We have recently solved the tumbling-snake model for concentrated polymer solutions and entangled melts in the presence of both steady-state and transient shear and uniaxial elongational flows, supplemented by a variable link tension coefficient. Here, we provide the transient and stationary solutions of the tumbling-snake model under biaxial elongation both analytically, for small and large elongation rates, and via Brownian dynamics simulations, for the case of planar elongational flow over a wide range of rates, times, and the model parameters. We show that both the steady-state and transient first planar viscosity predictions are similar to their uniaxial counterparts, in accord with recent experimental data. The second planar viscosity seems to behave in all aspects similarly to the shear viscosity, if shear rate is replaced by elongation rate.

This paper explores the critical role of biomathematics in cancer research, focusing on how mathematical models enhance our understanding of tumor growth and optimize treatment strategies. It begins with an overview of cancer biology, highlighting the complexities of tumor dynamics and the molecular mechanisms driving growth. The paper then delves into various mathematical modeling approaches, including deterministic, stochastic, and agent-based models, illustrating their applications in predicting tumor behavior and treatment responses. Case studies demonstrate the real-world impact of these models on optimizing chemotherapy, radiation therapy, and immunotherapy. Challenges such as data availability, model complexity, and clinical translation are discussed, alongside future directions in the field, including advances in computational power and personalized medicine. Ultimately, this research emphasizes the transformative potential of biomathematics in improving cancer treatment outcomes and underscores the importance of interdisciplinary collaboration in advancing the field.

The traditional understanding of brain function has predominantly focused on chemical and electrical processes. However, new research in fruit fly (Drosophila) binocular vision reveals ultrafast photomechanical photoreceptor movements significantly enhance information processing, thereby impacting a fly's perception of its environment and behaviour. The coding advantages resulting from these mechanical processes suggest that similar physical motion-based coding strategies may affect neural communication ubiquitously. The theory of neural morphodynamics proposes that rapid biomechanical movements and microstructural changes at the level of neurons and synapses enhance the speed and efficiency of sensory information processing, intrinsic thoughts, and actions by regulating neural information in a phasic manner. We propose that morphodynamic information processing evolved to drive predictive coding, synchronising cognitive processes across neural networks to match the behavioural demands at hand effectively.

The use of entropy concepts in the field of stochastic electrodynamics is briefly reviewed here. Entropy calculations to date that have been fully carried out are discussed in two main situations: first, where electric dipole oscillators interact with zero-point, or zero-point plus Planckian, or Rayleigh-Jeans radiation, and second where only these radiation fields exist within a cavity. The emphasis here will be on the first more difficult situation where both charged particles and radiation fields are present and interacting. Unlike the usual exposition on entropy in clasical statistical mechanics involving probabilistic notions of phase space occupation, the calculations to date for both particles and fields or for fields alone, follow the caloric entropy method where the notions of heat flow, adiabatic surfaces, and isothermal conditions, are utilized. Probability notions certainly still enter into the calculations, as the fields and charged particles interact stochastically together, following Maxwellian electrodynamics. Examples of phase-space calculations for harmonic oscillators and classical hydrogen atoms are carried out, emphasizing how much farther caloric entropy calculations have been successfully utilized.

The container relocation problem (CRP) is one of the important topics in container terminals, which aims to find the optimal sequence of movements to minimize the total number of relocations needed to retrieve all the containers within a bay according to a given specific layout and retrieval order. However, determining such an order may be difficult due to uncertainty. Various CRP solution methods proposed so far show a common pitfall concerning the complexity of the solving process, whose scale grows exponentially with the number of containers. Considering the retrieval operation process of the inbound containers in a bay consists of several operation rounds, this paper focuses on the real-time operation scenario of each round to minimize the actual number of relocations during the pick-up process, i.e., starting from the initial layout of the bay, we minimize the sum of the incremental number of blocking containers due to the layout change and the number of reallocated containers unrelated to the target container. We present a heuristic algorithm (called SPFH) based on the three rules (LL, MSS, and FSS), considering the adjustment of the pick-up order of containers. Numerical experiments on a set of instances generated from the literature are performed. The proposed methodology excels in both execution efficiency and solution quality and is capable of solving instances that were impossible to solve before. This also makes our methods appealing for being applied in practice. The source codes are available at https://github.com/zhou-sf/rt-scrp.

This paper addresses a mode-dependent state-feedback H∞ control for descriptor hybrid systems, considering both the absence and presence of actuator saturation. Firstly, the necessary and sufficient conditions for the stochastic admissibility criterion with H∞ performance ? of the closed-loop system is proposed. Given the proposed non-convex condition, the author reformulates it into linear matrix inequalities (LMIs). Then, to extend the result to the systems with actuator saturation, the actuator saturated control input is expressed as a linear combination of given state-feedback control input and a virtual control input that remains under the saturation level. To verify this expression, the set invariant condition is also suggested by using the singular mode-dependent Lyapunov function candidate. Therefore, the LMI conditions for the existence of the mode-dependent state-feedback H∞ control and the ellipsoidal shape of invariant set are successfully derived. Two numerical examples demonstrate the effectiveness of the proposed approach in optimizing H∞ performance $\gamma$ and identifying the largest invariant set.

By employing the stochastic extension of the Madelung quantum-hydrodynamic description within a discrete methodology, we establish a solution using the path integral approach to explore the progression of quantum states' superposition. This investigation aims to understand the eventual establishment of a stable end-state configuration amid the backdrop of gravitational background fluctuations. The model identifies the circumstances that lead to a limited range of interaction for the quantum potential, allowing for the emergence of sizeable, classically described macroscopic phenomena. The theory unveils the lowest achievable level of uncertainty in an open quantum system and investigate its congruence with the localized behaviors of macroscopic classical systems. The study examines agreements and differences with decoherence theory and the Copenhagen interpretation of quantum mechanics, and evaluates the impact of wave function decay on the measurement process.

In this paper, a model of the hub covering the location-routing problem with simultaneous delivery and pickup should be designed in order to minimize the total costs, minimize the maximum vehicles travel time and minimize the amount of CO_2 gas emissions. Two-stage stochastic programming is used in this paper to control the uncertainty parameters of the problem. The mathematical model aims to decide the appropriate location of hubs and vehicle routing for simultaneous delivery and pickup of products. In this regard, the results obtained from the LP-Metric method show that there is a conflict between the objective functions, and with the reduction of the amount of CO_2 gas emissions and the reduction of the maximum vehicles travel time, the total costs have increased. On the other hand, by examining the economical factor, it was observed that by reducing this factor, the robustness factors are changed and the total costs of the network are reduced. MOIWO and MOALO were used to solve the problem in large scale, the result of which was the existence of a significant difference between the calculation time averages. Also, the efficiency of these methods was very high compared to the LP-Metric method and the maximum relative difference was less than 2.83%. The results of numerical examples show a higher efficiency of the MOALO than the MOIWO.

The need to find the global minimum in multi-dimensional functions is a critical problem in many fields of science and technology. Effectively solving this problem requires the creation of initial solution estimates, which are subsequently used by the optimization algorithm to search for the best solution in the solution space. In the context of this article, a novel approach to generating the initial solution distribution is presented which is applied to a genetic optimization algorithm. Using the k-means clustering algorithm, a distribution based on data similarity is created. This helps in generating initial estimates that may be more tailored to the problem. Additionally, the proposed method employs a rejection sampling algorithm to discard samples that do not yield better solution estimates in the optimization process. This allows the algorithm to focus on potentially optimal solutions, thus improving its performance. Finally, the article presents experimental results from the application of this approach to various optimization problems, providing the scientific community with a new method for addressing this significant problem.

To quantitatively estimate the risk of power system operation under extreme rainfall, a multi-scenario stochastic risk assessment method is proposed. First, a scenario generation scheme considering waterlogged faults of power facilities is constructed based on the storm water management model (SWMM) and the extreme learning machine method. These scenarios will be merged to several typical scenario sets for further processing. The outage of power facilities will induce power flow transfer which may consequently lead to transmission lines’ thermal limit violation. Semi-invariant and Gram-Charlier level expansion methods are adopted to analytically depict the probability density function and cumulative probability function of each line’s power flow. The optimal solution is performed by a particle swarm algorithm to obtain proper load curtailment at each bus, and consequently the violation probability of line thermal violations can be controlled within an allowable range. The volume of load curtailment as well as their importance are considered to quantitatively access the risk of power supply security under extreme precipitation scenarios. The effectiveness of the proposed method is verified in case studies based on the IEEE 24-bus system.

Purpose- Betel nut (Areca catechu) is one of the major plantation crops grown in Assam. However, due to inefficiency in production, the productivity of betel nuts in the state is very low. Therefore, this study attempted to measure the level of technical efficiency and the factors affecting the technical inefficiency of betel nut growers in the Nagaon district of Assam.Design/methodology/approach – Primary data were collected from 240 households in the Nagaon district of Assam. Based on the Cobb-Douglas Production function for betel nut growers, the present study uses stochastic frontier analysis to estimate the production frontier and examine the effects of exogenous variables on farm-level technical inefficiency. Findings - The findings of the study reveal that, on average, 85 per cent of betel nut growers are technically efficient in the study area. Moreover, experience in betel nut plantations and gender have a significantly negative effect on technical inefficiency. In contrast, the age of the grower had a positive and significant effect on the technical inefficiency of betel nut cultivation. The findings suggest the availability of space for an increase in the productivity of betel nut plantations in the study area and scope for increasing the level of output through technical efficiency without raising inputs.Originality/Value: This study contribute to the estimation of the technical efficiency of betel nut growers and examines the factors responsible for technical inefficiency.The dataset is original and was especially collected for the present study.

The paper proves a theorem about the structure of the distribution function on which the extremum of fractionally linear functional is reached in the presence of an uncountable number of linear constraints. The problem of finding an extremal distribution function arises when determining the optimal control strategy in a class of Markov homogeneous randomized control strategies. The structure of extremal functions is described by a finite number of parameters, hence the problem is greatly simplified since it is reduced to the search for an extremum of some function.

Identifying productive, profitable and less risky cropping systems is important for sustaining farm-based livelihoods in the context of climatic uncertainties and market volatility in many developing nations. Reductionist field crop research identifies the best-bet solutions based on treatment replicates at a single point in time, which may not account for price instability under climatic uncertainties and volatile markets. Keeping this in mind, we estimated productivity, profitability and weather-related risk from eleven different rice-based cropping systems (eight existing and three potential systems) in the coastal region of West Bengal, India. Information on the crop management practices, yield and prices of the component crops of these eleven cropping systems, under ’best,’ ’normal’ and ‘worst’ situations (scenario), were collected through a ques-tionnaire survey on50 farms of Gosaba Block, West Bengal, India. Irrespective of the scenarios, the rice-lathyrus systems, followed by rice-onion and rice-lentil systems recorded the lowest rice-equivalent yields and system yields. However, the highest rice-equivalent yields and system yields were recorded for rice-chilli systems, followed by rice-tomato and rice-potato-green gram systems. Per hectare total paid-out cost (TPC) of rice-tomato systems was higher, followed by rice-chilli, rice-potato-green gram and rice-potato systems. However, irrespective of seasonal conditions (best, normal and worst), rice-chilli systems gave a higher net return followed by rice-tomato and rice-potato-green gram systems. The rice-fallow system recorded the lowest value for both parameters. Under the worst seasonal conditions, the rice-onion system gave a negative net return. Under all the scenarios, the highest B:C ratio was observed for rice-chilli, rice-tomato, rice-potato-green gram and rice-potato systems. The cumulative probability distribution of the rice-tomato system showed first-degree stochastic dominance over other systems and the rice-chilli system showed second-degree stochastic dominance over the rest of the systems. Only the rice-onion system had a small chance (< 1%) of a negative net return, while the rest of the cropping systems were highly likely to get a positive net return. Taking productivity, economics, and risk assessment of different rice-based systems into account, rice-vegetable systems, especially rice-tomato and rice-chilli among the existing systems and rice-potato-green gram system among the potential systems, can be recommended for sustainable intensification in these coastal saline tracts of the region. We also discuss additional socio-economic factors explored by in-depth in-terviews with the farmers, which might influence the adoption and upscaling of these cropping systems in the region.

