependable designs and regular maintenance. However, when these systems or their components operate at multiple working levels, optimizing reliability becomes a complex task for models and analyses. In the context of reliability modeling in solar energy generation systems, researchers often assume that random variables follow an exponential distribution (binary-state representation) as a simplification, although this may not always hold true for real-world engineering systems. In the present paper, a multi-state solar energy generating system with inverters in series configuration is investigated, in which unreliable by-pass changeover switches, common cause failures (CCFs), and multiple repairman vacations are also considered. Furthermore, the arrivals of CCFs and the repair processes of the failed system due to CCFs are governed by different Markovian arrival processes (MAPs), and the lifetimes and repair times of inverters and by-pass changeover switches and the repairman vacation time in the system have different phase-type (PH) distributions. Therefore, the behavior of the system is represented using a Markov process methodology, and reliability measures for the proposed system are derived utilizing aggregated stochastic process theory. Finally, a numerical example and a comparison analysis are presented to demonstrate the findings. [ABSTRACT FROM AUTHOR]

The step-stress accelerated degradation test (ADT) provides a feasible method for assessing the storage life of high-reliability, long-life products. However, this method results in a slower rate of performance degradation at the beginning of the test, significantly reducing the test efficiency. Therefore, this article proposes an assessment method for the step-down stress ADT that considers random effects and detection errors (SDRD). Firstly, a new Inverse Gaussian (IG) model is proposed. The model introduces the Gamma distribution to characterize the randomness of the product degradation path and uses the normal distribution to describe the detection errors of performance parameters. In addition, to solve the problem that the likelihood function of the IG model is complex and has no explicit expression, the Monte Carlo (MC) method is used to estimate unknown parameters of the model. This approach enhances computational accuracy and efficiency. Finally, to verify the effectiveness of the SDRD method, it is applied to the step-down stress ADT data from a specific missile tank to assess its storage life. Comparing the life assessment results of different methods, the conclusion shows that the SDRD method is more effective for assessing the storage life of high-reliability, long-life products. [ABSTRACT FROM AUTHOR]

A cruise was conducted in the summer of 2023 from the Pearl River Estuary (PRE) to the adjacent waters of the Xisha Islands in the northern South China Sea (NSCS) to investigate the distribution, community structure, and assembly patterns of eukaryotic and prokaryotic phytoplankton using high-throughput sequencing (HTS) and microscopic observation. Dinophyta were the most abundant phylum in the eukaryotic phytoplankton community based on HTS, accounting for 92.17% of the total amplicon sequence variants (ASVs). Syndiniales was the most abundant order among eukaryotic phytoplankton, whereas Prochlorococcus was the most abundant genus within cyanobacteria. The alpha diversity showed the lowest values in the PRE area and decreased gradually with depth, while cyanobacteria exhibited higher alpha diversity indices in the PRE and at depths ranging from 75 m to 750 m. The morphological results were different from the data based on HTS. Diatoms (37 species) dominated the phytoplankton community, with an average abundance of 3.01 × 104 cells L-1, but only six species of dinoflagellate were observed. Spearman correlation analysis and redundancy analysis (RDA) showed that the distribution and community structure of phytoplankton were largely influenced by geographical location and environmental parameters in the NSCS. The neutral community model (NCM) and null model indicated that deterministic processes played a significant role in the assembly of eukaryotic phytoplankton, with heterogeneous selection and homogeneous selection accounting for 47.27 and 29.95%, respectively. However, stochastic processes (over 60%) dominated the assembly of cyanobacteria and undominated processes accounted for 63.44%. In summary, the formation of eukaryotic phytoplankton was mainly influenced by environmental factors and geographic location, but the assembly of cyanobacteria was shaped by both stochastic processes, which accounted for over 60%, and environmental selection in the NSCS. [ABSTRACT FROM AUTHOR]

AbstractFunctional Time Series (FTS) are sequences of dependent random elements taking values on some functional space. Most of the research on this domain focuses on producing a predictor able to forecast the next function, having observed a part of the sequence. For this, the Autoregressive Hilbertian process is a suitable framework. Here, we address the problem of constructing simultaneous predictive confidence bands for a stationary FTS. The method is based on an entropy measure for stochastic processes. To construct predictive bands, we use a Reproducing Kernel Hilbert Space (RKHS) to represent the functions and a functional bootstrap procedure that allows us to estimate the prediction law and a Reproducing Kernel Hilbert Spaces (RKHS) to represent the functions, considering then the basis associated to the reproducing kernel. We then classify the points on the projected space according to those that belong to the minimum entropy set (MES) and those that do not. We map the minimum entropy set back to the functional space and construct a band using the regularity property of the RKHS. The proposed methodology is illustrated through artificial and real data sets. [ABSTRACT FROM AUTHOR]

