Nonlinear electrodynamics with two dimensional parameters is studied. The range of electromagnetic fields when principles of causality, unitarity and the classical stability hold are obtained. A singularity of the electric field at the center of charges is absent within our model and there are corrections to the Coulomb law as $r\rightarrow\infty$. The universe inflation takes place in the background of stochastic magnetic fields. The second stage of the universe evolution is the radiation era so that the graceful exit exists. We estimated the spectral index, the tensor-to-scalar ratio, and the running of the spectral index that are in an approximate agreement with the PLANK and WMAP data.

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.

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.

We address the process of discounting in random environments which allows to value the far future in economic terms. We review several approaches to the problem regarding different well-established stochastic market dynamics in the continuous-time context and include the Feynman-Kac approach. We also review the relation between bond pricing theory and discount and introduce the market price of risk and the risk neutral measures from an intuitive point of view devoid of excessive formalism. We provide the discount for each economic model and discuss their key results. We finally present a summary of our previous empirical studies on several countries of the long-run discount problem.

A thermal load dispatch problem minimizes the number of objectives viz operating cost and emission of gaseous pollutants together while allocating the power demand among the committed generating units subject to physical and technological system constraints. A stochastic thermal load dispatch problem is undertaken while taking into consideration, the uncertainties, errors in data measurements and nature of load demand which is random. Owing to uncertain load demand, variance due to mismatch of power demand termed as risk, is considered as another conflicting objective to be minimized. Generally multiobjective problems generate a set of non-inferior solutions are generated and supplied to a decision maker to select the best solution from the set of non-inferior solutions. This paper proposes opposition-based greedy heuristic search (OGHS) method to generate a set of non-inferior solutions. Opposition-based learning is applied to generate initial population to select good candidates. Migration to maintain diversity in the set of feasible solutions is also based on opposition-based learning. Mutation strategy is implemented by perturbing the genes heuristically in parallel and better one solution is sought for each member. Feasible solutions are achieved heuristically by modifying the generation-schedules in such a manner that violation of operating generation limits are avoided. The OGHS method is simple to implement and provides global solutions derived from the randomness of the population generated without tuning of parameters. Decision maker exploits fuzzy membership functions to decide the final decision. Validity of the method has been demonstrated by analysing systems in different scenarios consisting of six generators and forty generators.

A single Information security is of pivotal concern for consistently streaming information over the widespread internetwork. The bottleneck flow of incoming and outgoing data traffic introduces the issue of malicious activities taken place by intruders, hackers and attackers in the form of authenticity desecration, gridlocking data traffic, vandalizing data and crashing the established network. The issue of emerging suspicious activities is managed by the domain of Intrusion Detection Systems (IDS). The IDS consistently monitors the network for identifica-tion of suspicious activities and generates alarm and indication in presence of malicious threats and worms. The performance of IDS is improved by using different signature based machine learning algorithms. In this paper, the performance of IDS model is determined using hybridization of nestrov-accelerated adaptive moment estimation –stochastic gradient descent (HNADAM-SDG) algorithm. The performance of the algorithm is compared with other classi-fication algorithms as logistic regression, ridge classifier and ensemble algorithm by adapting feature selection and optimization techniques

We present a class of efficient parametric closure models for 1D stochastic Burgers equations. Casting it as statistical learning of the flow map, we derive the parametric form by representing the unresolved high wavenumber Fourier modes as functionals of the resolved variables’ trajectory. The reduced models are nonlinear autoregression (NAR) time series models, with coefficients estimated from data by least squares. The NAR models can accurately reproduce the energy spectrum, the invariant densities, and the autocorrelations. Taking advantage of the simplicity of the NAR models, we investigate maximal and optimal space-time reduction. Reduction in space dimension is unlimited, and NAR models with two Fourier modes can perform well. The NAR model’s stability limits time reduction, with a maximal time step smaller than that of the K-mode Galerkin system. We report a potential criterion for optimal space-time reduction: the NAR models achieve minimal relative error in the energy spectrum at the time step where the K-mode Galerkin system’s mean CFL number agrees with the full model’s.

