Search

Statistical depth, a commonly used analytic tool in nonparametric statistics, has been extensively studied for multivariate and functional observations over the past few decades. Although various forms of depth were introduced, they are mainly procedure based whose definitions are independent of the generative model for observations. To address this problem, we introduce a generative model-based approach to define statistical depth for both multivariate and functional data. The proposed model-based depth framework permits simple computation via a bootstrap sampling and improves the depth estimation accuracy. When applied to functional data, the proposed depth can capture important features such as continuity, smoothness or phase variability, depending on the defining criteria. We propose efficient algorithms to compute the proposed depths and establish estimation consistency. Through simulations and real data, we demonstrate that the proposed functional depths reveal important statistical information such as those captured by the median and quantiles, and detect outliers. [ABSTRACT FROM AUTHOR]

The epidemic type aftershock sequence (ETAS) model is used as a baseline model both for earthquake clustering and earthquake prediction. In most forecast experiments, the ETAS parameters are estimated based on a short and local catalog, therefore the model parameter optimization carried out by means of a maximum likelihood estimation may be not as robust as expected. We use Bayesian forecast techniques to solve this problem, where non-informative flat prior distributions of the parameters is adopted to perform forecast experiments on 3 mainshocks occurred in Southern California. A Metropolis–Hastings algorithm is employed to sample the model parameters and earthquake events. We also show, through forecast experiments, how the Bayesian inference allows to obtain a probabilistic forecast, differently from one obtained via MLE. [ABSTRACT FROM AUTHOR]

The integration of renewable energy resources into the smart grids improves the system resilience, provide sustainable demand-generation balance, and produces clean electricity with minimal leakage currents. However, the renewable sources are intermittent in nature. Therefore, it is necessary to develop scheduling strategy to optimise hybrid PV-wind-controllable distributed generator based Microgrids in grid-connected and stand-alone modes of operation. In this manuscript, a priority-based cost optimization function is developed to show the relative significance of one cost component over another for the optimal operation of the Microgrid. The uncertainties associated with various intermittent parameters in Microgrid have also been introduced in the proposed scheduling methodology. The objective function includes the operating cost of CDGs, the emission cost associated with CDGs, the battery cost, the cost of grid energy exchange, and the cost associated with load shedding. A penalty function is also incorporated in the cost function for violations of any constraints. Multiple scenarios are generated using Monte Carlo simulation to model uncertain parameters of Microgrid (MG). These scenarios consist of the worst as well as the best possible cases, reflecting the microgrid's real-time operation. Furthermore, these scenarios are reduced by using a k-means clustering algorithm. The reduced procedures for uncertain parameters will be used to obtain the minimum cost of MG with the help of an optimisation algorithm. In this work, a meta-heuristic approach, grey wolf optimisation (GWO), is used to minimize the developed cost optimisation function of MG. The standard LV Microgrid CIGRE test network is used to validate the proposed methodology. Results are obtained for different cases by considering different priorities to the sub-objectives using GWO algorithm. The obtained results are compared with the results of Jaya and PSO (particle swarm optimization) algorithms to validate the efficacy of the GWO method for the proposed optimization problem. [ABSTRACT FROM AUTHOR]

Three-phase induction motors are widely used in various industrial sectors and are responsible for a significant portion of the total electrical energy consumed. To ensure their efficient operation, it is necessary to apply control systems with specific algorithms able to estimate rotation speed accurately and with an adequate response time. However, the angular speed sensors used in induction motors are generally expensive and unreliable, and they may be unsuitable for use in hostile environments. This paper presents an algorithm for speed estimation in three-phase induction motors using the chaotic variable of maximum density. The technique used in this work analyzes the current signals from the motor power supply without invasive sensors on its structure. The results show that speed estimation is achieved with a response time lower than that obtained by classical techniques based on the Fourier Transform. This technique allows for the provision of motor shaft speed values when operated under variable load. [ABSTRACT FROM AUTHOR]

Understanding the mechanisms of community assembly is a key question in ecology. Metal pollution may result in significant changes in bird community structure and diversity, with implications for ecosystem processes and function. However, the relative importance of these processes in shaping the bird community at the polluted area is still not clear. Here, we explored bird species richness, functional, and phylogenetic diversity, and the assembly processes of community at the mine region of southwest China. Our results showed that the 3 dimensions of diversity at the mine area were lower than that at the reference sites. In the community assembly, the result was 0 < NRI/ NFRI < 1.96, which indicated deterministic processes (environmental filtering) might drive community clustering. The results of the neutral community model, and normalized stochasticity ratio, showed the dominant role of stochastic processes in shaping the bird community assembly. We further quantified the community-level habitat niche breadth (Bcom), and we found that there was no difference in Bcom -value between the mine area and reference sites. This indicates that the bird communities at the mine area and 3 reference sites were not subjected to extreme environmental selection (same or different resource allocation) to form a highly specialized niche. These findings provide insights into the distribution patterns and dominant ecological processes of bird communities under metal exposure, and extend the knowledge in community assembly mechanisms of bird communities living in the mine area. [ABSTRACT FROM AUTHOR]

Process simulations can be used to improve grinding circuit performance, which efficiently reduces operating costs. The population balance model (PBM) is widely accepted for grinding modeling because it can reproduce breakage events in tumbling mills, as described by Austin et al. (1984). In this study, a pseudodynamic model is introduced, integrating the PBM with the Monte Carlo Method to stochastically simulate variables in an industrial grinding circuit. This integrated approach enabled circuit simulations over a period of 2 hours, representing the operational variables as seen in historical data. Model validation showed a correlation of 0.74 in the product size distribution when comparing simulated outcomes with the original population. [ABSTRACT FROM AUTHOR]

In this paper, we studied the dynamic properties of predator-prey and scavenger three species system by using ergodic invariant measures. Pengyu Ma. find the five points of dynamical bifurcation of the stochastic model, which happened between extinction and survival of each species. Environmental noise was added and proved by the fact that driving force produced by environmental noise influence the system and it was find that system may extinct or partially extinct. Here, we have analysed the stochastic bifurcation phenomena of the prey-predator with scavenger system from the nature of dynamic bifurcation. The phase plots and time diagram plotted for the different values of parameters. We have verified all the results by numerical simulations. [ABSTRACT FROM AUTHOR]

