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.

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.

The aims of this study are to measure the technical efficiency (TE) of Cambodian household’s rice production and trying to determine its main influencing factors using the stochastic frontier production function. The study utilized primary data collected from 301 rice farmers in three selected districts of Battambang by structured questionnaires. The empirical results indicated the level of household rice output varied according to differences in the efficiency of production processes. The mean TE is 0.34 which means that famers produce 34% of rice at best practice at the current level of production inputs and technology, indicates that rice output has the potential of being increased further by 66% at the same level of inputs if farmers had been technically efficient. Furthermore, between 2013-2015 TE of household’s rice production recorded -14.3% decline rate due to highly affected of drought during dry season of 2015. Moreover, evidence reveals that land, fertilizer, and pesticide are the major influencing input factors of household’s rice production, while disaster, education of household head, family size and other crops’ cultivated area are core influencing factors decreasing TE. Conversely, the main influencing factors increasing TE are irrigated area, number of plot area and sex of household head.

Modern companies accumulate a vast amount of customer data that can be used for creating a personalized experience. Analyzing this data is difficult and most business intelligence tools cannot cope with the volume of the data. One example is churn prediction, where the cost of retaining existing customers is less than acquiring new ones. Several data mining and machine learning approaches can be used, but there is still little information about the different algorithm settings to be used when the dataset doesn't fit into a single computer memory. Because of the difficulties of applying feature selection techniques at a large scale, Incremental Probabilistic Component Analysis (IPCA) is proposed as a data preprocessing technique. Also, we present a new approach to large scale churn prediction problems based on the mini-batch Stochastic Gradient Decent (SGD) algorithm. Compared to other techniques, the new method facilitates training with large data volumes using a small memory footprint while achieving good prediction results.

The aims of this study are to measure the technical efficiency (TE) of Cambodian household’s rice production and trying to determine its main influencing factors using the stochastic frontier production function. The study utilized primary data collected from 301 rice farmers in three selected districts of Battambang by structured questionnaires. The empirical results indicated the level of household rice output varied according to differences in the efficiency of the production processes. The mean TE is 0.34 which means that famers produce 34% of rice at best practice at the current level of production inputs and technology, indicates that rice output has the potential of being increased further by 66% at the same level of inputs if farmers had been technically efficient. Furthermore, between 2013-2015, TE of household’s rice production recorded -14.3% decline rate due to highly affected of drought during dry season of 2015. Moreover, evidence reveals that land, fertilizer, and pesticide are the major influencing input factors of household’s rice production, while disaster, education of household head, family size and other crops’ cultivated area are core influencing factors decreasing TE. Conversely, the main influencing factors increasing TE are irrigated area, number of plot area and sex of household head.

The Vacuum Energy Parameter (VEP) of standard cosmology denotes the fraction of the critical density attributed to the accelerated expansion of the Universe. Astrophysical evidence sets the numerical range of VEP at 0.692 +, - 0.012, yet the root cause of these values is currently unknown. Drawing from the stochastic interpretation of early-Universe cosmology, we develop here a derivation of the VEP based on classical diffusion theory and the Langevin equation. Predictions are shown to be in reasonable agreement with observations.

This paper aimed to assess the technical efficiency of maize seed production and the major factors contributing on technical efficiency. Maize is the second most important staple crop in Nepal, but the average yield of maize is very low as compared to other countries having similar agro-climatic requirements. Inefficient use of resources had led to low yield in maize crop. The software Raosoft was used to determine the required sample size and total of 182 samples were selected using simple random technique in June, 2016. Stochastic production frontier model and Tobit model were used to derive the results. The average technical efficiency of maize seed production ranged from 0.25-0.92 with an average of 0.71which revealed the scope of increasing technical efficiency by 29 percent. The majority of the farmers (29.1%) were at higher technical efficiency level of 0.8-0.9 followed by 28.6 percent at 0.7-0.8 and 23.1 percent at 0.6-0.7. Age and schooling of household head, experience on maize seed production, area shared by maize crop and dummies variables such as livestock holding, source of seed and access to extension service had found significantly affecting on the technical efficiency level. For the least developed country like Nepal it would be better to use the available resources wisely and improvement of existing technologies would be more cost effective than that of discovering new technologies. The study recommended that the concerned organizations should focus on mixed agricultural farming system, access to better quality seed and provide technical knowledge which would help in improving technical efficiency.

Partial differential representation of self-similarity feature has been derived from notion of the homogenous function in general sense. This representation allows consideration of stochastic self-similar systems. As well as the partial differential representation allows consideration of Stochastic Partial Differential Equation.

Recently, there has been a growing interest in the production of electricity from renewable energy sources (RES). The RES investment is characterized by uncertainty, which is long-term, costly, depend on feed-in-tariff and support schemes. In this paper, we address the real option valuation (ROV) of a solar power plant investment. The real option framework is investigated. This framework considers the renewable certificate price, furthermore the cost of delay between establishing and operating the solar power plant. The optimal time of launching the project and assess the value of deferred option are discussed. The new three stage numerical methods are constructed, the Lobatto3C-Milstein (L3CM) methods. The numerical methods are integrated with concept of Black-Scholes option pricing theory, and applied in option valuation for solar energy investment with uncertainty. The numerical results of L3CM, finite difference and Monte Carlo methods are compared to show the efficiency of our methods. Our data set refers to the Arab Republic of Egypt.

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/.

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.

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.

Vibrations of blades and tower have important impact for wind turbine. This paper presents a active controller design to suppress blade edgewise vibrations under aerodynamic load and gravitational load.Treating the sum of aerodynamic load input in edgewise direction and gravitational load as unknown disturbance input,a stochastic disturbance accommodating control(SDAC) approach is proposed to design a controller which it utilizes a minimum-variance unbiased estimator(MVUE) to estimate both state and unknown input. The stability analysis proved that the proposed SDAC is bounded in mean square.In order to verify the performance of the minimum-variance unbiased estimator and the proposed SDAC, numerical simulations using Matlab/Simulink have been carried out for the National Renewable Energy Laboratory 5-MW wind turbine.Under the different circumstance which exists the random process and measure noise and noise free. It is shown that the estimation value by MVUE can tracking the real state and unknown input. The results are also compared to the traditional linear quadratic regulator(LQR) and show that the proposed stochastic disturbance accommodating control scheme can further reduce displacement in edgewise vibrations direction and the control strategy is more effective than the LQR.