We apply the stochastic thermodynamics formalism to describe the dynamics of systems of complex Langevin and Fokker-Planck equations. We provide in particular a simple and general recipe to calculate thermodynamical currents, dissipated and propagating heat for networks of nonlinear oscillators. By using the Hodge decomposition of thermodynamical forces and fluxes, we derive a formula for entropy production that generalises the notion of non-potential forces and makes transparent the breaking of detailed balance and of time reversal symmetry for states arbitrarily far from equilibrium. Our formalism is then applied to describe the off-equilibrium thermodynamics of a few examples, notably a continuum ferromagnet, a network of classical spin-oscillators and the Frenkel-Kontorova model of nano friction.

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.

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%.

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.

Porous materials can be characterized by well-trained neural networks. In this study, fibrous paper-type gas diffusion layers were trained with artificial data created by a stochastic geometry model. The features of the data were calculated by means of transport simulations using the Lattice–Boltzmann method based on stochastic micro-structures. A convolutional neural network was developed that can predict the permeability and tortuosity of the material, through-plane and in-plane. The characteristics of real data, both uncompressed and compressed, were predicted. The data was represented by reconstructed images of different sizes and image resolutions. Image artifacts are also a source of potential errors in the prediction. The Kozeny–Carman trend was used to evaluate the prediction of permeability and tortuosity of compressed real data. Using this method, it was possible to decide if the predictions on compressed data were appropriate.

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.

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.

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.

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.

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.

Real assets in the energy market are subject to ecological uncertainty due to the penetration of renewables. We illustrate this point by analysing electrolysers, a class of assets which recently became the subject of a large interest, as they lead to the production of the desirable green hydrogen and green ammonia. The latter has the advantage of being easily stored and has huge potential in decarbonising both the fertilizer and shipping industries. We consider the optimization of green ammonia production with different types of electricity procurement in the context of stochastic power and ammonia markets, a necessary assumption to translate the features of renewable, hence intermittent, electricity. We emphasise the importance of using stochastic prices to effectively model the volatile nature of the price dynamics, illustrating the project risks that can be mitigated by hedging activities. This study shows the pivotal role of flexibility when dealing with fluctuating renewable production and volatile electricity prices to maximise profits and better manage risks.

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.

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.

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 world population is aging, which along with recent shifts in the labor force participation (LFP), is having a significant longevity influence on state pension programs across the board, including Canada, Finland, Japan, and Germany. Except Japan, these countries have set their statutory re-tirement age at 65, but the impact of aging workforce and declined fertility rates create wonders on the estimate future trends in the LFP, as well as the length of retirement. In this study, we fit the LFP rates of these countries, representing continents from Asia, Europe and North America among the OECD countries, using the Lee-Carter and Cairns-Blake-Dowd (CBD) stochastic models. The es-timates are then used for the projection of future LFP rates (1989-2066), and by combining the mortality forecasts from the United Nations, we project the expected length of retirement (1989-2066). This study provided a novel comparison between the Lee-Carter and the CBD LFP models by fitting and forecasting the LFP rates of senior employees between 50- to 74-year-olds. The results revealed disparities between models that provided proof of the presence of model risk for longer retirement durations. The study findings emphasized the importance for decision-makers in pension industry to have awareness of potential risks and limits associated with the LFP models. The Lee-Carter model outperformed the CBD model even though the CBD model is known for its ac-curate prediction in higher ages. Population aging should be considered in any analysis of the long-term viability of pensions, together with the participation rate trends for a sustainable labor market future.

The ageing global population and changing labor force participation are having a profound impact on state pension programs worldwide, including Malaysia. However, the effects of an ageing workforce and declining fertility rates are having a significant impact on future trends in labor force participation and the duration of retirement. This paper presents an innovative examination of labor force participation rate (LFPR) forecasting within the context of an aging workforce, utilizing the Lee-Carter and Cairns-Blake Dowd stochastic models, traditionally applied to mortality data. By adapting these models to LFPR data, the study offers a novel perspective on predicting workforce participation trends and understanding the dynamics of retirement planning from year 2001 to 2047. Additionally, by incorporating the mortality forecasts from the United Nations, the research navigates through the complexities of applying actuarial methods to labor economics, revealing differentiated pathways for male and female participation in the labor market and the anticipated length of retirement. This study offers a unique comparison between the Lee-Carter and the Cairns-Blake-Dowd (CBD) LFPR models. It focuses on fitting and forecasting the LFPR of senior employees aged 50 to 64. The results highlighted discrepancies among models that demonstrated evidence of model risk for extended retirement duration.