We present a thorough empirical study on real interest rates by also including risk aversion through the introduction of the market price of risk. From the viewpoint of complex systems science and its multidisciplinary approach, we use the theory of bond pricing to study the long-term discount rate to estimate the rate when taking historical US and UK data, and to further contribute to the discussion about the urgency of climate action in the context of environmental economics and stochastic methods. Century-long historical records of 3-month bonds, 10-year bonds, and inflation allow us to estimate real interest rates for the UK and the US. Real interest rates are negative about a third of the time and the real yield curves are inverted more than a third of the time, sometimes by substantial amounts. This rules out most of the standard bond-pricing models, which are designed for nominal rates that are assumed to be positive. We, therefore, use the Ornstein–Uhlenbeck model, which allows negative rates and gives a good match to inversions of the yield curve. We derive the discount function using the method of Fourier transforms and fit it to the historical data. The estimated long-term discount rate is 1.7% for the UK and 2.2% for the US. The value of 1.4% used by Stern is less than a standard deviation from our estimated long-run return rate for the UK, and less than two standard deviations of the estimated value for the US. All of this once more reinforces the need for immediate and substantial spending to combat climate change. [ABSTRACT FROM AUTHOR]

In this work, we are concerned with generating solutions of a class of Convection–Diffusion–Reaction (CDR) equation from the solutions of another CDR equation through the Darboux transformations. The method is elucidated by cases with certain types of the reaction coefficients. We have also discussed briefly supersymmetric pairs of CDR equations connected through similarity solutions. [ABSTRACT FROM AUTHOR]

Soil microorganisms play vital roles in regulating multiple ecosystem functions. Recent studies have revealed that the rare microbial taxa (with extremely low relative abundances, which are still largely ignored) are also crucial in maintaining the health and biodiversity of the soil and may respond differently to environmental pressure. However, little is known about the soil community structures of abundant and rare taxa and their assembly processes in different soil layers on the Qinghai‐Tibet Plateau (QTP). The present study investigated the community structure and assembly processes of soil abundant and rare microbial taxa on the northeastern edge of the QTP. Soil microbial abundance was defined by abundant taxa, whereas rare taxa contributed to soil microbial diversity. The results of null model show that the stochastic process ruled the assembly processes of all sub‐communities. Dispersal limitation contributed more to the assembly of abundant microbial taxa in the different soil layers. In contrast, drift played a more critical role in the assembly processes of the rare microbial taxa. In addition, in contrast to previous studies, the abundant taxa played more important roles in co‐occurrence networks, most likely because of the heterogeneity of the soil, the sparsity of amplicon sequencing, the sampling strategy, and the limited samples in the present study. The results of this study improve our understanding of soil microbiome assemblies on the QTP and highlight the role of abundant taxa in sustaining the stability of microbial co‐occurrence networks in different soil layers. [ABSTRACT FROM AUTHOR]

Regional integration and pairing assistance are two forms of cross-regional emergency collaboration practice carried out by the Chinese government. Based on the Chinese government's emergency management practice, evolutionary game models of cross-regional emergency collaboration were constructed. Further, the traditional evolutionary game model was improved by introducing the stochastic process, and Gaussian white noise was introduced as a random disturbance. The stochastic evolutionary game model was constructed, and the existence and stability of the equilibrium solutions of the two kinds of stochastic evolutionary game systems for cross-regional emergency collaboration were verified based on the stability discrimination theorem of stochastic differential equations. We used numerical simulations to simulate the evolution trajectories of the regional integration and the pairing assistance stochastic evolutionary game system. In the regional integration game system, when the efficiency of emergency collaboration, the emergency capital stock, and the externality coefficients are higher, positive emergency strategies are more likely to become the stable state of the game subjects' strategy selection. In the pairing assistance game system, the efficiency of emergency collaboration, the rewards and benefits from the central government, and the matching degree between governments all had positive effects on the formation of the positive emergency strategies of the game subjects. In addition, the pairing assistance mechanism for sustainable development requires external support from the central government. [ABSTRACT FROM AUTHOR]

This study delves into the interplay of Rayleigh wave‐groundwater‐aquifer dynamics, utilizing seismic data from designated stations, particularly the magnitude 9 event on March 11, 2011 (02:46:23 PM epicenter), Tohoku earthquake, Japan. Auto spectra uncover significant peaks, linking groundwater level with the vertical motion of Rayleigh waves. High coherence between groundwater levels and seismogram vertical displacements confirms this connection. Coherence analysis validates it at the significant frequency bands. Groundwater storage coefficient estimation aligns with typical values of confined aquifers, ranging from 1.0E‐05 to 1.0E‐03. This consistency applies across different methods and other earthquake events, highlighting seismic impact. The findings enhance understanding of aquifer behavior during seismic events, aiding groundwater management and earthquake readiness in susceptible regions. Further research should expand datasets for coefficient accuracy. Insights advance aquifer behavior comprehension during seismic events, guiding groundwater management and earthquake readiness in prone areas. [ABSTRACT FROM AUTHOR]

This paper presents a novel estimator for a nonstandard restriction to both symmetry and low rank in the context of high-dimensional cointegrated processes. Furthermore, we discuss rank estimation for high-dimensional cointegrated processes by restricted bootstrapping of the Gaussian innovations. We demonstrate that the classical rank test for cointegrated systems is prone to underestimating the true rank and demonstrate this effect in a 100-dimensional system. We also discuss the implications of this underestimation for such high-dimensional systems in general. Also, we define a linearized Kuramoto system and present a simulation study, where we infer the cointegration rank of the unrestricted p\times p system and successively the underlying clustered network structure based on a graphical approach and a symmetrized low rank estimator of the couplings derived from a reparametrization of the likelihood under this unusual restriction. [ABSTRACT FROM AUTHOR]

The work is devoted to integro-differential equations related to stochastic processes. We study the relationship between differential equations with random perturbations — stochastic differential equations (SDEs) — and deterministic equations for the probability characteristics of processes determined by random perturbations. The resulting deterministic pseudodifferential equations are investigated by semigroup methods and Fourier transform methods. [ABSTRACT FROM AUTHOR]

