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The work is devoted to the analysis of non-standard methods for assessing reliability and the probability of uptime (operating time) to failure at a certain point in time. In the case of small deviations in the density of the failure distribution from the normal type, the perturbation function method is considered, which is applicable to a wide class of distributions decreasing at infinity no faster than the exponential function. For processing censored runs, when only the number of runs for certain periods of observation time is known, estimates of the distribution function from start to failure and the probability of uptime are obtained based on the application of the root method of nonparametric construction of the distribution density of a random variable. In contrast to strictly probabilistic methods of reliability analysis, diffusion distributions as probabilistic-physical models of reliability have a great practical advantage. The method of constructing the failure distribution function proposed in the article provides a reasonable choice of a theoretical distribution model from a fairly complete set of competing distribution models, which must necessarily include monotonic and non-monotonic diffusion distribution. The results of the study of reliability estimates and the probability of trouble-free operation in relation to dangerous failures allow to assess the level of safety of complex technical systems containing hazardous production facilities. An analytical expression has been obtained for the probability of trouble-free operation of a system with automatic protective devices that ensure the safety of maintenance personnel at hazardous production facilities. [ABSTRACT FROM AUTHOR]

To ensure the efficient functioning of solar energy generation systems, it is crucial to have dependable designs and regular maintenance. However, when these systems or their components operate at multiple working levels, optimizing reliability becomes a complex task for models and analyses. In the context of reliability modeling in solar energy generation systems, researchers often assume that random variables follow an exponential distribution (binary-state representation) as a simplification, although this may not always hold true for real-world engineering systems. In the present paper, a multi-state solar energy generating system with inverters in series configuration is investigated, in which unreliable by-pass changeover switches, common cause failures (CCFs), and multiple repairman vacations are also considered. Furthermore, the arrivals of CCFs and the repair processes of the failed system due to CCFs are governed by different Markovian arrival processes (MAPs), and the lifetimes and repair times of inverters and by-pass changeover switches and the repairman vacation time in the system have different phase-type (PH) distributions. Therefore, the behavior of the system is represented using a Markov process methodology, and reliability measures for the proposed system are derived utilizing aggregated stochastic process theory. Finally, a numerical example and a comparison analysis are presented to demonstrate the findings. [ABSTRACT FROM AUTHOR]

In many machine learning applications, there are many scenarios when performance is not satisfactory by single classifiers. In this case, an ensemble classification is constructed using several weak base learners to achieve satisfactory performance. Unluckily, the construction of the ensemble classification is empirical, i.e., to try an ensemble classification and if performance is not satisfactory then discard it. In this paper, a challenging analytical problem of the estimation of ensemble classification using the prediction performance of the base learners is considered. The proposed formulation is aimed at estimating the performance of ensemble classification without physically developing it, and it is derived from the perspective of probability theory by manipulating the decision probabilities of the base learners. For this purpose, the output of a base learner (which is either true positive, true negative, false positive, or false negative) is considered as a random variable. Then, the effects of logical disjunction-based and majority voting-based decision combination strategies are analyzed from the perspective of conditional joint probability. To evaluate the forecasted performance of ensemble classifier by the proposed methodology, publicly available standard datasets have been employed. The results show the effectiveness of the derived formulations to estimate the performance of ensemble classification. In addition to this, the theoretical and experimental results show that the logical disjunction-based decision outperforms majority voting in imbalanced datasets and cost-sensitive scenarios. [ABSTRACT FROM AUTHOR]

The multivariate random coefficient autoregression (RCAR) process is widely used in time series modeling applications. Random autoregressive coefficients are usually assumed to be independent and identically distributed sequences of random variables. This paper investigates the issue of coefficient constancy testing in a class of static multivariate first-order random coefficient autoregressive models. We construct a new test statistic based on the locally most powerful-type test and derive its limiting distribution under the null hypothesis. The simulation compares the empirical sizes and powers of the LMP test and the empirical likelihood test, demonstrating that the LMP test outperforms the EL test in accuracy by 10.2%, 10.1%, and 30.9% under conditions of normal, Beta-distributed, and contaminated errors, respectively. We provide two sets of real data to illustrate the practical effectiveness of the LMP test. [ABSTRACT FROM AUTHOR]

Background: Simulation is an important tool for assessing the performance of statistical methods for the analysis of data and for the planning of studies. While methods are available for the simulation of correlated binary random variables, all have significant practical limitations for simulating outcomes from longitudinal cluster randomised trial designs, such as the cluster randomised crossover and the stepped wedge trial designs. For these trial designs as the number of observations in each cluster increases these methods either become computationally infeasible or their range of allowable correlations rapidly shrinks to zero. Methods: In this paper we present a simple method for simulating binary random variables with a specified vector of prevalences and correlation matrix. This method allows for the outcome prevalence to change due to treatment or over time, and for a 'nested exchangeable' correlation structure, in which observations in the same cluster are more highly correlated if they are measured in the same time period than in different time periods, and where different individuals are measured in each time period. This means that our method is also applicable to more general hierarchical clustered data contexts, such as students within classrooms within schools. The method is demonstrated by simulating 1000 datasets with parameters matching those derived from data from a cluster randomised crossover trial assessing two variants of stress ulcer prophylaxis. Results: Our method is orders of magnitude faster than the most well known general simulation method while also allowing a much wider range of correlations than alternative methods. An implementation of our method is available in an R package NestBin. Conclusions: This simulation method is the first to allow for practical and efficient simulation of large datasets of binary outcomes with the commonly used nested exchangeable correlation structure. This will allow for much more effective testing of designs and inference methods for longitudinal cluster randomised trials with binary outcomes. [ABSTRACT FROM AUTHOR]

