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Chiral-induced-spin-selectivity of electron transport and its interplay with DNA's mechanical motion are explored in a double stranded DNA helix with spin–orbit-coupling. The mechanical degree of freedom is treated as a stochastic classical variable experiencing fluctuations and dissipation induced by the environment as well as force exerted by nonequilibrium, current-carrying electrons. Electronic degrees of freedom are described quantum mechanically using nonequilibrium Green's functions. Nonequilibrium Green's functions are computed along the trajectory for the classical variable taking into account dynamical, velocity dependent corrections. This mixed quantum-classical approach enables calculations of time-dependent spin-resolved currents. We showed that the electronic force may significantly modify the classical potential, which, at sufficient voltage, creates a bistable potential with a considerable effect on electronic transport. The DNA's mechanical motion has a profound effect on spin transport; it results in chiral-induced spin selectivity, increasing spin polarization of the current by 9% and also resulting in temperature-dependent current voltage characteristics. We demonstrate that the current noise measurement provides an accessible experimental means to monitor the emergence of mechanical instability in DNA motion. The spin resolved current noise also provides important dynamical information about the interplay between vibrational and spin degrees of freedom in DNA. [ABSTRACT FROM AUTHOR]

While the linear Pearson correlation coefficient represents a well-established normalized measure to quantify the inter-relation of two stochastic variables X and Y, it fails for multidimensional variables, such as Cartesian coordinates. Avoiding any assumption about the underlying data, the mutual information I(X, Y) does account for multidimensional correlations. However, unlike the normalized Pearson correlation, it has no upper bound (I ∈ [0, ∞)), i.e., it is not clear if say, I = 0.4 corresponds to a low or a high correlation. Moreover, the mutual information (MI) involves the estimation of high-dimensional probability densities (e.g., six-dimensional for Cartesian coordinates), which requires a k nearest-neighbor algorithm, such as the estimator by Kraskov et al. [Phys. Rev. E 69, 066138 (2004)]. As existing methods to normalize the MI cannot be used in connection with this estimator, a new approach is presented, which uses an entropy estimation method that is invariant under variable transformations. The algorithm is numerically efficient and does not require more effort than the calculation of the (un-normalized) MI. After validating the method by applying it to various toy models, the normalized MI between the Cα-coordinates of T4 lysozyme is considered and compared to a correlation analysis of inter-residue contacts. [ABSTRACT FROM AUTHOR]

We consider a production-inventory system in which the facility produces continuously, switching between two production rates: one faster and one slower than the average demand rate. Demand follows a compound Poisson process, and the size of each demand request is an exponential random variable. Unsatisfied demand is backordered. The production-inventory system is controlled by a two-critical number policy (r, R), whereby production switches from the slower rate to the faster rate when inventory drops below level r and from the faster rate to the slower rate when inventory reaches level R. A fixed cost occurs whenever production switches rates. Our analysis covers two cases: r ≥ 0 and the less studied case of r ≤ 0. We use a level crossing approach to derive the steadystate distribution of the inventory level. Using the steady-state distribution of the inventory level, we calculate the total expected inventory holding, backorder, and switchover costs for each of the two cases. We outline how to obtain the optimal policy through a search of the expected cost functions. We also propose heuristics that give simple closed-form solutions with near-optimal performance. Through a numerical study, we illustrate the importance of considering the r ≤ 0 case. [ABSTRACT FROM AUTHOR]

Planning and scheduling approaches in real manufacturing environments entail the need to cope with random attributes and variables to match the characteristics of real scheduling problems where uncertain events are frequent. Moreover, the capability of devising robust schedules, which are less sensitive to the disruptive effects of unexpected events, is a major request in real applications. In this paper, a branch-and-bound approach is proposed to solve the two-machine permutation flow shop scheduling problem with stochastic processing times. The objective is the minimisation of the value-at-risk of the makespan, to support decision-makers in the trade-off between the expected performance and the mitigation of the impact of extreme scenarios. A Markovian Activity Network (MAN) model is adopted to estimate the distribution of the makespan and assess the value-at-risk for both partial and complete schedules. Phase-type distributions are used to enable general distributions for processing times while maintaining the capability to exploit a Markovian approach. The effectiveness and performance of the proposed approach are demonstrated through a set of computational experiments. [ABSTRACT FROM AUTHOR]

Simulations of condensed matter systems often focus on the dynamics of a few distinguished components but require integrating the full system. A prime example is a molecular dynamics simulation of a (macro)molecule in a solution, where the molecule(s) and the solvent dynamics need to be integrated, rendering the simulations computationally costly and often unfeasible for physically/biologically relevant time scales. Standard coarse graining approaches can reproduce equilibrium distributions and structural features but do not properly include the dynamics. In this work, we develop a general data-driven coarse-graining methodology inspired by the Mori–Zwanzig formalism, which shows that macroscopic systems with a large number of degrees of freedom can be described by a few relevant variables and additional noise and memory terms. Our coarse-graining method consists of numerical integrators for the distinguished components, where the noise and interaction terms with other system components are substituted by a random variable sampled from a data-driven model. The model is parameterized using data from multiple short-time full-system simulations, and then, it is used to run long-time simulations. Applying our methodology to three systems—a distinguished particle under a harmonic and a bistable potential and a dimer with two metastable configurations—the resulting coarse-grained models are capable of reproducing not only the equilibrium distributions but also the dynamic behavior due to temporal correlations and memory effects. Remarkably, our method even reproduces the transition dynamics between metastable states, which is challenging to capture correctly. Our approach is not constrained to specific dynamics and can be extended to systems beyond Langevin dynamics, and, in principle, even to non-equilibrium dynamics. [ABSTRACT FROM AUTHOR]