Based on stochastic frontier analysis and translog input distance function, this paper examines the total factor energy efficiency of China’s industry using input-output data of 30 sub-industries from 2002 to 2014, and decomposes the changes in estimated total factor energy efficiency into the effects of technical change, technical efficiency change, scale efficiency change and input-mix effect. The results show that during this period the total factor energy efficiency in China’s industry grows annually at a rate of 3.63%, technical change, technical efficiency change and input-mix effect contribute positively to the change in total factor energy efficiency, while scale efficiency change contributes negatively to it.

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.

For evaluating probabilities of arbitrary random events with respect to a given multivariate probability distribution, specific techniques are of great interest. An important two-dimensional high risk limit law is the Gauss-exponential distribution whose probabilities can be dealt with based upon the Gauss-Laplace law. The latter will be considered here as an element of the newly introduced family of (p,q)-spherical distributions. Based upon a suitably defined non-Euclidean arc-length measure on (p,q)-circles we prove geometric and stochastic representations of these distributions and correspondingly distributed random vectors, respectively. These representations allow dealing with the new probability measures similarly like with elliptically contoured distributions and more general homogeneous star-shaped ones. This is demonstrated at hand of a generalization of the Box-Muller simulation method. En passant, we prove an extension of the sector and circle number functions.

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.

This study purposes the use of plug-in electric vehicles for demand side management (DSM) considering uncertainties in demand as well as uncertainties due to mobility of PEV to mitigate peak demand. The solution also seeks to reduce electric cost in addition to reducing the effects of greenhouse gases. In recent years DSM using distributed storage system such as battery energy management system (BESS) and plugged-in electric vehicles (PEV) have become very prevalent with most implementations resorting to deterministic load forecast. These methods do not consider the potential growth in demand making their solutions less robust. In this study we propose a real-time density demand forecast and stochastic optimization for robust operation of PEV for a building. This method accounts for demand uncertainties in addition to uncertainties in mobile energy storage as found in PEV, making the resulting solution robust as compared to the deterministic case. A case study on a real site in South Korea is used for verification and testing. The proposed study is verified and tested against existing algorithms. The result verifies the effectiveness of the proposed approach

This study analyzed the technical efficiency of barley production by smallholder farmers in Meket district, Amhara National Regional State, Ethiopia. A cross sectional data from a sample of 123 barley producers during the 2016/17 production season was collected by applying two stage random sampling. To address the objective of the study, both descriptive statistics and econometric models were used to analyze the data. The trans-log functional form of the production function simultaneously with single stage estimation approach was used to estimate the production of barley output and technical inefficiency factors. The estimated stochastic production frontier model indicated that input variables such as fertilizer, human labor and oxen power were the significant variables to increase the quantity of barley output while, barley seed had a negative effect. The estimated mean levels of technical efficiency of the sample farmers were about 70.9% which revealed that, presence of a room to increase their technical efficiency level on average by 29.1% with the existing resources. The discrepancy ratio gamma indicated that 63% of the total variation from the frontier comes due to technical inefficiency while, the remaining 37% comes due to factors outside the control of farmers. Among the hypothesized factors that affect technical inefficiency; education level, extension contact and number of barley plots significantly and negatively affected technical inefficiency score. Besides, practice of crop rotation, distance of residence from the nearest main market, total expenditure and soil fertility was found to have a positive and significant effect. Hence, emphasis should be given to decrease the inefficiency level of those more inefficient farm households via experience sharing among the farmers and usage of improved or certified barley seed. Besides to this, policies and strategies of the government should be directed towards increasing farmers’ education, improve the system of input distributions and institutional facilities.

Optimal dividend payment under a ruin constraint is a two objective control problem which—in simple models—can be solved numerically by three essentially different methods. One is based on a modified Bellman equation and the policy improvement method (see Hipp C., 2003). In this paper we use explicit formulas for running allowed ruin probabilities which avoid a complete search and speed up and simplify the computation. The second is also a policy improvement method, but without the use of a dynamic equation (see Hipp C., 2003). It is based on closed formulas for first entry probabilities and discount factors for the time until first entry (see Hipp C., 2016). Third a new, faster and more intuitive method which uses appropriately chosen barrier levels and a closed formula for the corresponding dividend value. Using the running allowed ruin probabilities, a simple test for admissibility—concerning the ruin constraint—is given. All these methods work for the discrete De Finetti model and are applied in a numerical example. The non stationary Lagrange multiplier method suggested in (see Hipp C., 2016), Section 2.2.2 does also yield optimal dividend strategies which differ from those in all other methods, and Lagrange gaps are present here. These gaps always exist in De Finetti models, see (see Hipp C., 2017).

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.

Rice is the most important food crop in Cambodia and its production is the most organized food production system in the country. The main objective of this study is to measure technical efficiency (TE) of Cambodian rice production and also trying to identify core influencing factors of rice TE at both national and household level, for explaining the possibilities of increasing productivity and profitability of rice, by using translog production function through Stochastic Frontier Analysis (SFA) model. Four-years dataset (2012-2015) generated from the government documents was utilized for the national analysis, while at household-level, the primary three-years data (2013-2015) collected from 301 rice farmers in three selected districts of Battambang province by structured questionnaires was applied. The results indicate that level of rice output varied according to the different level of capital investment in agricultural machineries, total actual harvested area, and technically fertilizers application within provinces, while level of household rice output varied according to the differences in efficiency of production processes, techniques, total annual harvested land, and technically application of fertilizers and pesticides of farmers. The overall mean TE was estimated at 78.4% (national-level) and 34% (household-level), indicates that rice output has the potential of being increased further by 21.6% (national production) and 66% (household) at the same level of inputs and technology if farmers had been technically efficient. The TE also recorded -7% decreasing rate at the national-level and -14.3% at household-level due to highly affected of natural disasters and various environmental and social factors during the study periods.