The probabilistic seismic demand model (PSDM) is essential to identify the seismic demand of the highway bridge during and after an earthquake. This paper aims to review the probabilistic seismic demand estimation and modeling methodology options associated with the procedure, analytical analysis, and mathematical framework for a highway bridge. As a result of the review, different techniques with features, applications, and limitations on highway bridges are reviewed and presented. A review has investigated the current PSDM and provides a comprehensive summary with formulas, tables, figures, and frameworks. PSDM steps are constructed and introduced to how scholars use them. Besides, analytical methods are the best choice for investigating the PSDA and PSDM for critical bridge components when damage data is insufficient. They are determined to predict each component's seismic response for a given deterministic or random variable. This work helps and motivates the decision-makers and stakeholders to extend the application of the PSDM methodology option for a more informed decision. [ABSTRACT FROM AUTHOR]

Comfort has traditionally been assessed as a single deterministic index that can be assigned to each railway vehicle type (at a given speed on a given track quality level). However, it is now well established that passengers influence vibration and, as a consequence, occupancy level and seating arrangement influence comfort, thus turning it into a stochastic variable. The concept of Compound Comfort, presented in Palomares et al. [Is the standard ride comfort index an actual estimation of railway passenger comfort? Veh Syst Dyn. 2022;1–14. doi: ], is used in this paper to evaluate several train types. Simplified models are used as a first approximation for vibration analysis. Despite model simplicity, since the number of possible seating arrangements is intractable, a Monte Carlo procedure is used to obtain compound comfort probability density distributions from a randomised subset of cases. The results from the work presented here will show that the information provided by stochastic distributions is much richer than a single deterministic index. Nevertheless, obtaining distributions from Monte Carlo tests (numerical or experimental) is impractical for any commercial assessment of comfort. Therefore, an inference procedure is called for and has been devised in order to obtain probability density function parameters from just one tare test, along with ten runs of a half laden test. This recipe has been adapted from one presented previously to be able to accommodate the skewed distributions that emerge when a wide range of train configurations is considered. [ABSTRACT FROM AUTHOR]

In this paper, we generalize two new statistical distributions, to improve the ability to model failure rates with non-monotonic, monotonic, and mainly bathtub curve behaviors. We call these distributions Generalized Powered Uniform Distribution and MOE-Powered Uniform. The proposed distributions' approach is based on incorporating a parameter k in the power of the values of the random variables, which is associated with the Probability Density Function and includes an operator called the Powered Mean. Various statistical and mathematical features focused on reliability analysis are presented and discussed, to make the models attractive to reliability engineering or medicine specialists. We employed the Maximum Likelihood Estimator method to estimate the model parameters and we analyzed its performance through a Monte Carlo simulation study. To demonstrate the flexibility of the proposed approach, a comparative analysis was carried out on four case studies with the proposed MOE-Powered Uniform distribution, which can model failure times as a bathtub curve. The results showed that this new model is more flexible and useful for performing reliability analysis. [ABSTRACT FROM AUTHOR]

This paper examines the Wasserstein metric between the empirical probability measure of n discrete random variables and a continuous uniform measure in the d-dimensional ball, providing an asymptotic estimation of their expectations as n approaches infinity. Furthermore, we investigate this problem within a mixed process framework, where n discrete random variables are generated by the Poisson process. [ABSTRACT FROM AUTHOR]

The complete characterization of the almost-entropic region yields rate regions for network coding problems. However, this characterization is difficult and open. In this paper, we propose a novel algorithm to determine whether an arbitrary vector in the entropy space is entropic or not, by parameterizing and generating probability mass functions by neural networks. Given a target vector, the algorithm minimizes the normalized distance between the target vector and the generated entropic vector by training the neural network. The algorithm reveals the entropic nature of the target vector, and obtains the underlying distribution, accordingly. The proposed algorithm was further implemented with convolutional neural networks, which naturally fit the structure of joint probability mass functions, and accelerate the algorithm with GPUs. Empirical results demonstrate improved normalized distances and convergence performances compared with prior works. We also conducted optimizations of the Ingleton score and Ingleton violation index, where a new lower bound of the Ingleton violation index was obtained. An inner bound of the almost-entropic region with four random variables was constructed with the proposed method, presenting the current best inner bound measured by the volume ratio. The potential of a computer-aided approach to construct achievable schemes for network coding problems using the proposed method is discussed. [ABSTRACT FROM AUTHOR]

