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Age and longevity are key parameters for demography and life-history evolution of organisms. In clonal species, a widespread life history among animals, plants, macroalgae and fungi, the sexually produced offspring (genet) grows indeterminately by producing iterative modules, or ramets, and so obscure their age. Here we present a novel molecular clock based on the accumulation of fixed somatic genetic variation that segregates among ramets. Using a stochastic model, we demonstrate that the accumulation of fixed somatic genetic variation will approach linearity after a lag phase, and is determined by the mitotic mutation rate, without direct dependence on asexual generation time. The lag phase decreased with lower stem cell population size, number of founder cells for the formation of new modules, and the ratio of symmetric versus asymmetric cell divisions. We calibrated the somatic genetic clock on cultivated eelgrass Zostera marina genets (4 and 17 years respectively). In a global data set of 20 eelgrass populations, genet ages were up to 1,403 years. The somatic genetic clock is applicable to any multicellular clonal species where the number of founder cells is small, opening novel research avenues to study longevity and, hence, demography and population dynamics of clonal species.

Cellular signaling, crucial for biological processes like immune response and homeostasis, relies on specificity and fidelity in signal transduction to accurately respond to stimuli amidst biological noise. Kinetic proofreading (KPR) is a key mechanism enhancing signaling specificity through time-delayed steps, although its effectiveness is debated due to intrinsic noise potentially reducing signal fidelity. In this study, we reformulate the theory of kinetic proofreading (KPR) by convolving multiple intermediate states into a single state and then define an overall processing time required to traverse these states. This simplification allows us to succinctly describe kinetic proofreading in terms of a single waiting time parameter, facilitating a more direct evaluation and comparison of KPR performance across different biological contexts such as DNA replication and T cell receptor (TCR) signaling. We find that loss of fidelity for longer proofreading steps relies on the specific strategy of information extraction and show that in the first-passage time (FPT) discrimination strategy, longer proofreading steps can exponentially improve the accuracy of KPR at the cost of speed. Thus, KPR can still be an effective discrimination mechanism in the high noise regime. However, in a product concentration-based discrimination strategy, longer proofreading steps do not necessarily lead to an increase in performance. However, by introducing activation thresholds on product concentrations, can we decompose the product-based strategy into a series of FPT-based strategies to better resolve the subtleties of KPR-mediated product discrimination. Our findings underscore the importance of understanding KPR in the context of how information is extracted and processed in the cell.

The brain produces diverse functions, from perceiving sounds to producing arm reaches, through the collective activity of populations of many neurons. Determining if and how the features of these exogenous variables (e.g., sound frequency, reach angle) are reflected in population neural activity is important for understanding how the brain operates. Often, high-dimensional neural population activity is confined to low-dimensional latent spaces. However, many current methods fail to extract latent spaces that are clearly structured by exogenous variables. This has contributed to a debate about whether or not brains should be thought of as dynamical systems or representational systems. Here, we developed a new latent process Bayesian regression framework, the orthogonal stochastic linear mixing model (OSLMM) which introduces an orthogonality constraint amongst time-varying mixture coefficients, and provide Markov chain Monte Carlo inference procedures. We demonstrate superior performance of OSLMM on latent trajectory recovery in synthetic experiments and show superior computational efficiency and prediction performance on several real-world benchmark data sets. We primarily focus on demonstrating the utility of OSLMM in two neural data sets: μECoG recordings from rat auditory cortex during presentation of pure tones and multi-single unit recordings form monkey motor cortex during complex arm reaching. We show that OSLMM achieves superior or comparable predictive accuracy of neural data and decoding of external variables (e.g., reach velocity). Most importantly, in both experimental contexts, we demonstrate that OSLMM latent trajectories directly reflect features of the sounds and reaches, demonstrating that neural dynamics are structured by neural representations. Together, these results demonstrate that OSLMM will be useful for the analysis of diverse, large-scale biological time-series datasets.

AbstractContinuous processes in most applications are measured discretely with error. This complicates the task of detecting intersections and the number of intersections between two continuous processes (i.e., when the processes have the same value). Intersections of continuous processes are scientifically important, but challenging to estimate from data. For example, in the field of animal ecology, intersections of the paths of moving animals tracked with satellite technologies can be used to understand disease transmission. We illustrate how to quantify contact between animals using telemetry data (i.e., the recorded locations of an animal over time). We introduce our method to quantify contact time with accessible concepts from introductory stochastic process literature, such as Brownian motion. Then, we provide two data examples using white-tailed deer (Odocoileus virginianus) and mule deer (Odocoileus hemionus) telemetry data in a region with high prevalence of chronic wasting disease. Our work provides a needed connection between existing model-based literature for animal movement and rule-based literature for animal interaction. Further, our work illustrates a unique statistical problem receiving minimal attention with broad applicability in human and livestock tracking. [ABSTRACT FROM AUTHOR]