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

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.

Many species of plants are found in regions to which they are alien. Their global distributions are characterised by a family of exponential functions of the kind that arise in elementary statistical mechanics (an example in ecology is MacArthur's broken stick). We show here that all these functions are quantitatively reproduced by a model containing a single parameter – some global resource partitioned at random on the two axes of species number and site number. A dynamical model generating this equilibrium is a two fold stochastic process and suggests a curious and interesting biological interpretation in terms of niche structures fluctuating with time and productivity; with sites and species highly idiosyncratic. Idiosyncrasy implies that attempts to identify a priori those species likely to become naturalized are unlikely to be successful. Although this paper is primarily concerned with a particular problem in population biology, the two fold stochastic process may be of more general interest.

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.

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.

A controlled ammonia (NH₃) release experiment was performed at a grassland site to quantify the effect of dry deposition, at the field scale between the source and the receptors (NH₃ measurement locations), on the estimates of emission rates by means of inverse dispersion modelling. NH₃ was released for 3 hours at a constant rate of Q = 6.29 mg s⁻¹ from a grid of 36 orifices spread over an area of 250 m². The increase in line-integrated NH₃ concentration was measured with open-path optical miniDOAS devices at different locations downwind of the artificial source. Using a backward Lagrangian stochastic (bLS) dispersion model (bLSmodelR), the fraction of the modelled release rate to the emitted NH₃ (Q_bLS/Q) was calculated from the measurements of the individual instruments. Q_bLS/Q was found to be systematically lower than 1, on average between 0.69 and 0.91, depending on the location of the receptor. We hypothesized that NH₃ dry deposition to grass and soil surfaces was the main factor responsible for the observed depletion of NH₃ between source and receptor. A dry deposition algorithm based on a deposition velocity approach was included in the bLS modelling. Model deposition velocities were evaluated from a ‘big‑leaf’ canopy resistance analogy. Canopy resistances (generally termed Rc) that provided Q_bLS/Q = 1 ranged from 75 to 290 s m⁻¹, showing that surface removal of NH₃ by dry deposition can plausibly explain the original underestimation of Q_bLS/Q. The inclusion of a dry deposition process in dispersion modelling is crucial for emission estimates, which are based on concentration measurements of depositing tracers downwind of homogeneous area sources or heterogeneously distributed hot spots, such as e.g. urine patches on pastures in the case of NH₃.

Historical maps constitute unique sources of retrospective geographic information. Recently, several map archives containing map series covering large spatial and temporal extents have been systematically scanned and made available to the public. The geographic information contained in such data archives allows extending geospatial analysis retrospectively beyond the era of digital cartography. However, given the large data volumes of such archives and the low graphical quality of older map sheets, the processes to extract geographic information need to be automated to the highest degree possible. In order to understand the salient characteristics, data quality variation, and potential challenges in large-scale information extraction tasks, preparatory analytical steps are required to efficiently assess spatio-temporal coverage, approximate map content, and spatial accuracy of such georeferenced map archives across different cartographic scales. Such preparatory steps are often neglected or ignored in the map processing literature but represent highly critical phases that lay the foundation for any subsequent computational analysis and recognition. In this contribution we demonstrate how such preparatory analyses can be conducted using classical analytical and cartographic techniques as well as visual-analytical data mining tools originating from machine learning and data science, exemplified for the United States Geological Survey topographic map and Sanborn fire insurance map archives.

Little in the scholarly economics literature is directed specifically to the performance of sta­ble value funds, although they occupy a leading place among retirement investment vehicles. They are currently offered in more than one-third of all defined contribution plans in the USA, with more than $800 billion of assets under management. This paper rigorously ex­amines their performance throughout the entire period since their inception in 1973. We produce a composite index of stable value returns. We next conduct mean-variance analysis, Sharpe and Sortino ratio analysis, stochastic dominance analysis, and optimal multi-period portfolio composition analysis. Our evidence suggests that stable value funds dominate (on average) two major asset classes based on a historical analysis, and that they often occupy a significant position in optimized portfolios across a broad range of risk aversion levels. We discuss factors that contributed to stable value funds’ past performance and whether they can continue to perform well into the future. We also discuss considerations regarding whether or not to include stable value as an element in target date funds within defined con­tribution pension plans.

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.

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.

Capsule endoscopy, which uses a wireless camera to take images of the digestive tract, is emerging as an alternative to traditional colonoscopy. The diagnostic values of these images depend on the quality of revealed underlying tissue surfaces. In this paper, we consider the problem of enhancing the visibility of detail and shadowed tissue surfaces for capsule endoscopy images. Using concentric circles at each pixel for random walks combined with stochastic sampling, the proposed method enhances the details of vessel and tissue surfaces. The framework decomposes the image into two detail layers that contain shadowed tissue surfaces and detail features. The target pixel value is recalculated for the smooth layer using similarity of the target pixel to neighboring pixels by weighting against the total gradient variation and intensity differences. In order to evaluate the diagnostic image quality of the proposed method, we used clinical subjective evaluation with a rank order on selected KID image database and compared to state of the art enhancement methods. The result showed that the proposed method provides a better result in terms of diagnostic image quality and objective quality contrast metrics and structural similarity index.

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.

Breast cancer is the most common cause of death for women worldwide. Thus, the ability of artificial intelligence systems to predict and classify breast cancer is very important. In this paper, a hybrid ensemble method classification mechanism is proposed based on a majority voting mechanism. First, the performance of different state-of-the-art machine learning classification algorithms for the Wisconsin Breast Cancer Dataset (WBCD) were evaluated. The three best classifiers were then selected based on their F3 score. F3 score is used to emphasize the importance of false negatives (recall) in breast cancer classification. Then, these three classifiers, simple logistic Regression learning, stochastic gradient descent learning and multilayer perceptron network, are used for ensemble classification using a voting mechanism. We also evaluated the performance of hard and soft voting mechanism. For hard voting, majority-based voting mechanism was used and for soft voting we used average of probabilities, product of probabilities, maximum of probabilities and minimum of probabilities-based voting methods. The hard voting (majority-based voting) mechanism shows better performance with 99.42% as compared to the state-of-the-art algorithm for WBCD.