In the last two decades, survey researchers have intensively used computerised methods for the collection of different types of paradata, such as keystrokes, mouse clicks and response times, to evaluate and improve survey instruments as well as to understand the survey response process. With the growing popularity of web surveys, the importance of paradata has further increased. Within this context, response time measurement is the prevailing paradata approach. Papers typically analyse the time (measured in milliseconds or seconds) a respondent needs to answer a certain item, question, page or questionnaire. One of the key challenges when analysing the response time is to identify and separate units that are answering too quickly or too slowly. These units can have a poor response quality and are typically labelled as response time outliers. This paper focuses on approaches for identifying and processing response time outliers. It presents a systematic overview of scientific papers on response time outliers in web surveys. The key observed characteristics of the papers are the approaches used, the level of time measurement, the processing of response time outliers and the relationship between response time and response quality. The results show that knowledge on response time outliers is scattered, inconsistent and lacking systematic comparisons of approaches. Consequently, there is a need to improve and upgrade the knowledge on this issue and to develop new approaches that will overcome existing deficiencies and inconsistencies in identifying and dealing with response time outliers. [ABSTRACT FROM AUTHOR]

This paper studies the downlink of a cloud radio access network (C-RAN) in which a centralized processor (CP) communicates with mobile users through base stations (BSs) that are connected to the CP via finite-capacity fronthaul links. Information theoretically, the downlink of a C-RAN is modeled as a two-hop broadcast-relay network. Among the various transmission and relaying strategies for such model, this paper focuses on the compression strategy, in which the CP centrally encodes the signals to be broadcast jointly by the BSs, then compresses and sends these signals to the BSs through the fronthaul links. We characterize an achievable rate region for a generalized compression strategy with Marton’s multicoding for broadcasting and multivariate compression for fronthaul transmission. We then compare this rate region with the distributed decode-forward (DDF) scheme, which achieves the capacity of the general relay networks to within a constant gap, and show that the difference lies in that DDF performs Marton’s multicoding and multivariate compression jointly as opposed to successively as in the compression strategy. A main result of this paper is that under the assumption that the fronthaul links are subject to a sum capacity constraint, this difference is immaterial; so, for the Gaussian network, the compression strategy based on successive encoding can already achieve the capacity region of the C-RAN to within a constant gap, where the gap is independent of the channel parameters and the power constraints at the BSs. As a further result, for C-RAN under individual fronthaul constraints, this paper also establishes that the compression strategy can achieve to within a constant gap to the sum capacity. [ABSTRACT FROM AUTHOR]

This paper studies the problem of estimating the covariance of a collection of vectors using only highly compressed measurements of each vector. An estimator based on back-projections of these compressive samples is proposed and analyzed. A distribution-free analysis shows that by observing just a single linear measurement of each vector, one can consistently estimate the covariance matrix, in both infinity and spectral norm, and this analysis leads to precise rates of convergence in both norms. Through information-theoretic techniques, lower bounds showing that this estimator is minimax-optimal for both infinity and spectral norm estimation problems are established. These results are also specialized to give matching upper and lower bounds for estimating the population covariance of a collection of Gaussian vectors, again in the compressive measurement model. The analysis conducted in this paper shows that the effective sample complexity for this problem is scaled by a factor of $m^{2}/d^{2}$ , where $m$ is the compression dimension and $d$ is the ambient dimension. Applications to subspace learning (principal components analysis) and learning over distributed sensor networks are also discussed. [ABSTRACT FROM AUTHOR]

In this paper we consider two random variables in a cell in the network of mobile users. The first random variable (RV) is the distance of active mobile user from a base station. The second RV is emission power for the random active user if the control of emission power exists. RV emission power is dependent RV of the first RV. That's why the calculations of mean values for these RVs differ one from the other. The first RV depends only on the users' density area distribution. The second RV depends on the signal attenuation value in the considered environment. It is proved that, in real conditions, emission power to a user at the mean value of distance from a base station is always lower than mean value of emission power to a user. The difference between these two power values increases as the signal attenuation coefficient increases. These two values are calculated for three characteristic user density distributions in a cell. The results are verified by original computer simulation programs. [ABSTRACT FROM AUTHOR]

The authors study the complete convergence and complete moment convergence for weighted sums of m-extended negatively dependent (m-END) random variables. The results obtained in this paper extend and improve the corresponding results of Wu, Zhai and Peng [Y. F. Wu, M. Q. Zhai and J. Y. Peng, On the complete convergence for weighted sums of extended negatively dependent random variables, Journal of Mathematical Inequalities, 13 (1) (2019), 251–260] and Zarei and Jabbari [H. Zarei and H. Jabbari, Complete convergence of weighted sums under negative dependence, Statistical Papers, 52 (2011), 413–418]. [ABSTRACT FROM AUTHOR]

This paper provides new insight into the theoretical principle and the practical applicability of the ranked nodes method (RNM) that is used to construct conditional probability tables (CPTs) for Bayesian networks (BNs) by expert elicitation. RNM is designed for specific types of discrete random variables called ranked nodes that are common in real-world applications of BNs. Despite its active use in recent years, there remains ambiguity about the exact theoretical basis of RNM which can hamper its effective employment. In addition, there are a lack of studies about the general ability of CPTs generated with RNM to represent probabilistic relationships in real-world applications. In this paper, it is shown how the generation of probabilities with RNM is underpinned by a regression model of continuous random variables. Then, it is experimentally determined that in typical applications of RNM, one can generate in a matter of seconds CPTs whose elements reflect well probabilities given by the underlying regression model. Another experiment discovers that CPTs generated with RNM provide a good average fit to a large portion of various real-world CPTs investigated. This confirms the usefulness of RNM in practical applications. The results of the experiment also indicate that choices made by the user of RNM can considerably impact the ability of a generated CPT to represent a given probabilistic relationship. This paper then provides practical advice on the efficient use of RNM with regard to the user-controlled features explored in the experiment. [ABSTRACT FROM AUTHOR]