In this study, for the first time, a study on optical soliton solutions of the stochastic perturbed Schrödinger-Hirota equation which models the propagation of solitons through optical fibers having the Kerr law is carried out. For this purpose, the nonlinear partial differential equation of the examined model is first reduced to the nonlinear ordinary differential equation form using the complex wave transformation. Then, using the new Kudryashov and the Kudryashov methods, bright, dark and singular soliton solutions are derived as a basic step. The next part is devoted to the examination of the noise effect, and first of all, soliton solutions are obtained in the absence of noise strength. Afterwards, the same soliton solutions are obtained, taking into account the noise effect, and comparison and comments are made. In addition to the fact that the form of the examined equation has not been presented and studied before. Considering that, in today's world, taking into account the effect of noise is an inevitably important factor for engineering models to be designed correctly and to operate efficiently, it is obvious that the results obtained will contribute to the literature. [ABSTRACT FROM AUTHOR]

We study a system of M particles with jump dynamics on a network of N sites. The particles can exist in two states, active or inactive. Only the former can jump. The state of each particle depends on its position. A given particle is inactive when it is at a given site, and active when it moves to a change site. Indeed, each sleeping particle activates at a rate λ > 0 , leaves its initial site, and moves for an exponential random time of parameter μ > 0 before uniformly landing at a site and immediately returning to sleep. The behavior of each particle is independent of that of the others. These dynamics conserve the total number of particles; there is no limit on the number of particles at a given site. This system can be represented by a continuous-time Pólya urn with M balls where the colors are the sites, with an additional color to account for particles on the move at a given time t. First, using this Pólya interpretation for fixed M and N, we obtain the average number of particles at each site over time and, therefore, those on the move due to mass conservation. Secondly, we consider a large system in which the number of particles M and the number of sites N grow at the same rate, so that the M / N ratio tends to a scaling constant α > 0 . Using the moment-generating function technique added to some probabilistic arguments, we obtain the long-term distribution of the number of particles at each site. [ABSTRACT FROM AUTHOR]

The article provides proof that the diagnostics of marine internal combustion engines and other ship power plant machines should take into account the randomness and unpredictability of certain events, such as wear, damage, the variations of mechanical and thermal loads, etc., which take place during machine operation. In the article, the energy E, like the other forms (methods) that it can be converted into (heat and work), is considered the random variable Et; at time t, this variable has the mean value E ¯ t , which is the observed value of the statistic E ¯ s t with an asymptotically normal distribution N (E ( E t) , σ t n ) , irrespective of the functional form of the random variable Et. A proof is given that shows that the expected value estimated in the above way, considering the time t of the performance of task Z by a marine internal combustion engine or other ship power plant machine, can be used to determine the machine's possible action (DM). When compared to the required action (DW) needed for task Z to be performed, this possible action makes it possible to formulate an operating diagnosis concerning whether the engine or machine of concern is able to perform task Z. It is assumed that an energy device of this type is able to perform a given task when the inequality DM≥DW holds. Otherwise, when DM < DW, the device cannot perform the task for which it was adopted in the design and manufacturing phase, which means that it is in the incapability state, although it still can be started and convert energy into the form of heat or work.. [ABSTRACT FROM AUTHOR]

Matching and pickup processes are core features of ride-sourcing services. Previous studies have adopted abundant analytical models to depict the two processes and obtain operational insights; while the goodness of fit between models and data was dismissed. To simultaneously consider the fitness between models and data and analytically tractable formations, we propose a data-driven approach based on the additive Gaussian Process Model (AGPM) for ride-sourcing market modelling. The framework is tested based on real-world data collected in Hangzhou, China. We fit analytical models, machine learning models, and AGPMs, in which the number of matches or pickups are used as outputs and spatial, temporal, demand, and supply covariates are utilized as inputs. The results demonstrate the advantages of AGPMs in recovering the two processes in terms of estimation accuracy. Furthermore, we illustrate the modelling power of AGPM by utilizing the trained model to design and estimate idle vehicle relocation strategies. [ABSTRACT FROM AUTHOR]

Forecasting disease spread is a critical tool to help public health officials design and plan public health interventions. However, the expected future state of an epidemic is not necessarily well defined as disease spread is inherently stochastic, contact patterns within a population are heterogeneous, and behaviors change. In this work, we use time-dependent probability generating functions (PGFs) to capture these characteristics by modeling a stochastic branching process of the spread of a disease over a network of contacts in which public health interventions are introduced over time. To achieve this, we define a general transmissibility equation to account for varying transmission rates (e.g. masking), recovery rates (e.g. treatment), contact patterns (e.g. social distancing) and percentage of the population immunized (e.g. vaccination). The resulting framework allows for a temporal and probabilistic analysis of an intervention's impact on disease spread, which match continuous-time stochastic simulations that are much more computationally expensive. To aid policy making, we then define several metrics over which temporal and probabilistic intervention forecasts can be compared: Looking at the expected number of cases and the worst-case scenario over time, as well as the probability of reaching a critical level of cases and of not seeing any improvement following an intervention. Given that epidemics do not always follow their average expected trajectories and that the underlying dynamics can change over time, our work paves the way for more detailed short-term forecasts of disease spread and more informed comparison of intervention strategies. [ABSTRACT FROM AUTHOR]

Homeostatic balance in the intestinal epithelium relies on a fast cellular turnover, which is coordinated by an intricate interplay between biochemical signalling, mechanical forces and organ geometry. We review recent modelling approaches that have been developed to understand different facets of this remarkable homeostatic equilibrium. Existing models offer different, albeit complementary, perspectives on the problem. First, biomechanical models aim to explain the local and global mechanical stresses driving cell renewal as well as tissue shape maintenance. Second, compartmental models provide insights into the conditions necessary to keep a constant flow of cells with well-defined ratios of cell types, and how perturbations can lead to an unbalance of relative compartment sizes. A third family of models address, at the cellular level, the nature and regulation of stem fate choices that are necessary to fuel cellular turnover. We also review how these different approaches are starting to be integrated together across scales, to provide quantitative predictions and new conceptual frameworks to think about the dynamics of cell renewal in complex tissues. • Intestinal homeostasis as a paradigm to study cell fate choices and tissue mechanics. • Different types of theoretical modelling frameworks recently proposed. • Can help to understand cell movements, organ shape or fate choice robustness. • Emerging frontier on how to couple different scales and modelling frameworks. [ABSTRACT FROM AUTHOR]