In a randomly moving particle swarm with fixed kinetic energy, the particle speeds follow the Maxwell distribution. In a certain period, the moving directions of particles in a sub-particle swarm may aggregate. Thus, the movements of the particles have the characteristics of biased stochastic movement. Regarding the biased particle swarm formed by a series of randomly moving particles (with a uniform average velocity c) with a greater probability of moving in a certain direction and the same probability of moving in other directions, there is a certain group velocity u in this direction, while the diffusion rate in other directions is slower than that of unbiased moving particles with the same average speed c. Moreover, the degree of slowing follows the Lorentz-like factor. In this article, the characteristics of this kind of biased random process are deduced starting from a biased random walk by using probability theory, and the expression of the Ito equation is provided. This article is expected to provide a reference to understand the nature of the special relativity effect.

By combining stochastic variational inference with message passing algorithms we show how to solve the highly complex problem of navigation and avoidance in distributed multi-robot systems in a computationally tractable manner, allowing online implementation. Subsequently, the proposed variational method lends itself to more flexible solutions than prior methodologies. Furthermore, the derived method is verified both through simulations with multiple mobile robots and a real world experiment with two mobile robots. In both cases the robots shares the operating space and needs to cross each other’s paths multiple times without colliding.

The ongoing COVID-19 pandemic has raised numerous questions concerning the shape and range of state interventions whose goals are to reduce the number of infections and deaths. The lockdowns, which have become the most popular response worldwide, are assessed as being an outdated and economically inefficient way to fight the disease. However, in the absence of efficient cures and vaccines, there is a lack of viable alternatives. In this paper we assess the economic consequences of the epidemic prevention and control schemes that were introduced in order to respond to the COVID-19 pandemic. The analyses report the results of epidemic simulations that were obtained using the agent-based modelling methods under the different response schemes and their use in order to provide conditional forecasts of the standard economic variables. The forecasts were obtained using the DSGE model with the labour market component.

We applied a generalized SEIR epidemiological model to the recent SARS-CoV-2 outbreak in the world, with a focus on Italy and its Lombardia, Piemonte, and Veneto regions. We focus on the application of a stochastic approach in fitting the model numerous parameters using a Particle Swarm Optimization (PSO) solver, to improve the reliability of predictions in the medium term (30 days). We analyze the official data and the predicted evolution of the epidemic in the Italian regions, and we compare the results with data and predictions of Spain and South Korea. We link the model equations to the changes in people’s mobility, with reference to Google’s COVID-19 Community Mobility Reports. We discuss the effectiveness of policies taken by different regions and countries and how they have an impact on past and future infection scenarios.

In this paper, we compare the performance between systems of ordinary and (Caputo) fractional differential equations depicting the susceptible-exposed-infectious-recovered (SEIR) models of diseases. In order to understand the origins of both approaches as mean-field approximations of integer and fractional stochastic processes, we introduce the fractional differential equations as approximations of some type of fractional nonlinear birth--death processes. Then, we examine validity of the two approaches against empirical courses of epidemics; we fit both of them to case counts of three measles epidemics that occurred during the pre-vaccination era in three different locations. While FDEs appear more flexible in fitting empirical data, our ODEs offered better fits to two out of three data sets. Important differences in transient dynamics between these modeling approaches are discussed.

Dams design and their operation cause strong environmental alteration and therefore a long-term debate is ongoing for the scale of these projects. At the same time, the concept of Environmental Flow Assessment (EFA) is a crucial element of modified ecosystems featuring large infrastructure such as dams and reservoirs for mitigating potential environmental degradation while they operate. Nowadays, integrated scientific frameworks are required to quantify the risks caused by large infrastructure. Through the use of stochastic analysis, it is possible to quantify these uncertainties, and present a solution that incorporates long-term persistence and environmental sustainability into a balanced reservoir simulation model. In this work, an attempt is made to determine a benchmark reservoir size incorporating hydrological and ecological criteria though stochastic analysis. The primary goal is to ensure the best possible conditions for the ecosystem, and then secondarily to allow a steady supply of water for other uses. Using a synthetic timeseries based on historical inputs, it is possible to determine and preserve essential statistical characteristics of a river’s streamflow, and use these to detect the optimal reservoir capacity that maximizes environmental and local water demand reliability.

Imperceptible vibratory noise stimulation has shown to be an effective means of improving stability for both whole body postural control and simple motor control tasks. While the physiological mechanism affording this improvement is uncertain, it is suspected that sensory noise stimulation may elicit a stochastic resonance-like effect within the somatosensory system. A stochastic resonance effect describes the phenomenon in which noise added to a non-linear system improves signal detection rather than degrading it. One hallmark of stochastic resonance is the existence of an optimal noise level which elicits the best system performance. There is disagreement in the literature regarding the presence of an optimal stimulation level for motor stability in humans. The goals of this study were to: 1) determine optimal stimulation level as a function of an individual’s sub-sensory threshold level, and 2) to determine whether performance of a force stability task was significantly better when subjects received stimulation at this identified optimal level compared to other sub-sensory threshold stimulation levels. Eighteen (18) participants completed an isometric finger flexion task with visual feedback while receiving noise stimulation scaled to varying percentages of their individual sub-sensory threshold level. Performance for this force stabilization task was quantified as the root-mean-square (RMS) error between the target force and the actual generated force values. Despite controlling all other signal properties and varying only amplitude, optimal noise stimulation values still varied widely across participants (10-100% sub-sensory threshold level). Statistical modeling revealed a significant improvement in task performance with optimal noise stimulation compared to other sub-sensory stimulation levels (p ≤ 0.019) with estimated marginal mean differences in force errors ranging from 0.13 to 0.23 N. Moderate significant Spearman correlations (r_s = 0.49 and r_s = 0.56, respectively) were found between finger flexion maximal voluntary contraction (MVC) and sub-sensory threshold level and MVC and optimal stimulation level. A strong, significant Spearman correlation (r_s = 0.65) was observed between sub-sensory threshold level and optimal stimulation level. Although these correlations do not provide a means to predict optimal stimulation level as a function of these other measures, optimal stimulation level appears to increase with sub-sensory threshold and MVC.

This review paper deals with recently proposed algorithms for distributed blind macro-calibration of sensor networks based on consensus (synchronization), not requiring any fusion center. The basic algorithm, performing the estimation of the local calibration parameters, is derived commencing from appropriate local criteria, and developing the corresponding gradient descent scheme. It is shown that the estimated parameters of the calibration functions asymptotically converge, in the mean-square sense and with probability one (w.p.1), to such values that ensure consensus on calibrated sensor gains and calibrated sensor offsets. For the more realistic case in which additive measurement noise, communication dropouts and additive communication noise are present, two algorithm modifications are introduced: one using a simple compensation term, and a more robust one based on an instrumental variable. By utilizing stochastic approximation arguments it is shown that the modified algorithms also achieve asymptotic agreement for calibrated sensor gains and offsets, in the mean-square sense and w.p.1. Convergence rate is analyzed in terms of an upper bound of the mean-square error. It is also shown that the communications between nodes can be completely asynchronous, which is of substantial importance for real-world applications. Suggestions for design of \textit{a priori} adjustable weights are given. Finally, it is shown that, if there is a subset of (precalibrated) reference sensors with fixed calibration parameters, the calibrated sensor gains and offsets of the rest of the sensors do not achieve consensus - they converge to different points dictated by the reference sensors and the network characteristics. Wide applicability and efficacy of these algorithms are illustrated on several simulation examples.

Protein-DNA interactions are critical for the successful functioning of all natural systems. The key role in these interactions is played by processes of protein search for specific sites on DNA. Although it has been studied for many years, only recently microscopic aspects of these processes became more clear. In this work, we present a review on current theoretical understanding of the molecular mechanisms of the protein target search. A comprehensive discrete-state stochastic method to explain the dynamics of the protein search phenomena is introduced and explained. Our theoretical approach utilizes a first-passage analysis and it takes into account the most relevant physical-chemical processes. It is able to describe many fascinating features of the protein search, including unusually high effective association rates, high selectivity and specificity, and the robustness in the presence of crowders and sequence heterogeneity.

In a wireless network, locations of base stations (BSs)/access points (APs)/sensor nodes can be modeled based on stochastic processes, e.g., a Poisson point process (PPP) or a deterministic pattern planned ahead by providers. While deterministic deployment does not provide tractable interference analysis in general, PPP yields tractable analysis for interference. However, PPP allows APs to be deployed very close to each other and gives pessimistic results compared to the field measurements. In this study, in order to address this issue, Lloyd’s algorithm, which functions as a bridge between random and structural APs deployments, is investigated for analyzing coverage probability in a network. The link distance distribution is modeled as a mixture of Weibull distributions and its parameters are obtained by using the expectation-maximization (EM) algorithm for each iteration of Lloyd’s algorithm. The link distance distribution is further utilized for calculating the coverage probability approximately by exploiting the tractability of PPP.

In this paper, a two-stage stochastic programming modelling is proposed to design a multi-period, multistage, and single-commodity integrated forward/reverse logistics network design problem under uncertainty. The problem involves both strategic and tactical decision levels. The first stage deals with strategic decisions, which are the number, capacity, and location of forward and reverse facilities. At the second stage tactical decisions such as base stock level as an inventory policy is determined. The generic introduced model consists of suppliers, manufactures, and distribution centers in forward logistic and collection centers, remanufactures, redistribution, and disposal centers in reverse logistic. The strength of proposed model is its applicability to various industries. The problem is formulated as a mixed-integer linear programming model and is solved by using Benders’ Decomposition (BD) approach. In order to accelerate the Benders’ decomposition, a number of valid inequalities are added to the master problem. The proposed accelerated BD is evaluated through small-, medium-, and large-sized test problems. Numerical results reveal that proposed solution algorithm increases convergence of lower bound and upper bound of BD and is able to reach an acceptable optimality gap in a convenient CPU time.

Markov chain Monte Carlo sampling propagators, including numerical integrators for stochastic dynamics, are central to the calculation of thermodynamic quantities and determination of structure for molecular systems. Efficiency is paramount, and to a great extent, this is determined by the integrated autocorrelation time (IAcT). This quantity varies depending on the observable that is being estimated. It is suggested that it is the maximum of the IAcT over all observables that is the relevant metric. Reviewed here is a method for estimating this quantity. For reversible propagators (which are those that satisfy detailed balance), the maximum IAcT is determined by the spectral gap in the forward transfer operator, but for irreversible propagators, the maximum IAcT can be far less than or greater than what might be inferred from the spectral gap. This is consistent with recent theoretical results (not to mention past practical experience) suggesting that irreversible propagators generally perform better if not much better than reversible ones. Typical irreversible propagators involve a parameter controlling the mix of ballistic and diffusive movement. To gain insight into the effect of the damping parameter for Langevin dynamics, its optimal value is obtained here for a multidimensional quadratic potential energy function.