Microorganisms in lakes are sensitive to salinity fluctuations. Despite extensive prior research on bacterial communities, our understanding of their characteristics and assembly mechanisms in lakes, especially in desert lakes with different salinities. To address this issue, we collected three samples from freshwater lakes, six from brackish lakes, and five from salt lakes in the Badanjilin Desert. The 16S rRNA gene sequencing was applied to investigate the bacterial interactions with rising salinity, community coexistence patterns, and assembly mechanisms. Our findings suggested that the increased lake salinity significantly reduces the bacterial community diversity and enhanced the community differentiation. Significant variations were observed in the contribution of biomarkers from Cyanobacteria, Chloroflexi, and Halobacterota to the composition of the lake bacterial communities. The bacterial communities in the salt lakes exhibited a higher susceptibility to salinity limitations than those in the freshwater and brackish lakes. In addition, the null modeling analyses confirmed the quantitative biases in the stochastic assembly processes of bacterial communities across freshwater, brackish, and saline lakes. With the increasing lake salinity, the significance of undominated and diffusion limitation decreased slightly, and the influence of homogenizing dispersal on community assembly increased. However, the stochasticity remained the dominant process across all lakes in the Badanjilin Desert. The analysis of co-occurring networks revealed that the rising salinity reduced the complexity of bacterial network structures and altered the interspecific interactions, resulting in the increased interspecies collaboration with increasing salinity levels. Under the influence of salinity stress, the key taxon Cyanobacteria in freshwater lakes (Schizothrix_LEGE_07164) was replaced by Proteobacteria (Thalassobaculum and Polycyclovorans) in brackish lakes, and Thermotogota (SC103) in salt lakes. The results indicated the symbiotic patterns of bacterial communities across varying salinity gradients in lakes and offer insights into potential mechanisms of community aggregation, thereby enhancing our understanding of bacterial distribution in response to salinity changes. [ABSTRACT FROM AUTHOR]

Introduction: Accurately predicting the remaining mechanical equipment is of great significance for ensuring the safe operation of the equipment and improving economic efficiency. Methods: To accurately assess the mechanical equipment degradation, predict its remaining useful life, and ensure efficient, stable, and safe operation, a degradation and life prediction model for mechanical equipment based on multivariate stochastic processes is studied. The study innovatively predicts the remaining life of mechanical equipment using multivariate stochastic processes, and facilitates the correlation analysis between performance indicators based on the characteristics of Copula functions. Results and discussion: The results showed that the Root Mean Squared Error value of the prediction results based on the trivariate Wiener process was 2.58, which decreased by 46.91% and 35.82% compared with the univariate and bivariate Wiener processes, respectively. The prediction value based on the trivariate gamma process was 3.49, which decreased by 44.95% and 40.54% compared with the univariate and bivariate gamma processes, respectively. In conclusion, the degradation and life prediction model with multivariate stochastic processes can effectively assess the mechanical equipment degradation and predict its remaining useful life. This provides an important reference for the maintenance and management of mechanical equipment, improving equipment efficiency and extend its service life. [ABSTRACT FROM AUTHOR]

The Strauss point process is a very popular model for describing the random cellular networks, yet several key statistical properties such as intensity, empty space function, and probability generating functional have remained elusive. This article addresses these issues by first leveraging the Poisson saddle point method to approximate the distance‐conditioned intensity for Strauss point processes. Subsequently, the author derives an analytically tractable expression for the distribution of empty space distance based on a conditional thinning mechanism. Additionally, the author establishes an upper bound for the probability generating functional in Strauss point processes, which is crucial for evaluating the Laplace transform of cumulative interference in relevant cellular networks. These findings facilitate the systematic derivation of spatially averaged probability of coverage, and the accuracy of analytic results is validated through simulations. [ABSTRACT FROM AUTHOR]

Without heritable variation natural selection cannot effect evolutionary change. In the case of group selection, there must be variation in the population of groups. Where does this variation come from? One source of variation is from the stochastic birth–death processes that occur within groups. This is where variation between groups comes from in most mathematical models of group selection. Here, we argue that another important source of variation between groups is fission, the (generally random) group-level reproduction where parent groups split into two or more offspring groups. We construct a simple model of the fissioning process with a parameter that controls how much variation is produced among the offspring groups. We then illustrate the effect of that parameter with some examples. In most models of group selection in the literature, no variation is produced during group reproduction events; that is, groups "clone" themselves when they reproduce. Fission is often a more biologically realistic method of group reproduction, and it can significantly increase the efficacy of group selection. [ABSTRACT FROM AUTHOR]

This work studies how the Elo rating system can be applied to score-based sports, where it is gaining popularity, and in particular for predicting the result at any point of a game, extending its statistical basis to stochastic processes. We derive some new theoretical results for this model and use them to implement Elo ratings for basketball and soccer leagues, where the assumptions of our model are tested and found to be mostly accurate. We showcase several metrics for comparing the performance of different rating systems and determine whether adding a feature has a statistically significant impact. Finally, we propose an Elo model based on a discrete process for the score that allows us to obtain draw probabilities for soccer matches and has a performance competitive with alternatives like SPI ratings. [ABSTRACT FROM AUTHOR]

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]

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]

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 data set. [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]

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]

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]

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]

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]

Utilizing the holographic dictionary from the proposal that treats Newton's constant as a thermodynamic variable, we establish a thermodynamic topological equivalence between the AdS black holes in the bulk and the thermal states in the dual CFT. The findings further reveal that the thermodynamic topological characteristics of the RegMax AdS black holes are strongly influenced by the characteristic parameter of the regularized Maxwell theory. Additionally, we investigate the phase transition between low and high entropy thermal states within a canonical ensemble in the dual CFT. Our observations indicate that the phase transition behavior of the thermal states mirrors that of the black holes. By modeling the phase transition process as a stochastic process, we are able to calculate the rates of phase transition between the thermal states. This result enhances our understanding of the dominant processes involved in the phase transition of the thermal states in the dual CFT. [ABSTRACT FROM AUTHOR]

In this article, convolution-type fractional derivatives generated by Dickman subordinator and inverse Dickman subordinator are discussed. The Dickman subordinator and its inverse are generalizations of stable and inverse stable subordinators, respectively. The series representations of densities of the Dickman subordinator and inverse Dickman subordinator are also obtained, which could be helpful for computational purposes. Moreover, the space and time-fractional Poisson-Dickman processes, space-fractional Skellam Dickman process and non-homogenous Poisson-Dickman process are introduced and their main properties are studied. [ABSTRACT FROM AUTHOR]