A novel approach to the construction of absolutely continuous distributions over the unit interval is proposed. Considering two absolutely continuous random variables with positive support, this method conditions on their convolution to generate a new random variable in the unit interval. This approach is demonstrated using some popular choices of positive random variables, such as the exponential, Lindley, and gamma. Some existing distributions, like the uniform, the beta, and the Kummer-beta, are formulated with this method. Several new structures of density functions having potential for future applications in real-life problems are also provided. One of the new distributions, namely the LCG, is considered for detailed study along with a related distribution, namely the GCL. The moments, hazard rate, cumulative distribution function, stress-strength reliability, random sample generation using the quantile function, method of moments along with maximum likelihood estimation, and regression modeling are discussed for both the distributions. Real-life applications of the proposed models and the corresponding regression models show promising results. [ABSTRACT FROM AUTHOR]

In this article, the complete convergence for the partial sum of the moving average process { X n = ∑ i = − ∞ ∞ a i Y i + n , n ≥ 1 } is established under some mild conditions, where { Y i , − ∞ < i < ∞ } is a sequence of extended negatively dependent and identically distributed random variables that is stochastically dominated by a random variable Y under a sub-linear expectation (Ω , H , E ̂) , and { a i , − ∞ < i < ∞ } is an absolutely summable sequence of real numbers. These conclusions promote and improve the corresponding results of moving the average process under extended negatively dependent random variables from the traditional probability space to the sub-linear expectation space. [ABSTRACT FROM AUTHOR]

Recently developed inerter-based dampers have been installed at the base layer to reduce base displacement and simultaneously improve the superstructure's performance. However, in the existing research on optimizing damper parameters, the nonlinear property of base isolation is simplified and stochastic linearization technique is introduced to approximate such nonlinearity, which would inevitably introduce errors. In this paper, an improved method is proposed for stochastic optimization of electromagnetic inertial mass dampers (EIMD) in nonlinear hybrid isolation systems subject to seismic excitations. First, a stochastic seismic excitation is represented by one elementary random variable adopting the dimension-reduction spectral representation method. Then, statistical moments of nonlinear base-isolated structural responses are estimated using two-point estimation method (2PEM). Finally, the EIMD optimal parameters are obtained via the modified directional bat algorithm (MDBA) recently proposed by the authors through minimizing base layer response moments. This proposed improved method could fully consider the base isolation nonlinearity compared with the previous stochastic linearization technique. Moreover, the proposed stochastic optimization of the EIMD only requires two dynamic analyses to achieve its efficiency. A seven-story base-isolated frame building equipped with an EIMD is investigated in the numerical simulation, and results indicate that EIMD optimized by this proposed method obviously outperforms the results by the stochastic linearization technique and the conventional viscous damper (VD) in the base layer displacement reduction. [ABSTRACT FROM AUTHOR]

Performing reliability analysis for reinforced concrete structures is a tedious and challenging task because it requires conducting a four-nested loop calculation procedure involving millions of data samples to account for the complex behaviours of the structures and multiple random variables. Therefore, the study proposes a novel, practical, and accurate reliability framework that is applicable for multi-component RC frame structures exhibiting different behaviours ranging from linear elastic and non-linear elastic to non-linear plastic. For this purpose, this study first employs a tree-based boosting ensemble model combined with quantile regression, dubbed as QR-LightGBM to calculate the structures' limit state function and the associated uncertainty estimation at the same time. Next, an active learning process is implemented to improve the computed reliability results progressively. During each active learning step, relevant data samples with potentially high impacts on the model accuracy are determined based on their uncertainty, and then QR-LightGBM is retrained utilizing these samples. By doing so, the prediction performance of the surrogate model is enhanced with a minimized number of actual data samples, thus significantly reducing overall computational resources. The viability and effectiveness of the proposed framework are validated through three case studies involving a simple 1D reinforced concrete beam, a 2D three-story frame, and a 3D five-story building structure. Furthermore, its performance is quantitatively demonstrated via comparison studies with competing methods such as Monte Carlo simulation, Kriging-based models, and an original LightGBM without active learning. [ABSTRACT FROM AUTHOR]

Let X, Y be continuous random variables with unknown distributions. The aim of this paper is to study the problem of estimating the probability θ : = P (X < Y) based on independent random samples from the distributions of X ′ , Y ′ , ζ and η , where X ′ = X + ζ , Y ′ = Y + η and X, Y, ζ , η are mutually independent random variables. In this context, ζ , η are referred to as measurement errors. We apply the ridge-parameter regularization method to derive a nonparametric estimator for θ depending on two parameters. Our estimator is shown to be consistent with respect to mean squared error if the characteristic functions of ζ , η only vanish on Lebesgue measure zero sets. Under some further assumptions on the densities of X, Y, ζ and η , we obtain some upper and lower bounds on the convergence rate of the estimator. A numerical example is also given to illustrate the efficiency of our method. [ABSTRACT FROM AUTHOR]