Based on productivity and efficiency indicators, we investigated the performance of the Brazilian oil and gas exploration industry, comparing the performance of this sector with other industrial sectors. We associate productivity with the concept of total factor productivity (TFP), while efficiency is measured using the stochastic frontier production model. Our sample was assembled from the Annual Industrial Survey (PIA) for 29 Brazilian industrial sectors from 2007 to 2019. The results derived from both methods allow us to affirm that the policies resulting from the Pre-Salt have significantly boosted the oil and natural gas extraction sector in terms of technological progress and efficiency. Between 2007 and 2009, the sector was among the least efficient, ranking 29th. However, in 2019 it reached first place in terms of efficiency. This structural change, which began in 2010 as a result of the technological innovations resulting from investments in R&D, has undergone a change since 2010, reflected in the upward trend towards pre-salt exploration promoted by Petrobras, as well as the new regulatory framework and government incentives for oil exploration in Brazil. Unfortunately, these productivity gains have not been exported to other branches of industry connected to the oil industry.

As an important part of urban terminal delivery, automated guided vehicle (AGV) has been widely used in the field of takeout delivery. Due to the real-time generation of takeout orders, the delivery system is required to be extremely dynamic, so the AGV needs to be dynamically scheduled. At the same time, the uncertainty in the delivery process (such as the meal preparation time) further increases the complexity and difficulty of AGV scheduling. Considering the influence of these two factors, the method of embedding stochastic programming model into rolling mechanism is adopted to optimize the AGV delivery routing. Specifically, To handle real-time orders under dynamic demand, an optimization mechanism based on rolling scheduling framework is proposed, which allows the AGV route to be continuously updated. Different from most VRP models, open chain structure is used to describe the dynamic delivery path of AGV. In order to deal with the impact of uncertain meal preparation time on route planning, a stochastic programming model is formulated with the purpose of minimizing the expectation of order timeout rate and the total customer waiting time. In addition, an effective path merging strategy and after-effects strategy are also considered in the model. In order to solve the proposed mathematical programming model, a multi-objective optimization algorithm based on NSGA-III framework is developed. Finally, a series of experimental results demonstrate the effectiveness and superiority of the proposed model and algorithm.

The Mara River basin (MRB) has a world-famous ecosystem, but the vegetation has been damaged due to economic development in recent years, and there is little known about the area that will experience severe vegetation damage in the future. Based on the vegetation vulnerability system, principal component analysis, and three CMIP6 scenarios (SSP1-2.6, SSP2-4.5, SSP5-8.5), vegetation vulnerability was calculated in the base period (2010-2019), near-term period (2020-2059) and long-term period (2060-2099) in the MRB. The spatial cluster of vegetation vulnerability was revealed by spatial correlation analysis, and the transition of vegetation vulnerability of different periods was analyzed by stochastic matrix. The results showed that in all periods, the vulnerability showed a high-high cluster in the east, and a low-low cluster midstream and downstream. From the stochastic matrix, the area of high vulnerability increased the least under the SSP1-2.6, while it increased the most under the SSP5-8.5. The vegetation vulnerability upstream increased the most from the base period to the near-term period and long-term period in the MRB. By comparing the vegetation vulnerability under different scenarios, and pointing out the areas with the highest vulnerability increase, this study can better provide comprehensive decision-making for vegetation protection in the MRB.

This paper provides the numerical investigation of two-dimensional stochastic Navier-Stokes equation driven by additive white noises. The vorticity-stream function method is presented to calculate the incompressible fluid flow. In order to solve the formulation of steam function equation, we propose a Crank-Nicolson Fourier pseudo-spectral method. Numerical results obviously show that the presence of stochastic forcing can have an impact upon the shapes of vortex in fluid flow. To a certain extent, the phenomenon of eddy shedding and the formation of some new vortex in a random medium can be observed, which make it possible for us to conduct optimal control experiments in the development of vortex structures.

This paper studies the finite-time synchronization problem of fractional-order stochastic memristive bidirectional associative memory neural networks (MBAMNNs) with discontinuous jumps. A novel criterion for finite-time synchronization is obtained by utilizing the properties of quadratic fractional-order Gronwall inequality with time delay and the comparison principle. This criterion provides a new approach to analyze the finite-time synchronization problem of neural networks with stochasticity. Finally, numerical simulations are provided to demonstrate the effectiveness and superiority of the obtained results.

Recently, federated learning (FL) has been receiving great attention as an effective machine learning method to avoid the security issue in raw data collection as well as to distribute the computing load to edge devices. However, even though wireless communications is a essential part for implementing FL in edge networks, there have been a few works that analyze the effect of wireless networks on FL. In this paper, we investigate FL in small-cell networks where multiple base stations (BSs) and users are located according to homogeneous Poisson point process (PPP) with different densities. We comprehensively analyze the effects of geographic node deployment on the model aggregation in FL on the basis of stochastic geometry-based analysis. We derive the closed-form expressions of coverage probability with tractable approximations and discuss the minimum required BS density for achieving a target model aggregation rate in small-cell networks. Our analysis and simulation results provide insightful information for understanding the behaviors of FL in small-cell networks, and it can be exploited as a guideline for designing the network facilitating the wireless FL.

In this paper, we first establish upper stochastic bounds on the lifetime of a used cold standby system with arbitrary age, using the likelihood ratio order and the usual stochastic order. Then, stochastic comparisons are made between the lifetime of a used cold standby system with age t and the lifetime of a cold standby system consisting of used components with age t using the likelihood ratio order and the usual stochastic order. We use illustrative examples to explore the results presented.

One of the key challenges of stock trading is the stock prices follow a random walk process, which is a special case of a stochastic process, and are highly sensitive to new information. A random walk process is difficult to predict in the short-term. Many linear process models that are being used to predict financial time series are structural models that provide an important decision boundary, albeit not adequately considering the correlation or causal effect of market sentiment on stock prices. This research seeks to increase the predictive capability of linear process models using the SPDR S\&P 500 ETF (SPY) and the CBOE Volatility (VIX) Index as a proxy for market sentiment. Three econometric models are considered to forecast SPY prices: (i) Auto-Regressive Integrated Moving Average (ARIMA), (ii) Generalized Auto Regressive Conditional Heteroskedasticity (GARCH), and (iii) Vector Autoregression (VAR). These models are integrated into two technical indicators, Bollinger Bands and Moving Average Convergence Divergence (MACD), focusing on forecast performance. The profitability of various algorithmic trading strategies is compared based on a combination of these two indicators. This research finds that linear process models that incorporate the VIX Index do not improve the performance of algorithmic trading strategies.

The purpose of this paper is to find the time optimal control to a target set for semilinear stochastic functional differential equations involving time delays or memories under general conditions on a target set and nonlinear terms even though the equations contain unbounded principal operators. Our research approach is construct a fundamental solution for corresponding linear systems and establish variations of constant formula of solutions for given stochastic equations. The existence result of time optimal controls for one point target set governed by the given semilinear stochastic equation is also established.

Water is essential to all life-forms including various ecological, geological, hydrological, and climatic processes/activities. With changing climate, associated El Nino/Southern Oscillation (ENSO) events appear to stimulate highly uncertain patterns of precipitation (P) and evapotranspiration (EV) processes across the globe. Changes in P and EV patterns are highly sensitive to temperature variation and thus also affecting natural streamflow processes. This paper presents a novel suite of stochastic modelling approaches for associating streamflow sequences with climatic trends. The present work is built upon a stochastic modelling framework HMM_GP that integrates a Hidden Markov Model with a Generalised Pareto distribution for simulating synthetic flow sequences. The GP distribution within HMM_GP model is aimed to improve the model's efficiency in effectively simulating extreme events. This paper further investigated the potentials of Generalised Extreme Value Distribution (EVD) coupled with an HMM model within a regression-based scheme for associating impacts of precipitation and evapotranspiration processes on streamflow. The statistical characteristic of the pioneering modelling schematic has been thoroughly assessed for their suitability to generate/predict synthetic river flows sequences for a set of future climatic projections. The new modelling schematic can be adapted for a range of applications in the area of hydrology, agriculture and climate change.

An exploding demand for processing capabilities related to the emergence of the IoT, AI and big data, has led to the quest for increasingly efficient ways to expeditiously process the rapidly increasing amount of data. These ways include different approaches like improved devices capable of going further in the more Moore path, but also new devices and architectures capable of going beyond Moore and getting more than Moore. Among the solutions being proposed, Stochastic Computing has positioned itself as a very reasonable alternative for low-power, low-area, low-speed, and adjustable precision calculations; four key-points beneficial to edge computing. On the other hand, chaotic circuits and systems appear to be an attractive solution for (low-power, green) secure data transmission in the frame of edge computing and IoT in general. Classical implementations of this class of circuits require intensive and precise calculations. This paper discusses the use of the SC framework for the implementation of nonlinear systems, showing that it can provide results comparable to those of classical integration, with much simpler hardware, paving the way for relevant applications.

This paper inquires on the options pricing modeling using Artificial Neural Networks to price Apple(AAPL) European Call Options. Our model is based on the premise that Artificial Neural Networks can be used as functional approximators and can be used as an alternative to the numerical methods to some extent, for a faster and an efficient solution. This paper provides a neural network solution for two financial models, the BlackScholes-Merton model, and the calibrated-Heston Stochastic Volatility Model, we evaluate our predictions using the existing numerical solutions for the same, the analytic solution for the Black-Scholes equation, COS-Model for Heston’s Stochastic Volatility Model and Standard Heston-Quasi analytic formula. The aim of this study is to find a viable time-efficient alternative to existing quantitative models for option pricing.

Supplier selection/replacement strategies and optimized purchasing policies play a key role in efficient supply chain management in today’s dynamic market. Here we study supplier replacement in a one-level assembly system (OLAS) producing one type of finished product. To assemble the product, we need to provide multi-type components, but assembly will be interrupted if any single component is missing, and incoming units will get hoarded until the missing component arrives. The assembly process can be interrupted by various sources of uncertainty, including delays in component deliveries. There is consequently a non-negligible risk that the assembly process may get stopped any moment. This brings inventory-related costs, which should be minimized. Here we consider discrete lead-time distributions to mimic industry-world reality. We present a model that takes into account not only optimal assignment of component order release dates but also replacement of a critical supplier. For a given unit, we model several alternative suppliers with alternative pricing and lead-time uncertainties, and we evaluate the impact on the total assembly system. For a more general case where several suppliers may be replaced, we propose a genetic algorithm.

The unprecedented demand for services and applications, coupled with large network architecture calls for a radical melioration in evolving wireless networks. Massive multiple-input and multiple-out (massive MIMO) systems, small cell networks (SCN) and Heterogeneous networks (HetNet) are envisioned to meet the new quality of service (QoS) objectives of evolving networks. In this paper, we investigate massive MIMO with HetNet, where the intended macro BS signal follows Ricean fading and interfering Femto BS signals follow Rayleigh fading. Subject to the Ricean assumption, strong line-of-sight (LOS) channel exists in the coverage area, when the high power macro BS is mounted at a high altitude. Then, by exploiting matrix and stochastic geometric tools, we evaluate the signal-to-interference (SIR). And obtain QOS objectives: coverage and outage probabilities, and area spectral efficiency (ASE). Further, we investigate the role of multiple antenna system in improving the SIR. This involves massive MIMO beamforming coordination of the macro BSs through power control with max-min optimization for users at the cell-edge. Numerical results show that the coverage and outage performance converge for different user locations, pathloss and Ricean factor. Also, the monotonic increase in Ricean factor improves the SIR of a user located within coverage region. That is, a user is in an outage at a distance where the Ricean factor is very small. And, optimal macro BS antennas and Ricean factor that achieve the ASE performance guarantee a rate-fairness between the cooperating macrocells, and avoid strong Ricean channel correlation. The performance gain is dependent on Ricean factor and user location, but independent of cell size.