Following Dirac's notation in Quantum Mechanics (QM), we propose the Probability Bracket Notation (PBN), by defining a probability-bra (P-bra), P-ket, P-bracket, P-identity, etc. Using the PBN, many formulae, such as normalizations and expectations in systems of one or more random variables, can now be written in abstract basis-independent expressions, which are easy to expand by inserting a proper P-identity. The time evolution of homogeneous Markov processes can also be formatted in such a way. Our system P-kets are identified with probability vectors and our P-bra system is comparable with Doi's state function or Peliti's standard bra. In the Heisenberg picture of the PBN, a random variable becomes a stochastic process, and the Chapman–Kolmogorov equations are obtained by inserting a time-dependent P-identity. Also, some QM expressions in Dirac notation are naturally transformed to probability expressions in PBN by a special Wick rotation. Potential applications show the usefulness of the PBN beyond the constrained domain and range of Hermitian operators on Hilbert Spaces in QM all the way to IT. [ABSTRACT FROM AUTHOR]

As stated in the no-free-lunch (NFL) theory, there is not any optimizer suitable for all problems. This circumstance becomes the motivation of introducing a new swarm-based metaheuristic called best couple algorithm (BCA). BCA is constructed as a swarm-based metaheuristic where the swarm is split into two sub-swarms. There are two types of splitting. The first split is dividing the swarm into the first half and second half of swarms. The second split is dividing the swarm into the odd indexed swarm members and even indexed swarm members. There is a sub swarm leader representing the highest quality swarm member in every sub swarm. There are two sequential searches for every split: the motion toward the middle between two sub swarm leaders and the motion relative to the middle between two randomly picked sub swarm members. In the benchmark assessment, BCA is compared with total interaction algorithm (TIA), coati optimization algorithm (COA), language education algorithm (LEO), osprey optimization algorithm (OOA), and walrus optimization algorithm (WaOA). The result shows that BCA is superior to these five contenders as it is better than TIA, COA, LEO, OOA, and WaOA in 18, 18, 16, 18, and 18 functions respectively out of 23 functions. [ABSTRACT FROM AUTHOR]

Atherosclerosis, a leading cause of cardiovascular disease, necessitates advanced and innovative modeling techniques to better understand and predict plaque dynamics. The present work presents two distinct hypothetical models inspired by different research fields: the logistic map from chaos theory and Markov models from stochastic processes. The logistic map effectively models the nonlinear progression and sudden changes in plaque stability, reflecting the chaotic nature of atherosclerotic events. In contrast, Markov models, including traditional Markov chains, spatial Markov models, and Markov random fields, provide a probabilistic framework to assess plaque stability and transitions. Spatial Markov models, visualized through heatmaps, highlight the spatial distribution of transition probabilities, emphasizing local interactions and dependencies. Markov random fields incorporate complex spatial interactions, inspired by advances in physics and computational biology, but present challenges in parameter estimation and computational complexity. While these hypothetical models offer promising insights, they require rigorous validation with real-world data to confirm their accuracy and applicability. This study underscores the importance of interdisciplinary approaches in developing theoretical models for atherosclerotic plaques. [ABSTRACT FROM AUTHOR]

• A new SM model of the CDS with multi-different and S-dependent components is studied. • The diverse and dependent component degradation is depicted by an extended DRI model. • Explicit reliability functions of systems with arbitrary configurations are provided. • Examples verified the great effects of multi-difference and S-dependency on strategy. Selective maintenance (SM) is often performed on systems having limited maintenance resources to enhance mission reliability. In practical engineering, components within a system are typically distinct and correlated, leading to differences in the degradation processes and sensitivity to working conditions, as well as stochastic dependencies (S-dependencies) among the components. However, in most studies on the SM of continuously degrading systems (CDSs), these features are not considered, thereby limiting the accuracy of reliability evaluations and the efficiency of maintenance strategies. Therefore, considering the differences and S-dependencies of components, we investigate SM optimization for CDSs. Focusing on the diverse and stochastically dependent degradation processes of non-identical components, we first propose an extended degradation rate interaction model integrated with a general stochastic process to describe the multiple degradation processes of components and manifest the sensitivity differences to working conditions in the degradation states and rates. Next, a derivation method is developed to obtain explicit mission reliability functions for systems with arbitrary configurations. Subsequently, an SM optimization model that incorporates the effects of multiple differences and S-dependencies of the components is formulated and used to obtain an optimal maintenance strategy that considers resource and mission reliability constraints. Finally, the effectiveness of the proposed method is demonstrated using two numerical examples. [ABSTRACT FROM AUTHOR]

In this study, we explore optimal service allocation within the Chinese hierarchical healthcare system with green channels, providing valuable insights for practitioners to understand how optimal service allocation is affected by various realistic factors. These green channels are designed to streamline referrals from community healthcare centers to comprehensive hospitals. We aim to determine the optimal capacity allocation for these green channels within comprehensive hospitals. Our research employs techniques from queuing theory and stochastic processes, e.g., diffusion analysis, to develop a mathematical model that approximates the optimal allocation of resources. We uncover both closed-form and numerical solutions for this optimal capacity allocation. By analyzing the impact of various cost factors, we find that an increase in costs within the green channel results in a lower optimal service rate. Additionally, patient preferences for specific treatments influence allocation, reducing the optimal share of services provided by general hospitals. The optimal solution is also affected by the proportions of different patient types. Through extensive simulations, we validate the accuracy of our model approximations under heavy traffic conditions, further examining sources of error to ensure robustness. Our findings provide valuable insights into optimizing resource allocation in hierarchical healthcare systems, ensuring efficient and cost-effective patient care. [ABSTRACT FROM AUTHOR]