The benefits of less repetitive practice schedules on motor learning are usually described in terms of greater demand for memory processes. The present study aimed to investigate the interactions between working memory and practice schedule and their effects on motor learning. Forty female participants had their WMC evaluated by the N-back test and were randomly allocated to either the variable random (VP) or the constant practice (CP) groups. In the acquisition phase, participants practiced 120 trials of a sequential key-pressing task with two goals: learning the relative and the absolute timing. Delayed retention and transfer tests occurred 24 h after the acquisition phase. Participants performed 12 trials of the motor task. Results showed that in the CP, learners with a high level of WMC presented better motor performance in the transfer test than learners with a low level of WMC. In the RP, no difference between WMC levels was found. Learners with a high level of WMC in the CP presented the same motor performance as learners in the RP regardless of the WMC level in the transfer test. In conclusion, learners with a high WMC could compensate for the poor working memory stimulation of a more repetitive practice schedule. The high WMC did not seem to exert an additional benefit when learners were well stimulated by a less repetitive practice schedule. [ABSTRACT FROM AUTHOR]

For each \alpha \in (0, 1), we construct a bounded monotone deterministic sequence (c_k)_{k \geqslant 0} of real numbers so that the number of real roots of the random polynomial f_n(z) = \sum _{k=0}^n c_k \varepsilon _k z^k is n^{\alpha + o(1)} with probability tending to one as the degree n tends to infinity, where (\varepsilon _k) is a sequence of i.i.d. (real) random variables of finite mean satisfying a mild anti-concentration assumption. In particular, this includes the case when (\varepsilon _k) is a sequence of i.i.d. standard Gaussian or Rademacher random variables. This result confirms a conjecture of O. Nguyen from 2019. More generally, our main results also describe several statistical properties for the number of real roots of f_n, including the asymptotic behavior of the variance and a central limit theorem. [ABSTRACT FROM AUTHOR]

In the analysis of a train–bridge coupled system, fuzzy uncertainty is a factor that must be considered in the prediction of coupled vibration response, but it has not been considered so far. In this work, the concept of information entropy is used to unify the fuzzy uncertainty and random variables into the train–bridge coupled system, and the fuzzy random train–bridge coupled system is established. The fuzzy dynamic response of trains and bridges with fuzzy parameters of the bridge structures and the mass of the carriage were studied, and the mean and variance of the response quantities were calculated using the new point estimation method (NPEM). The combined effect of the fuzziness is considered and the fuzzy value of the system dynamics is obtained. The feasibility of applying this method to train–bridge problems was verified. The calculation results indicated that the maximum amplitude of the fuzzy vertical displacement of the bridge exceeded the conventional vertical displacement by 25.57%, and the maximum amplitude of the fuzzy vertical acceleration of the train exceeded the conventional vertical acceleration by 23.42%. Obviously, in this case, the traditional deterministic calculation method cannot comprehensively and accurately analyze the dynamic response of the train–bridge system. The method in this paper can provide theoretical guidance for evaluating the safety of bridge structures and running safety research in the future. [ABSTRACT FROM AUTHOR]

In this paper, a model with integration of interval programming (IP), chance-constrained programming (CCP), and fuzzy random variables (FRVs), termed as an inexact fuzzy random chance-constrained programming (IFRCCP) model, was proposed to deal with the fuzzy and random uncertainties in optimization of booster cost for a water distribution system (WDS) under uncertainty. The IFRCCP model was applied to a WDS to verify the efficiency of the method. After formulating the IFRCCP model, the booster cost intervals were obtained under various violation levels and confidence levels. The results indicated that the lower and upper booster costs increased with the confidence levels of the lower limits, and decreased with the violation levels of the lower limits. Moreover, the nodal chlorine concentrations are more uniform with the increase of booster numbers. The booster costs under trapezoidal distribution FRVs are greater than that under triangular distribution FRVs. Moreover, the uniformity of nodal chlorine concentration under triangular fuzzy distributions is larger than that under trapezoidal fuzzy distributions. The results obtained can help managers to make schemes on booster optimization under fuzzy and random uncertainties. [ABSTRACT FROM AUTHOR]

Suppose X 1 ,... , X n are independent survival exponentiated location-scale random variables, and I p 1 , ... , I p n are independent Bernoulli random variables, independently of Xi's, i = 1 , ... , n. Let Y i = I p i X i , for i = 1 , ... , n. Then, in actuarial context, Yi corresponds to the claim amount in a portfolio of heterogeneous risks. In this work, we compare the largest and smallest order statistics arising from two heterogeneous portfolios in the sense of usual stochastic order. The results obtained here are based on multivariate chain majorization with heterogeneity in different parameters, and generalize some of the results known in the literature. Some examples and counterexamples are also presented for illustrating the results established here. [ABSTRACT FROM AUTHOR]

In current researches on belief rule base (BRB), input parameters are tended to be expressed in the form of quantitative values through expert knowledge combined with optimization methods. A singular quantitative value fails to capture the statistical properties, leading to irrational outcomes. Therefore, an attempt on attribute weights is made in this paper, and a new model with probability distribution attribute weights (pdw) called BRB-pdw is proposed. The combination of two attributes is in detail discussed, where attribute weights are described as random variables with specific probability distribution. To characterize the output of probability distribution attribute weight, a new concept of expectation of activation weight is proposed. In addition, the BRB-pdw is extended to multiple attributes to demonstrate its universality. Furthermore, fundamental properties and characteristics of the BRB-pdw are further validated by rigorous mathematical derivation. Finally, practicability of the BRB-pdw is validated with NASA lithium battery open dataset, and experiments show that the BRB-pdw model is more robust while maintaining precision. [ABSTRACT FROM AUTHOR]