In this paper, a kind of single-walled carbon nanotube nonlinear model is developed, and the strongly nonlinear dynamic characteristics of such carbon nanotubes subjected to random magnetic field are studied. The nonlocal effect of microstructure is considered based on the theory of nonlocal elasticity. The natural frequency of the strongly nonlinear dynamic system is obtained by the energy function method, the drift coefficient and the diffusion coefficient are verified. The stationary probability density function of the system dynamic response is given and the fractal boundary of the safe basin is provided. Theoretical analysis and numerical simulation show that stochastic resonance occurs when varying the random magnetic field intensity. The boundary of safe basin has fractal characteristics and the area of safe basin decreases when the intensity of the magnetic field permeability increases.

In this paper, we study the asymptotic properties of slowly varying functions of one real variable in the sense of Karamata. We establish analogs of fundamental theorems on uniform convergence and integral representation for slowly varying functions with remainder depending on the types of remainder. We also prove several important theorems on the asymptotic representation of integrals of Karamata functions. Under certain conditions, we observe a “narrowing” of classes of slowly varying functions concerning the types of remainder. At the end of the paper, we discuss the possibilities of application of slowly varying functions in the theory of stochastic branching systems. In particular, under the condition of the finiteness of the moment of the type Exlnx for the particle transformation intensity, it is established that the property of slow variation with remainder is implicitly present in the asymptotic structure of a non-critical Markov branching random system.

When limited area models of the hydrodynamics of the atmosphere and of the ocean are 1 run over an extended time, variability unrelated to external "drivers" emerge - this variability is 2 colloquially named "hydrodynamical noise" or just "noise". This article summarises what we have 3 learned in the past few years about the properties of such noise, and the implications for numerical 4 experimentation and analysis. The presence of this noise can be identified easily in ensembles of 5 numerical simulations, and it turns out that the intensity of the noise is closely linked to the scale- 6 dependent "memory". At the system level, this "memory" term as given by Hasselmann’s Stochastic 7 Climate model plays a key role. In the case of marginal seas, the process of baroclinic instability 8 modulated by tides and the formation of seasonal thermoclines are significant aspects. Some more 9 general aspects are discussed, such as the applicability of the Stochastic Climate model to systems 10 outside of atmospheric and oceanic dynamics, the irreversibility of tipping points and the challenges 11 of detecting changes beyond a noise level and of the attribution of causes of change.

This manuscript presents a new two-parameter unit stochastic distribution, obtained by transforming the Laplace distribution, using generalized logistic map, into a unit interval. The distribution thus obtained is named the Laplace-logistic unit (abbreviated LLU) distribution, and its basic stochastic properties are examined in detail. Also, the procedure for estimating parameters based on quantiles is provided, along with the asymptotic properties of the obtained estimates and the appropriate numerical simulation study. Finally, the application of the LLU distribution in dynamic and regression analysis of real-world data with accentuated "peaks" and "fat" tails is also discussed.

Coronavirus disease 2019 (COVID-19) is a high contagious respiratory infectious disease that has afiected millions of people worldwide. Initially, basic public health measures were implemented to control specially the spread of such virus. However, vaccination has emerged as a highly efiective strategy in combating COVID-19 and reducing its transmission. Several efiective and safe vaccines have been approved to prevent the inadvertent spread of the disease. In this study, a modeling approach is used to analyze the impact of these vaccines on the dynamics of COVID-19. By applying a higher-order numerical method, the model is solved based on reported cases in Pakistan. A spectral method is employed for the numerical solution, and the model is simulated to assess the efiects of vaccination. The Next-generation method is used to calculate the threshold quantity, known as R0, which indicates the potential for disease transmission. The study also includes a detailed stability analysis, examining the invariance properties of the model solution and discussing equilibrium points and their stability in disease-free and endemic states. Furthermore, the study presents graphical representations of the influence of special parameters on the dynamics of the pandemic.

At present paper, we aim to study the long-time behavior of a stochastic semi-linear degenerate parabolic equation on bounded or unbounded domain and driven by a nonlinear noise and defined. Since the theory of pathwise random dynamical systems can not be applied directly to the equation with nonlinear noise, first, we establish the existence of weak pullback mean random attractors for the equation by applying the theory of mean-square random dynamical systems; then, we prove the existence of (pathwise) pullback random attractors for the Wong-Zakai approximate system of the equation. In addition, we establish the upper semicontinuity of pullback random attractors for the Wong-Zakai approximate system of the equation under consideration driven by a linear multiplicative noise.

The passenger prediction flow is very significant to transportation sustainability. This is due to some chaos of traffic jams encountered by the road users during their movement to the offices, schools, or markets at earlier of the days and during closing periods. This problem is peculiar to the transportation system of the Federal University of Technology Minna, Nigeria. However, the prevailing technique of passenger flow estimation is non-parametric which depends on the fixed planning and is easily affected by noise. In this research, we proposed the development of a hybrid intelligent passenger frequency prediction model using the Auto-Regressive Integrated Moving Average (ARIMA) linear model, Convolutional Neural Network (CNN), and Kalman Filter Algorithm (KFA). The passengers’ frequency of arrival at the bus terminals is obtained and enumerated through the closed-circuit television (CCTV) and demonstrated using the Markovian Queueing Systems Model (MQSM). The ARIMA model was used for learning and prediction and compared the result with the combined techniques of using CNN-KFA. The autocorrelation coefficient functions (ACF) and partial autocorrelation coefficient functions (PACF) are used to examine the stationary data with different features. The performance of the models was analyzed and evaluated in describing the short-term passenger flow frequency at each terminal using the Mean Absolute Percentage Error (MAPE) and Mean Squared Error (MSE) values. The CNN-Kalman-filter model was fitted into the short-term series and the MAPE values are below 10%. The Mean Square Error (MSE) shows that the CNN-Kalman Filter model has the overall best performance with 83.33% of the time better than the ARIMA model and provides high accuracy in forecasting.

Uncertainty relations in hydrodynamics are numerically studied. We first give a review for the formulation of the generalized uncertainty relations in the stochastic variational method (SVM), following the work by two of the present authors [Phys.\ Lett.\ A\textbf{382}, 1472 (2018)]. In this approach, the origin of the finite minimum value of uncertainty is attributed to the non-differentiable (virtual) trajectory of a quantum particle and then both of the Kennard and Robertson-Schr\"{o}dinger inequalities in quantum mechanics are reproduced. The same non-differentiable trajectory is applied to the motion of fluid elements in the Navier-Stokes-Fourier equation or the Navier-Stokes-Korteweg equation. By introducing the standard deviations of position and momentum for fluid elements, the uncertainty relations in hydrodynamics are derived. These are applicable even to the Gross-Pitaevskii equation and then the field-theoretical uncertainty relation is reproduced. We further investigate numerically the derived relations and find that the behaviors of the uncertainty relations for liquid and gas are qualitatively different. This suggests that the uncertainty relations in hydrodynamics are used as a criterion to classify liquid and gas in fluid.

The so-called Born-Huang ansatz is a fundamental tool in the context of ab-initio molecular dynamics, viz., it allows to effectively separate fast and slow degrees of freedom and thus treating electrons and nuclei at different mathematical footings. Here we consider the use of a Born-Huang-like expansion of the three-dimensional time-dependent Schr\"odinger equation to separate transport and confinement degrees of freedom in electron transport problems that involve geometrical constrictions. The resulting scheme consists of an eigenstate problem for the confinement degrees of freedom (in the transverse direction) whose solution constitutes the input for the propagation of a set of coupled one-dimensional equations of motion for the transport degree of freedom (in the longitudinal direction). This technique achieves quantitative accuracy using an order less computational resources than the full dimensional simulation for a prototypical two-dimensional constriction.

Bello's stochastic linear time-varying system theory has been widely used in the wireless communications literature to characterize multipath fading channel statistics. In the context of radar backscatter, this formulation allows for statistical characterization of distributed radar targets in range and Doppler using wide-sense stationary uncorrelated scattering (WSSUS) models. WSSUS models separate the channel from the effect of the waveform and receive filter, making it an ideal formulation for waveform design problems. Of particular interest in the radar waveform design community is the ability to suppress unwanted backscatter from the earth's surface, known as clutter. Various methods for estimating WSSUS system functions have been studied in the literature, but to date, no analytic expressions for radar surface clutter range-Doppler scattering functions exist. In this work we derive a wideband generalization of the Jakes Doppler spectrum model, which is widely used in the wireless communications literature, adapt it for use in radar problems, and show how the maximum entropy method can be used to extend this model to account for internal clutter motion. Validation of the spectral and stationarity properties of the proposed model against a subset of the Australian Ingara sea clutter database is performed, and good agreement is shown.

In this paper, we introduce the evolve-then-filter (EF) regularization method for reduced order modeling of convection-dominated stochastic systems. The standard Galerkin projection reduced order model (G-ROM) yield numerical oscillations in a convection-dominated regime. The evolve-then-filter reduced order model (EF-ROM) aims at the numerical stabilization of the standard G-ROM, which uses explicit ROM spatial filter to regularize various terms in the reduced order model (ROM). Our numerical results based on a stochastic Burgers equation with linear multiplicative noise. It shows that the EF-ROM is significantly better results than G-ROM.

A probabilistic description is essential for understanding the dynamics of stochastic systems far from equilibrium. To compare different Probability Density Functions (PDFs), it is extremely useful to quantify the difference among different PDFs by assigning an appropriate metric to probability such that the distance increases with the difference between the two PDFs. This metric structure then provides a key link between stochastic processes and geometry. For a non-equilibrium process, we define an infinitesimal distance at any time by comparing two PDFs at times infinitesimally apart and sum these distances in time. The total distance along the trajectory of the system quantifies the total number of different states that the system undergoes in time and is called the information length. By using this concept, we investigate classical and quantum systems and demonstrate the utility of the information length as a unique Lagrangian diagnostic to quantify the information change as a system continuously evolves in time and to map out attractor structure. We further elucidate quantum effects (uncertainty relation) and the dual role of the width of PDF in quantum systems.

In this paper we investigate the optimal investment strategy for a defined contribution (DC) pension plan during the decumulation phrase which is risk-averse and pays close attention to inflation risk. The plan aims to maximize the expected constant relative risk aversion (CRRA) utility from the terminal wealth by investing the wealth in a financial market consisting of an inflation-indexed bond, an ordinary zero coupon bond and a risk-free asset. We derive the optimal investment strategy in closed-form using the dynamic programming approach by solving the corresponding Hamilton-Jacobi-Bellman (HJB) equation. Our theoretical and numerical results reveal that under some rational assumptions, an inflation-indexed bond do has significant advantage to hedge inflation risk.