The formation of congestion on an urban road network is a key issue for the development of sustainable mobility in future smart cities. In this work, we propose a reductionist approach by studying the stationary states of a simple transport model using a random process on a graph, where each node represents a location and the link weights give the transition rates to move from one node to another, representing the mobility demand. Each node has a maximum flow rate and a maximum load capacity, and we assume that the average incoming flow equals the outgoing flow. In the approximation of the single-step process, we are able to analytically characterize the traffic load distribution on the single nodes using a local maximum entropy principle. Our results explain how congested nodes emerge as the total traffic load increases, analogous to a percolation transition where the appearance of a congested node is an independent random event. However, using numerical simulations, we show that in the more realistic case of synchronous dynamics for the nodes, entropic forces introduce correlations among the node states and favor the clustering of empty and congested nodes. Our aim is to highlight the universal properties of congestion formation and, in particular, to understand the role of traffic load fluctuations as a possible precursor of congestion in a transport network. [ABSTRACT FROM AUTHOR]

In this study, we compare the performance of stochastic processes, namely, the Vasicek, Cox–Ingersoll–Ross (CIR), and geometric Brownian motion (GBM) models, with that of machine learning algorithms, such as Random Forest, Support Vector Machine (SVM), and k-Nearest Neighbors (KNN), for predicting the trends of stock indices XLF (financial sector), XLK (technology sector), and XLV (healthcare sector). The results showed that stochastic processes achieved remarkable prediction performance, especially the CIR model. Additionally, this study demonstrated that the metrics of machine learning algorithms are relatively lower. However, it is important to note that stochastic processes use the actual current index value to predict tomorrow's value, which may overestimate their performance. In contrast, machine learning algorithms offer a more flexible approach and are not as dependent on the current index value. Therefore, optimizing the hyperparameters of machine learning algorithms is crucial for further improving their performance. [ABSTRACT FROM AUTHOR]

In Chile and worldwide, life expectancy has consistently increased over the past six decades. Thus, the purpose of this study was to identify, measure, and estimate the population mortality ratios in Chile, mortality estimates are used to calculate life expectancy when constructing life tables. The Bayesian approach, specifically through Approximate Bayesian Computation (ABC) is employed to optimize parameter selection for these calculations. ABC corresponds to a class of computational methods rooted in Bayesian statistics that could be used to estimate the posterior distributions of the model parameters. For this research, ABC was applied to estimate the mortality ratios in Chile, using information available from 2004 to 2021. The results showed heterogeneity in the results when selecting the best model. Additionally, it was possible to generate projections for the next 10 years for the series analysed in the research. Finally, the main contribution of this research is that we measured and estimated the population mortality rates in Chile, defining the optimal selection of parameters, in order to contribute to creating a link between social and technical sciences for the advancement and implementation of current knowledge in the field of social structures. [ABSTRACT FROM AUTHOR]

In this study, we focused on the treatment of random forces in a semi-implicitly discretized overdamped Langevin (OL) equation with large time steps. In the usual implicit approach for a nonstochastic mechanical equation, the product of the time interval and Hessian matrix was added to the friction matrix to construct the coefficient matrix for solution updates, which were performed using Newton iteration. When large time steps were used, the additional term, which could be regarded as an artificial friction term, prevented the amplification of oscillations associated with large eigenvalues of the Hessian matrix. In this case, the damping of the high-frequency terms did not cause any discrepancy because they were outside of our interest. However, in OL equations, the friction coefficient was coupled to the random force; therefore, excessive artificial friction may have obscured the effects caused by the stochastic properties of the fluctuations. Consequently, we modified the random force in the proposed semi-implicit scheme so that the total random force was consistent with the friction including the additional artificial term. By deriving a discrete Fokker-Planck (FP) equation from the discretized OL equation, we showed how our modification improved the distribution of the numerical solutions of discrete stochastic processes. Finally, we confirmed the validity of our approach in numerical simulations of a freely jointed chain. [ABSTRACT FROM AUTHOR]

The issue of black-odorous water (BOW) represents a formidable challenge to the current aquatic ecosystems, and its governance exhibits characteristics of low efficiency, susceptibility to relapse, and fragmented management under the Central Environmental Protection Inspection, thereby emerging as a dynamically complex issue in the ecological governance of urban and rural settings. This study introduces Gaussian white noise to simulate environmental uncertainty and design a stochastic evolutionary game model encompassing the central government, local governments, and societal forces based on evolutionary game theory and classical governance theories and concepts. Numerical simulations are conducted to explore trajectories of the strategic evolution of various subjects influenced by numerous factors. Results indicate that under the environment of random disturbances, the strategies of the game subjects show significant fluctuations, but actively cultivating the subject's initial willingness facilitates collaboration governance in inspection. Moreover, joint construction of a "belief system" by multi-subjects, the intensity of inspection interventions, the integration of heterogeneous resources, and effective punitive measures all influence the governance of BOW, but the efficiency of resource allocation should be considered throughout the governance process. Recommendations are made finally for collaborative governance of urban and rural BOW, promoting the sustainable development of the ecological environment. [ABSTRACT FROM AUTHOR]