• Reliability-based non-probabilistic multiscale topology optimization (NRBMTO) with stress constrained is proposed. • The p-norm function aggregates global unit stresses. • Mechanical and thermo-mechanical loads are considered as non-probabilistic uncertain parameters. • Ellipsoid modeling describes uncertainty in non-probabilistic random variables. • NRBMTO results in more security than the traditional deterministic multiscale topology optimization (DMTO) approach. A reliability-based non-probabilistic multiscale topology optimization (NRBMTO) method with stress constraints is proposed for thermo-mechanical continuous structures with uncontrollable stresses. The physical parameters, external loads and temperature values at the macro scale, are regarded as non-probabilistic uncertain parameters in the optimization of structural topologies with complex physical fields at multi-scale. The homogenization-based finite element method is employed to quantify thermo-mechanical structures with multi-scale uncertain parameters in the established multi-scale topology model. The ellipsoid model is applied to describe the uncertainty of non-probabilistic random variables, and the non-probabilistic reliability index is obtained by estimating the failure probability based on the first-order reliability method (FORM). The unit stresses are aggregated to the global maximum stresses with the normalized p-norm function, taking into account the mechanical and thermal stresses. The sensitivity information of the compliance and stress constraint to the macro- and micro-design variables and uncertain variables are derived simultaneously. The macro- and micro- design variables are solved by the method of moving asymptotes (MMA), respectively. Several numerical examples are given to verify the effectiveness and feasibility of the proposed NRBMTO method. The results demonstrate that the optimized structure based on the NRBMTO method provides better security with reliability index β =3 and minimum compliance (244.39) while stress is controlled below 235 MPa compared to the classical deterministic multiscale topology optimization (DMTO) method. [ABSTRACT FROM AUTHOR]

Understanding the probabilistic nature of brittle materials due to inherent dispersions in their mechanical properties is important to assess their reliability and safety for sensitive engineering applications. This is all the more important when elements composed of brittle materials are exposed to dynamic environments, resulting in catastrophic fatigue failures. The authors propose the application of a non-intrusive polynomial chaos expansion method for probabilistic studies on brittle materials undergoing fatigue fracture when geometrical parameters and material properties are random independent variables. Understanding the probabilistic nature of fatigue fracture in brittle materials is crucial for ensuring the reliability and safety of engineering structures subjected to cyclic loading. Crack growth is modelled using a phase-field approach within a finite element framework. For modelling fatigue, fracture resistance is progressively degraded by modifying the regularised free energy functional using a fatigue degradation function. Number of cycles to failure is treated as the dependent variable of interest and is estimated within acceptable limits due to the randomness in independent properties. Multiple 2D benchmark problems are solved to demonstrate the ability of this approach to predict the dependent variable responses with significantly fewer simulations than the Monte Carlo method. This proposed approach can accurately predict results typically obtained through 10 5 or more runs in Monte Carlo simulations with a reduction of up to three orders of magnitude in required runs. The independent random variables' sensitivity to the system response is determined using Sobol' indices. The proposed approach has low computational overhead and can be useful for computationally intensive problems requiring rapid decision-making in sensitive applications like aerospace, nuclear and biomedical engineering. The technique does not require reformulating existing finite element code and can perform the stochastic study by direct pre/post-processing. [ABSTRACT FROM AUTHOR]

The Method of Moments (MoM) is a non-embedded uncertainty analysis method that has been widely used in Electromagnetic Compatibility (EMC) simulations in recent years due to its two major advantages of high computational efficiency and immunity from dimensional disaster. A random variable sensitivity calculation method based on the Complex Number Method of Moments (CNMoM) is proposed in this paper to improve the accuracy of the MoM in standard deviation prediction and thereby enhance the credibility of EMC simulation uncertainty analysis results. In the parallel cable crosstalk prediction example in the literature, the result of the Monte Carlo Method (MCM) is used as the standard, and the accuracy of the new method proposed in this paper is quantitatively verified using the Feature Selective Validation (FSV) method. Compared with the MoM, the proposed method can significantly improve the calculation accuracy of the standard deviation results without sacrificing simulation efficiency. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to analyze the reliability and characteristics of the non‐series‐parallel network. The illustrative non‐series parallel networks, that is, the Twin T‐Network and the network with six components of resistor and capacitor, have been converted into a series of parallel network combinations by use of the minimal path technique. The stochastic variables related to component failure rate have been demonstrated using exponential decay distribution. We obtain the reliability, mean time to failure, and sensitivity with the use of the exponential decay distribution. The reliability and its attributes are examined by assuming different values of scale and shape parameters at different points of time. Using Owen's methodology, we obtained minimal signature, tail signature, expected time, expected cost, and Barlow‐Proschan index were determined. The performance of all reliability characteristics has been observed graphically for arbitrary values of parameters. A real‐world example is used to introduce the point. [ABSTRACT FROM AUTHOR]