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.

The present paper deals with the stochastic modeling of bio-colonization for the computation of stochastic hydrodynamic loading on jacket-type offshore structures. It relies on a multidisciplinary study gathering biological and physical research fields that accounts of uncertainties at all the levels. Indeed, bio-colonization of offshore structures is a complex phenomenon with two major but distinct domains (i) marine biology whose processes are modeled with biomathematics methods and (ii) hydrodynamic processes. This paper aims to connect these two domains. It proposes a stochastic model for the marine organism’s growth and then continues with transfers for assessment of drag coefficient and forces probability density functions that accounts for marine growth evolution. A case study relies on the characteristics (growth and shape) of the blue mussel (Mytilus edulis) in northeastern Atlantic.

The paper is concerned with a class of stochastic differential equations in infinite dimensional Hilbert space with random coefficients driven by Teugel's martingales which are more general processes. and its optimal control problem. Here Teugels martingales are a family of pairwise strongly orthonormal martingales associated with L\'{e}vy processes (see Nualart and Schoutens). There are three major ingredients. The first is to prove the existence and uniqueness of the solutions by continuous dependence theorem of solutions combining with the parameter extension method. The second is to establish the stochastic maximum principle and verification theorem for our optimal control problem by the classicconvex variation method and dual technique.The third is to represent an example of a Cauchy problem for a controlled stochastic partial differential equation driven by Teugels martingales which our theoretical results can solve.

The disastrous 2017 fire season in Portugal lead to widespread recognition of the need for a paradigm shift in forest and fire management. We focused our study on Alvares, a parish in central Portugal which had 60% of its area burned in 2017, with a large record of historical. We evaluated how different fuel treatment strategies can reduce wildfire hazard in Alvares, through i) a fuel break network with different priorities and ii) random fuel treatments resulting from stand-level management intensification. To assess this, we developed a stochastic fire simulation system (FUNC-SIM) that integrates uncertainties in fuel distribution over the landscape. If the landscape remains unchanged, Alvares will have large burn probabilities in the north, northeast, and center-east areas of the parish that are very often associated with high fire line intensities. The different fuel treatment scenarios decreased burned area between 12.1-31.2%, resulting from 1%-4.6% increases in annual treatment area, and reduced 10%-40% the likelihood of wildfires larger than 5000 ha. On average, simulated burned area decreased 0.22% per each ha treated, and effectiveness decreased with increasing area treated. Overall, both fuel treatment strategies effectively reduced wildfire hazard and should be part of a larger, holistic and integrated plan to reduce the vulnerability of the Alvares parish to wildfires.

The novel Coronavirus (COVID-19) is spreading and has caused a large-scale infection in China since December 2019. Thefirst infected person was declared on March 18, 2020 in Djibouti. This has led to a signicant impact on the lives and economy in Djibouti and other countries. In this study, we propose a double compartment stochastic model which describes the evolution of the infection rate and the evolution of the number of infected in the period from May 20 to June 23, 2020. We will also propose the evolution of people infected in two states, recovered and deceased.

The vibration feature of weak gear fault is often covered in strong background noise, which makes it necessary to establish weak feature enhancement methods. Among the enhancement methods, stochastic resonance (SR) has the unique advantage of transferring noise energy to weak signals and has a great application prospection in weak signal extraction. But the traditional SR potential model cannot form a richer potential structure and may lead to system instability when the noise is too great. To overcome these shortcomings, the article presents a periodic potential underdamping stochastic resonance (PPUSR) method after investigating the potential function and system signal-to-noise ratio (SNR). In addition, system parameters are further optimized by using ant colony algorithm. Through simulation and gear experiments, the effectiveness of the proposed method was verified. We concluded that compared with the traditional underdamped stochastic resonance (TUSR) method, the PPUSR method had a higher recognition degree and better frequency response capability.

In this paper, we propose a new mathematical model based on the association between susceptible and recovered individual, where the association between susceptible and recovered individual is disturbed by white noise. This model is based on demographic changes and is used for long term behavior. We study the stability of equilibria of the deterministic model and prove the conditions for the extinction of diseases. Then, we investigate and obtain the critical condition of the stochastic epidemic model for the extinction and the permanence in mean of the disease with the white noise. To verify our results, we present some numerical simulations for real data related to disease.

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.

Activation Functions are crucial parts of the Deep Learning Artificial Neural Networks. From the Biological point of view, a neuron is just a node with many inputs and one output. A neural network consists of many interconnected neurons. It is a “simple” device that receives data at the input and provides a response. The function of neurons is to process and transmit information; the neuron is the basic unit in the nervous system. Carly Vandergriendt (2018) stated the human brain at birth consists of an estimated 100 billion Neurons. The ability of a machine to mimic human intelligence is called Machine Learning. Deep Learning Artificial Neural Networks was designed to work like a human brain with the aid of arbitrary choice of Non-linear Activation Functions. Currently, there is no rule of thumb on the choice of Activation Functions, “Try out different things and see what combinations lead to the best performance”, however, sincerely; the choice of Activation Functions should not be Trial and error. Jamilu (2019) proposed that Activation Functions shall be emanated from AI-ML-Purified Data Set and its choice shall satisfy Jameel’s ANNAF Stochastic and or Deterministic Criterion. The objectives of this paper are to propose instances where Deep Learning Artificial Neural Networks are SUPERINTELLIGENT. Using Jameel’s ANNAF Stochastic and or Deterministic Criterion, the paper proposed four classes where Deep Learning Artificial Neural Networks are Superintelligent namely; Stochastic Superintelligent, Deterministic Superintelligent, and Stochastic-Deterministic 1^st and 2^nd Levels Superintelligence. Also, a Normal Probabilistic-Deterministic case was proposed.

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.

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.