The non-Gaussian feature of seismic ground motion has been reported in some works. However, there remains a lack of research on the influence of the ground motion non-Gaussianity on the seismic performance of buildings, which motivates this study. By employing a non-Gaussian non-stationary random process simulation method previously proposed by the authors, 40,000 ground motion acceleration signals are efficiently generated, including 20,000 Gaussian and 20,000 non-Gaussian records. As computational examples, a four-story frame building and a three-tower super-tall building are selected. The generated acceleration signals serve as external excitations for the two buildings, allowing for a comparison of the differences in seismic structural responses caused by the Gaussian and non-Gaussian earthquake groups. Probability analysis is performed using top-layer displacement and maximum inter-story drift ratio as damage indicators. The results show that the structural responses induced by both Gaussian and non-Gaussian earthquake groups have identical first- and second-order moments but different higher-order moments. The responses from non-Gaussian earthquakes display distinct non-Gaussian traits, with their distribution of extreme values exhibiting a longer tail compared to the Gaussian counterparts. This leads to a notably larger value of non-Gaussian responses under high crossing probabilities, with an amplification that can surpass 18%. [ABSTRACT FROM AUTHOR]

In the recent past, the Gravity Recovery and Climate Experiment (GRACE) satellite mission and its successor GRACE Follow‐On (GRACE‐FO), have become invaluable tools for characterizing drought through measurements of Total Water Storage Anomaly (TWSA). However, the existing approaches have often overlooked the uncertainties in TWSA that stem from GRACE orbit configuration, background models, and intrinsic data errors. Here we introduce a fresh view on this problem which incorporates the uncertainties in the data: the Probabilistic Storage‐based Drought Index (PSDI). Our method leverages Monte Carlo simulations to yield realistic realizations for the stochastic process of the TWSA time series. These realizations depict a range of plausible drought scenarios that later on are used to characterize drought. This approach provides probability for each drought category instead of selecting a single final category at each epoch. We have compared PSDI with the deterministic approach (Storage‐based Drought Index, SDI) over major global basins. Our results show that the deterministic approach often leans toward an overestimation of storage‐based drought severity. Furthermore, we scrutinize the performance of PSDI across diverse hydrologic events, spanning continents from the United States to Europe, the Middle East, Southern Africa, South America, and Australia. In each case, PSDI emerges as a reliable indicator for characterizing drought conditions, providing a more comprehensive perspective than conventional deterministic indices. In contrast to the common deterministic view, our probabilistic approach provides a more realistic characterization of the TWS drought, making it more suited for adaptive strategies and realistic risk management. Plain Language Summary: Total Water Storage (TWS) is defined as the sum of water stored as surface water (e.g., lakes and rivers), groundwater, soil moisture, snow, ice, and vegetation biomass. Since its launch in 2002, the Gravity Recovery and Climate Experiment (GRACE) satellite mission has provided unique TWS change measurements with many applications in hydrology, including characterizing drought events. Scientists have been using satellites like GRACE and its successor, GRACE‐FO, to understand drought by measuring the Total Water Storage Anomaly (TWSA). However, previous methods didn't consider uncertainties from satellite orbits, models, and data errors. This study offers a novel probabilistic approach for characterizing drought, Probabilistic Storage‐based Drought Index (PSDI), which acknowledges the uncertainties in the GRACE TWS change. We use simulations to create different drought scenarios, offering probabilities for each category instead of one fixed category. Comparing PSDI to traditional methods, we found that traditional methods tend to overestimate drought severity. We tested PSDI across different regions, and it consistently proved to be a reliable way to understand drought conditions, offering a more comprehensive perspective. Our probabilistic approach offers a more realistic view of TWS drought, making it suitable for adaptive strategies and risk management. Key Points: A novel probabilistic framework is introduced to characterize drought using Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow‐On observations and propagating their stochasticsOur study suggests a tendency of deterministic approaches to overestimate storage‐based drought severityThe probabilistic approach captures global hydrological droughts while delivering more realistic results suited for risk management [ABSTRACT FROM AUTHOR]

Anthropogenic stresses are intensively affecting the structure and function of microbial communities in coastal ecosystems. Despite being essential components of coastal ecosystems, the environmental influences and assembly processes of protist communities remain largely unknown in areas with severe disturbance. Here, we used 18S rRNA gene high-throughput sequencing to compare the composition, assembly process, and functional structure of the protist communities from the coastal areas of the Northern Yellow Sea (NYS) and the Eastern Bohai Sea (EBS). These two areas are separated by the Liaodong Peninsula and experience different anthropogenic stresses due to varying degrees of urbanization. We detected significant differences between the protist communities of the two areas. Environmental and geographic factors both influenced the composition of protist communities, with environmental factors playing a greater role. The neutral community model indicated that the assembly of protist communities was governed by deterministic processes, with stochastic processes having a stronger influence in the EBS area compared to the NYS area. The phototrophic and consumer communities, influenced by different environmental factors, differed significantly between the two areas. Our results provide insights into the biogeography and assembly of protist communities in estuaries under anthropogenic stresses, which may inform future coastal management. [ABSTRACT FROM AUTHOR]

This paper investigates the decision-making behaviors of opinion leaders and netizens in the context of uncertain information dissemination with the aim of effectively managing online public opinion crises triggered by major sudden events. The decision-making behaviors of opinion leaders are categorized into positive and negative guidance, while those of netizens are classified into acceptance and nonacceptance. Using an evolutionary game model, this study introduces random factors to examine their influence on the decisionmaking processes of both groups. A stochastic evolutionary game model is constructed to analyze the behaviors of opinion leaders and netizens in the context of uncertain information dissemination. The evolutionary stability strategies and stochastic evolutionary processes of the model are analyzed based on the theory of Itô stochastic differential equations. The impacts of key variables such as random disturbances, the degree of psychological identification of netizens with opinion leaders, and the intensity of government penalties for those spreading negative information are examined through numerical simulations. The findings indicate that opinion leaders evolve to make stable strategies more rapidly than netizens do; random disturbances slow the evolution of stable strategies for both groups but do not alter their strategic choices; a higher degree of psychological identification increases the likelihood of netizens adopting the views of opinion leaders; and as punitive measures intensify, both opinion leaders and netizens are inclined to choose strategies of positive guidance and acceptance. The results of this study offer theoretical insights and decision-making guidance for future government strategies for managing similar online collective behaviors. [ABSTRACT FROM AUTHOR]