Sustainable forest management is an important way to deal with climate change, and optimal rotation period decision-making is an important condition for sustainable forest management. In the optimal rotation period decision-making process, the static assumptions of the classical Faustmann model about forest growth and market price cannot be satisfied. Therefore, it is necessary to clarify the fluctuation form of the price in the real market and use the dynamic model to make flexible decisions according to market conditions, so as to achieve the goal of maximizing profits in a market with fluctuating prices. Based on the classical framework of the Faustmann model, this paper summarizes the origin and evolution of this model and identifies the research trends of stochastic price in optimal rotation period decision-making. The results show that: ① In modern capital market theory, the stochastic process is an important model to describe price fluctuations, which mainly includes geometric Brownian motion in accordance with the efficient market hypothesis or the mean reversion process in accordance with the perfect competitive market hypothesis. In addition, more complex stochastic process models can also be used based on the test of empirical price data. ② Discounted cash flow is mostly used for static Faustmann model analysis, but it ignores the impact of new information on decision-making. Real option analysis allows forest owners to conduct dynamic analysis, compare the expected returns of immediate and delayed logging at each decision point, and adjust their business strategies at any time according to market conditions. ③ The Bellman equation, which aims at maximizing the immediate return value and the continuous return value, is an effective method to solve the Faustmann model with stochastic prices. The construction of partial differential equation, Monte Carlo simulation and Markov decision process can effectively solve the Bellman equation when the price follows a normal distribution, when there are multiple stochastic prices, and when the price has Markov property, respectively. The future research trend of stochastic price in optimal rotation period decision-making also involves the following aspects: expanding the Faustmann model to complete forestry carbon sequestration benefits in the context of climate change, modeling price fluctuation more accurately and reasonably by using a variety of methods, including machine learning, and considering multiple risk sources in the Faustmann model, including risks from resource and preferences of decision makers. [ABSTRACT FROM AUTHOR]

The present study devotes to introducing and analyzing the use of the adaptive Fourier decomposition (AFD)‐type methods in the area of stochastic processes and random fields. We involve two types of algorithms, namely, stochastic AFD (SAFD) and stochastic pre‐orthogonal AFD (SPOAFD), for, respectively, the Hardy space format and non‐Hardy space ones, as may be regarded. We provide both their theoretical results and practical algorithms and compare them with the well adopted and, in fact, dominating Karhunen–Loève (KL)‐type expansions. The AFD methods involve a finite or infinite sequence of optimally chosen parameters; they, in contrast, do not rely on and hence not have to compute the eigenpairs of the second type Fredholm integral equation with the covariance function as the kernel. Apart from such computational conveniences, they with the same convergence rate have flexibility of choosing best suitable dictionaries for doing the specific task in the practice. We include a number of experiments showing that in terms of effectiveness, the AFD methods give better approximations before all the positive eigenvalues running out in the case the integral operator being of a finite rank or before the KL iteration step becomes excessively large: The AFD methods normally give better approximations from the very beginning of the iterations. [ABSTRACT FROM AUTHOR]

Constructing a renewable energy-based power system has become an important development path for the power industry's low-carbon transformation. However, as the proportion of renewable energy generation (REG) increases, the power grid gradually changes to uncertainty. Technologies to address this issue have been introduced. However, the majority of existing reviews focus on specific uncertainty modeling approaches and applications, lacking the consideration of temporal and spatial interdependence. Therefore, this paper provides a comprehensive review of the uncertainty modeling of temporal and spatial interdependence. It includes the discrete and continuous stochastic process-based methods to address temporal interdependence, the correlation coefficient and copula functions in modeling spatial interdependence, and the Itô process and random fields theory to describe temporal and spatial interdependence. Finally, their applications in power system stability, control, and economic scheduling are summarized. [ABSTRACT FROM AUTHOR]

Metalliferous mine tailings ponds are generally characterized by low levels of nutrient elements, sustained acidic conditions, and high contents of toxic metals. They represent one kind of extreme environments that are believed to resemble the Earth's early environmental conditions. There is increasing evidence that the diversity of fungi inhabiting mine tailings ponds is much higher than previously thought. However, little is known about functional guilds, community assembly, and co-occurrence patterns of fungi in such habitats. As a first attempt to address this critical knowledge gap, we employed high-throughput sequencing to characterize fungal communities in 33 mine tailings ponds distributed across 18 provinces of mainland China. A total of 5842 fungal phylotypes were identified, with saprotrophic fungi being the major functional guild. The predictors of fungal diversity in whole community and sub-communities differed considerably. Community assembly of the whole fungal community and individual functional guilds were primarily governed by stochastic processes. Total soil nitrogen and total phosphorus mediated the balance between stochastic and deterministic processes of the fungal community assembly. Co-occurrence network analysis uncovered a high modularity of the whole fungal community. The observed main modules largely consisted of saprotrophic fungi as well as various phylotypes that could not be assigned to known functional guilds. The richness of core fungal phylotypes, occupying vital positions in co-occurrence network, was positively correlated with edaphic properties such as soil enzyme activity. This indicates the important roles of core fungal phylotypes in soil organic matter decomposition and nutrient cycling. These findings improve our understanding of fungal ecology of extreme environments. [ABSTRACT FROM AUTHOR]

The evolution of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in humans has been monitored at an unprecedented level due to the public health crisis, yet the stochastic dynamics underlying such a process is dubious. Here, considering the number of acquired mutations as the displacement of the viral particle from the origin, we performed biostatistical analyses from numerous whole genome sequences on the basis of a time-dependent probabilistic mathematical model. We showed that a model with a constant variant-dependent evolution rate and nonlinear mutational variance with time (i.e., anomalous diffusion) explained the SARS-CoV-2 evolutionary motion in humans during the first 120 wk of the pandemic in the United Kingdom. In particular, we found subdiffusion patterns for the Primal, Alpha, and Omicron variants but a weak superdiffusion pattern for the Delta variant. Our findings indicate that non-Brownian evolutionary motions occur in nature, thereby providing insight for viral phylodynamics. [ABSTRACT FROM AUTHOR]