This special issue of the journal is a compilation of papers from the 41 SP st sp IAPSP Annual Conference entitled "Vienna-Kohut-Self Psychology: Searching for Creativity in Times of Crisis." Kottler and Ben co-create a unique, shared visual language in treatment, giving voice to Ben's less articulated and nascent self-states. As they work through their painful encounter, Kottler and Ben confront their largely hidden, alienated alter-ego self-states, "between different parts within a person and between people" (p. 74), which Togashi links to Buber's notion of I-Thou authentic dialogue. [Extracted from the article]

This paper presents secrecy analyses of a full-duplex MIMOME network which consists of two full-duplex multi-antenna users (Alice and Bob) and an arbitrarily located multi-antenna eavesdropper (Eve). The paper assumes that Eve's channel state information (CSI) is completely unknown to Alice and Bob except for a small radius of secured zone. The first part of this paper aims to optimize the powers of jamming noises from both users. To handle Eve's CSI being unknown to users, the focus is placed on Eve at the most harmful location, and the large matrix theory is applied to yield a hardened secrecy rate to work on. The performance gain of the power optimization in terms of maximum tolerable number of antennas on Eve is shown to be significant. The second part of this paper shows two analyses of anti-eavesdropping channel estimation (ANECE) that can better handle Eve with any number of antennas. One analysis assumes that Eve has a prior statistical knowledge of its CSI, which yields lower and upper bounds on secure degrees of freedom of the system as functions of the number (N) of antennas on Eve and the size (K) of information packet. The second analysis assumes that Eve does not have any prior knowledge of its CSI but performs blind detection of information, which yields an approximate secrecy rate for the case of K being larger than N. [ABSTRACT FROM AUTHOR]

This paper discusses the dissipative filtering problem for discrete-time nonlinear networked systems with dynamic quantization and data packet dropouts. The Takagi–Sugeno (T–S) fuzzy model is employed to approximate the considered nonlinear plant. Both the measurement and performance outputs are assumed to be quantized by the dynamic quantizers before being transmitted. Moreover, the Bernoulli stochastic variables are utilized to characterize the effects of data packet dropouts on the measurement and performance outputs. The purpose of this paper is to design full- and reduced-order filters, such that the stochastic stability and dissipative filtering performance for the filtering error system can be guaranteed. The collaborative design conditions for the desired filter and the dynamic quantizers are expressed in the form of linear matrix inequalities. Finally, simulation results are used to illustrate the feasibility of the proposed filtering scheme. [ABSTRACT FROM AUTHOR]

In recent years, uncertainty analysis is a hot topic in the field of electromagnetic compatibility simulation. The actual electromagnetic environment is simulated by considering the randomness of the model input parameters. However, there are currently two key issues that have not been resolved. One is the curse of dimensionality problem that occurs when there are many random variables. The other is how to establish a random input model with generality and portability. In order to address these issues, this paper proposes a new random input modeling method called random variable black box model. When applying to the Stochastic Collocation Method with dimensionality reduction sparse grid strategy, the applicability of this uncertainty analysis method can be extended to any probability density function, then enabling efficient electromagnetic compatibility simulation uncertainty analysis of high-dimensional random variable models and fundamentally solving the curse of dimensionality problem. Finally, this paper implements a joint simulation technology of the MATLAB software and COMSOL software to verify the strong portability of the random variable black box model, ensuring that advanced uncertainty analysis methods can be smoothly introduced into commercial electromagnetic simulation software and expanding the application scope of uncertainty analysis. [ABSTRACT FROM AUTHOR]

Let X1, X2, . . ., Xn be a sequence of coherent random variables, i.e., satisfying the equalities Xj = P(A|Gj), j = 1, 2, . . ., n, almost surely for some event A. This paper contains the proof of the estimate P (max 1=i

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In the paper, we establish the complete convergence for weighted sums of random variables satisfying generalized Rosenthal-type inequalities. Our results partially extend some known results and weaken their conditions. As statistical applications, we study the nonparametric regression model and obtain the complete consistency of the weighted regression estimator for the unknown regression functions. [ABSTRACT FROM AUTHOR]

In this paper, the asmptotics is considered for the distribution tail of a randomly stopped sum Sν = X1 + ··· + Xν of independent identically distributed consistently varying random variables with zero mean, where ν is a counting random variable independent of {X1,X2, . . .}. The conditions are provided for the relation P(Sν > x) ∼ Eν P(X1 > x) to hold, as x →∞, involving the finiteness of E|X1|. The result improves that of Olvera-Cravioto [14], where the finiteness of a moment E|X1|r for some r > 1 was assumed. [ABSTRACT FROM AUTHOR]