ABSTRACT This article investigates the robust secure output tracking control for a class of uncertain two‐dimensional (2‐D) networked control systems. The 2‐D systems are described by the well‐known Fornasini–Marchesini (FM) local state‐space model, the parameter uncertainties are assumed to reside in a polytopic region, and the deception attacks are supposed to occur randomly in the transmission process. In the problem formulation, Bernoulli random variables are used to characterize the phenomena of deception attacks. As main results, a novel H∞$$ {H}_{\infty } $$ performance analysis condition for the augmented closed‐loop system is proposed by using a novel parameter‐dependent Lyapunov function and some zero equalities. Furthermore, both parameter‐dependent and parameter‐independent controllers have been designed, respectively, such that the output of the 2‐D systems tracks the output of a given reference model well in the H∞$$ {H}_{\infty } $$ sense. The design conditions are presented in terms of linear matrix inequalities (LMIs). In the end, a numerical simulation on a practical thermal process is applied to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract.In this article, we introduce a new concept of integrability called extended residually h-integrability with exponent r, which deals with weighted sums of arrays under sublinear expectation. The classical copy of this concept extends the residually h-integrability given by Wang, Hu, and Volodin (2018). On this basis, we obtain three forms of weak laws of large numbers for weighted sums of arrays of rowwise negatively dependent or rowwise independent random variables, respectively, under sublinear expectation. As corollaries, we get some weak laws of large numbers for arrays of random variables with normalizing factor kn under sublinear expectation. [ABSTRACT FROM AUTHOR]

In this paper, we develop a multi-item inventory model with stochastic demand, and the demand is considered as a random variable following a power demand pattern. A cumulative cycle demand is first identified for each product, and then the demand is gradually released to the inventory system by the power patterns within a cycle. The replenishment schedule is predetermined and well-known. Shortages are permitted but partially backlogged, and the rest are taken as lost sales. An effective inventory policy is utilized to reduce the total expected cost per unit of time by acquiring the optimal amount of stock to be stored at the start of the inventory cycle, which may protect against excessive lost sales and also avoid overstocking. This model is better suited for use in online purchases and the offline market where the buyer is assured that the goods will be shipped within a few days rather than at the time of purchase. We evaluated the system with items deteriorating instantaneously, which makes it appropriate to have a larger initial demand with a power pattern index greater than one. Numerical illustrations and sensitivity analysis provide an efficient tool for the insights of the theoretical solutions over the managerial foundation. [ABSTRACT FROM AUTHOR]

This article introduces co-quantiles, a new concept in rank statistics that generalizes quantiles, order statistics, and concomitants. In contrast to conventional order statistics that rank and record the same attribute of a population, or concomitants that consider different attributes observed over the same time period, co-quantiles allow for the ranking and recording of different attributes, and more generally their functions, across different time periods. In the special case of affine co-quantiles (defined formally in the article), we derive explicit expressions for their probability density functions and moments under the assumption that the distribution of the underlying data is multivariate normal. In particular, we establish that the former is a sum of unified skew-normal distributions introduced in Arellano-Valle and Azzalini (2006). The co-quantile results naturally reduce to those for order statistics and concomitants, and generalize those on the distributions of linear combinations and the maxima of vector-valued random variables obtained in Arellano-Valle and Genton (2007, 2008) and on cross-sectional momentum returns obtained in Kwon and Satchell (2018). As an example that has not been analyzed in the financial literature, we consider momentum spill-over returns and establish theoretically that these returns are susceptible to sudden changes in skewness and kurtosis during periods of market uncertainty. [ABSTRACT FROM AUTHOR]

In this article, some results on the complete f-moment convergence for randomly weighted sums of extended negatively dependent (END, for short) random variables are established. The results extend the results of Xu and Yan (2021) from complete moment convergence to complete f-moment convergence for randomly weighted sums of END random variables. [ABSTRACT FROM AUTHOR]

In this article, the Marcinkiewicz-Zygmund-type moment inequality and Rosenthal-type moment inequality for m-extended negatively dependent (m-END, for short) random variables are established. As applications of Marcinkiewicz-Zygmund-type moment inequality and Rosenthal-type moment inequality, we further investigate the Lr convergence properties for arrays of rowrise m-END random variables. Some sufficient conditions are provided. Finally, some simulations are presented to verify the validity of theoretical results. The results obtained in the article generalize some known ones for independent random variables and some dependent random variables. [ABSTRACT FROM AUTHOR]

In this article, we establish complete convergence for randomly weighted sums of negatively orthant-dependent random variables. We also establish complete convergence for the maximums of randomly weighted sums of negatively associated random variables. As a corollary, a Marcinkiewicz-Zygmund-type strong law for randomly weighted sums of negatively associated random variables is obtained. The results can be applied to the bootstrap sample means, and an open problem in a convergence rate of the bootstrap sample means posed by Csörgő (2004) is solved completely. [ABSTRACT FROM AUTHOR]

In this paper, we extend a Central Limit Theorem, recently established for the Thompson group F = F2 by Krishnan, to the Brown–Thompson groups Fp, where p is any integer greater than or equal to 2. The non-commutative probability space considered is the group algebra ℂ[Fp], equipped with the canonical trace. The random variables in question are an := (xn + xn−1)/2, where {xi}i≥0 represents the standard family of infinite generators. Analogously to the case of F = F2, it is established that the limit distribution of sn = (a0 + ⋯ + an−1)/n converges to the standard normal distribution. Furthermore, it is demonstrated that for a state corresponding to Jones’s oriented subgroup is denoted by F→, such a Central Limit Theorem does not hold. [ABSTRACT FROM AUTHOR]