Statistical depth, a commonly used analytic tool in nonparametric statistics, has been extensively studied for multivariate and functional observations over the past few decades. Although various forms of depth were introduced, they are mainly procedure based whose definitions are independent of the generative model for observations. To address this problem, we introduce a generative model-based approach to define statistical depth for both multivariate and functional data. The proposed model-based depth framework permits simple computation via a bootstrap sampling and improves the depth estimation accuracy. When applied to functional data, the proposed depth can capture important features such as continuity, smoothness or phase variability, depending on the defining criteria. We propose efficient algorithms to compute the proposed depths and establish estimation consistency. Through simulations and real data, we demonstrate that the proposed functional depths reveal important statistical information such as those captured by the median and quantiles, and detect outliers. [ABSTRACT FROM AUTHOR]

Background: The time between the appearance of successive leaves, or phyllochron, characterizes the vegetative development of annual plants. Hypothesis testing models, which allow the comparison of phyllochrons between genetic groups and/or environmental conditions, are usually based on regression of thermal time on the number of leaves; most of the time a constant leaf appearance rate is assumed. However regression models ignore auto-correlation of the leaf number process and may lead to biased testing procedures. Moreover, the hypothesis of constant leaf appearance rate may be too restrictive. Methods: We propose a stochastic process model in which emergence of new leaves is considered to result from successive time-to-events. This model provides a flexible and more accurate modeling as well as unbiased testing procedures. It was applied to an original maize dataset collected in the field over three years on plants originating from two divergent selection experiments for flowering time in two maize inbred lines. Results and conclusion: We showed that the main differences in phyllochron were not observed between selection populations but rather between ancestral lines, years of experimentation and leaf ranks. Our results highlight a strong departure from the assumption of a constant leaf appearance rate over a season which could be related to climate variations, even if the impact of individual climate variables could not be clearly determined. [ABSTRACT FROM AUTHOR]

The nonlinearly stochastic Schrödinger equation (NLSSE) predicts the nonlinear process that produces the waves decay in many physics applications. The unified method has been used in obtaining different new stochastic forms for NLSSE damped by noises in Itô sense. The derived structures appear in the form of rational, solitons, soliton-like shocks, and explosive propagations. The new stochastic solutions investigated the change of frequencies by noise term in NLSSE in nonlinear process that may be produced in many nonlinear wave applications. Finally, wave picture properties may controlled by noise term in Itô sense effect, which gives new information's for NLSSE in physics applications which is believed to be affected by the influence of Brownian motion that change the shape and structures of the generated decaying and damping waves. [ABSTRACT FROM AUTHOR]

This article presents a study with the aim of optimizing a production system, consisting of a machine that produces a single type of parts, that degrades over time. This degradation affects the availability of the deployed machine and increases the defective rate of the manufactured products. The machine is subject to random failures and repairs. It has a defective rate which increases with its degradation. An overhaul of the machine allows to reduce this defective rate and bring it back to its initial condition. The objective of this study is to find a joint policy for production, maintenance and quality control, in order to increase the availability of the machine, improve the quality of the manufactured products and minimize the total cost of production. To achieve this goal, we formulated the research problem and used a stochastic dynamic programming approach to develop the Hamilton-Jacobi-Bellman (HJB) type optimum conditions. Then, we simulated a practical hybrid application to optimize the production of a Router class R CNC cutting machine that transforms polypropylene sheets in a Quebec (Canada) company specialized in the production of fire pumps. The obtained results allowed us to propose a critical threshold production policy, corrective and preventive maintenance strategies, and a sampling type of quality control to the company. Finally, we performed a sensitivity analysis to ensure the validation of the proposed policies. [ABSTRACT FROM AUTHOR]

Earthquakes are prominent natural hazards that cause loss of life and property in residential areas in the world. The Aegean Graben system is geologically under the influence of the Western Anatolian Opening Regime. There are many active fault lines that can be a source of earthquake activity in the Aegean Graben system. Many earthquakes have been recorded in the region, which have caused serious material and moral damages from the past to the present. This situation reveals the importance of investigation this region in detail and by this way is possible to reduce the risks and consequences of earthquakes. In the study, earthquake data from three different earthquake catalogs were examined, and the earthquakes recorded between 1970 and 2020 in the region were declustered and homogenized in the scale of magnitude wave (Mw). Then, the data are clustered based on the seismic classification via k-means cluster analysis. By this way, the predictions for sequential transition of earthquakes within time and magnitude of the earthquakes are analyzed with a stochastic model, namely Markov chain. It has been concluded that the row probability values of the transition matrices of the earthquake transition probabilities between the clusters of the Aegean Region are fixed values depending on time. We also found an equilibrium distribution for the region. Hence, the probability of an earthquake in Cluster 1 in the region is 30%, Cluster 2–33% and Cluster 3–37%, respectively. We then obtain mean passage time of the earthquakes in each cluster. The results suggest that all clusters have similar characteristics as regard to earthquake sequencing. For these reasons, we finally study the without clustering to find the magnitude transitions depending on the time with Markov chain analysis. [ABSTRACT FROM AUTHOR]

We introduce five nonparametric kriging‐type predictors for spatial data where only the variable of interest, without covariates, is recorded. The proposed methods seek to fully exploit the information contained in the spatial closeness and also in the similarity between neighbourhoods of the variable of interest. This is managed using different combinations of kernels (one or two kernels), and different combinations of distances (multiplicative and additive). The good performance of the proposed methods is shown via simulation studies and housing price prediction applications. [ABSTRACT FROM AUTHOR]

The batch clustering algorithm for classification application requires the initial parameters and also has a drifting phenomenon for the stochastic process. The initial parameters are critical for the clustering to converge to the partial optimum. The drifting phenomenon in original batch clustering still has space to be improved thus to speed up the convergence based on the initial parameters. This paper proposes an unsupervised clustering method by addressing these two issues. Firstly, the estimation method for the initial parameters has been given in preliminary with a hierarchical manner of principal component analysis (PCA). The nonlinear parameters have been estimated based on a mathematical connection between PCA and clusters membership. With initial parameters, the drifting issue is addressed by combing the gradient descent and the batch clustering on an auxiliary objective to refine the initial parameters. The efficiency of the clustering process is proved based on the relationship between two quadratic functions followed by a justification. In addition, the effectiveness of the proposed method has been validated with the statistical F measure in classification application. The validation results show that the efficiency of the proposed gradient descent batch clustering has been improved significantly with trade-off to the accuracy in comparison of the original algorithms under the mean squared error (MSE) criterion. [ABSTRACT FROM AUTHOR]