This paper establishes a new fractional frSIS model utilizing a continuous time random walk method. There are two main innovations in this paper. On the one hand, the model is analyzed from a mathematical perspective. First, unlike the classic SIS infectious disease model, this model presents the infection rate and cure rate in a fractional order. Then, we proved the basic regeneration number R0 of the model and studied the influence of orders a and b on R0. Second, we found that frSIS has a disease-free equilibrium point E0 and an endemic equilibrium point E∗. Moreover, we proved frSIS global stability of the model using R0. If R0<1, the model of E0 is globally asymptotically stable. If R0>1, the model of E∗ is globally asymptotically stable. On the other hand, from the perspective of infectious diseases, we discovered that appropriately increasing a and decreasing b are beneficial for controlling the spread of diseases and ultimately leading to their disappearance. This can help us provide some dynamic adjustments in prevention and control measures based on changes in the disease. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with a stochastic semilinear differential equations driven by both Brownian motion and fractional Brownian motion. Firstly, we establish an inequality for the distance between finite‐dimensional distributions of a random process at two different moments. Then, using the properties of stochastic integrals, fixed point theorems, and based on this inequality, we establish the existence and uniqueness of Besicovich almost automorphic solutions in finite‐dimensional distributions for this type of semilinear equation. Finally, we provide an example to demonstrate the effectiveness of our results. Our results are new to stochastic differential equations driven by Brownian motion or stochastic differential equations driven by fractional Brownian motion. [ABSTRACT FROM AUTHOR]

Properties of the intervals between zero-crossings of non-Gaussian stable random processes are investigated. The classes of process considered are divided into those having short- and long-term memories, characterized by a coherence function that imbues dependence between a random variable measured at different times, which replaces the auto-correlation function, which exists only for the Gaussian case. For exponential coherence functions, all moments of probability densities for the intervals exist and a persistence parameter is determined that characterizes the rate of decay of the exponential tail of the probability densities, together with the full form of the density functions for selected values of the stability index. Results are verified with numerical simulation of a Cauchy process using a method independent of the theoretical development. For power-law coherence functions, the existence of moments of the distribution is conditional upon the indices characterizing the stable process and coherence function. The probability densities of the intervals have power-law tails depending on the product of these indices, with a logarithmic correction for specific combinations of these. An outer-scale or cut-off to power-law coherence functions regains a persistence parameter to the densities and the existence of all moments of the intervals. [ABSTRACT FROM AUTHOR]

Fluorescence microscopic imaging is essentially a convolution process distorted by random noise, limiting critical parameters such as imaging speed, duration, and resolution. Though algorithmic compensation has shown great potential to enhance these pivotal aspects, its fidelity remains questioned. Here we develop a physics-rooted computational resolution extension and denoising method with ensured fidelity. Our approach employs a multi-resolution analysis (MRA) framework to extract the two main characteristics of fluorescence images against noise: across-edge contrast, and along-edge continuity. By constraining the two features in a model-solution framework using framelet and curvelet, we develop MRA deconvolution algorithms, which improve the signal-to-noise ratio (SNR) up to 10 dB higher than spatial derivative based penalties, and can provide up to two-fold fidelity-ensured resolution improvement rather than the artifact-prone Richardson-Lucy inference. We demonstrate our methods can improve the performance of various diffraction-limited and super-resolution microscopies with ensured fidelity, enabling accomplishments of more challenging imaging tasks. [ABSTRACT FROM AUTHOR]