Cellular Nonlinear Networks (CNN) are a concept introduced in 1988 by Leon Chua and Lin Yang as a bio-inspired architecture, capable of massively parallel computation. Later on, CNN have been enhanced by incorporating designs that incorporate memristors to profit from their processing and memory capabilities. In addition, Stochastic Computing (SC) can be used to optimize the quantity of required processing elements; thus it provides a lightweight approximate computing framework, quite accurate and effective, though. In this work, we propose utilization of SC in designing and implementing a memristor-based CNN. As a proof of the proposed concept, an example of application is presented. This application combines Matlab and a FPGA in order to create the CNN. The implemented CNN has then been used to perform three different real-time applications on a 512x512 gray-scale and a 768x512 color image: storage of the image, edge detection, and image sharpening. It has to be pointed out that the same CNN has been used for the three different tasks, with the sole change of some programmable parameters. Results show an excellent capability with significant accompanying advantages, like the low number of needed elements further allowing for a low cost FPGA-based system implementation, something confirming the system’s ability for real time operation.

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.

Based on a previous risk calculation study along a road corridor, risk is recalculated using stochastic simulation by introducing variability for most of the parameters in the risk equation. This leads to an exceedance curve comparable to that of catastrophe models. This approach introduces uncertainty into the risk calculation in a simple way, which can be used for poorly documented cases to fulfil lack of data. This approach seems to tend to minimize risk or to question risk calculations.

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.

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.

Here we are concerning with two problems of a coupled system of random and stochastic nonlinear differential equations with two coupled systems of nonlinear nonlocal random and stochastic integral conditions. The existence of solutions will be studied. The sufficient condition for the uniqueness of the solution will be given. The continuous dependence of the unique solution on the nonlocal conditions will be proved.

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, mean-field type games between two players with backward stochastic dynamics are defined and studied. They make up a class of non-zero-sum differential games where the players' state dynamics solve backward stochastic differential equations (BSDEs) that depend on the marginal distributions of player states. Players try to minimize their individual cost functionals, also depending on the marginal state distributions. Under some regularity conditions, we derive necessary and sufficient conditions for existence of Nash equilibria. Player behavior is illustrated by numerical examples, and is compared to a centrally planned solution where the social cost, the sum of player costs, is minimized. The inefficiency of a Nash equilibrium, compared to socially optimal behavior, is quantified by the so-called price of anarchy. Numerical simulations of the price of anarchy indicate how the improvement in social cost achievable by a central planner depends on problem parameters.

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.

The paper describes a method of solving some stochastic processes using generating functions. A general theorem of generating functions of a particular type is derived. A generating function of this type is applied to a stochastic process yielding polynomial time algorithms for certain partitions. The method is generalized to a stochastic process describing a rather general linear transform. Finally, the main idea of the method is used in deriving a theoretical polynomial time algorithm to the knapsack problem.

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.

In this paper, we investigate some kind of Dynkin game under $g$-expectation induced by backward stochastic differential equation (shortly for BSDE). We define the lower and upper value functions $\underline{V}_t=ess\sup\limits_{\tau\in{\mathcal{T}_t}} ess\inf\limits_{\sigma\in{\mathcal{T}_t}}\mathcal{E}^g_t[R(\tau,\sigma)]$ and $\overline{V}_t=ess\inf\limits_{\sigma\in{\mathcal{T}_t}}ess\sup\limits_{\tau\in{\mathcal{T}_t}}\mathcal{E}^g_t[R(\tau,\sigma)]$, respectively. Under some regular assumptions, a pair of saddle point is obtained and the value function of Dynkin game $V(t)=\underline{V}_t=\overline{V}_t$ follows. Furthermore, the constrained case of Dynkin game is also considered.

The world’s human population is reaching record longevities. Consequently, our societies are experiencing the impacts of prolonged longevity, such as increased retirement age. A major hypothesised influence on ageing patterns is resource limitation, formalised under calorie restriction theory. This theory predicts extended organismal longevity due to reduced calorie intake without malnutrition. However, several challenges face current calorie restriction (CR) research and, although several attempts have been made to overcome these challenges, there is still a lack of holistic understanding of how CR shapes organismal vitality. Here, we conduct a literature review of 222 CR peer-reviewed publications to summarise the state-of-the-art in the field. We use this summary to highlight challenges of CR research in our understanding of its impacts on longevity. Our review demonstrates that experimental research in this field is biased towards short-lived species (98.2% of studies examine species with <5 years of mean life expectancy) and lacks realism in key areas, such as stochastic environments or interactions with other environmental drivers such as temperature. We argue that only by considering a range of short- and long-lived species and by taking more realistic approaches can the impacts of CR on longevity be examined and validated in natural settings. We conclude by proposing experimental designs and study species that will allow the discipline to gain a much-needed understanding of how restricting caloric intake affects long-lived species in realistic settings. Through incorporating more experimental realism, we anticipate crucial insights that will ultimately shape the myriad of socio-bio-economic impacts of senescence in humans and other species across the Tree of Life.

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.

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.

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.

We outline and test a new methodology for genuine simulation of stochastic processes with any dependence and any marginal distribution. We reproduce time dependence with a generalized, time symmetric or asymmetric, moving-average scheme. This implements linear filtering of non-Gaussian white noise, with the weights of the filter determined by analytical equations in terms of the autocovariance of the process. We approximate the marginal distribution of the process, irrespective of its type, using a number of its cumulants, which in turn determine the cumulants of white noise in a manner that can readily support the generation of random numbers from that approximation, so that it be applicable for stochastic simulation. The simulation method is genuine as it uses the process of interest directly without any transformation (e.g. normalization). We illustrate the method in a number of synthetic and real-world applications with either persistence or antipersistence, and with non-Gaussian marginal distributions that are bounded, thus making the problem more demanding. These include distributions bounded from both sides, such as uniform, and bounded form below, such as exponential and Pareto, possibly having a discontinuity at the origin (intermittence). All examples studied show the satisfactory performance of the method.