The article is devoted to Bayes optimization problems of nonlinear observable stochastic systems (NLOStSs) based on wavelet canonical expansions (WLCEs). Input stochastic processes (StPs) and output StPs of considered nonlinearly StSs depend on random parameters and additive independent Gaussian noises. For stochastic synthesis we use a Bayes approach with the given loss function and minimum risk condition. WLCEs are formed by covariance function expansion coefficients of two-dimensional orthonormal basis of wavelet with a compact carrier. New results: (i) a common Bayes' criteria synthesis algorithm for NLOStSs by WLCE is presented; (ii) partial synthesis algorithms for three of Bayes' criteria (minimum mean square error, damage accumulation and probability of error exit outside the limits) are given; (iii) an approximate algorithm based on statistical linearization; (iv) three test examples. Applications: wavelet optimization and parameter calibration in complex measurement and control systems. Some generalizations are formulated. [ABSTRACT FROM AUTHOR]

With the dramatically increased demand for data analysis, statistical techniques play a key role in modern society for both academics and practitioners. Statistical techniques have been evolving from descriptive statistics to statistical inference in fields that require the evaluation of uncertainty and the quantification of risks. With the growing complexity of various fields, such as manufacturing and industrial applications, as well as business decision-making, modeling and quantifying risks has become essential. In this paper, we aimed to use statistical risk analysis and Value at Risk (VaR) to address the decision problem for project portfolios. Traditional economic evaluation criteria used in the management of project portfolios, as they pertain to new product development (NPD), are based on the assumption that pinpoint estimations will remain constant in the future. The assumption that NPD is static, however, is clearly unrealistic due to the inherent uncertainty of NPD projects. In this study, we stress the critical role that uncertainty plays in the selection of NPD portfolios, and clarify the reasons why it must not be overlooked. Using Value at Risk measurements, we show how uncertainty plays a critical role in evaluating and prioritizing NPD portfolios. The implications of this study regarding statistically modeling NPD portfolio decisions are provided for academics and practitioners. [ABSTRACT FROM AUTHOR]

Transportation logistics aims to deliver products at the right time and place at the lowest possible cost. Within this activity are the problems of optimizing the routing of cargo vehicles that must travel a minimum cost route for the delivery of goods. The impact of the use of information technologies in the context of the supply chain can be measured basically in integration and in the benefits it brings. The objective of this research is to use computational simulation to evaluate restrictions of a messaging system and to show the shortest route found for three package delivery lines, optimizing the time and allocation of packages for each line. The project was developed under an empirical and exploratory methodology, where four phases followed. An algorithm was designed that used a voracious and stochastic approach, with an objective function that was evaluated in each of the n-simulations, to find the shortest route on the three delivery lines. To test the effectiveness of the algorithm, two test scenarios were carried out. In both scenarios, it was possible to show that the greater the number of simulations, the distance found was shorter, which was the objective of the investigation. [ABSTRACT FROM AUTHOR]

There is continuing pressure to improve the cost effectiveness of quality control (QC) for clinical laboratory testing. Risk-based approaches are promising but recent research has uncovered problems in some common methods. There is a need for improvements in risk-based methods for quality control. We provide an overview of a dynamic model for assay behavior. We demonstrate the practical application of the model using simulation and compare the performance of simple Shewhart QC monitoring against Westgard rules. We also demonstrate the utility of trade-off curves for analysis of QC performance. Westgard rules outperform simple Shewhart control over a narrow range of the trade-off curve of false-positive and false negative risk. The risk trade-off can be visualized in terms of risk, risk vs. cost, or in terms of cost. Risk trade-off curves can be "smoothed" by log transformation. Dynamic risk-models may provide advantages relative to static models for risk-based QC analysis. [ABSTRACT FROM AUTHOR]

Mathematical programming and optimization problems related to fluid dynamics are heavily influenced by stochastic processes associated with integral and variational inequalities. Furthermore, symmetry and convexity are intrinsically related. Over the last few years, both have become increasingly interconnected so that we can learn from one and apply it to the other. The objective of this note is to convert ordinary stochastic processes into interval stochastic processes due to the wide range of applications in various disciplines. We have developed Hermite–Hadamard ( H. H ), Ostrowski-, and Jensen-type inequalities using interval h-convex stochastic processes. Our main results can be applied to a variety of new and well-known outcomes as specific situations. The results of this study are expected to stimulate future research on inequalities using fractional and fuzzy integral operators. Furthermore, we validate our main findings by providing some non-trivial examples. To demonstrate their general properties, we illustrate the connections between the examined results and those that have already been published. The results discussed in this article can be seen as improvements and refinements to results that have already been published. This is a fascinating subject that can be investigated in the future to identify equivalent inequalities for various convexity types. [ABSTRACT FROM AUTHOR]

The revise abstract is given as follows: The rapid emergence of the super-spreader COVID-19 with severe economic calamities with devastating social impact worldwide created the demand for effective research on the spread dynamics of the disease to combat and create surveillance systems on a global scale. In this study, a novel hybrid Deterministic Autoregressive Fractional Integral Moving Average (ARFIMA) model is presented to forecast the bimodal COVID-19 transmission dynamics. The heterogeneity of multimodal behavior of the COVID-19 pandemic in Pakistan is modeled by a hybrid paradigm, in which a deterministic pattern is combined with the ARFIMA model to absorb the inherent chaotic pattern of the pandemic spread. The fractional fluctuation of the real epidemic system is effectively taken as a paradigm by stochastic type improved the deterministic model and ARFIMA process. Special transformations are also introduced to enhance the convergent rate of the bimodal paradigm in deterministic modeling. The outcome of the improved deterministic model is combined with the ARFIMA model is evaluated on the spread pattern of pandemic data in Pakistan for the next 30 days. The performance-indices of the hybrid-model based on Relative-Errors and RMSE statistics confirmed the effectiveness of the proposed paradigm for long-term epidemic modeling compared to other classical and machine learning algorithms. [ABSTRACT FROM AUTHOR]