This paper analyses the disruptions occurring in a production system determining the operating states of a single machine. A system with a convergent production character, in which both single flows (streams) and multi-stream flows occur, was considered. In this paper, a two-level formalisation of the production system (PS) was made according to complex systems theory. The continuity analysis was performed at the operational level (manufacturing machine level). The definition of the kth survival value and the quasi-coherence property defined on chains of synchronous relations were used to determine the impact of interruption of the processed material flow on uninterrupted machine operation. The developed methodology is presented in terms of shaping the energy efficiency of technical objects with the highest power demand (the furnace of an automatic paint shop and the furnace of a glass tempering line were taken into consideration). The proposed methodology is used to optimise energy consumption in complex production structures. The model presented is utilitarian in nature—it can be applied to any technical system where there is randomness of task execution times and randomness of unplanned events. This paper considers the case in which two mutually independent random variables determining the duration of correct operation T P and the duration of breakdown T B are determined by a given distribution: Gaussian and Gamma family distributions (including combinations of exponential and Erlang distributions). A formalised methodology is also developed to determine the stability of system operation, as well as to assess the potential risk for arbitrary system evaluation parameters. [ABSTRACT FROM AUTHOR]

In this paper, the asymptotic normality and strong consistency for M estimators of the unknown regression coefficients in classical linear models are established under the assumptions that the errors are identically distributed φ-mixing random variables. The results obtained in this paper generalize the corresponding ones of Chen and Zhao [M-methods in linear model. Shanghai: Scientific and Technical Publishers; 1996] and Zhao [Strong consistency of M-estimates in linear model. Sci China Ser A. 2002;45:1420–1427] for independent errors. Finally, the simulation study is provided to verify the finite sample performance of the theoretical results and a real example is analysed for illustration. [ABSTRACT FROM AUTHOR]

Theoretical analysis and empirical study results all show that there are situations in reality where observed data are not random variables. Thus, decision-making criteria based on probability theory are not suitable for people to make decisions. This paper proposes an uncertain dominance based on uncertainty theory to offer an alternative decision-making criterion for such situations. The paper first defines a new criterion of first- and second-order uncertain dominance, then proves some necessary conditions of them based on uncertainty theory. Some sufficient and necessary conditions of the first- and second-order uncertain dominance are given when uncertain variables are all normal or linear uncertain variables. In addition, the paper proves the link between the uncertain dominance criterion and the expected utility criterion and shows that the first-order uncertain dominance is suitable for all people to make decisions and the second-order uncertain dominance is suitable for risk-averse people to make decisions. [ABSTRACT FROM AUTHOR]

The generalized Kaiser–Bessel window function is defined via the modified Bessel function of the first kind and arises frequently in tomographic image reconstruction. In this paper, we study in details the properties of the Kaiser–Bessel distribution, which we define via the symmetric form of the generalized Kaiser–Bessel window function. The Kaiser–Bessel distribution resembles to the Bessel distribution of McKay of the first type, it is a platykurtic or sub-Gaussian distribution, it is not infinitely divisible in the classical sense and it is an extension of the Wigner's semicircle, parabolic and n-sphere distributions, as well as of the ultra-spherical (or hyper-spherical) and power semicircle distributions. We deduce the moments and absolute moments of this distribution and we find its characteristic and moment generating function in two different ways. In addition, we find its cumulative distribution function in three different ways and we deduce a recurrence relation for the moments and absolute moments. Moreover, by using a formula of Ismail and May on quotient of modified Bessel functions of the first kind, we deduce a closed-form expression for the differential entropy. We also prove that the Kaiser–Bessel distribution belongs to the family of log-concave and geometrically concave distributions, and we study in details the monotonicity and convexity properties of the probability density function with respect to the argument and each of the parameters. In the study of the monotonicity with respect to one of the parameters we complement a known result of Gronwall concerning the logarithmic derivative of modified Bessel functions of the first kind. Finally, we also present a modified method of moments to estimate the parameters of the Kaiser–Bessel distribution, and by using the classical rejection method we present two algorithms for sampling independent continuous random variables of Kaiser–Bessel distribution. The paper is closed with conclusions and proposals for future works. [ABSTRACT FROM AUTHOR]

In this paper we study the Marcinkiewicz–Zygmund-type strong law of large numbers with general normalizing sequences under sublinear expectation. Specifically, we establish complete convergence in the Marcinkiewicz–Zygmund-type strong law of large numbers for sequences of negatively dependent and identically distributed random variables under certain moment conditions. We also give results for sequences of independent and identically distributed random variables. The moment conditions in this paper are based on a class of slowly varying functions that satisfy some convergence properties. Moreover, some special examples and comparisons to existing results are also given. [ABSTRACT FROM AUTHOR]

The paper has two main objectives. Firstly, it explores the properties of hyperbolic cosine and hyperbolic sine functions by using Volkenborn and the fermionic p-adic integrals, respectively. It also investigates interesting identities involving Bernoulli and degenerate Bernoulli numbers from differential equations with their solutions. Secondly, it introduces a random variable whose mass function is given in terms of Euler polynomials and find some expressions for the expectation of the random variable. [ABSTRACT FROM AUTHOR]