Many systems in nature and laboratories are far from equilibrium and exhibit significant fluc- tuations, invalidating the key assumptions of small fluctuations and short memory time in or near equilibrium. A full knowledge of Probability Distribution Functions (PDFs), especially time- dependent PDFs, becomes essential in understanding far-from-equilibrium processes. We consider a stochastic logistic model with multiplicative noise, which has gamma distributions as stationary PDFs. We numerically solve the transient relaxation problem, and show that as the strength of the stochastic noise increases the time-dependent PDFs increasingly deviate from gamma distributions. For sufficiently strong noise a transition occurs whereby the PDF never reaches a stationary state, but instead forms a peak that becomes ever more narrowly concentrated at the origin. The addition of an arbitrarily small amount of additive noise regularizes these solutions, and re-establishes the existence of stationary solutions. In addition to diagnostic quantities such as mean value, standard deviation, skewness and kurtosis, the transitions between different solutions are analyzed in terms of entropy and information length, the total number of statistically distinguishable states that a system passes through in time.

In this paper, we propose a novel stochastic model to study prime distribution in almost-short intervals, inspired by a corollary of the Maynard-Guth theorem. The model uses the equation \[ x_{n+1} = x_n + \frac{y}{\log x_n} + \epsilon_n, \] where \(\epsilon_n\) follows a Laplace distribution, and demonstrates that our new bound surpasses both Walfisz and Maynard-Guth bounds, particularly for large \(x\): \[ \left| \pi(x + y) - \pi(x) - \frac{y}{\log x} \right| \leq C \cdot y \exp(-\sqrt[4]{\log x}). \] Additionally, we explore a modulated Hamiltonian \(\hat{H}(x)\), derived from a potential \(V(x)\) and a test function \(f(x)\), that exhibits behavior akin to the energy levels of the heavy nucleus \(H_{38}\). The gaps between these energy levels resemble the distribution of zeros of the Riemann zeta function near the critical line, suggesting that \(\zeta(0.5 + i \hat{H}(x))\) corresponds to the energy levels of \(\hat{H}(x)\), thus supporting a quantum mechanical interpretation of the Riemann hypothesis. Furthermore, assuming the Elliott-Halberstam conjecture, which implies that prime gaps can be as small as 12, we find that the transition rate \(\Gamma_{p \to p+12}\) between quantum states associated with prime numbers increases with larger primes. This observation indicates that the distribution of prime gaps reflects an underlying discrete structure in the "energy" landscape of primes, offering a novel perspective on the connection between number theory and quantum physics.

This study considers the values of the credit payments that are made at random values for both payment size and number. The simultaneous existence of the two random variables increases the total value of the volatility of the payment process. The dependence for the simultaneous influence of the two random variables is derived by applying conditional probabilistic formulations. Formal relations apply to animal husbandry credit payments. The credit policy was analyzed for the cases of regular payments and with a stochastic number of payments. A recommendation for the upper level of credit payments is proposed based on a model predictive approach using historical payment data. A credit management algorithm is derived, in which decision-making for credit payments is formally derived and numerically discussed. The application of derived quantitative relations is empirically applied to real data on animal husbandry. The recommendations from the dependencies obtained allow a reduction in the mean values of credit payments, which correspond to a reduction in the credits used for business management, without a change in business policy.

This paper addresses the optimal stochastic allocation of Distributed Energy Resources in distribution Networks. Typically, uncertain problems are analyzed in multi-stage formulations including case generation routines, resulting in computationally exhaustive programs. In this article, two probabilistic approaches are proposed resulting in a single-stage, convex, stochastic optimal power flow problem: The Range-Probability Optimization (RPO) and Value-Probability Optimization (VPO). The RPO maximizes probabilities within a range of uncertainty, whilst the VPO optimizes the values of the random variables and maximizes their probabilities. Random variables are modeled with hourly measurements fitted to the logistic distribution. These formulations were tested on two systems and compared against the deterministic case built from expected values. Results indicate that assuming deterministic conditions ends in highly underestimated losses. The RPO showed that by including a ±10 % uncertainty, the losses can be increased up to 40 % with up to −72 % photovoltaic capacity, depending on the system, whereas the VPO resulted in up to 85 % increases in power losses despite PV installations, with 20 % greater probabilities in average. By implementing any of the proposed approaches, it was possible to obtain more probable upper envelopes in the objective, avoiding case generation stages and heuristic methods.

The article is devoted to algebraic modeling of universal rules of stochastic organization of genomic DNA of higher and lower organisms, previously published by the author. The proposed algebraic apparatus, which uses formalisms of quantum mechanics and quantum informatics and which is based on the so-called tensor-unitary transformations of vectors that generate families of interrelated stochastic-deterministic vectors of increased dimensions. The features of the vectors' interconnections in these families model the stochastic-deterministic properties of the named phenomenological rules. There are new approaches to modeling of developing multi-parameter biosystems, whose number of parameters increases in the course of step-by-step development. In the light of the presented materials, the issues of fractal-like organization in genetically inherited biosystems are considered. The development of the theory of stochastic determinism as an antipode of deterministic chaos is discussed.

Bayesian techniques for engineering problems, that rely on Gaussian process (GP) regression, are known for their ability to quantify epistemic and aleatory uncertainties and for being data efficient. The mathematical elegance of applying these methods usually comes at a high computational cost when compared to deterministic and empirical Bayesian methods. Furthermore, using these methods becomes practically infeasible in scenarios characterized by a large number of inputs and thousands of training data. The focus of this work is on enhancing Gaussian Process-based metamodeling and model calibration tasks, when the size of the training datasets is significantly large. To achieve this goal, we employ a stochastic variational inference algorithm that enables rapid statistical learning of the calibration parameters and hyperparameter tuning, while retaining the rigor of Bayesian inference. The numerical performance of the algorithm is demonstrated on multiple metamodeling and model calibration problems with thousands of training data.

The part transportation efficiency is a main factor of aircraft sortie generation rate. Part transportation is used to transport spare part from base to carrier. Transportation strategy depends on both demand on carrier and inventory in transportation base. The transportation time and stochastic demand will induce fluctuations of cost and inventory. Thus, a Takagi-Sugeno fuzzy system of dynamic part transportation is established considering transportation time and stochastic demand. And a novel Takagi-Sugeno fuzzy robust control is designed for dynamic part transportation, which will keep transportation cost and part inventory stable. First of all, a fuzzy model with stochastic demand and transportation time is proposed. Then, a novel robust control with cross rule groups is conducted according to production and transportation strategy, which will reduce fluctuations induced by strategies switch. Moreover, robust stability is guaranteed and part can be supplied in time under a low cost. Finally, simulation illustrates usefulness and quickness of the novel Takagi-Sugeno fuzzy robust control. Besides, the proposed method will be useful in other transportation electrification systems with delay time and uncertainty.

The study of pain requires a balance between subjective methods that rely on self-reports and complementary objective biometrics that ascertain physical signals associated with subjective accounts. There are at present no objective scales that enable the personalized assessment of pain, as most work involving electrophysiology rely on summary statistics from a priori theoretical population assumptions. Along these lines, recent work has provided evidence of differences in pain sensations between participants with Sensory Over Responsivity (SOR) and controls. While these analyses are useful to understand pain across groups, there remains a need to quantify individual differences more precisely in a personalized manner. Here we offer new methods to characterize pain using the moment-by-moment standardized fluctuations in EEG brain activity centrally reflecting the person’s experiencing temperature-based stimulation at the periphery. This type of gross data is often disregarded as noise, yet here we show its utility to characterize the lingering sensation of discomfort raising to the level of pain, individually, for each participant. We show fundamental differences between the SOR group in relation to controls and provide an objective account of pain congruent with the subjective self-reported data. This offers the potential to build a standardized scale useful to profile pain levels in a personalized manner across the general population.

In the fifth generation communication system, millimeter wave (mmWave) networks will coexist with traditional micro wave (μWave) networks, which allows for higher data transmission rate and better user experience. In this paper, we give a comprehensive framework of mathematical models and analytical methods for multi-tier mmWave and μWave hybrid caching networks based on stochastic geometry. We propose an association strategy by assuming average biased-received power association and Rayleigh fading. Accordingly, by using a D-ball approximating blockage model of mmWave networks, expressions of the cell association probability and the coverage probability of the hybrid networks are derived. Also, we use the average successful delivery probability as the performance metric to analyze the existing caching placement strategies. Simulation results validate the accuracy of our analytical conclusions.

This research aims to explore factors that influence sustainable music education from a psychological perspective, and innovatively constructs a combination of qualitative and quantitative approaches. For first time, combines stochastic nonlinear system of control theory and identifies relevant factors affecting sustainable music learning by establishing a data system for questionnaire answering and a quantitative model for actual academic performance. Existing research mainly looks at several factors that affect fragmented music education from perspective of teachers' teaching rules, emphasizing phased teaching state and learning goals of teachers as main body, thus ignoring sustainable music education and students, who are a large group of music learning objects. The research fills gap in this type of research object, focusing on sustainable music education from an emotional perspective and students who occupy a dominant position in music learning, so as to more accurately explore impact of their emotional influencing factors on sustainable music learning. The most prominent innovation of this study lies in construction of stochastic nonlinear system for psychological influencing factors of sustainable student music learning and a quantitative model for actual learning effect. Through analysis of nonlinear system, weight values of several negative emotions on sustainable music learning are obtained.

A simple bounded stochastic motion is employed for modelling equity price dynamics under shocks, where the prices are constrained to lie between two positive bounds. While the stochastic process has an inaccessible boundary, the other boundary is quasi-bounded, implying that the boundary can be breached if the probability leakage condition is met. The quasi-boundedness of the process at the boundary can thus provide an indicator of possible risk of equities under price shocks. Empirical calibration of model parameters of the proposed process for equities can be performed easily due to the availability of an analytically tractable probability density function which generates fat-tailed distributions consistent with empirical observations. The volatility and mean-reversion of the S&P500 dynamics calibrated by the process is positively and negatively co-integrated respectively with the VIX index representing the level of market distress. The process captures the high likelihood of Hertz’s default about two months earlier, using only information until that point, and before the firm filed for Chapter 11 bankruptcy in May 2020 as a result of the Covid-19 pandemic. Empirical calibration of the process for GameStop’s stock price shows that the short squeeze of the stock occurred when the condition for breaching an upper boundary was met on 14 January 2021, i.e., about two weeks before major short sellers closed out their positions with significant losses. The trading volume of the stock was positively co-integrated with the probability leakage ratio.

This paper proposes a non-extensive entropy econometric technique to predict energy efficiency at province (NUT-2) level based on imperfect knowledge of the national overall efficiency in the sectors of industry, transport, households and services. The model is applied to the polish case. As acknowledged in recent literature, non-extensive entropy model should remain a valuable device for econometric modelling even in the case of low frequency series since outputs provided by the Gibbs-Shannon entropy approach correspond to the Tsallis entropy limiting case of the Gaussian law when the Tsallis q-parameter converges to unity. Therefore, we set up a q-Tsallis-Kullback-Leibler entropy criterion function with a priori consistency moment and model data constraints, including province energy intensity (known with uncertainty), regional climate differentiation and regular conditions. The model outputs continue to conform to empirical expectations. In spite of the close to unity q-Tsallis parameter, this Tsallis related approach reflects higher stability for parameter computation in comparison with the Shannon-Gibbs entropy econometrics technique. The proposed technique can be applied in different EU countries and elsewhere for example in the context of experimental official statistics.

We develop the process of discounting when underlying rates follow a jump-diffusion process, that is, when, in addition of diffusive behavior, rates suffer a series of finite discontinuities located at random Poissonian times. Jump amplitudes are also random and governed by an arbitrary density. Such a model may describe the economic evolution specially when extreme situations occur (pandemics, global wars, etc.). When between jumps the dynamical evolution is governed by an Ornstein-Uhlenbeck diffusion process, we obtain exact and explicit expressions for the discount function and the long-run discount rate and show that the presence of discontinuities may drastically reduce the discount rate, a fact that has significant consequences for environmental planning. We also discuss as a specific example the case when rates are described by the continous time random walk.