Introduction: Arbuscular mycorrhizal fungi (AMF) are pivotal in plant resource acquisition, mediating plant interactions, and influencing soil carbon dynamics. However, their biogeographical distribution in Tibetan alpine grasslands remains understudied. Methods: In this research, we examined the distribution pattern of AMF communities and their key determinants along a 2000-km transect across the Tibetan plateau, encompassing 7 alpine meadows and 8 alpine steppes. Results: Our findings indicate that AMF community diversity and composition exhibit similarities between alpine meadows and alpine steppes, primarily influenced by latitude and evapotranspiration. At the genus level, Glomus predominated in both alpine meadow (36.49%±2.67%) and alpine steppe (41.87%±2.36%) soils, followed by Paraglomus (27.14%±3.69%, 32.34%±3.28%). Furthermore, a significant decay relationship of AMF community was observed over geographical distance. Null model analyses revealed that random processes predominantly (>50%) drove the assembly of AMF communities. Discussion: In summary, our study elucidates the spatial distribution pattern of AMF in Tibetan plateau grasslands and underscores the significant influence of geographical and climatic factors on AMF community dynamics. [ABSTRACT FROM AUTHOR]

A geometrically symmetric gear with asymmetric surface wettability exhibits one-way spin on a vibrating water bed. On the side face of the gear, a parafilm was coated to create asymmetry in the surface energy. The gear shows fluctuations in both directions within a shorter timescale; however, for a longer timescale, the gear exhibits a one-way spin. This unique motion is generated by a stochastic process with a biased driving force produced by the interaction between the vibrating water surface and the side face of the gear. This new model resembles an active Brownian ratchet. Until now, most ratchet motors, which obtain regular motion from nonthermal fluctuations, utilize a geometrical ratchet structure. However, in this study, the surface energy forms a ratchet that rectifies the noisy motion. [ABSTRACT FROM AUTHOR]

This paper is concerned with pullback measure attractors of the non-autonomous stochastic reaction-diffusion equations defined in thin domains. We first prove the existence and uniqueness of pullback measure attractors for the inhomogeneous Markov process associated with the stochastic equations. We also introduce the concept of complete orbits for this sort of systems and use these special solutions to characterize the structures of pullback measure attractors. Then we establish the upper semi-continuity of these attractors as a family of thin domains collapses into a lower-dimensional domain. [ABSTRACT FROM AUTHOR]

As the hunt for an Earth-like exoplanets has intensified in recent years, so has the effort to characterize and model the stellar signals that can hide or mimic small planetary signals. Stellar variability arises from a number of sources, including granulation, supergranulation, oscillations, and activity, all of which result in quasi-periodic or stochastic behaviour in photometric and/or radial velocity observations. Traditionally, the characterization of these signals has mostly been done in the frequency domain. However, the recent development of scalable Gaussian process regression methods makes direct time-domain modelling of stochastic processes a feasible and arguably preferable alternative, obviating the need to estimate the power spectral density of the data before modelling it. In this paper, we compare the two approaches using a series of experiments on simulated data. We show that frequency-domain modelling can lead to inaccurate results, especially when the time-sampling is irregular. By contrast, Gaussian process regression results are often more precise, and systematically more accurate, in both the regular and irregular time-sampling regimes. While this work was motivated by the analysis of radial velocity and photometry observations of main-sequence stars in the context of planet searches, we note that our results may also have applications for the study of other types of astrophysical variability such as quasi-periodic oscillations in X-ray binaries and active galactic nuclei variability. [ABSTRACT FROM AUTHOR]

Delays in nerve transmission are an important topic in the field of neuroscience. Spike signals fired or received by the dendrites of a neuron travel from the axon to a presynaptic cell. The spike signal then triggers a chemical reaction at the synapse, wherein a presynaptic cell transfers neurotransmitters to the postsynaptic cell, regenerates electrical signals via a chemical reaction through ion channels, and transmits them to neighboring neurons. In the context of describing the complex physiological reaction process as a stochastic process, this study aimed to show that the distribution of the maximum time interval of spike signals follows extreme-order statistics. By considering the statistical variance in the time constant of the leaky Integrate-and-Fire model, a deterministic time evolution model for spike signals, we enabled randomness in the time interval of the spike signals. When the time constant follows an exponential distribution function, the time interval of the spike signal also follows an exponential distribution. In this case, our theory and simulations confirmed that the histogram of the maximum time interval follows the Gumbel distribution, one of the three forms of extreme-value statistics. We further confirmed that the histogram of the maximum time interval followed a Fréchet distribution when the time interval of the spike signal followed a Pareto distribution. These findings confirm that nerve transmission delay can be described using extreme value statistics and can therefore be used as a new indicator of transmission delay. [ABSTRACT FROM AUTHOR]