For the current problems of complex network state, difficulty in fast response to intrusion and poor adaptation of response decision in fog computing environment, in this paper, we propose an intrusion response decision method based on a combination of deep learning and reinforcement learning based on game theory (Minimax-DQN). First, a Markov game is used as the standard to construct the intrusion response decision model in the fog computing environment. Second, two different sets of random variables are defined considering the possible behavioral choices taken by the attacker and the fog computing intrusion detection systems (FC-IDS), and the continuous state space formed by the game between the attacker and the FC-IDS is processed using a deep Q-network. Finally, the Minimax algorithm is used to solve the optimal value function in a specific state, and the best intrusion response strategy is obtained according to the training output after the training is completed. Three sets of experiments are conducted to compare the results of the Minimax-DQN algorithm, the DQN algorithm and the random strategy. The experimental results data prove that the model and the proposed algorithm can greatly improve the probability of IDS winning in the game process with the attacker, and thus effectively solve the problem of intrusion response decision in fog environment. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to solve the problem that pipes conveying fluid are faced with severe reliability failures under the complicated working environment. Design/methodology/approach: This paper proposes a dynamic reliability and variance-based global sensitivity analysis (GSA) strategy with non-probabilistic convex model for pipes conveying fluid based on the first passage principle failure mechanism. To illustrate the influence of input uncertainty on output uncertainty of non-probability, the main index and the total index of variance-based GSA analysis are used. Furthermore, considering the efficiency of traditional simulation method, an active learning Kriging surrogate model is introduced to estimate the dynamic reliability and GSA indices of the structure system under random vibration. Findings: The variance-based GSA analysis can measure the effect of input variables of convex model on the dynamic reliability, which provides useful reference and guidance for the design and optimization of pipes conveying fluid. For designers, the rankings and values of main and total indices have essential guiding role in engineering practice. Originality/value: The effectiveness of the proposed method to calculate the dynamic reliability and sensitivity of pipes conveying fluid while ensuring the calculation accuracy and efficiency in the meantime. [ABSTRACT FROM AUTHOR]

The takeoff point in this paper is a random variable X for which large positive values are desired. When its probability distribution is highly skewed, the possibility of a long fat-tailed distribution can lead to an expected value, \mu =\mathbb E[ X] , which is unduly optimistic. For the reverse case when small values of X are desired, the ideas in this paper are applied to - X . This issue of over-optimism in the expected value is particularly important when a mission-critical random variable is involved. For example, when considering earthquake intensity or flood levels, reporting an understated expected value to a technically unsophisticated general public would be considered by many as highly undesirable. The Conservative Expected Value (CEV) of X , denoted by \mathbb CEV ( X ) is a new definition provided in this paper. It is a metric which we argue is particularly useful when risk aversion must be highly emphasized. At the same time, while being conservative, the CEV is also aimed at avoiding reflection of excessive pessimism. When, then \mathbb CEV ( X ), while being conservative, is defined in such a way so as not to be unduly pessimistic. In classical analysis, enhancement of a calculation often includes the variance \sigma ^ 2 \,\, = var( X ). However, when large X -values are desired, this may further distort one’s overview of the risk at hand; e.g., if X is profit, values above the mean should not be penalized. With these one-sidedness considerations in mind, we work with a new reward-risk pair, the CEV and the so-called Conservative Semi-Variance (CSV) of X , denoted by \mathbb CSV ( X ). Whereas the CEV definition is entirely new, the CSV definition is motivated by ideas in the area of finance. This paper also illustrates calculation of the CEV and CSV pair for a number of classical probability distributions and includes description of a number of properties of these metrics which suggest that this new theory is mathematically rich. Finally, we demonstrate the potential for application of the theory via two numerical examples. [ABSTRACT FROM AUTHOR]

This paper considers a general stochastic resource allocation problem that arises widely in wireless networks, cognitive radio, networks, smart-grid communications, and cross-layer design. The problem formulation involves expectations with respect to a collection of random variables with unknown distributions, representing exogenous quantities such as channel gain, user density, or spectrum occupancy. We consider the constant step-size stochastic dual subgradient descent (SDSD) method that has been widely used for online resource allocation in networks. The problem is solved in dual domain, which results in a primal resource allocation subproblem at each time instant. The goal here is to characterize the non-asymptotic behavior of such stochastic resource allocations in an almost sure sense. It is well known that with a step size of \epsilon , SDSD converges to an \mathcal {O}(\epsilon) -sized neighborhood of the optimum. In practice, however, there exists a trade-off between the rate of convergence and the choice of \epsilon $ . This paper establishes a convergence rate result for the SDSD algorithm that precisely characterizes this trade-off. Toward this end, a novel stochastic bound on the gap between the objective function and the optimum is developed. The asymptotic behavior of the stochastic term is characterized in an almost sure sense, thereby generalizing the existing results for the stochastic subgradient methods. For the stochastic resource allocation problem at hand, the result explicates the rate with which the allocated resources become near-optimal. As an application, the power and user-allocation problem in device-to-device networks is formulated and solved using the SDSD algorithm. Further intuition on the rate results is obtained from the verification of the regularity conditions and accompanying simulation results. [ABSTRACT FROM PUBLISHER]

In his article Willems (Clim Chang 120(4):931-944, ) proposed a methodology to analyse extremes in rainfall series. When applying it to artificially generated, non-cyclic random variables we were able to detect cyclic behavior. Therefor we had a closer look on the methodology. Here we discuss our considerations, why this method generates cycles, depending on chosen subperiods and their coherence between detected cycle lengths. To verify these relationships some examples based on random data samples are given. [ABSTRACT FROM AUTHOR]