Applications in high-performance computing (HPC) may not use all available computational resources, leaving some of them underutilized. By co-scheduling, i.e. running more than one application on the same computational node, it is possible to improve resource utilization and overall throughput. Some applications may have conflicting requirements on resources and co-scheduling may cause performance degradation, so it is important to take it into account in scheduling decisions. In this paper, we formalized co-scheduling problem and proposed multiple scheduling strategies to solve it: an optimal strategy, an online strategy and heuristic strategies. These strategies vary in terms of the optimality of the solution they produce and a priori information about the system they require. We showed theoretically that the online strategy provides schedules with a competitive ratio that has a constant upper limit. This allowed us to solve the co-scheduling problem using heuristic strategies that approximate this online strategy. Numerical simulations showed how heuristic strategies compare to the optimal strategy for different input systems. We proposed a method for measuring input parameters of the model in practice and evaluated this method on HPC benchmark applications. We showed high accuracy of measurement method, which allows to apply proposed scheduling strategies in scheduler implementation.

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 describes a stochastic clustering architecture that is used in the paper for making predictions over energy data. The design is discrete, localised optimisations based on similarity, followed by a global aggregating layer, which can be compared with the recent random neural network designs, for example. The topic relates to the IDEAS Smart Home Energy Project, where a client-side Artificial Intelligence component can predict energy consumption for appliances. The proposed data model is essentially a look-up table of the key energy bands that each appliance would use. Each band represents a level of consumption by the appliance. This table can replace disaggregation from more complicated methods, usually constructed from probability theory, for example. Results show that the table can accurately disaggregate a single source to a set of appliances, because each appliance has quite a unique energy footprint. As part of predicting energy consumption, the model could possibly reduce costs by 50% and more than that if the proposed schedules are also included. The hyper-grid has been changed to consider rows as single units, making it more tractable. A second case study considers wind power patterns, where the grid optimises over the dataset columns in a self-similar way to the rows, allowing for some level of feature analysis.

To sample from complex, high-dimensional distributions, one may choose algorithms based on the Hybrid Monte Carlo (HMC) method. HMC-based algorithms generate nonlocal moves alleviating diffusive behavior. Here, I build on an already defined HMC framework, Hybrid Monte Carlo on Hilbert spaces [A. Beskos, F.J. Pinski, J.-M. Sanz-Serna and A.M. Stuart, Stoch. Proc. Applic. 121, 2201 - 2230 (2011); doi:10.1016/j.spa.2011.06.003] that provides finite-dimensional approximations of measures π which have density with respect to a Gaussian measure on an infinite-dimensional Hilbert (path) space. In all HMC algorithms, one has some freedom to choose the mass operator. The novel feature of the algorithm described in this article lies in the choice of this operator. This new choice defines a Markov Chain Monte Carlo (MCMC) method which is well defined on the Hilbert space itself. As before, the algorithm described herein uses an enlarged phase space Π having the target π as a marginal, together with a Hamiltonian flow that preserves Π. In the previous method, the phase space π was augmented with Brownian bridges. With the new choice for the mass operator, π is augmented with Ornstein-Uhlenbeck (OU) bridges. The covariance of Brownian bridges grows with its length, which has negative effects on the Metropolis-Hasting acceptance rate. This contrasts with the covariance of OU bridges which is independent of the path length. The ingredients of the new algorithm include the definition of the mass operator, the equations for the Hamiltonian flow, the (approximate) numerical integration of the evolution equations, and finally the Metropolis-Hastings acceptance rule. Taken together, these constitute a robust method for sampling the target distribution in an almost dimension-free manner. The behavior of this novel algorithm is demonstrated by computer experiments for a particle moving in two dimensions, between two free-energy basins separated by an entropic barrier.

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.

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.

An increase of seismic activity is often observed before large earthquakes. Events responsible for this increase are usually named foreshock and their occurrence probably represents the most reliable precursory pattern. Many foreshocks statistical features can be interpreted in terms of the standard mainshock-to-aftershock triggering process and are recovered in the Epidemic Type Aftershock Sequence ETAS model. Here we present a statistical study of instrumental seismic catalogs from four different geographic regions. We focus on some common features of foreshocks in the four catalogs which cannot be reproduced by the ETAS model. In particular we find in instrumental catalogs a significantly larger number of foreshocks than the one predicted by the ETAS model. We show that this foreshock excess cannot be attributed to catalog incompleteness. We therefore propose a generalized formulation of the ETAS model, the ETAFS model, which explicitly includes foreshock occurrence. Statistical features of aftershocks and foreshocks in the ETAFS model are in very good agreement with instrumental results.

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.

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.

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.

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.

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.

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.

This study focuses on the decisions of picking, inventory, ripening, delivering, and selling mangoes in a harvesting season. Demand, supply, and prices are uncertain, and their probability density functions are fitted based on actual trading data collected from the largest spot market in Taiwan. A stochastic programming model is formulated to minimize the expected cost under the considerations of labor, storage space, shelf life, and transportation restrictions. We implement the sample-average approximation to obtain a high-quality solution of the stochastic program. The analysis compares deterministic and stochastic solutions to assess the uncertain effect on the harvest decisions. Finally, the optimal harvest schedule of each mango type is suggested based on the stochastic program solution.

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.

The article is devoted to the new results of the author, which add his previously published ones, of studying hidden rules and symmetries in structures of long single-stranded DNA sequences in eukaryotic and prokaryotic genomes. The author uses the existence of different alphabets of n-plets in DNA: the alphabet of 4 nucleotides, the alphabet of 16 douplets, the alphabet of 64 triplets, etc. Each of such DNA alphabets of n-plets can serve for constructing a text as a chain of these n-plets. Using this possibility, the author represents any long DNA nucleotide sequence as a bunch of many so-called n-texts, each of which is written on the basis of one of these alphabets of n-plets. Each of such n-texts has its individual percents of different n-plets in its genomic DNA. But it turns out that in such multi-alphabetical or multilayer presentation of each of many genomic DNA, analyzed by the author, universal rules of probabilities and symmetry exist in interrelations of its different n-texts regarding their percents of n-plets. In this study, the tensor product of matrices and vectors is used as an effective analytical tool borrowed from the arsenal of quantum mechanics. Some additions to the topic of algebra-holographic principles in genetics are also presented. Taking into account the described genomic rules of probability, the author puts also forward a concept of the important role of stochastic resonances in genetic informatics.