Probability is an open question in the ontological interpretation of quantum mechanics. It has been discussed in some trajectory interpretations such as Bohmian mechanics and stochastic mechanics. New questions arise when the domain of probability extends to the complex space, including the generation of complex trajectories, the definition of the complex probability, the relation of the complex probability to the real quantum probability, and so on. The complex treatment proposed here applies the optimal quantum guidance law to derive the stochastic differential (SD) equation governing the particle’s random motions in the complex plane. The ensemble of the complex quantum random trajectories (CQRTs) solved from the complex SD equation is used to construct the probability distribution ρc(t,x,y) of the particle’s position over the complex plane z=x+iy. The correctness of the obtained complex probability is confirmed by the solution of the complex Fokker-Planck equation. The significant contribution of the complex probability is that it can be used to reconstruct both quantum probability and classical probability, and to clarify their relationship. Although quantum probability and classical probability are both defined on the real axis, they are obtained by projecting complex probability onto the real axis in different ways. This difference explains why the quantum probability cannot exactly converge to the classical probability when the quantum number is large.

Recently, the properties of bouncing oil droplets, also known as `walkers', have attracted much attention because they are thought to offer a gateway to a better understanding of quantum behaviour. They indeed constitute a macroscopic realization of wave-particle duality, in the sense that their trajectories are guided by a self-generated surrounding wave. The aim of this paper is to try to describe walker phenomenology in terms of de Broglie-Bohm dynamics and of a stochastic version thereof. In particular, we first study how a stochastic modification of the de Broglie pilot-wave theory, à la Nelson, affects the process of relaxation to quantum equilibrium, and we prove an H-theorem for the relaxation to quantum equilibrium under Nelson-type dynamics. We then compare the onset of equilibrium in the stochastic and the de Broglie-Bohm approaches and we propose some simple experiments by which one can test the applicability of our theory to the context of bouncing oil droplets. Finally, we compare our theory to actual observations of walker behavior in a 2D harmonic potential well.

This paper aims to propose a stochastic linear parameter varying (LPV) model approach to design a state feedback controller for three-phase two-level inverters. To deal with the parameter changes, stochastic noise and delays faced by the inverter, it is modeled as a stochastic LPV system with time delay. The stability analysis and control synthesis are conducted for the LPV system. With parameter-dependent Lyapunov functionals, the sufficient stability condition for asymptotical mean-square stability is obtained. In addition, the slack matrix technique is employed to improve the feasibility and reduce the conservatism of the conditions. The obtained theoretical results are applied to the three-phase two-level inverter, whose currents are treated as state variables and controlled to reach the equilibrium point. The simulation results validate the effectiveness of the proposed theories and demonstrate the advantages of using the slack matrix.

Our recent analysis of empirical limit order flow data in financial markets reveals a power-law distribution in limit order cancellation times. These times are modeled using a discrete probability mass function derived from the Tsallis q-exponential distribution, closely aligned with the second form of the Pareto distribution. We elucidate this distinctive power-law statistical property through the lens of agent heterogeneity in trading activity and asset possession. Our study introduces a novel modeling approach that combines fractional Lévy stable motion for limit order inflow with this power-law distribution for cancellation times, significantly enhancing the prediction of order imbalances. This model not only addresses gaps in current financial market modeling but also extends to broader contexts such as opinion dynamics in social systems, capturing the finite lifespan of opinions. Characterized by stationary increments and a departure from self-similarity, our model provides a unique framework for exploring long-range dependencies in time series. This work paves the way for more precise financial market analyses and offers new insights into the dynamic nature of opinion formation in social systems.

The impacts of inflation on international finance are generally reflected in the decline of buying power, risks of investment and deposit loss from currency devaluation. For the purpose of optimized allocation and management of asset values, i.e., annual income or research grants, a framework of a three-level model for static financial management is presented to maximize banking interests, bonuses, and the remaining balance after spending necessary expenditures. Meanwhile, in retrospect to higher-level financial inflation, strategies of dynamic investment, i.e., posing regular tests of flipping coins, exploiting variations of the currency exchange rate, as well as applying the theory of broad money, are presented to increase the appreciation rate of net assets in and post the era of COVID-19. Quantitative evaluations in case studies verify the feasibility of improving the financial situation, indicating broader applications for budgeting and investing when US inflation rate is below 3.0%. Besides, combining approaches of static and dynamic strategies, the expected annual growth rate of individual zero-risk asset investment is predicted as within the range of 8.30~9.62% according to budgeted appreciation on net assets in 12 months, which is capable of overcoming negative impacts from higher level annual inflation, i.e., those as highest as 8.01% in the Year 2022.

The present paper reports an alternative solution of the measurement problem in quantum theory. The measurement problem can be characterized as that the U-procedure verses the R-procedure. The R-procedure is tested by the Yes/No measurement originally proposed by von Neuman and discussed in details by Penrose. We propose a novel stochastic sampling method to tackle the measurement paradox. Each testing sample produces a pair of Yes-number c and No-number d, which in turn generates a sample phase with respect to the exponential form of (c+id). All the sample phases forms a group G_R. Taking G_R as the sampling potential, combined with the dynamic phase group G_U，we establish a unified model of U-procedure and R-procedure for the evolution of wavefunction. Based on the Born rule, the probability of a sample is given by the squared magnitude of （c+id）. Some metaproperties of the new U-R model, such as natural transformation, consistency, and completeness, are presented. The present work provides a new picture of quantum mechanics and alike. The measurement problem widely exists in dynamic analysis, higher cognition, and large data modeling. Thus, the work reported here has a wide range of applications. Keywords: The measurement problem; U-R procedures; the Yes/No type measurement; stochastic sampling; sample phase; Born probability.

Low-intensity noisy galvanic vestibular stimulation (nGVS) can improve static and dynamic postural deficits in patients with bilateral vestibular loss (BVL). In this study, we aimed to explore the neurophysiological and neuroanatomical substrates underlying nGVS treatment effects in a rat model of BVL. Regional brain activation patterns and behavioral responses to repeated 30-min nGVS treatment in comparison to sham stimulation were investigated by serial whole-brain [18F]-FDG-PET measurements and quantitative locomotor assessments before and at 9 consecutive time points up to 60 days after chemical bilateral labyrinthectomy (BL). [18F]-FDG-PET revealed a broad nGVS-induced modulation on regional brain activation patterns encompassing biologically plausible brain networks in the brainstem, cerebellum, multisensory cortex and basal ganglia during the entire observation period post-BL. nGVS broadly reversed brain activity adaptions occurring in the natural course post-BL. Parallel behavioral locomotor assessment demonstrated a beneficial treatment effect of nGVS on sensory-ataxic gait alterations, particularly in the early stage of post-BL recovery. Stimulation-induced locomotor improvements were finally linked to nGVS brain activity responses in the brainstem, hemispheric motor and limbic networks. In conclusion, combined [18F]-FDG-PET and locomotor analysis discloses the potential neurophysiological and neuroanatomical substrates that mediate previously observed therapeutic nGVS effects on postural deficits in patients with BVL.

In this work, optimal consumption and investment strategies are derived for risk-averse investors under the 4/2 stochastic volatility class of models. We work under an expected utility (EUT) framework and consider a Constant Relative Risk Aversion (CRRA) investor, who might also be ambiguity-averse. The corresponding Hamilton-Jacobi-Bellman (HJB) and HJB-Isaacs (HJBI) equations are solved in closed-form for a subset of the parametric space and under some restrictions on the portfolio setting, for complete markets. Conditions for proper changes of measure and well defined solutions are provided. These are the first analytical solutions for the 4/2 stochastic volatility model and the embedded 3/2 model for the type of excess returns established in .

Oestrogen receptor expression in breast cancer (BC) cells is a marker of high cellular differentiation and allows the identification of two BC groups (ER-positive and ER-negative) that, although not completely homogeneous, differ in biological characteristics, clinical behaviour and therapeutic options. The study, based on three publicly available EWAS datasets, focuses on the comparison between these two groups of breast cancer using an epimutation score. The score is calculated not only based on the presence of the epimutation but also on the deviation amplitude of the methylation outlier value. For each dataset, we performed a functional analysis based first on the functional gene region of each annotated gene (we aggregated the data per gene region TSS1500, TSS200, first-exon, body-gene identified by the information from the Illumina Data Sheet) and then we performed a pathway enrichment analysis through the REACTOME database based on the genes with the highest epimutation score. Thus, we blended our results and found common pathways for all three data sets. We found that a higher and significant epimutation score due to hypermethylation in ER-positive BC is present in the promoter region of the genes belonging to the SUMOylation pathway, the NOTCH pathway, the IFN-$\gamma$ signalling pathway and the deubiquitination protease pathway; while a higher and significant level of epimutation due to hypomethylation in ER-positive BC is present in the promoter region of the genes belonging to the ESR-mediated pathway. The presence of this state of promoter hypomethylation in the ESR-mediated signalling genes is consistent and coherent with an active signalling pathway mediated by oestrogen function in the group of ER-positive BC. SUMOylation and NOTCH pathways are associated with BC pathogenesis and have been found to play distinct roles in the two BC subgroups. We speculated that the altered methylation profile may play a role in regulating signalling pathways with specific functions in the two subgroups of ER-BC.

Many problems in the fields of finance and actuarial science can be transformed into the problem of solving backward stochastic differential equations (BSDE) and partial differential equations (PDE) with jumps, which are often difficult to solve in high-dimensional cases. To solve this problem, this paper applies the deep learning algorithm to solve a class of high-dimensional nonlinear partial differential equations with jump terms and their corresponding backward stochastic differential equations (BSDE) with jump terms. Using the nonlinear Feynman-Kac formula, the problem of solving this kind of PDE is transformed into the problem of solving the corresponding backward stochastic differential equations with jump terms, and the numerical solution problem is turned into a stochastic control problem. At the same time, the gradient and jump process of the unknown solution are separately regarded as the strategy function and they are approximated respectively by using two multilayer neural networks as function approximators. Thus, deep learning-based method is used to overcome the “curse of dimensionality” caused by high-dimensional PDE with jump, and the numerical solution is obtained. In addition, this paper proposes a new optimization algorithm based on the existing neural network random optimization algorithm, and compares the results with the traditional optimization algorithm, and achieves good results. Finally, the proposed method is applied to three practical high-dimensional problems: Hamilton-Jacobi-Bellman equation, bond pricing under the jump Vasicek model and high-dimensional option pricing model with default risk. The proposed numerical method has obtained satisfactory accuracy and efficiency. The method has important application value and practical significance in investment decision-making, option pricing, insurance and other fields.

The article is devoted to applications of 2-dimensional hyperbolic numbers and their algebraic 2ⁿ-dimensional extensions in modeling some genetic and cultural phenomena. Mathematical properties of hyperbolic numbers and their bisymmetric matrix representations are described in a connection with their application to analyze the following structures: alphabets of DNA nucleobases; inherited phyllotaxis phenomena; Punnett squares in Mendelian genetics; the psychophysical Weber-Fechner law; long literary Russian texts (in their special binary representations). New methods of algebraic analysis of the harmony of musical works are proposed, taking into account the innate predisposition of people to music. The hypothesis is put forward that sets of eigenvectors of matrix representations of basis units of 2ⁿ-dimensional hyperbolic numbers play an important role in transmitting biological information. A general hyperbolic rule regarding the oligomer cooperative organization of different genomes is described jointly with its quantum-information model. Besides, the hypothesis about some analog of the Weber-Fechner law for sequences of spikes in single nerve fibers is formulated. The proposed algebraic approach is connected with the theme of the grammar of biology and applications of bisymmetric doubly stochastic matrices. Applications of hyperbolic numbers reveal hidden interrelations between structures of different biological and physical phenomena. They lead to new approaches in mathematical modeling genetic phenomena and innate biological structures.