Environmental change exerts a profound effect on soil microbial domains—including bacteria, fungi, and protists—that each perform vital ecological processes. While these microbial domains are ubiquitous and extremely diverse, little is known about how they respond to environmental changes in urban soil ecosystems and what ecological processes shape them. Here we investigated the community assembly processes governing bacteria, fungi, and protists through the lens of four distinct subcommunities: abundant, conditionally rare, conditionally abundant, and rare taxa. We show that transient taxa, including the conditionally rare and conditionally rare or abundant taxa, were the predominant subcommunities. Deterministic processes (e.g., environmental filtering) had major roles in structuring all subcommunities of fungi, as well as conditionally rare and abundant protists. Stochastic processes had strong effects in structuring all subcommunities of bacteria (except rare taxa) and conditionally rare protists. Overall, our study underscores the importance of complementing the traditional taxonomy of microbial domains with the subcommunity approach when investigating microbial communities in urban soil ecosystems. [ABSTRACT FROM AUTHOR]

The present paper deals with the problem of nonparametric estimation for stochastic processes driven by alpha-stable processes of the second kind. The consistency and the asymptotic distribution of the nonparametric estimator are discussed. [ABSTRACT FROM AUTHOR]

This paper discusses how to derive multidimensional conformable diffusion equation from continuous time random walks process by employing fractional Laplace transform and the conformable fractional derivative defined by Khalil et al in [10]. The results show that there exists intimate relationship between the stretched exponential function and conformable diffusion equation involving the conformable fractional derivative. The relationship is analogous to the relationship between the exponential function and usual diffusion equation involving usual derivative and the relationship between the Mittag-Leffler function and subdiffusion or slow diffusion equation involving Caputo fractional derivative. Multidimensional conformable FokkerPlanck equation is also derived here. The equation describes diffusion process influenced by external force fields. Conformable semigroup associated with the solution to the conformable diffusion equation has similar properties to the properties of the semigroup associated with the solution to usual diffusion except the semigroup property. For sufficiently large time, the graphs of the solution to the conformable diffusion equation and the subdiffusion equation involving Caputo fractional derivative are sufficiently close. Especially, for, the graphs are sufficiently close for . In presence of nonzero constant external force fields, the particle involved in the diffusion process moves faster toward the directions of the external force fields. [ABSTRACT FROM AUTHOR]

This paper introduces a methodology for computing expected values associated with compression networks resulting from the application of compression algorithms to independent and identically distributed random time series. Our analysis establishes a robust correspondence between the calculated expected values and empirically derived results obtained from constructing networks using nondeterministic time series. Notably, the ratio of the average indegree of a network to the computed expected indegree for stochastic time series serves as a versatile metric. It enables the assessment of inherent randomness in time series and facilitates the distinction between nondeterministic and chaotic systems. The metric demonstrates high sensitivity to nondeterminism in both synthetic and real-world datasets, highlighting its capacity to detect subtle disturbances and high-frequency noise, even in series characterized by a deficient sample rate. Our results extend and confirm previous findings in the field. [ABSTRACT FROM AUTHOR]

The current investigation examines the numerical performance of the fractional-order endemic disease model based on the direct spreading of cholera by applying the neuro-computing Bayesian regularization (BR) neural network process. The purpose is to present the numerical solutions of the fractional-order model, which provides more precise solutions as compared to the integer-order one. Real values based on the parameters can be obtained and one can achieve better results by utilizing these values. The mathematical form of the fractional direct spreading cholera disease is categorized as susceptible, infected, treatment, and recovered, which represents a nonlinear model. The construction of the dataset is performed through the implicit Runge–Kutta method, which is used to lessen the mean square error by taking 74% of the data for training, while 8% is used for both validation and testing. Twenty-two neurons and the log-sigmoid fitness function in the hidden layer are used in the stochastic neural network process. The optimization of BR is performed in order to solve the direct spreading cholera disease problem. The accuracy of the stochastic process is authenticated through the valuation of the outputs, whereas the negligible calculated absolute error values demonstrate the approach's correctness. Furthermore, the statistical operator performance establishes the reliability of the proposed scheme. [ABSTRACT FROM AUTHOR]

We propose a new definition of the γ -convex stochastic processes (C SP) using center and radius (CR) order with the notion of interval valued functions (C. R I. V) . By utilizing this definition and Mean-Square Fractional Integrals, we generalize fractional Hermite–Hadamard–Mercer-type inclusions for generalized   C. R I. V versions of convex, tgs-convex, P-convex, exponential-type convex, Godunova–Levin convex, s-convex, Godunova–Levin s-convex, h-convex, n-polynomial convex, and fractional n-polynomial (C SP) . Also, our work uses interesting examples of   C. R I. V (C SP) with Python-programmed graphs to validate our findings using an extension of Mercer's inclusions with applications related to entropy and information theory. [ABSTRACT FROM AUTHOR]

Rooted in dynamic systems theory, convergent cross mapping (CCM) has attracted increased attention recently due to its capability in detecting linear and nonlinear causal coupling in both random and deterministic settings. One limitation with CCM is that it uses both past and future values to predict the current value, which is inconsistent with the widely accepted definition of causality, where it is assumed that the future values of one process cannot influence the past of another. To overcome this obstacle, in our previous research, we introduced the concept of causalized convergent cross mapping (cCCM), where future values are no longer used to predict the current value. In this paper, we focus on the implementation of cCCM in causality analysis. More specifically, we demonstrate the effectiveness of cCCM in identifying both linear and nonlinear causal coupling in various settings through a large number of examples, including Gaussian random variables with additive noise, sinusoidal waveforms, autoregressive models, stochastic processes with a dominant spectral component embedded in noise, deterministic chaotic maps, and systems with memory, as well as experimental fMRI data. In particular, we analyze the impact of shadow manifold construction on the performance of cCCM and provide detailed guidelines on how to configure the key parameters of cCCM in different applications. Overall, our analysis indicates that cCCM is a promising and easy-to-implement tool for causality analysis in a wide spectrum of applications. [ABSTRACT FROM AUTHOR]