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.

ABSTRACT The present study aimed to investigate the presence of asymmetric stochastic volatility and leverage effects within the Nasdaq-100 index. This index is widely regarded as an important indicator for investors. We focused on the nine leading stocks within the index, which are highly popular and hold significant weight in the investment world. These stocks are Netflix, PayPal, Google, Intel, Microsoft, Amazon, Tesla, Apple, and Meta. The study covered the period between 03/01/2017 and 30/01/2023, and we employed the Eviews and WinBUGS applications to conduct the analysis. We began by calculating the logarithmic difference to obtain the return series. We then performed a sample test with 100,000 iterations, excluding the first 10,000 samples to eliminate the initial bias of the coefficients. This left us with 90,000 samples for analysis. Using the results of the asymmetric stochastic volatility model, we evaluated both the Nasdaq-100 index as a whole and the volatility persistence, predictability, and correlation levels of individual stocks. This allowed us to evaluate the ability of individual stocks to represent the characteristics of the Nasdaq-100 index. Our findings revealed a dense clustering of volatility, both for the Nasdaq-100 index and the nine individual stocks. We observed that this volatility is continuous but has a predictable impact on variability. Moreover, with the exception of Intel, all the stocks in the model exhibited both leverage effects and the presence of asymmetric relationships, as did the Nasdaq-100 index as a whole. Overall, our results show that the characteristics of stocks in the model are similar to the volatility characteristic of the Nasdaq-100 index and have the ability to represent it.

In this paper we present a successful implementation of the Hindmarsh–Rose model within a SC environment. The merits of the proposed approach are design simplicity, due to stochastic computing, and the ease of implementation. Simulation results showed that the approximation achieved is equivalent to introducing a noise source into the original model. A study for the level of noise introduced, according to the number of bits in the stochastic sequence, has been performed. Additionally, we demonstrate that such an approach, even though it is noisy, it reproduces the behaviour of biological systems, which are intrinsically noisy. It is also demonstrated that a speedup of x2 compared to biological systems is easily achievable, with a very small number of gates, thus paving the road for the in silico implementation of large neuron networks.

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.

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.

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.

Machinery parts gradually wear out over time due to regular usage. To improve machinery health and prevent critical issues, a reliable prognosis framework can be implemented by monitoring the behaviour of machinery parts and issuing warnings before they reach a critical state. To achieve this, vibration data from roller bearings experiencing various fault conditions have been collected. Different techniques from the literature were combined to analyze the distinct configurations in the vibration data sets and identify the main defects in roller bearings. The significant features extracted from this analysis were then used to create optimized stochastic model equations, separately regressing inner and outer race fault features to healthy bearing features under random conditions. These models can help engineers design more dependable systems, optimize their performance, and minimize the risk of failures and downtime.

A stochastic dominance (SD) relation can be defined by two different perspectives: One from the view of distributions, and the other one from the view of expected utilities. In early days, Fishburn investigated SD from the view of distributions and we refer this perspective as Fishburn’s SD. One of his many results was the development of fractional-order SD for continuous distributions. However, discrete fractional-order SD may not be generalized directly since some properties of fractional calculus do not have a discrete counterpart. In this paper, we develop a discrete analogue of fractional-order SD from the view of distributions. We generalize the order of SD by Lizama’s fractional delta operator, show the preservation of SD hierarchy, and formulate the utility classes that are congruent with our SD relations. This work brings a message that some results of discrete SD cannot be generalized directly from continuous SD. We characterize the difference between discrete and continuous fractional-order SD, as well as the way to handle them.

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.

Stochastic mortality models seek to forecast future mortality rates; thus, apparently the objective variable should be the mortality rate expressed in the original scale. However, the performance of stochastic mortality models - in terms, that is, of their goodness-of-fit and prediction accuracy - is often based on the logarithmic scale of the mortality rate. In this article, we examine whether the same forecast outcomes are obtained when the performance of mortality models is assessed based on the original and log scales of the mortality rate. We compare four different stochastic mortality models: the original Lee-Carter model, the Lee-Carter model with (log-)normal distribution, the Lee-Carter model with Poisson distribution and the median Lee-Carter model. We show that the preferred model will depend on the scale of the objective variable, the selection criteria measure and the range of ages analysed.