Abstract–Multistate Markov models are a canonical parametric approach for data modeling of observed or latent stochastic processes supported on a finite state space. Continuous-time Markov processes describe data that are observed irregularly over time, as is often the case in longitudinal medical data, for example. Assuming that a continuous-time Markov process is time-homogeneous, a closed-form likelihood function can be derived from the Kolmogorov forward equations—a system of differential equations with a well-known matrix-exponential solution. Unfortunately, however, the forward equations do not admit an analytical solution for continuous-time, time- inhomogeneous Markov processes, and so researchers and practitioners often make the simplifying assumption that the process is piecewise time-homogeneous. In this article, we provide intuitions and illustrations of the potential biases for parameter estimation that may ensue in the more realistic scenario that the piecewise-homogeneous assumption is violated, and we advocate for a solution for likelihood computation in a truly time-inhomogeneous fashion. Particular focus is afforded to the context of multistate Markov models that allow for state label misclassifications, which applies more broadly to hidden Markov models (HMMs), and Bayesian computations bypass the necessity for computationally demanding numerical gradient approximations for obtaining maximum likelihood estimates (MLEs). Supplemental materials are available online. [ABSTRACT FROM AUTHOR]

In this paper, a three-dimensional mathematical model of cancer, incorporating tumor cells, host normal cells, and effector immune cells, is examined. The chaotic nature of this cancer model is explored within the framework of Caputo fractional calculus. The analysis employs local stability assessment using the Matignon criteria, Lyapunov exponents (LEs) for various fractional orders of derivatives, bifurcation plots reflecting changes in the fractional derivative order, simulation outcomes of a novel chaotic attractor, Kaplan–Yorke dimension, and sensitivity to initial conditions. The results demonstrate that the Caputo fractional cancer model exhibits chaotic behavior for selected parameters. Moreover, the fractional derivative orders significantly influence the extent of chaotic behavior. Specifically, as the fractional derivative order increases from zero to one, the intensity of chaos diminishes, evidenced by a decrease in both the LE and the Kaplan–Yorke dimension. A piecewise modeling approach is applied to the cancer model, incorporating deterministic, stochastic, and power-law behaviors. Three distinct scenarios are developed within this framework, revealing several novel crossover behaviors through simulation. Notably, it is observed that when cancer dynamics initially follow a power-law behavior and subsequently transition into a stochastic process, the disease dynamics can stabilize, suggesting a positive outlook for disease control. Conversely, if the cancer dynamics begin with a deterministic process and then shift to a stochastic process, the system may enter a chaotic state, complicating disease management efforts. [ABSTRACT FROM AUTHOR]

The magnetic topology is a critical issue in fusion plasma research. An example is the Resonant Magnetic Perturbation (RMP), which controls the edge transport in tokamaks. However, the physics of how the RMP affects edge transport is not clear. One reason is the transport process on the stochastic magnetic field is poorly understood. This study examines anisotropic heat diffusion numerically to understand heat transport in stochastic magnetic fields. We developed a numerical model of an anisotropic temperature diffusion model, where the significant deviation of the parallel and perpendicular thermal conductivity exists. We applied this implementation to the realistic stellarator geometry with the stochastic magnetic field in the edge. The smooth temperature profile is obtained for the large perpendicular diffusion, although the magnetic field is stochastic. However, for another case of significant parallel diffusion, the small flattening of the temperature on the magnetic island in the stochastic region appears. That result suggests that the stochastic magnetic field can keep the finite temperature gradient if the connection length of the magnetic field line in the stochastic region is sufficiently long. [ABSTRACT FROM AUTHOR]

In studies of impurity transport in quasi-stationary hot plasma, the initial kinetic equation and the diffusive-convective transport model take into account ionization and recombination as "sources and sinks" of particles. Due to the incompatible representation of the radial dynamics and charge kinetics of impurity charge states, this approach and the results obtained appear to be out of system. The basis for their systematic criticism is the ideas of the theory of random processes proposed by M.A. Leontovich in 1935 as a theoretical alternative to the gas-kinetic equation. In this case, the charge-radial transport of an impurity in a quasi-stationary plasma is defined as a syncretic vector random Markov process of charge state transport. Its coupling (ergodicity) in a two-dimensional Markov system excludes "sources and sinks" from it in principle, and the relaxation convergence is directed to the formation of equilibrium invariant density profiles. The impurity equilibrium and density profiles are specified by a system of invariant functions that provide analysis of any types of density profiles observed in experiments. Modeling of radial profiles of helium, boron and carbon impurities allows us to find variants of their transformation from accumulation in the center to concentration near the plasma edge, transport coefficients and systematic connection with plasma parameters. [ABSTRACT FROM AUTHOR]