In recent years, the scientific community has increasingly recognized the complex multi-scale competency architecture (MCA) of biology, comprising nested layers of active homeostatic agents, each forming the self-orchestrated substrate for the layer above, and, in turn, relying on the structural and functional plasticity of the layer(s) below. The question of how natural selection could give rise to this MCA has been the focus of intense research. Here, we instead investigate the effects of such decision-making competencies of MCA agential components on the process of evolution itself, using in silico neuroevolution experiments of simulated, minimal developmental biology. We specifically model the process of morphogenesis with neural cellular automata (NCAs) and utilize an evolutionary algorithm to optimize the corresponding model parameters with the objective of collectively self-assembling a two-dimensional spatial target pattern (reliable morphogenesis). Furthermore, we systematically vary the accuracy with which the uni-cellular agents of an NCA can regulate their cell states (simulating stochastic processes and noise during development). This allows us to continuously scale the agents' competency levels from a direct encoding scheme (no competency) to an MCA (with perfect reliability in cell decision executions). We demonstrate that an evolutionary process proceeds much more rapidly when evolving the functional parameters of an MCA compared to evolving the target pattern directly. Moreover, the evolved MCAs generalize well toward system parameter changes and even modified objective functions of the evolutionary process. Thus, the adaptive problem-solving competencies of the agential parts in our NCA-based in silico morphogenesis model strongly affect the evolutionary process, suggesting significant functional implications of the near-ubiquitous competency seen in living matter. [ABSTRACT FROM AUTHOR]

In many applications, modeling based on a normal kernel is preferred because not only does the normal kernel belong to the family of stable distributions, but also it is easy to satisfy the stationary condition in the stochastic process. However, the characteristic of the data, such as count or proportion, is a major obstacle to complete modeling based on a normal distribution. To solve a limited boundary or non-normal distribution problem, we provided a novel transformation method and proposed a nonparametric Bayesian approach based on a normal kernel of the transformed variable. In particular, the provided transformation transforms any probability space into a real space and is free from the constraints of the previous transformation, such as skewness, presence of power, and bounded domains. Another advantage was that it was possible to use the Dirichlet process mixture model with full conditional posterior distributions for all parameters, leading to a fast convergence rate in the Markov chain Monte Carlo. The proposed methodology was illustrated with simulated datasets and two real datasets with non-normal distribution problems. In addition, to demonstrate the superiority of the proposed methodology, the comparison with the transformed Bernstein polynomial model was made in the real data analysis. [ABSTRACT FROM AUTHOR]

Exploring the effects of seasonal variation on the gut microbiota of cold-water fish plays an important role in understanding the relationship between seasonal variation and cold-water fish. Gut samples of cold-water fish and environmental samples were collected during summer and winter from the lower reaches of the Yalong River. The results of the 16S rRNA sequencing showed that significant differences were identified in the composition and diversity of gut bacteria of cold-water fish. Co-occurrence network complexity of the gut bacteria of cold-water fish was higher in summer compared to winter (Sum: nodes: 256; edges: 20,450; Win: nodes: 580; edges: 16,725). Furthermore, from summer to winter, the contribution of sediment bacteria (Sum: 5.3%;Win: 23.7%) decreased in the gut bacteria of cold-water fish, while the contribution of water bacteria (Sum: 0%; Win: 27.7%) increased. The normalized stochastic ratio (NST) and infer community assembly mechanisms by phylogenetic bin-based null model analysis (iCAMP) showed that deterministic processes played a more important role than stochastic processes in the microbial assembly mechanism of gut bacteria of cold-water fish. From summer to winter, the contribution of deterministic processes to gut bacteria community assembly mechanisms decreased, while the contribution of stochastic processes increased. Overall, these results demonstrated that seasonal variation influenced the gut bacteria of cold-water fish and served as a potential reference for future research to understand the adaptation of fish to varying environments. [ABSTRACT FROM AUTHOR]

The rare and endangered plant species Abies fanjingshanensis, which has a limited habitat, a limited distribution area, and a small population, is under severe threat, particularly due to poor leaf health. The plant endophytic microbiome is an integral part of the host, and increasing evidence indicates that the interplay between plants and endophytic microbes is a key determinant for sustaining plant fitness. However, little attention has been given to the differences in the endophytic microbial community structure, network complexity, and assembly processes in leaves with different leaf health statuses. Here, we investigated the endophytic bacterial and fungal communities in healthy leaves (HLs) and non-healthy leaves (NLs) of A. fanjingshanensis using 16S rRNA gene and internal transcribed spacer sequencing and evaluated how leaf health status affects the co-occurrence patterns and assembly processes of leaf endophytic microbial communities based on the co-occurrence networks, the niche breadth index, a neutral community model, and C-score metrics. HLs had significantly greater endophytic bacterial and fungal abundance and diversity than NLs, and there were significant differences in the endophytic microbial communities between HLs and NLs. Leaf-health-sensitive endophytic microbes were taxonomically diverse and were mainly grouped into four ecological clusters according to leaf health status. Poor leaf health reduced the complexity of the endophytic bacterial and fungal community networks, as reflected by a decrease in network nodes and edges and an increase in degrees of betweenness and assortativity. The stochastic processes of endophytic bacterial and fungal community assembly were weakened, and the deterministic processes became more important with declining leaf health. These results have important implications for understanding the ecological patterns and interactions of endophytic microbial communities in response to changing leaf health status and provide opportunities for further studies on exploiting plant endophytic microbes to conserve this endangered Abies species. [ABSTRACT FROM AUTHOR]