As a model for economic and ecological systems, replicator dynamics represents a basic form of agent competition for finite resources. Here, we investigate the effects of stochastic resetting in this kind of processes. Random reset events abruptly lead individual resources to a small value from which dynamics must start anew. Numerical results show that resource distribution over the population of competing agents develops highly nonuniform profiles, exhibiting clustering and fluctuations with anomalous dependence on the population size. This non-standard statistical behavior jeopardizes an analytical treatment based on mean-field assumptions. We propose alternative simplified analytical approaches which provide a stylized description of entropy evolution for the clustered distribution of resources and explain the unusually slow decrease of fluctuations.

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.

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.

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.

We introduce a novel stochastically correlated two-factor (i.e., bivariate) diffusion process under the square-root format, for which we obtained, analytically, the corresponding solutions for the conditional moment generating functions and conditional characteristic functions. Such solutions recover verbatim those of the uncorrelated case. We believe that the The aforementioned model encompasses a range of processes similar to that produced by a bivariate square-root process in which entries are correlated in the standard way, i.e., via a constant correlation coefficient. Note that, for the latter, closed-form solutions for the conditional characteristic functions are not available. We focus on the financial scenario of obtaining closed-form expressions for the exact price of a zero-coupon bond and Asian option prices via a Fourier cosine series method.

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.

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.

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.

When there is uncertainty in the value of parameters of the input random components of a stochastic simulation model, two-level nested simulation algorithms are used to estimate the expectation of performance variables of interest. In the outer level of the algorithm (n) observations are generated for the parameters, and in the inner level (m) observations of the simulation model are generated with the value of parameters fixed at the value generated in the outer level. In this article, we consider the case in which the observations at both levels of the algorithm are independent, showing how the variance of the observations can be decomposed into the sum of a parametric variance and a stochastic variance. Next, we derive central limit theorems that allow us to compute asymptotic confidence intervals to assess the accuracy of the simulation-based estimators for the point forecast and the variance components. Under this framework, we derive analytical expressions for the point forecast and the variance components of a Bayesian model to forecast sporadic demand; and we use these expressions to illustrate the validity of our theoretical results by performing simulation experiments using this forecast model.

The classical Lotka-Volterra predator-prey model is globally stable and uniformly persistent. However, in real-life biosystems extinction of species due to stochastic effects is possible. In this paper, we consider the classical Lotka-Volterra predator-prey model under stochastic perturbations. For this model, using an analytical technique based on the direct Lyapunov method and a development of the ideas of R.Z. Khasminskii, we find the precise sufficient conditions for the stochastic extinction of one and both species and the precise necessary conditions for the stochastic system persistence. The stochastic extinction occurs via a process known as the stabilization by noise of the Khasminskii type, and, in order to establish the sufficient conditions for extinction, we found the conditions for the stabilization. The analytical results are illustrated by numerical simulations. {\bf Keywords:} stochastic perturbations, white noise, Ito's stochastic differential equation, the Lyapunov functions method, stability in probability, stabilization by noise, stochastic extinction, persistence.

This paper is concerned with variational methods for open quantum systems with Markovian dynamics governed by Hudson-Parthasarathy quantum stochastic differential equations. These QSDEs are driven by quantum Wiener processes of the external bosonic fields and are specified by the system Hamiltonian and system-field coupling operators. We consider the system response to perturbations in these operators and introduce a transverse Hamiltonian which encodes the propagation of the perturbations through the unitary system-field evolution. This approach provides an infinitesimal perturbation analysis tool which can be used for the development of optimality conditions in quantum control and filtering problems. Such settings employ, as performance criteria, quadratic (or more complicated) cost functionals of the system and field variables to be minimised over the energy and coupling parameters of system interconnections. We demonstrate an application of the transverse Hamiltonian variational approach to a mean square optimal coherent quantum filtering problem for a measurement-free field-mediated cascade connection of a quantum system with a quantum observer.