Fokker-Planck PDEs (incl. diffusions) for stable Lévy processes (incl. Wiener processes) on the joint space of positions and orientations play a major role in mechanics, robotics, image analysis, directional statistics and probability theory. Exact analytic designs and solutions are known in the 2D case, where they have been obtained using Fourier transform on $SE(2)$. Here we extend these approaches to 3D using Fourier transform on the Lie group $SE(3)$ of rigid body motions. More precisely, we define the homogeneous space of 3D positions and orientations $\mathbb{R}^{3}\rtimes S^{2}:=SE(3)/(\{\mathbf{0}\} \times SO(2))$ as the quotient in $SE(3)$. In our construction, two group elements are equivalent if they are equal up to a rotation around the reference axis. On this quotient we design a specific Fourier transform. We apply this Fourier transform to derive new exact solutions to Fokker-Planck PDEs of $\alpha$-stable Lévy processes on $\mathbb{R}^{3}\rtimes S^{2}$. This reduces classical analysis computations and provides an explicit algebraic spectral decomposition of the solutions. We compare the exact probability kernel for $\alpha = 1$ (the diffusion kernel) to the kernel for $\alpha=\frac12$ (the Poisson kernel). We set up SDEs for the Lévy processes on the quotient and derive corresponding Monte-Carlo methods. We verify that the exact probability kernels arise as the limit of the Monte-Carlo approximations.

In this paper, we obtain the existence and uniqueness theorem for solutions of Caputo type fractional stochastic delay differential systems (FSDDSs) with Poisson jumps by utilizing delayed perturbation of Mittag-Leffler function. Moreover, by using Burkholder-Davis-Gundy's inequality, Doob's martingale inequality and Holder inequality, we prove that the solution of the averaged FSDDSs converges to that of the standard FSDDSs in the sense of Lp. Some known results in the literature are extended.

Continuous greenhouse gas emissions are causing global warming and impacting the habitats of many animals. Researchers in the field of electric power are making efforts to mitigate this situation. Operating and maintaining the power grid in an economic, low-carbon, and stable is challenging. To address the issue, we propose a grid dispatching technique that combines prediction technology, reinforcement learning, and optimization technology. Prediction technology can forecast future power demand and solar power generation, while reinforcement learning and optimization technology can make charging and discharging decisions for energy storage devices based on current and future grid conditions. In the power system, the aggregation of distributed energy resources increases uncertainty, particularly due to the fluctuating generation of renewable energy. This requires the use of advanced predictive control techniques to ensure long-term economic and decarbonization goals. In this paper, we present a real-time dispatching framework that integrates deep learning-based prediction, reinforcement learning-based decision-making, and stochastic optimization techniques. The framework can rapidly adapt to target uncertainty caused by various factors in real-time data distribution and control processes. The proposed framework achieved global Champion in the NeurIPS Challenge 2022 competition and demonstrated its effectiveness in practical scenarios of intelligent building energy management.

Results from a behavioral economic laboratory experiment are used to enhance our understanding of public health decisions made during the COVID-19 pandemic. The identification of systematic biases from optimal decision theory found in controlled experiments could help inform public policy design for future public health crises. The laboratory and the shelter-in-place decisions made during COVID-19 included elements of risk, uncertainty and ambiguity. The lab findings found individuals adopt different decision rules depending on both personal attributes and on the context and environment in which the decision task is conducted. Key observations to consider in the context of the COVID-19 decision environment include the importance of past experience, the ability to understand and calculate the odds of each action, the size and differences in economic payoffs given the choice, the value of information received, and how past statistical independent outcomes influence future decisions. The academic space encompassing both public health and behavioral economics is small, yet important, particularly in the current crisis. The objective of continued research in this area would be to develop a more representative model of decision-making processes, particularly during crisis, that would serve to enhance future public health policy design.

The article shows materials to the question about algebraic features of the genetic code and about the dictatorial influence of the DNA and RNA molecules on the whole organism. Presented results testify in favor that the genetic code is an algebraic code related with a wide class of algebraic codes, which are a basis of noise-immune coding of information in communication technologies. Structural features of the genetic systems are associated with hypercomplex double (or hyperbolic) numbers and with bisymmetric doubly stochastic matrices. The received results confirm that represented matrix approaches are effective for modeling genetic phenomena and revealing the interconnections of structures of biological bodies at various levels of their organization. This allows one to think that living organisms are algebraically encoded entities where structures of genetic molecules have the dictatorial influence on inherited structures of the whole organism. New described algebraic approaches and results are discussed.

In recent times, with the increase of Artificial Neural Network (ANN), deep learning has brought a dramatic twist in the field of machine learning by making it more Artificial Intelligence (AI). Deep learning is used remarkably used in vast ranges of fields because of its diverse range of applications such as surveillance, health, medicine, sports, robotics, drones etc. In deep learning, Convolutional Neural Network (CNN) is at the center of spectacular advances that mixes Artificial Neural Network (ANN) and up to date deep learning strategies. It has been used broadly in pattern recognition, sentence classification, speech recognition, face recognition, text categorization, document analysis, scene, and handwritten digit recognition. The goal of this paper is to observe the variation of accuracies of CNN to classify handwritten digits using various numbers of hidden layer and epochs and to make the comparison between the accuracies. For this performance evaluation of CNN, we performed our experiment using Modified National Institute of Standards and Technology (MNIST) dataset. Further, the network is trained using stochastic gradient descent and the backpropagation algorithm.

Fluctuation theorems are a class of equalities each of which links a thermodynamic path functional such as heat and work to a state function such as entropy and free energy. Jinwoo and Tanaka [L. Jinwoo and H. Tanaka, Sci. Rep. 5, 7832 (2015)] have shown that each microstate of a fluctuating system can be regarded as an ensemble (or a 'macrostate') if we consider trajectories that reach each microstate. They have revealed that local forms of entropy and free energy are true thermodynamic potentials of each microstate, encoding heat, and work, respectively, within an ensemble of paths that reach each state. Here we show that information that is characterized by the local form of mutual information between two subsystems in a heat bath is also a true thermodynamic potential of each coupled state and encodes the entropy production of the subsystems and heat bath during a coupling process. To this end, we extend the fluctuation theorem of information exchange [T. Sagawa and M. Ueda, Phys. Rev. Lett. 109, 180602 (2012)] by showing that the fluctuation theorem holds even within an ensemble of paths that reach a coupled state during dynamic co-evolution of two subsystems.

Research within the field of hydrology often focuses on comparing stochastic to machine learning (ML) forecasting methods. The comparisons performed are all based on case studies, while an extensive study aiming to provide generalized results on the subject is missing. Herein, we compare 11 stochastic and 9 ML methods regarding their multi-step ahead forecasting properties by conducting 12 large-scale computational experiments based on simulations. Each of these experiments uses 2 000 time series generated by linear stationary stochastic processes. We conduct each simulation experiment twice; the first time using time series of 100 values and the second time using time series of 300 values. Additionally, we conduct a real-world experiment using 405 mean annual river discharge time series of 100 values. We quantify the performance of the methods using 18 metrics. The results indicate that stochastic and ML methods perform equally well.

It is strongly desirable to accurately detect the clouds in hyperspectral images onboard before compression. However, conventional onboard cloud detection methods are not appropriate to all situation such as shadowed cloud or darken snow covered surfaces which are not identified properly in the NDSI test. In this paper, we propose a new spectral–spatial classification strategy to enhance the orbiting cloud screen performances obtained on hyperspectral images by integrating threshold exponential spectral angle map (TESAM), adaptive Markov random field (aMRF) and dynamic stochastic resonance (DSR). TESAM is performed to classify the cloud pixels coarsely based on spectral information. Then aMRF is performed to do optimal process by using spatial information, which improved the classification performance significantly. Some misclassification points still exist after aMRF processing because of the noisy data in the onboard environment. DSR is used to eliminate misclassification points in binary labeling image after aMRF. Taking level 0.5 data from hyperion as dataset, the average overall accuracy of the proposed algorithm is 96.28% after test. The method can provide cloud mask for the on-going EO-1 images and related satellites with the same spectral settings without manual intervention. The experiment indicate that the proposed method reveals better performance than the classical onboard cloud detection or current state-of-the-art hyperspectral classification methods.

This paper proposes a new dynamic analysis of reasoning. It makes the following contributions. First, the current states of the psychology of reasoning are critically reviewed from theoretical and empirical perspectives. The long-standing controversies between logicians and psychologists are clarified by introducing the gauge theoretic structure. The debates between the mental logic theory and the mental models theory are carefully reviewed by identifying the problem types used in the empirical studies. Certain mental fluctuations are found and a quantum theoretic solution is examined. Second, it solves the measurement problem within the Hamiltonian framework. The modeling structure underlying reasoning dynamics is the electrodynamics. They are both the single-charge dynamic systems sharing the U(1) symmetry. The mental logic theory and the mental models theory are now characterized as wavefunctions in a unified account of the dynamic analysis with the yes/no measurements. The stochastic sampling method is introduced to solve the measurement problem, which has a wide range of applications in social sciences. Third, a novel metatheoretic framework of reasoning dynamics within Lagrangian framework is proposed. It solves the “Man vs. Men” problem via gauge theoretic modeling, by making the distinction between the global level and the local level. At each level, the gauge transformations are applied to achieve the global symmetry and the local gauge symmetry. It explains the meanings of the gauge principle and the Nether theorem. Fourth, the special theory of relativity is applied to address the “Man vs. Men” problem. It explains how to draw the global language cone and the individualized local language cones. Finally, it points out that borrowing modeling methods from physics has a long tradition in psychology. The present work utilizes the conceptual and modeling methods found in modern theoretical physics.

A Demand-side management technique are deployed along with battery energy-storage systems (BESSs) to lower the electricity cost by mitigating the peak load of a building. Most of the existing methods rely on manual operation of the BESS, or even an elaborate building energy-management system resorting to a deterministic method that is susceptible to unforeseen growth in demand. In this study we propose a real-time optimal operating strategy for BESS based on density demand forecast and stochastic optimization. This method takes into consideration uncertainties in demand when accounting for an optimal BESS schedule, making it robust compared to the deterministic case. The proposed method is verified and tested against existing algorithms. Data obtained from a real site in South Korea is used for verification and testing. The results show that the proposed method is effective, even for the cases where the forecasted demand deviates from the observed demand

Iterative Stochastic decoding is an alternative to standard fixed-point decoding of Low-density parity check codes (LDPC) to reduce inter-node routing. In this paper, we propose a Flexible Field-Programmable Gate Array (FPGA)-Based Stochastic decoding (SD) hardware architecture for LDPC codes in the Fifth-Generation (5G) New Radio (NR) Standard that supports decoding of set of various code rates. This decoder’s runtime flexibility is desirable to switch a better performing code rate automatically based on the channel conditions without the extra time needed for reprogramming of FPGA. An offline design method is implemented to generate the hardware description language (HDL) code description of the decoder for the required code-rate set, which is further synthesized and integrated into the Xilinx Kintex-7 series FPGA board to determine the hardware resource utilisation and processing throughput. The Synopsys design tools were employed during both the simulation and synthesis stages, in combination with TSMC 65-nm CMOS standard cell technology, to facilitate comparative analysis. Compared with state-of-the-art designs, the proposed architecture reduces hardware utilization by up to 26% and achieved energy efficiency by 52%.