AbstractLet {pn;n≥1} be a sequence of positive integers. Let X1,…,Xpn be i.i.d. random vectors in ℝn with i.i.d. components that are centered and have variance 1. Consider the maximum interpoint distance Mn=max1≤iMn under the polynomial and the exponential growth regimes for the dimension. The proofs rely on the moderate deviation principle of the partial sum of i.i.d. random variables, the Chen–Stein Poisson approximation method, and Gaussian approximation techniques. [ABSTRACT FROM AUTHOR]

Process capability indices (PCIs), are widely used to gauge how well a process performs within its requirements. While greater PCIs are indicative of improved process “quality,” they do not necessarily translate into lower rejection rates. Therefore, using a loss‐based PCI to gauge process capability makes more sense. In this paper, the PCI Spk′$ S^{\prime }_{pk}$ has been considered for normal random variable. The article attempts to study the classical and the Bayesian estimation of Spk′$ S^{\prime }_{pk}$ for type‐II progressive right censored sample under symmetric as well as asymmetric loss functions, namely squared error loss function, and LINEX loss function, respectively. The Markov chain Monte Carlo simulation technique has been efficiently used here to have the approximate solution for Spk′$S^{\prime }_{pk}$. Through an extensive Monte Carlo simulation study along with two real life examples related to electronic industry, we compare the performances of the classical and the Bayes estimates based on symmetric and asymmetric loss functions and compared among the asymptotic confidence interval and highest posterior density credible intervals, in terms of average width and corresponding coverage probabilities of Spk′$S^{\prime }_{pk}$, respectively. [ABSTRACT FROM AUTHOR]

Photovoltaic (PV) systems offer cost-effective power solutions for outlying islands but often compromise system stability due to reduced inertia. This study introduces a Virtual Synchronous Generator (VSG) control strategy, integrated with Energy Storage Systems (ESS) and PV, to enhance system inertia. By optimizing coordination between these energy sources, the proposed method mitigates oscillations and improves grid stability. However, PV-VSG systems are generally not favored by energy providers due to the requirement for pre-curtailment of power output. To address this, the paper proposes a parameter design method for VSG control of ESS and PV, utilizing multi-objective genetic algorithm (MOGA) optimization to simultaneously increase the frequency nadir and minimize the settling time after disturbances. Additionally, an adaptive curtailment decision and parameter design method based on artificial neural networks is introduced to enhance the feasibility of PV-VSG systems by reducing PV pre-curtailment and prioritizing PV power release and ESS charging during frequency oscillations. Real data from the Penghu Archipelago in Taiwan are used to build a dynamic model in DIgSILENT, enabling interaction with MOGA. The Value at Risk (VaR) method with dual stochastic variables is employed to assess the allowable PV installed capacity. The results show that when VaR is set at 1%, the proposed PV-VSG method can increase PV penetration by 57.5% compared to scenarios without VSG. Furthermore, compared to traditional PV-VSG methods, the proposed approach achieves a 16.8% increase in PV penetration and reduces annual PV curtailment by 25 MWh. This study also evaluates the economic impact of planners choosing different risk levels, offering valuable insights for grid development in remote or island regions. [ABSTRACT FROM AUTHOR]

Graphical models are pivotal in studying the conditional independence structure of a set of random variables. Circular variables, arising in several contexts and fields, are characterized by periodicity. Models for studying the dependence/independence structure of circular variables are under-explored but of increasing interest. This paper delves into two multivariate circular distributions, the Wrapped Normal and the Inverse Stereographic Normal distribution as undirected graphical models. For each of these distributions, we study their key properties with respect to conditional independence and introduce specific classes of graphical models. The usefulness of the proposal is shown by modelling the conditional independence among dihedral angles that play a critical role in defining the three-dimensional structure and functionality of proteins. This can provide valuable insights, for instance, into the multiform protein folding understanding. [ABSTRACT FROM AUTHOR]

For a sequence consisting of independent random variables having a Bernoulli distribution with the parameter p = 1 2 the limit joint distribution of the statistics T1, T2, T3 of the following three tests of the NIST package is obtained: «Monobit Test», «Frequency Test within a Block»and «Test for the Longest Run of Ones in a Block». It is proved that the covariance matrix C of the limit distribution of the vector (T1, T2, T3) satisfies the relations C12 = C21 = C13 = C31 = 0, C23 = C32 ≥ 0. For arbitrary p necessary and sufficient conditions for asymptotic uncorrelatedness and/or asymptotic independence of these statistics are obtained. The limit behavior of the vector (T1, T2, T3) is described for a wide class of values p ≠ 1 2 . [ABSTRACT FROM AUTHOR]

Dynamic latent scale GAN is an architecture‐agnostic encoder‐based generative model inversion method. This paper introduces a method to efficiently integrate perceptual VAE into dynamic latent scale GAN to improve the performance of dynamic latent scale GAN. When dynamic latent scale GAN is trained with a normal i.i.d. latent random variable and the latent encoder is integrated into the discriminator, a sum of a predicted latent random variable of real data and a scaled normal noise follows the normal i.i.d. random variable. Since this random variable is paired with real data and follows the latent random variable, it can be used for both VAE and GAN training. Furthermore, by considering the intermediate layer output of the discriminator as the feature encoder output, the VAE can be trained to minimise the perceptual reconstruction loss. The forward propagation & backpropagation for minimising this perceptual reconstruction loss can be integrated with those of GAN training. Therefore, the proposed method does not require additional computations compared to typical GAN or dynamic latent scale GAN. Integrating perceptual VAE to dynamic latent scale GAN improved the generative and inversion performance of the model. [ABSTRACT FROM AUTHOR]