The distribution laws of various natural and anthropogenic processes in the world around us are stochastic in nature. The development of mathematics and, in particular, of stochastic modelling allows us to study regularities in such processes. In practice, stochastic modelling finds a huge number of applications in various fields, including finance and economics. In this work, some particular applications of stochastic processes in finance are examined in the conditions of financial crisis. More specifically, Autoregressive Integrated Moving Average (ARIMA) models and Modified Ordinary Differential Equations (ODE) models, which have been previously developed by the authors to predict assets’ prices of four Bulgarian companies, are validated on a time period during the crisis. Estimated rates of return are calculated from the models for one period ahead. The errors are estimated and the models are compared. The predicted return values with each of the two approaches are used to derive optimal risk portfolios based on the Markowitz Model. The resulting portfolios are compared in terms of distribution (weights of the stocks), risk and rate of return.

The stochastic modelling of chemical physical processes is essentially based on a coarse-grained formulation of fluctuations, usually described by means of Wiener processes. By taking the paradigmatic example of chemical reaction kinetics, we propose a simple representation of microscopic stochastic dynamics grounded on the use of distributional derivatives of counting processes that account for elementary reactive events. This approach is consistent with the statistical analysis based on the Chemical Master Equation, and provides the formal setting for the existing algorithmic approaches (Gillespie algorithm). Some practical advantages of this formulation are addressed, and several other examples are discussed in connection with cluster formation, velocity fluctuations in liquid systems, and quantum transitions (radiative interactions) at the molecular level.

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.

Starting from the analysis of the lack of positivity of the Cattaneo heat equation, the article addresses the thermodynamic relevance of the positivity constraint in irreversible thermodynamics, than is at least as important as the entropic constraints. The fulfillment of this condition in hyperbolic models leads to the parametrization of the concentration fields with respect to internal variables associated with the microscopic dynamics. Using Brownian motion theory as a landmarking example for deriving macroscopic transport equations from the equations of motion at the particle/molecular level, we discuss two typical problems involving hydrodynamic interactions at microscale: surface chemical reactions at a solid interface of a diffusing reactant, and mass-balance equations in a complex viscoelastic fluid, in which the physics of the interaction leads either to the overcome the parabolic diffusion model or to consider the parametrization of the concentration with respect to the degrees of freedom associated with the relaxation dynamics of the solvent fluid.

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.

Discretization in time and in the state space of the system leads to the necessity to solve the parameter identification problems for dynamic systems in a limited time (at a finite time interval) using observations obtained under the influence of unknown-but-bounded noise. Finding the solution in this case is more difficult compared to traditional identification problem setting which considers random independent zero-mean noise. For system parameter identification problem under unknown-but-bounded noise, a randomized stochastic optimization algorithm is given in the paper, estimates for the mean square values of the residuals for a finite observation interval are obtained. An example of application of the given method to the problem of tuning the parameters of a multi-mirror telescope is considered.

In a recent article, the author derived a new generalized Langevin equation and its associated Fokker-Planck equation of a Brownian particle in a parabolic potential where the thermal bath, consisting of $N$ harmonic oscillators, interacts bilinearly with the external field. The time needed for the system to reach a steady state is longer than that for the classical version where such an interaction is off. We find that there is a marked effect of the field-bath interaction on the average heat and entropy production of the bath represented through strong oscillations in such properties. The new theory applied to the system should improve the physical description of previous works done with the classical approach.

In this paper we consider a failed cold standby systems and obtain some stochastic bounds on the idle time of such systems. It is assumed that, at a time t the failure of a cold standby system is observed, but the actual time of the failure is a time before t. The idle time of the inactive cold standby system is measured as the time between the exact time of failure, which is a random variable, and time t. We use the idle times of the components of the system to obtain lower and upper bounds on the lifetime of the standby system to which they are assembled. We bring some examples to show that the results and the conditions imposed to get them are achievable.

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.

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.