This article characterizes topological duals of spaces of cadlag processes. We extend functional analytic results of Dellacherie and Meyer that underlie many fundamental results in stochastic analysis and optimization. We unify earlier duality results on L p and Orlicz spaces of cadlag processes and extend them to general Fréchet functions spaces. In particular, we obtain a characterization of the dual of cadlag processes of class (D) in terms of optional measures of essentially bounded variation. When applied to regular processes, we extend (Bismut, 1978) on projections of continuous processes. More interestingly, our argument yields characterizations of dual spaces of regular processes. [ABSTRACT FROM AUTHOR]

This paper provides a useful supplement note for implementing the Kalman filters. The material presented in this work points out several significant highlights with emphasis on performance evaluation and consistency validation between the discrete Kalman filter (DKF) and the continuous Kalman filter (CKF). Several important issues are delivered through comprehensive exposition accompanied by supporting examples, both qualitatively and quantitatively for implementing the Kalman filter algorithms. The lesson learned assists the readers to capture the basic principles of the topic and enables the readers to better interpret the theory, understand the algorithms, and correctly implement the computer codes for further study on the theory and applications of the topic. A wide spectrum of content is covered from theoretical to implementation aspects, where the DKF and CKF along with the theoretical error covariance check based on Riccati and Lyapunov equations are involved. Consistency check of performance between discrete and continuous Kalman filters enables readers to assure correctness on implementing and coding for the algorithm. The tutorial-based exposition presented in this article involves the materials from a practical usage perspective that can provide profound insights into the topic with an appropriate understanding of the stochastic process and system theory. [ABSTRACT FROM AUTHOR]

PVA chemical hydrogel can absorb a large amount of water to produce swelling, and the degree of swelling impact on its physical properties and applications significantly. Polymer and crosslinking agent concentration in the gelation stage can modulate degree of swelling and the structure of the hydrogel network. In order to further understand the modulation mechanism, it is necessary to develop method to establish model of hydrogel network and use it to calculate the degree of swelling. In this paper, a method for simulating PVA chemical hydrogel cross-linking reaction process and constructing a hydrogel network structure based on stochastic process is proposed. Using this method, the influences of amount of PVA and the amount of crosslinking agent on the network structure are obtained. The free energy and swelling degree of the hydrogel are calculated using the constructed hydrogel network. The quantitative relationship between the amount of PVA, crosslinking agent and the actual swelling degree of the hydrogel is obtained. The calculation results show that the increase of the PVA concentration and the decrease of the amount of the cross-linking agent can promote the swelling of the hydrogel. The calculated results of swelling degree are in good agreement with the experimental results. The method proposed in this paper can be used as an effective tool to study the network structure and mechanical properties of hydrogels. [ABSTRACT FROM AUTHOR]

Revealing planktonic fungal ecology under coastal eutrophication is crucial to our understanding of microbial community shift in marine pollution background. We investigated the diversity, putative interspecies interactions, assembly processes and environmental responses of abundant and rare planktonic fungal communities along a eutrophication gradient present in the Beibu Gulf. The results showed that Dothideomycetes and Agaricomycetes were the predominant classes of abundant and rare fungi, respectively. We found that eutrophication significantly altered the planktonic fungal communities and affected the abundant taxa more than the rare taxa. The abundant and rare taxa were keystone members in the co-occurrence networks, and their interaction was enhanced with increasing nutrient concentrations. Stochastic processes dominated the community assembly of both abundant and rare planktonic fungi across the eutrophication gradient. Heterogeneous selection affected abundant taxa more than rare taxa, whereas homogenizing dispersal had a greater influence on rare taxa. Influences of environmental factors involving selection processes were detected, we found that abundant fungi were mainly influenced by carbon compounds, whereas rare taxa were simultaneously affected by carbon, nitrogen and phosphorus compounds in the Beibu Gulf. Overall, these findings highlight the distinct ecological adaptations of abundant and rare fungal communities to marine eutrophication. [ABSTRACT FROM AUTHOR]

Introduction: Surveys are common research tools, and questionnaires revisions are a common occurrence in longitudinal studies. Revisions can, at times, introduce systematic shifts in measures of interest. We formulate that questionnaire revision are a stochastic process with transition matrices. Thus, revision shifts can be reduced by first estimating these transition matrices, which can be utilized in estimation of interested measures. Materials and method: An ideal survey response model is defined by mapping between the true value of a participant's response to an interval in the grouped data type scale. A population completed surveys multiple times, as modeled with multiple stochastic process. This included stochastic processes related to true values and intervals. While multiple factors contribute to changes in survey responses, here, we explored the method that can mitigate the effects of questionnaire revision. We proposed the Version Alignment Method (VAM), a data preprocessing tool, which can separate the transitions according to revisions from all transitions via solving an optimization problem and using the revision-related transitions to remove the revision effect. To verify VAM, we used simulation data to study the estimation error and a real life MJ dataset containing large amounts of long-term questionnaire responses with several questionnaire revisions to study its feasibility. Result: We compared the difference of the annual average between consecutive years. Without adjustment, the difference is 0.593 when the revision occurred, while VAM brought it down to 0.115, where difference between years without revision was in the 0.005, 0.125 range. Furthermore, our method rendered the responses to the same set of intervals, thus comparing the relative frequency of items before and after revisions became possible. The average estimation error in L infinity was 0.0044 which occupied the 95% CI which was constructed by bootstrap analysis. Conclusion: Questionnaire revisions can induce different response bias and information loss, thus causing inconsistencies in the estimated measures. Conventional methods can only partly remedy this issue. Our proposal, VAM, can estimate the aggregate difference of all revision-related systematic errors and can reduce the differences, thus reducing inconsistencies in the final estimations of longitudinal studies. [ABSTRACT FROM AUTHOR]

Computer simulation in the field of pharmacokinetics and pharmacodynamics or in silico modelling is the need of the hour in the biomedical field. A computer simulation (CS) is a program run on a computer that uses step-by-step methods to explore the approximate behaviour of a mathematical model. The mathematical models enable the computational simulation of real-world systems. As the program is executed, the mathematical dynamics that arise constitute an analogue of the real-world system's behaviour. Computer simulations thus offer a means of quantitatively and qualitatively simulating, analysing, and visualising complex biological processes. Furthermore, in silico studies may help facilitate the research process by embedding ease and efficiency through computational simulations. This article explores the importance of computer programs for the simulation of in silico experiments with the help of mathematical descriptions or models. The current review summarises the various CS models for different drugs with their outcomes. The major challenge that seems to emerge is the need for quantitative, testable, and validated frameworks for the joint analysis of large data sets available in disparate formats and focused on different biological scales. The solution(s) to this problem will require a diverse set of disciplines, including not only biology and pharmacology but also (bio) engineering, computer science, (applied) mathematics and physics, and (bio) statistics. The study summarises and gives a brief review of recent biocomputation developments that are potentially relevant to drug development. [ABSTRACT FROM AUTHOR]