In various applications, observed variables are missing some information that was intended to be collected. The estimations of both loading and path coefficients could be biased when ignoring the missing data. Inverse probability weighting (IPW) is one of the well-known methods helping to reduce bias in regressions, while belonging to a promising but new category in structural equation models. The paper proposes both parametric and nonparametric IPW estimation methods for dynamic structural equation models, in which both loading and path coefficients are developed into functions of a random variable and of the quantile level. To improve the computational efficiency, modified parametric IPW and modified nonparametric IPW are developed through reducing inverse probability computations but making fuller use of completely observed information. All the above IPW estimation methods are compared to existing complete case analysis through simulation investigations. Finally, the paper illustrates the proposed model and estimation methods by an empirical study on digital new-quality productivity. [ABSTRACT FROM AUTHOR]

In this paper, three-dimensional nonlinear dynamic finite-element analyses are conducted to examine the effect of soil property variability on the lateral displacement (D) of liquefiable ground reinforced by granular columns. A suite of 20 ground motions is selected from the NGA-West2 database as input. A soil-granular column ground system consisting of an intermediate liquefiable layer is modeled in OpenSees. Both the random variable (RV) and random filed (RF) methods are adopted to model the variability of soil property parameters. Dynamic analyses are then conducted to estimate the earthquake-induced deformation of the soil-granular column system. It is found that modeling the variability of soil parameters based on the RV method generally increases the geometric mean and standard deviation (σlnD) of D for the soil-granular column system. Enlarging the spatial correlation of soil parameters in the RF model brings in a slight increase of the mean D and comparable σlnD values, respectively. Hence, incorporating the spatially correlated soil property parameters may not be necessarily increase the variation of D for the soil-granular column system. Specifically, the statistical distribution of D is more sensitive to the vertical scale of fluctuation rather than the horizontal one. The results presented could aid in addressing the variability issue for performance-based design of granular column-reinforced liquefiable ground in engineering applications. [ABSTRACT FROM AUTHOR]

This paper aims at assessing the failure time of a 7‐story reinforced concrete (RC) frame in a post‐earthquake fire (PEF) event probabilistically. Cumulative distribution functions (CDF) of the studied frame's failure time in various seismic load intensities have been calculated and presented with the aid of Monte Carlo analysis. Seismic load intensity, failure time, and failure probability are three parameters that are correlated through probabilistic analysis. The effects of cracking, spalling, and residual deformations resulted from the seismic load are considered in the strength of structure against the fire load. Seismic load intensity, materials properties, gravity load, and geometry are considered as random variables and one probabilistic analysis has been carried out for each seismic load intensity. The results have illustrated that in low seismic load intensities, probabilistic values of failure time in a structure subjected to pure fire load are equal to the one exposed to PEF. With the increase of seismic load intensity, the effects of cracking, spalling, and residual deformations would lead to a decline in the strength of structural elements against PEF scenario. The failure time in 50% failure probability for Sa = 0.2 g, Sa = 1 g, and Sa = 2 g intensities has been calculated as 14,300, 12,200, and 5100 s, respectively. The analysis results have shown that in an unspecified seismic load intensity, the failure time of the 7‐story RC frame for the 50% occurrence probability is equal to 9750 s. [ABSTRACT FROM AUTHOR]

In the present analysis, the homogeneous, updated and complete seismic catalog of the Kohat-Potwar plateau was analyzed through dynamic time dependent statistical models. The study region earthquake interoccurrence times are assumed as a stochastic study variable and it follows one of the renewal models. A rich and updated class of statistical models was used to identify the most parsimonious one. The developed models will serve the purpose of describing, analyzing and forecasting the earthquake occurrence probabilities in the future. The model parameters were estimated through the method of maximum likelihood. Different statistical evaluation criteria were used to prioritize the estimated models according to their fitting performance to the observed data. We have found that the interoccurrence times of the study region can plausibly be described through the log-logistic model. Based on the log-logistic model, it has been found that there is a significantly high probability (>90%) of another earthquake occurrence of Mw ≥ 5.3 in the region in near future (2023‒2028). These probabilities increase with increasing time periods since the last event occurrence. The mean recurrence period of another earthquake of Mw ≥ 5.3, based on the most suitable log-logistic model, is almost three and half years with 1.80 years as standard error, i.e., 3.38 ± 1.80 years. The quantification of earthquake occurrence uncertainties in the study region provides many useful quantitative estimates that have crucial importance in seismic hazard and risk analysis studies of a region. [ABSTRACT FROM AUTHOR]

The Katz centrality of a node in a complex network is a measure of the node's importance as far as the flow of information across the network is concerned. For ensembles of locally tree-like undirected random graphs, this observable is a random variable. Its full probability distribution is of interest but difficult to handle analytically because of its "global" character and its definition in terms of a matrix inverse. Leveraging a fast Gaussian Belief Propagation-Cavity algorithm to solve linear systems on tree-like structures, we show that i) the Katz centrality of a single instance can be computed recursively in a very fast way, and ii) the probability P(K) that a random node in the ensemble of undirected random graphs has centrality K satisfies a set of recursive distributional equations, which can be analytically characterized and efficiently solved using a population dynamics algorithm. We test our solution on ensembles of Erdős-Rényi and Scale Free networks in the locally tree-like regime, with excellent agreement. The analytical distribution of centrality for the configuration model conditioned on the degree of each node can be employed as a benchmark to identify nodes of empirical networks with over- and underexpressed centrality relative to a null baseline. We also provide an approximate formula based on a rank-1 projection that works well if the network is not too sparse, and we argue that an extension of our method could be efficiently extended to tackle analytical distributions of other centrality measures such as PageRank for directed networks in a transparent and user-friendly way. [ABSTRACT FROM AUTHOR]