It is known that the source of a tectonic earthquake in the framework of the theory of elasticity and viscoelasticity is considered as a displacement along a certain fault surface. Usually, when describing the source, the geometry of the fault surface is simplified to a flat rectangular area. The displacement vector is assumed to be constant. In this paper, we propose a model of an earthquake source in the form of a displacement with a constant vector along a stochastic surface. A number of standard assumptions were made when modeling. We take into account only the elastic properties of the medium. We consider the Earth’s crust as a half-space and assume that the medium is homogeneous and isotropic. For the mathematical description of the earthquake source, we use the classical force equivalent of displacement along the fault. This is the distribution of double pairs of forces. The field of displacements under the action of body forces is found through a combination of Mindlin nuclei of strain. The paper presents solutions for strike-slip fault. To obtain a stochastic fault surface, we propose to introduce a random deformation of a rectangular flat surface. The paper presents the results of a computational experiment comparing the levels and regions of relative deformations of the Earth’s crust in the case of displacement along a flat rupture surface and along a stochastic one. In the case of a stochastic surface, the regions of relative deformations become asymmetric. The developed model will help to indirectly take into account various mechanical properties of the Earth’s crust when modeling deformations caused by earthquakes.

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 study investigates the stochastic dynamics of hepatitis B virus (HBV) infection using a newly proposed stochastic model. Contrary to deterministic models that fail to encapsulate the inherent randomness and fluctuations in biological processes, our stochastic model provides a more realistic representation of HBV infection dynamics. It incorporates random variability, thereby acknowledging the changes in viral and cellular populations and uncertainties in parameters such as infection rates and immune responses. We examine the solution's existence, uniqueness, and positivity for the proposed model, followed by a comprehensive stability analysis. We provide the necessary and sufficient conditions for local and global stability, offering deep insight into the infection dynamics. Furthermore, we utilize numerical simulations to corroborate our theoretical results. This research provides a robust tool for understanding the complex behavior of HBV dynamics, contributing significantly to the ongoing quest for more effective HBV control and prevention strategies.

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 .

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.

Polynomial recurrence bounds for a class of stochastic differential equations with a gradient type drift and an additive Wiener process are studied without Lyapunov functions.

In this paper, we investigate the cumulative historical entropy of the lifetime of an n-component coherent system under the assumption that all system components have failed at time t. Using the system signature, we can calculate the cumulative historical entropy of the system’s lifespan, which is an important aspect in determining a system’s predictability. This research produces a number of significant results, including expressions, bounds, and ordering aspects for this measure. In addition, we offer a method for finding a preferred system based on cumulative Kullback-Leibler discriminating information that is closely related to the parallel system. These findings provide important insights into the predictability and dependability of coherent systems, emphasizing the importance of this field.

The focus of this paper is on analyzing the role and the choice of parameters in sociophysics diffusion models, by leveraging the potentialities of sociophysics from a mathematical programming perspective. We first present a generalised version of Galam’s opinion diffusion model (see, e.g. , ). For a given selection of the coefficients in our model, this proposal yields the original Galam’s model. The generalised model suggests guidelines for possible alternative selection of its parameters that allow to foster diffusion. Examples of the parameters selection process as steered by numerical optimisation, taking into account various objectives, are provided.

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.

The temporo-spatial theory of consciousness postulates that the brain implements its own inner time and space for conscious processing of outside world. In line with this hypothesis, I present a mechanistic model of mutually connected processes that encode the inner space and time. The model is used to elaborate the binding mechanism between two sets of processes representing the inner space and time, respectively. Further, a stochastic version of the model is developed to investigate the interplay between the binding strength and noise. The spectral entropy is used to characterize the noise effects on the systems of processes when the binding strength is varied. The stochastic modeling results reveal that the spectral entropy values for strongly bound systems have similar entropy values for weakly bound or even decoupled systems. Thus, the analysis performed in this study allows to conclude that the binding mechanism is noise-resilient.

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.

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.

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.

We consider the problem of scheduling tasks on a single machine subject to an uncertain breakdown to minimize the flowtime. Assume the machine is unavailable during the breakdown; the starting time of the breakdown is a random variable s with distribution function D(s) and the terminating time of the breakdown has no any other information; jobs are non-resumable. Under the assumptions, starting from the perspective of statistical optimization, we first define the expected competitive ratio of an algorithm to find the optimized solution with the considered problem. Further, we propose and prove a certain result on the expected competitive ratio of the SPT rule. In particular, we show that under a quite loose condition the expected competitive ratio of the SPT rule is no more than 5/4. Meanwhile, we also make some discussions about our studies. What we have done will rich and improve the studying results on the area of scheduling to minimize flowtime and advance the development of online optimization and statistical optimization.