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.

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.

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.

This study has developed a Matlab application for simulating statistical models project (SMp) probabilistic distributions that are similar to binomial and Poisson, which were created by mathematical procedures. The simulated distributions are graphically compared with these popular distributions. The application allows to obtain many probabilistic distributions, and shows the trend (τ ) for n trials with success probability p, i.e. the maximum probability as τ=np. While the Poisson distribution PD(x;µ) is a unique probabilistic distribution, where PD=0 in x=+∞, the application simulates many SMp(x;µ,Xmax) distributions, where µ is the Poisson parameter and value of x with generally the maximum probability, and Xmax is the upper limit of x with SMp(x;µ,Xmax) ≥ 0 and limit of the stochastic region of a random discrete variable. It is shown that by simulation via, one can get many and better probabilistic distributions than by mathematical one.

Deterministic-stochastic empirical mode decomposition (EMD) is used to obtain low-frequency (non-diffusive, i.e., background velocity) and high-frequency (diffusive, i.e., eddies) components from a Lagrangian drifter‘s trajectory. Eddy characteristics are determined from the time series of eddy trajectories from individual Lagrangian drifter such as the eddy radial scale, eddy velocity scale, eddy Rossby number, and eddy-background kinetic energy ratio. A long-term dataset of the SOund Fixing And Ranging float time series obtained near the California coast by the Naval Postgraduate School from 1992 to 2004 at depth between 150 and 600 m (http://www.oc.nps.edu/npsRAFOS/) is used as an example to demonstrate the capability of the deterministic-stochastic EMD.

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.

The prediction of capacity degradation, and more generally of the behaviors related to battery aging, is useful in the design and use phases of a battery to help improve the efficiency and reliability of energy systems. In this paper, a stochastic model for the prediction of battery cell degradation is presented. The proposed model takes its cue from an approach based on Markov chains, although it is not comparable to a Markov process, as the transition probabilities vary as the number of cycles that the cell has performed varies. The proposed model can reproduce the abrupt decrease in the capacity that occurs near the end of life condition (80% of the nominal value of the capacity) for the cells analyzed. Furthermore, we illustrate the ability of this model to predict the capacity trend for a lithium-ion cell with nickel-manganese-cobalt (NMC) at the cathode and graphite at the anode subjected to a life cycle in which there are different aging factors, using the results obtained for cells subjected to single aging factors.

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 present a novel method for interpolating univariate time series data. The proposed method combines multi-point fractional Brownian bridges, a genetic algorithm, and Takens’ theorem for reconstructing a phase space from univariate time series data. The basic idea is to first generate a population of different stochastically interpolated time series data, and secondly, to use a genetic algorithm to find the pieces in the population which generate the smoothest reconstructed phase space trajectory. A smooth trajectory curve is hereby found to have a low variance of second derivatives along the curve. For simplicity, we refer to the developed method as PhaSpaSto-interpolation, which is an abbreviation for phase-space-trajectory-smoothing stochastic interpolation. The proposed approach is tested and validated with a univariate time series of the Lorenz system, five non-model data sets and tested against a cubic spline interpolation and a linear linear interpolation. We find that the criterion for smoothness guarantees low errors on known model and non-model data. Finally, we interpolate the discussed non-model data sets, and show the corresponding improved phase space portraits. The proposed method is useful for interpolating low-sampled time series data sets for, e.g., machine learning, regression analysis, or time series prediction approaches.

A multiscale modeling concept for numerical simulation of multiphysics turbulent flow utilizing map-based advection is described. The approach is outlined with emphasis on its theoretical foundations and physical interpretations in order to establish the context for subsequent presentation of the associated numerical algorithms and the results of validation studies. The model formulation is a synthesis of existing methods, modified and extended in order to obtain a qualitatively new capability. The salient feature of the approach is that time advancement of the flow is fully resolved both spatially and temporally, albeit with modeled advancement processes restricted to one spatial dimension. This one-dimensional advancement is the basis of a bottom-up modeling approach in which three-dimensional space is discretized into under-resolved mesh cells, each of which contains an instantiation of the modeled one-dimensional advancement. Filtering is done only to provide inputs to a pressure correction that enforces continuity and to obtain mesh-scale-filtered outputs if desired. The one-dimensional advancement, the pressure correction, and coupling of one-dimensional instantiations using a Lagrangian implementation of mesh-resolved volume fluxes is sufficient to advance the three-dimensional flow without time advancing coarse-grained equations, a feature that motivates the designation of the approach as autonomous microscale evolution (AME). In this sense, the one-dimensional treatment is not a closure because there are no unclosed terms to evaluate. However, the approach is additionally suitable for use as a subgrid-scale closure of existing large-eddy-simulation methods. The potential capabilities and limitations of both of these implementations of the approach are assessed conceptually and with reference to demonstrated capabilities of related methods.

We propose a model for medium-term hydropower scheduling (MTHS) with variable head and uncertainty in inflow, reserve capacity, and energy price. With an increase of intermittent energy sources in the generation mix, it is expected that a flexible hydropower producer can obtain added profits by participating in other markets than just the energy market. To capture this added potential the hydropower system should be modeled with a higher level of details. In this context, we apply an algorithm based on stochastic dual dynamic programming (SDDP) to solve the nonconvex MTHS problem, and show that the use of Strengthened Benders (SB) cuts to represent the expected future profit (EFP) function provide accurate scheduling results for slightly nonconvex problems. A method to visualize the EFP function in a dynamic programming setting is provided, serving as a useful tool for a priori inspection of the EFP shape and its nonconvexity.