The present paper is the second part of a series of papers aimed at assessing the accuracy of alchemical computational approaches based on nonequilibrium techniques for solvation free energy of organic molecules in the context of molecular dynamics simulations. In Paper I [Procacci, J. Chem. Phys. 151, 144113 (2019)], we dealt with bidirectional estimates of solvation free energies using nonequilibrium approaches. Here, we assess accuracy and precision of unidirectional estimates with the focus on the Gaussian and Jarzynski estimators. We present a very simple methodology to increase the statistics in the work distribution, hence boosting the accuracy and precision of the Jarzynski unidirectional estimates at no extra cost, exploiting the observed decorrelation between the random variables represented by the Lennard-Jones solute-solvent recoupling or decoupling work and by the electrostatic work due to the charging/discharging of the solute in the solvent. [ABSTRACT FROM AUTHOR]

In this paper, we study bounds for the total variation distance between distributions of second order polynomials in normal random variables provided that they essentially depend on at least three variables. Moreover, we partially extend some recent bounds for the Kolmogorov distance between the distributions of norms of Gaussian random vectors to the case of the total variation distance. [ABSTRACT FROM AUTHOR]

A considerable body of prior research has been dedicated to devising efficient and high‐order numerical methods for solving stochastic partial differential equations (SPDEs) driven by discrete or continuous random variables. The majority of these efforts have concentrated on introducing numerical approaches for SPDEs involving independent random variables, with limited exploration into solving SPDEs driven by dependent and discrete random variables. In this paper, we introduce a Galerkin spectral method tailored for addressing SPDEs driven by multivariate Poisson variables. Our novel numerical method is applied to solve the one‐ and two‐dimensional stochastic Poisson equations, as well as the one and two‐dimensional stochastic heat equation, stochastic KdV equation, and stochastic Burgers equation, respectively. Notably, all the presented stochastic equations are governed by two dependent Poisson random variables. [ABSTRACT FROM AUTHOR]

This paper considers a repairable system whose periods of operations and repairs alternate during the run time. The residual lifetime of the system and its age, when the system operates at time $t$ t , are proposed, and their properties are investigated. Under the condition that the system is under repair, the remaining time until the end of system repair time and the elapsed time of a repair are studied. Since computing a renewal function is not straightforward, we use phase-type approximation to find the best-fitted distribution of corresponding random variables. We provide some examples and utilize a real data set to demonstrate the results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate an extended version of the elephant random walk model. Unlike the traditional approach where step sizes remain constant, our model introduces a novel feature: step sizes are generated as a sequence of positive independent and identically distributed random variables, and the step of the walker at time n+1 depends only on the steps of the walker between times 1, ..., mn, where (mn)n⩾1 is a sequence of positive integers growing to infinity as n goes to infinity. Our main results deal with the validity of the central limit theorem for this new variation of the standard ERW model introduced by Schutz and Trimper in 2004. [ABSTRACT FROM AUTHOR]

This paper generalizes the concept of capacity from the portfolio level to the investment process for systematic equity strategies. Capacity is often understood as the maximum asset under management, above which additional inflows would have too great a negative impact on performance. The concept of capacity is often limited to the study of a given portfolio. However, setting up a capacity management framework must consider what the portfolio might look like in the future. This is obviously complicated for discretionary portfolios but theoretically conceivable for portfolios implementing systematic strategies, if we can simulate all possible scenarios. In our framework, we extend the traditional definition of capacity from a number to a random variable, allowing portfolio managers to integrate it into their risk considerations. We provide examples of how portfolio managers can approach this problem, with full-search or modelling methods. Our framework includes several capacity metrics that can be used jointly or selected to align better with the features of each strategy. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of H∞ performance analysis of 2D discrete singular stochastic system described by Roesser model which is challenging since it involves 2D random variables and the disturbance simultaneously. Sufficient conditions are established for the regularity, causality and stability of the system. The proposed results are expressed in terms of strict linear matrix inequalities. Furthermore, a mean square asymptotic stability with an $ H_{\infty } $ H ∞ disturbance level is developed. Simulation example is provided in order to illustrate the relevance of our approach. [ABSTRACT FROM AUTHOR]

In this paper, we construct a class of Z 4 Z 4 Z 4 -additive cyclic codes generated by 3-tuples of polynomials. We discuss their algebraic structure and show that generator matrices can be constructed for all codes in this class. We study asymptotic properties of this class of codes by using a Bernoulli random variable. Moreover, let 0 < δ < 1 be a real number such that the entropy h 4 ((k + l + t) δ 6) < 1 4 , we show that the relative minimum distance converges to δ and the rate of the random codes converges to 1 k + l + t , where k, l, and t are pairwise co-prime positive odd integers. Finally, we conclude that the Z 4 Z 4 Z 4 -additive cyclic codes are asymptotically good. [ABSTRACT FROM AUTHOR]