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 main issue in this work is to study limit functions necessary for the reliability assessment of the structural steel with the use of the relative entropy apparatus. This would be done using a few different mathematical theories relevant to this relative entropy, namely those proposed by Bhattacharyya, Kullback-Leibler, Jeffreys, and Hellinger. Probabilistic analysis in the presence of uncertainty in material characteristics would be delivered using three different numerical strategies – Monte-Carlo simulation, stochastic perturbation method as well as the semi-analytical approach. All these methods are based on the Weighted Least Squares Method approximations of the structural response functions versus the given uncertainty source and they would allow efficient determination of the first two probabilistic moments of the structural responses including stresses, displacements, and strains. The entire computational implementation would be delivered using the Finite Element Method system ABAQUS and computer algebra program MAPLE, where relative entropies, as well as polynomial response functions, would be determined. This study would demonstrate that the relative entropies may be efficiently used in reliability assessment close to the widely engaged First Order Reliability Method (FORM).

Long-range interactions are relevant for a large variety of quantum systems in quantum optics and condensed matter physics. In particular, the control of quantum-optical platforms promises to gain deep insights in quantum-critical properties induced by the long-range nature of interactions. From a theoretical perspective, long-range interactions are notoriously complicated to treat. Here, we give an overview of recent advancements to investigate quantum magnets with long-range interactions focusing on two techniques based on Monte Carlo integration. First, the method of perturbative continuous unitary transformations where classical Monte Carlo integration is applied within the embedding scheme of white graphs. This linked-cluster expansion allows to extract high-order series expansions of energies and observables in the thermodynamic limit. Second, stochastic series expansion quantum Monte Carlo which enables calculations on large finite systems. Finite-size scaling can then be used to determine physical properties of the infinite system. In recent years, both techniques have been applied successfully to one- and two-dimensional quantum magnets involving long-range Ising, XY, and Heisenberg interactions on various bipartite and non-bipartite lattices. Here, we summarise the obtained quantum-critical properties including critical exponents for all these systems in a coherent way. Further, we review how long-range interactions are used to study quantum phase transitions above the upper critical dimension and the scaling techniques to extract these quantum critical properties from the numerical calculations.

We suppose that a Cooper pair (CP) will experience a damping force exerted by the condensed matter. A Langevin equation of a CP in two dimensional condensed matter is established. Following a method similar to Nelson's stochastic mechanics, generalized Schr\"{o}dinger equation of a CP in condensed matter is derived. If the CPs move with a constant velocity, then the corresponding direct current (DC) electrical conductivity can be calculated. Therefore, a Drude like formula of resistivity of CPs is derived. We suppose that the damping coefficient of CPs in two dimensional cuprate superconductors is a linear function of temperature. Then the resistivity and scattering rate of CPs turn out to be also linear-in-temperature. The origin of linear-in-temperature resistivity and Planckian dissipation in cuprate superconductors may be the linear temperature dependence of the damping coefficient of CPs.

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 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.

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.

For concrete structures exposed to offshore areas, chloride ion erosion is one of the main factors affecting the durability. It is crucial to evaluate chloride ion permeability resistance of concrete structures. In this article, a finite element simulation of the chloride ion diffusion process in concrete is conducted. A mass diffusion finite element model based on random aggregate approach is established to investigate the influence of aggregate, interface transition zone, and micro-cracks on chloride ion diffusion coefficients in concrete. The results show that the mass diffusion finite element analysis based on the exponential function model and power function model can effectively simulate the chloride ion diffusion process in concrete. In addition, the data reveal that coarse aggregate is the most important factor affecting chloride ion diffusivity in concrete. However, the interface transition zone significantly accelerates chloride ion diffusion in concrete. Moreover, this acceleration effect exceeds the barrier effect of aggregate.

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.

Global optimization is widely adopted nowadays in a variety of practical and scientific problems. In this context, a group of techniques that is widely used is that of evolutionary techniques. A relatively new evolutionary technique in this direction is that of Giant Armadillo Optimization, which is based on the hunting strategy of giant armadillos. In this paper, a number of modifications to this technique are proposed, such as the periodic application of a local minimization method as well as the use of modern termination techniques based on statistical observations. The proposed modifications have been tested on a wide - series test functions, available from the relevant literature and it was compared against other evolutionary methods.