In this paper, we identify several relative ordering properties of the modified proportional hazard rate and modified proportional reversed hazard rate models. For this purpose, we use two well-known relative orderings, namely the relative hazard rate ordering and the relative reversed hazard rate ordering. The investigation is to see how a relative ordering between two possible base distributions for the response distributions in these models is preserved when the parameters of the underlying models are changed. We will give some examples to illustrate the results and the conditions under which they are obtained.

In this manuscript we use an exactly solvable stochastic binary model for regulation of gene expression to analyse the dynamics of response to a treatment aiming to modulate the number of transcripts of RKIP gene. We demonstrate the usefulness of our method simulating three treatment scenarios aiming to reestablish RKIP gene expression dynamics towards pre-cancerous state: i. to increase the promoter’s ON state duration; ii. to increase the mRNAs’ synthesis rate; iii. to increase both rates. We show that the pre-treatment kinetic rates of ON and OFF promoter switching speeds and mRNA synthesis and degradation will affect the heterogeneity and time for treatment response. Hence, we present a strategy for reducing drug dosage by simultaneously targeting multiple kinetic rates. That enables a reduction of treatment response time and heterogeneity which in principle diminishes the chances of emergence of resistance to treatment. This approach may be useful for inferring kinetic constants related to expression of antimetastatic genes or oncogenes and on the design of multi-drug therapeutic strategies targeting master regulatory genes.

Classical models of gene expression were built using genetics and biochemistry. Although these approaches are powerful, they have very limited consideration of the spatial and temporal organization of gene expression. Although the spatial organization and dynamics of RNA polymerase II (RNAPII) transcription machinery has fundamental functional consequences for gene expression, its detailed studies have been for long time abrogated by the limits of classical light microscopy. The advent of super-resolution microscopy (SRM) techniques allowed for the visualization of the RNAPII transcription machinery with nanometer resolution and millisecond precision. In this review, we summarize the recent methodological advances in SRM, focus on its application for studies of the nanoscale organization in space and time of RNAPII transcription, and discuss its consequences for the mechanistic understanding of gene expression.

The evaluation of geometric defects is necessary in order to maintain the integrity of structures over time. These assessments are designed to detect damages of structures and ideally help inspectors to estimate the remaining life of structures. Current methodologies for monitoring structural systems, while providing useful information about the current state of a structure, are limited in the monitoring of defects over time and in linking them to predictive simulation. This paper presents a new approach to the predictive modeling of geometric defects. A combination of segmented from point clouds are parametrized using the convex hull algorithm to extract features from detected defects, and a stochastic dynamic model is then adapted to these features to model the evolution of the hull over time. Describing a defect in terms of its parameterized hull enables consistent temporal tracking for predictive purposes, while implicitly reducing data dimensionality and complexity as well. In this study, 2D point clouds analogous to information derived from point clouds were first generated over simulated life-cycles. The evolutions of point cloud hull parameterizations were modeled as stochastic dynamical processes via autoregressive integrated moving average (ARIMA) and vectorized autoregression (VAR) and compared against ground truth. The results indicate that this convex hull approach provides consistent and accurate representations of defect evolution across a range of defect topologies and is reasonably robust to noisy measurements, however assumptions regarding the underlying dynamical process play a significant the role in predictive accuracy. The results were then validated on experimental data from fatigue testing with high accuracy. Longer term, the results of this work will support finite element model updating for predictive analysis of structural capacity.

A system of two nonlinear difference equations under stochastic perturbations is considered. Nonlinearity of the exponential type in each equation of the system under consideration depends on all variables of the system. The stability in probability of a positive equilibrium of the system is studied via the general method of Lyapunov functionals construction and the method of linear matrix inequalities (LMIs). The obtained results are illustrated via examples and figures with numerical simulations of solutions of a considered system of stochastic difference equations. The proposed way of investigation can be applied to nonlinear systems of higher dimension and with other types of nonlinearity, for both difference equations and for delay differential equations.

Demographic change is leading to the aging of German society. As long as the baby boom co-horts are still of working age, the working population will also age - and decline as soon as this baby boom generation gradually reaches retirement age. At the same time, there has been a trend towards increasing absenteeism (times of inability to work) in companies since the zero years, with the number of days of absence increasing with age. We present a novel stochastic forecast approach that combines population forecasting with forecasts of labor force participation trends, considering epidemiological aspects. For this, we combine a stochastic Monte Carlo-based cohort-component forecast of the population with projections of labor force participation rates and morbidity rates. This article examines the purely demographic effect on the economic costs associated with such absenteeism due to the inability to work. Under expected future employment patterns and constant morbidity patterns, absenteeism is expected by close to 5 percent by 2050 relative to 2020, associated with increasing economic costs of almost 3 percent. Our results illustrate how strongly the pronounced baby boom/ baby bust phenomenon determines demographic development in Germany in the midterm.

Summary: Studying biological systems generally relies on computational modeling and simulation, e.g., for model-driven discovery and hypothesis testing. Progress in standardization efforts led to the development of interrelated file formats to exchange and reuse models in systems biology, such as SBML, the Simulation Experiment Description Markup Language (SED-ML), or the Open Modeling EXchange format (OMEX). Conducting simulation experiments based on these formats requires efficient and reusable implementations to make them accessible to the broader scientific community and to ensure the reproducibility of the results. The Systems Biology Simulation Core Library (SBSCL) provides interpreters and solvers for these standards as a versatile open-source API in Java™. The library simulates even complex bio-models and supports deterministic Ordinary Differential Equations (ODEs); Stochastic Differential Equations (SDEs); constraint-based analyses; recent SBML and SED-ML versions; exchange of results, and visualization of in silico experiments; open modeling exchange formats (COMBINE archives); hierarchically structured models; and compatibility with standard testing systems, including the Systems Biology Test Suite and published models from the BioModels and BiGG databases. Availability and implementation: SBSCL is freely available at https://draeger-lab.github.io/SBSCL/.

Paratemporal methods based on tree expansion have proven to be effective in efficiently generating trajectories of stochastic systems. However, combinatorial explosion of branching arising from multiple choice points presents a major hurdle that must be overcome to implement such techniques. In this paper we tackle this scalability problem by developing a systems theory-based framework covering both conventional and proposed tree expansion algorithms for speeding up discrete event system stochastic simulations while preserving desired accuracy. An example is discussed to illustrate the tree expansion framework in which a discrete event system specification (DEVS) Markov stochastic model takes the form of a tree isomorphic to a free monoid over the branching alphabet. We derive the computation times for baseline, non-merging, and merging tree expansion algorithms to compute the distribution of output values at any given depth. The results show the remarkable reduction from exponential to polynomial dependence on depth effectuated by node merging. We relate these results to the similarly reduced computation time of binomial coefficients underlying Pascal’s triangle. Finally, we discuss application of tree expansion to estimating temporal distributions in stochastic simulations involving serial and parallel compositions with potential real world use cases.

This article introduces a novel approach, termed the Asymmetric Probabilistic Tsetlin (APT) Machine, which incorporates the Stochastic Point Location (SPL) algorithm with the Asymmetric Steps technique into the Tsetlin Machine (TM). APT introduces stochasticity into the state transitions of Tsetlin Automata (TA) by leveraging the SPL algorithm, thereby enhancing pattern recognition capabilities. To enhance random search processes, we introduced a decaying normal distribution into the procedure. Meanwhile, the Asymmetric Steps approach biases state transition probabilities towards specific input patterns, further elevating operational efficiency. The efficacy of the proposed approach is assessed across diverse benchmark datasets for classification tasks. The performance of APT is compared with traditional machine learning algorithms and other Tsetlin Machine models, including the Asymmetric Tsetlin (AT) Machine, characterized by deterministic rules for Asymmetric transitions, and the Classical Tsetlin (CT) Machine, employing deterministic rules for symmetric transitions. Strikingly, the introduced APT methodology demonstrates highly competitive outcomes compared to established machine learning methods. Notably, both APT and AT exhibit state-of-the-art performance, surpassing the Classical Tsetlin Machine, emphasizing the efficacy of asymmetric models for achieving superior outcomes. Remarkably, APT exhibits even better performance than AT, particularly in handling complex datasets.

Regular regimes of oil and oil products pipelines are studied. The problem is to develop an algorithm of effective pipeline system control that ensures the fulfillment of specified boundary conditions at the system boundaries. The product is pumped in batches, the flow is characterized by a change in temperature and pressure flow parameters over time. The developed solution method uses the principle of decomposition in the sense that each computational iteration is im-plemented in 3 stages, in three nested loops. The inner cycle is connected with the material bal-ance relations, at the next cycle the flow equations are introduced and the fulfillment of the 2nd Kirchhoff's law is monitored. If the flow process is significantly affected by temperature, then an external cycle is also implemented, correcting the solution so that the energy conservation equa-tion is satisfied. In the calculation procedure, some computational difficulties may arise, which consist in choosing an appropriate optimization method. On a specific example, the possibility of using various library programs to solve the problem was checked. The developed method is suita-ble for the analysis of systems of arbitrary topology. Since the method is not time-consuming, it can be recommended for online control of oil and oil products supply systems. The paper opens a new direction in the theory of hydraulic circuits. It uses both traditional methods of continuum mechanics and stochastic models.

This paper develops Bayesian inference in reliability of a class of scale mixtures of log-normal failure time (SMLNFT) models with stochastic (or uncertain) constraint in their reliability measures. The class is comprehensive and includes existing failure time (FT) models (such as log-normal, log-Cauchy, and log-logistic FT models) as well as new models that are robust in terms of heavy-tailed FT observations. Since classical frequency approaches to reliability analysis based on the SMLNFT model with stochastic constraint are intractable, the Bayesian method is pursued utilizing a Markov chain Monte Carlo (MCMC) sampling based approach. This paper introduces a two-stage maximum entropy (MaxEnt) prior, which elicits a priori uncertain constraint and develops Bayesian hierarchical SMLNFT model by using the prior. The paper also proposes an MCMC method for Bayesian inference in the SMLNFT model reliability and calls attention to properties of the MaxEnt prior that are useful for method development. Finally, two data sets are used to illustrate how the proposed methodology works.

Utilizing groundwater offers a promising solution to alleviate water stress in Ethiopia, providing a dependable and sustainable water source, particularly in regions with limited or unreliable surface water availability. However, effective decision-making regarding well drilling and placement is essential to maximize groundwater resource potential, enhancing agricultural productivity, reducing hunger, and bolstering food security in Ethiopia. This study concentrates on the development of two-stage stochastic mixed integer programming (SMIP) models to optimize well placement for sustainable agricultural irrigation, considering uncertain demand scenarios. Additionally, a deterministic mixed integer programming model is formulated for comparison with the two-stage SMIP. Experiments are conducted to explore various demand scenario distributions, revealing that the optimized total cost for the two-stage SMIP generally exceeds that of a deterministic setting, aligning with the two-stage SMIP's focus on long-term benefits. Moreover, slight differences are observed in well layouts under different assumption scenarios. The study also examines the impact of selected parameters, such as fixed construction costs, per-meter drilling costs, and demand scenarios. The out-of-sample performance shows that the stochastic model is more flexible and resilient, with 11% and 4% lower costs than deterministic cases 1 and 3, respectively. This flexibility provides a more robust long-term strategy for well placement and resource allocation in groundwater management.