Cyber-security research on networked multi-sensor systems is crucial due to the vulnerability to various types of cyberattacks. For the development of effective defense measures, attention is required to gain insight into the complex characteristics and behaviors of cyber attacks from the attacker's perspective. This paper aims to tackle the problem of distributed consensus estimation for networked multi-sensor systems subject to hybrid attacks and missing measurements. To account for both random denial of service (DoS) attacks and false data injection (FDI) attacks, a hybrid attack model on the estimator-to-estimator communication channel is presented. The characteristics of missing measurements are defined by random variables that satisfy the Bernoulli distribution. Then a modified consensus-based distributed estimator, integrated with the characteristics of hybrid attacks and missing measurements, is presented. For reducing the computational complexity of the optimal distributed estimation method, a scalable suboptimal distributed consensus estimator is designed. Sufficient conditions are further provided for guaranteeing the stability of the proposed suboptimal distributed estimator. Finally, a simulation experiment on aircraft tracking is executed to validate the effectiveness and feasibility of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Because it is generally impossible to completely characterize the uncertainty in complex model variables after assimilation of data, it is common to approximate the uncertainty by sampling from approximations of the posterior distribution for model variables. When minimization methods are used for the sampling, the weights on each of the samples depend on the magnitude of the data mismatch at the critical points and on the Jacobian of the transformation from the prior density to the sample proposal density. For standard iterative ensemble smoothers, the Jacobian is identical for all samples, and the weights depend only on the data mismatch. In this paper, a hybrid data assimilation method is proposed which makes it possible for each ensemble member to have a distinct Jacobian and for the approximation to the posterior density to be multimodal. For the proposed hybrid iterative ensemble smoother, it is necessary that a part of the mapping from the prior Gaussian random variable to the data be analytic. Examples might include analytic transformation from a latent Gaussian random variable to permeability followed by a black-box transformation from permeability to state variables in porous media flow, or a Gaussian hierarchical model for variables followed by a similar black-box transformation from permeability to state variables. In this paper, the application of weighting to both hybrid and standard iterative ensemble smoothers is investigated using a two-dimensional, two-phase flow problem in porous media with various degrees of nonlinearity. As expected, the weights in a standard iterative ensemble smoother become degenerate for problems with large amounts of data. In the examples, however, the weights for the hybrid iterative ensemble smoother were useful for improving forecast reliability. [ABSTRACT FROM AUTHOR]

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

This paper analyzes the co-fluctuation between a scalar response random variable and a curve regressor using quantile regression. We focus on the situation wherein the output variable is observed with random missing. For this incomplete functional data situation, we estimate the quantile regression by combining two principal nonparametric methods: the local linearity approach (LLA) and the kernel nearest neighbor (KNN) algorithm. We study the asymptotic properties of the constructed estimator by establishing, under general assumptions, uniform consistency over the number of neighborhoods. This asymptotic result provides good mathematical support for the selection of the optimal neighborhood. We examine the feasibility of the constructed estimator using artificially generated data. Moreover, we apply the quantile regression technique in food quality by predicting the riboflavin quantity in yogurt using spectrometry data. [ABSTRACT FROM AUTHOR]

In this paper, for a wide class of nonparametric regression models, new local linear kernel estimators are proposed that are uniformly consistent under close-to-minimal and visual conditions on design points. These estimators are universal in the sense that their designs can be either fixed and not necessarily satisfying the traditional regularity conditions, or random, while not necessarily consisting of independent or weakly dependent random variables. With regard to the design elements, only dense filling of the regression function domain with the design points without any specification of their correlation is assumed. This study extends the dense data methodology and main results of the authors' previous work for the case of regression functions of several variables. [ABSTRACT FROM AUTHOR]

For the RRT* algorithm, there are problems such as greater randomness, longer time consumption, more redundant nodes, and inability to perform local obstacle avoidance when encountering unknown obstacles in the path planning process of autonomous vehicles. And the artificial potential field method (APF) applied to autonomous vehicles is prone to problems such as local optimality, unreachable targets, and inapplicability to global scenarios. A fusion algorithm combining the improved RRT* algorithm and the improved artificial potential field method is proposed. First of all, for the RRT* algorithm, the concept of the artificial potential field and probability sampling optimization strategy are introduced, and the adaptive step size is designed according to the road curvature. The path post-processing of the planned global path is carried out to reduce the redundant nodes of the generated path, enhance the purpose of sampling, solve the problem where oscillation may occur when expanding near the target point, reduce the randomness of RRT* node sampling, and improve the efficiency of path generation. Secondly, for the artificial potential field method, by designing obstacle avoidance constraints, adding a road boundary repulsion potential field, and optimizing the repulsion function and safety ellipse, the problem of unreachable targets can be solved, unnecessary steering in the path can be reduced, and the safety of the planned path can be improved. In the face of U-shaped obstacles, virtual gravity points are generated to solve the local minimum problem and improve the passing performance of the obstacles. Finally, the fusion algorithm, which combines the improved RRT* algorithm and the improved artificial potential field method, is designed. The former first plans the global path, extracts the path node as the temporary target point of the latter, guides the vehicle to drive, and avoids local obstacles through the improved artificial potential field method when encountered with unknown obstacles, and then smooths the path planned by the fusion algorithm, making the path satisfy the vehicle kinematic constraints. The simulation results in the different road scenes show that the method proposed in this paper can quickly plan a smooth path that is more stable, more accurate, and suitable for vehicle driving. [ABSTRACT FROM AUTHOR]