There is paucity of the statistical model that is specified for data on imported COVID-19 cases with the unique global information on infectious properties of SARS-CoV-2 variant different from local outbreak data used for estimating transmission and infectiousness parameters via the established epidemic models. To this end, a new approach with a four-state stochastic model was proposed to formulate these well-established infectious parameters with three new parameters, including the pre-symptomatic incidence rate, the median of pre-symptomatic transmission time (MPTT) to symptomatic state, and the incidence (proportion) of asymptomatic cases using imported COVID-19 data. We fitted the proposed stochastic model to empirical data on imported COVID-19 cases from D614G to Omicron with the corresponding calendar periods according to the classification GISAID information on the evolution of SARS-CoV-2 variant between March 2020 and Jan 2022 in Taiwan. The pre-symptomatic incidence rate was the highest for Omicron followed by Alpha, Delta, and D614G. The MPTT (in days) increased from 3.45 (first period) ~ 4.02 (second period) of D614G until 3.94–4.65 of VOC Alpha but dropped to 3.93–3.49 of Delta and 2 days (only first period) of Omicron. The proportion of asymptomatic cases increased from 29% of D-614G period to 59.2% of Omicron. Modeling data on imported cases across strains of SARS-CoV-2 not only bridges the link between the underlying natural infectious properties elucidated in the previous epidemic models and different disease phenotypes of COVID-19 but also provides precision quarantine and isolation policy for border control in the face of various emerging SRAS-CoV-2 variants globally. [ABSTRACT FROM AUTHOR]

Purpose: This paper studies the integration of production and maintenance planning for an unreliable production system subject to gradual deterioration. The goal of this planning is to optimize production and maintenance while reducing workers' exposure to silica dust. The objective will therefore be to offer manufacturers a production strategy that minimizes the total cost of production while considering the health of employees. Design/methodology/approach: Adequate prevention methods are determined and integrated into the granite transformation production system, which evolves in a stochastic environment. With the failure rate of the dust reduction unit being a function of its degradation state, the authors solve the optimization problem using stochastic dynamic programming in the context of nonhomogeneous Markov chain. Findings: The resulting planning strategy shows that one can manage stock optimally while ensuring a healthy environment for workers. It ensures that crystalline silica prevention equipment is available and effective and defines the production rate according to a critical threshold, which is a function of the age of the dust reduction unit. Research limitations/implications: This article illustrates that it is possible to integrate silica dust reduction measures into production planning while remaining optimal and ensuring the health of operators. In the present study, the machined granite was assumed to be a natural granite, and production takes place in a closed environment. Originality/value: The originality of this work lies in its development of an optimal joint production and maintenance strategy, which considers limits of exposure to crystalline silica. An optimal production and maintenance control policy considering employees' health is therefore proposed. [ABSTRACT FROM AUTHOR]

The paper presents a stochastic approach to generate randomly rough surfaces with a prescribed mean angular intensity distribution for elastic wave scattering. The analytical and numerical technique is implemented for a linearly elastic medium-vacuum interface, to generate band-limited uniform diffusers which may have applications for wave manipulation and ultrasonic non-destructive evaluation. Longitudinal incidence is assumed, and the theory allows for bulk wave mode conversions, with the surfaces designed to produce prescribed intensity distributions for both reflected compression wave modes, as well as the mode-converted vertically polarized shear wave modes. The angular distribution of these two cases is shown to be significantly different; additional, more exotic intensity distributions are also demonstrated to highlight the versatility of the model. [ABSTRACT FROM AUTHOR]

A characterization and numerical scheme to control problem governed by a three-dimensional (3D) time-dependent Fokker–Planck (FP) equation is presented. We formulate a control formulation that controls the drift of the stochastic (FP) process. In this way, the probability density function attains a specific configuration. Moreover, a FP control strategy for collective motion is investigated and first-order optimality conditions are presented. On staggered grids, the Chang–Cooper discretization scheme that ensures the positivity, second-order accuracy, and conservativeness to the FP equation is employed to the discretized state (respectively adjoint) system. Furthermore, a line search strategy is applied to update the control variable. Results of numerical experiments show the efficiency of the proposed numerical scheme to stochastic (FP) control problems. [ABSTRACT FROM AUTHOR]

Revision game is a very recent advance in dynamic game theory and it can be used to analyze the trading in the pre-opening stock market. In such games, players prepare actions that will be implemented at a given deadline, before which they may have opportunities to revise actions. For the first time, we study the role of the deadline in revision games, which is the core component that distinguishes revision games from classic games. We introduce the deadline distribution into revision game model and characterize the sufficient and necessary condition for players' strategies to constitute an equilibrium. The equilibrium strategy with respect to the deadline uncertainty is given by a simple differential equation set. Governed by this differential equation set, players initially fully cooperate, and the cooperation level decreases as time progresses. The uncertainty has a great impact on players' behavior. As the uncertainty increases, players become more risk averse, in the sense that they prefer lower mutual cooperation rate rather than higher payoff with higher uncertainty. Specifically, they will not stay in full cooperation for a long time, while after they deviate from the full cooperation, they adjust their plans more slowly and cautiously. The deadline uncertainty can improve the competition and avoid collusion in games, which could be utilized for auction design and pre-opening stock market regulations. [ABSTRACT FROM AUTHOR]

Unmanaged high penetration of customer-scale photovoltaic on the distribution network results in voltage rises along the network. However, the performance of the implemented battery energy storage system (BESS) to prevent voltage rise under that high penetration condition was unclear because the previous penetration models did not consider the intermittency and variability characteristics of the penetration due to their model simplifications. Therefore, this research proposes a BESS control scheme to mitigate impermissible voltage rises by considering the penetration characteristics of intermittency and variability. As a result, the proposed model outperformed the previous model by providing a more complete representation of the actual penetration issues, and thus the expected contribution of the BESS control scheme in reducing voltage rises could be provided. [ABSTRACT FROM AUTHOR]