Air sampling using vortex air samplers combined with species specific amplification of pathogen DNA, was carried out over two years in four or five locations in the Salinas Valley of California. The resulting time series data for the abundance of pathogen DNA trapped per day displayed complex dynamics with features of both deterministic (chaotic) and stochastic dynamics. Methods of nonlinear time series analysis developed for the reconstruction of low dimensional attractors provided new insights into the complexity of the pathogen abundance data, but also indicated that practicality may limit the capacity for definitively classifying the dynamics of air borne plant pathogen inoculum. Over the two years of the study five location/year combinations were classified as having stochastic linear dynamics and four were not. Calculation of entropy values for either the number of pathogen DNA copies or for a binary string indicating the pathogen abundance data were increasing or not, revealed (1) some robust differences in the dynamics between seasons that were not obvious in the time series data themselves, and also (2) that the series were almost all at their theoretical maximum entropy value when considered from the simple perspective of whether instantaneous change along the sequence is positive or not.

Due to the increased use of memristors, and its many applications, the use of emulators has grown in parallel to avoid some of the difficulties presented by real devices such as variability and reliability. In this paper, we present a memristive emulator designed using a Switched Capacitor (SC), this is, an analog component/ block and a control part or block implemented using stochastic computing (SCo) and therefore fully digital. Our design is thus a mixed signal circuit. Memristor equations are implemented using stochastic computing to generate the control signals necessary to work with the controllable resistor implemented as switched capacitor.

This study has developed a Matlab application for simulating statistical models project (SMp) probabilistic distributions that are similar to binomial and Poisson, which were created by mathematical procedures. The simulated distributions are graphically compared with these legendary distributions. The application allows to obtain many probabilistic distributions, and shows the trend (τ ) for n trials with success probability p, i.e. the maximum probability as τ=np. While the Poisson distribution PD(x;µ) is a unique probabilistic distribution, where PD=0 in x=+∞, the application simulates many SMp(x;µ,Xmax) distributions, where µ is the Poisson parameter and value of x with generally the maximum probability, and Xmax is upper limit of x with SMp(x;µ,Xmax) ≥ 0 and limit of the stochastic region of the random discrete variable X. It is shown that by simulation via, one can get many and better probabilistic distributions than by mathematical one.

This feature study attempts on setting a granules involving mesoscopic matter-aggregation context as a problem of passing locally by the matter-aggregating system from classical stochastic (mesoscopic limit) to a quantum description (nanoscale quantum-size effect limit). A d-dimensional entropy-production aggregation of the granules-involving matter is considered in terms of a (sub)diffusive realization. It turns out that when taking a full d-dimensional pathway of the aggregation toward the nanoscale, one is capable of disclosing a Heisenberg type (diffusional) relation, setting up an upper uncertainty bound for the (sub)diffusive very slow granules-including environment that matches the quantum limit of h/2pm (m– average mass of a granule; h – the Planck’s constant) for the diffusion coefficient of the aggregation, likely first proposed by Fürth in 1933, and qualitatively foreseen by Schrödinger some years before, both in the context of a diffusing particle cluster. The classical-quantum passage uncovered here, also termed insightfully the quantum-size effect (as borrowed from the quantum dots’ parlance), works properly for the three-dimensional (d=3) case, making use of a substantial physical fact that the (nano)granules interact readily via their surfaces with the also granular surroundings in which they are immersed. This natural observation is embodied in the basic averaging construction of the diffusion coefficient of the aggregation of interest. Certain, possibly biomedical, applications of the model can also be viewed by prospective inspection of tiny inhomogeneities in nanofibrillar and/or lamellar matter for which certain numerical realizations are plausible to prepare based on thorough nanoscale experiments.

The COVID-19 epidemic and the measures adopted to contain it have had a significant impact on energy patterns throughout the world. The pandemic and movement restrictions led to unpredictable fluctuations in power systems demand and the fuel price for a delayed period. Monkeypox, another viral disease, appeared during the post-COVID period. It is assumed that the outbreak of monkeypox is unlikely due to the implication of preventive measures experienced by COVID-19. At the same time, the probability of an epidemic cannot be blindly overlooked. This paper aims to examine and analyze historical data to look at how much petroleum fuel was used for generating power and how the price of petroleum fuel changed over seven years, from January 2016 to August 2022. This period covers the time before the COVID-19 pandemic, during the pandemic, and after the pandemic. Several time-series forecasting models, including all four benchmark methods (Mean, Naïve, Drift, and Snaïve), Seasonal and Trend decomposition using Loess (STL), Exponential Smoothing (ETS), and Autoregressive Integrated Moving Average (ARIMA) methods have been applied for both fuel consumption and price prediction. The best forecasting method for fuel price and consumption has been identified among these methods. The paper also utilizes the ARIMAX model by incorporating multiple exogenous variables, such as monthly mean temperature, mean fuel price, and mileage of vehicles traveling during a certain period of pandemic lock-down. It will assist in capturing the non-smooth and stochastic pattern of fuel consumption and price due to the pandemic by separating the seasonal influence and thus provide a prediction of the consumption pattern in the event of any future pandemic.

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.

A Robust Optimization framework with original concepts and fundamentals also admitting a fusion of ideals from relative regret models and static robust optimization, containing conservatism concepts is disclosed. The algorithm uses a fine-tune strategy to tune the model so the robustness and a target ideality can be mutually achieved with a specified risk. The framework comprises original concepts, a mathematical approach and an algorithm. The statistical treatment of the data with the original concepts from the framework make it able to make short, middle or long-term decision-making setting. The framework has high tractability since the algorithm forces the creation of a setting that makes a robust optimization with the specified risk. The framework can be applied in linear and nonlinear mathematical models since that the objective function is monotonic in the domain of the active convex region. Several examples are solved to best understand the framework and all results demonstrated high tractability and performance. There is a wide range of applications. Along all the text, there is a profound discussion about its philosophy, objective, original concepts, fields of application, statistical and probabilistic fundamentals.

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.

This paper analyzes the robust dissipativity of uncertain stochastic generalized neural networks (USGNNs) with Markovian jumping parameters and time-varying delays. In practical applications most of the systems refer to uncertainties, hence, the norm-bounded parameter uncertainties and stochastic disturbance are considered. Then, by constructing an appropriate Lyapunov-Krasovskii functional (LKF) and by employing integral inequalities LMI-based sufficient conditions of the considered systems are established. Numerical simulations are given to show the merit of the presented results.