The Central Limit Theorem (CLT) is a fundamental result in probability theory with numerous applications in various disciplines. There are a wide variety of CLT‐like theorems, for example the De Moivre–Laplace, Lindeberg and Lyapounov theorems. Independent and identically distributed random variables with a finite second moment are usually considered assumptions in CLTs. However, in this article we present a CLT for a sum of dependent and nonidentically distributed Bernoulli random variables that arises in the well‐known matching experiment. [ABSTRACT FROM AUTHOR]

AbstractFor grouped covariates, we propose a framework for boosting that allows for sparsity within and between groups. By using component-wise and group-wise gradient ridge boosting simultaneously with adjusted degrees of freedom or penalty parameters, a model with similar properties as the sparse-group lasso can be fitted through boosting. We show that within-group and between-group sparsity can be controlled by a mixing parameter, and discuss similarities and differences to the mixing parameter in the sparse-group lasso. Furthermore, we show under which conditions variable selection on a group or individual variable basis happens and provide selection bounds for the regularization parameters depending solely on the singular values of the design matrix in a boosting iteration of linear Ridge penalized boosting. In special cases, we characterize the selection chance of an individual variable vs. a group of variables through a generalized beta prime distribution. With simulations as well as two real datasets from ecological and organizational research data, we show the effectiveness and predictive competitiveness of this novel estimator. The results suggest that in the presence of grouped variables, sparse-group boosting is associated with less biased variable selection and higher predictability compared to component-wise or group-component-wise boosting. [ABSTRACT FROM AUTHOR]

This study proposes an integrated dimension-reduction representation strategy for simulating multivariate mainshock-aftershock stochastic ground motions based on measured motion records. The strategy includes a parameter identification method for modeling evolutionary power spectrum density (EPSD) of mainshock-aftershocks, a coherence function describing the spectrum correlation between mainshock and aftershock, and the EPSD function matrix establishment for mainshock-aftershock field combining with complex spatial coherence function. Furthermore, the dimension-reduction representation for simulating the ground motions considering the sequence and spatial variability simultaneously is presented with merely two elementary random variables. Numerical results effectively demonstrate the accuracy, efficiency, and engineering applicability of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an R package EATME, which is known as Exponentially weighted moving average (EWMA) control chart with Adjustments To Measurement Error. The main purpose of this package is to correct for measurement error effects in continuous or binary random variables and develop the corrected control charts based on the EWMA statistic. In addition, the corrected control charts can detect out-of-control process accurately. The package contains a function to generate synthetic data and includes functions to determine the reasonable coefficient of control limit as well as estimate average run length. Moreover, for the visualization, we also provide the control charts to show the monitoring of in-control and out-of-control process. Finally, the functions in this package are clearly demonstrated, and numerical studies show the validity of the package. [ABSTRACT FROM AUTHOR]

The notion of (real-valued) almost measurable functions on probability spaces is introduced and some of their properties are considered. It is shown that any almost measurable function may be treated as a quasi-random variable in the sense of [A. Kharazishvili, On some version of random variables, Trans. A. Razmadze Math. Inst. 177 2023, 1, 143–146]. [ABSTRACT FROM AUTHOR]

Summary: In this article, the issue of resilient filtering for descriptor nonhomogeneous Markovian jump cyber‐physical systems under hybrid cyber‐attacks has been studied. First, occurrences of both deception attacks and replay attacks are modeled as two mutually independent Bernoulli distributed random variables. To depress the ratio of sampled data transmissions over the network, the dynamic version of event‐triggered transmission policy is properly proposed. Then, criteria of stochastically admissible for the filtering error systems guaranteeing mixed H∞$$ {H}_{\infty } $$ and passive performance are addressed via linear matrix inequalities (LMIs). The gains of resilient filter and the dynamic event‐based transmission policy can be simultaneously gained by optimizing the LMIs. Finally, two examples that include a numerical example and a direct current motor system are provided to testify the feasibility and effectiveness of the developed technique. [ABSTRACT FROM AUTHOR]

AbstractIn the present paper, we consider a sequence of the general random variables, which include the sequences of martingale differences, and establish the weak law of large numbers and the convergence in Lp under some weaker conditions. [ABSTRACT FROM AUTHOR]

The submarine massive mud transports of several seas around the world, including the Shenhu Sea, are thought to relate with hydrate decomposition, which occur even at small gradients. This article investigates the stability and reliability of marine slopes considering three factors related to hydrate decomposition and earthquake, namely decrease in sediment strength, increase in excess pore pressure, and activation by external seismic force. Taking the SH2 hole, implemented by the first Chinese offshore hydrate drilling mission (GMGS-1), as an example, the impacts of three factors mentioned above on marine slopes stability are analyzed with infinite slope theory. In addition, the space distribution of physical and mechanical parameters in hydrate deposits is under consideration. The cohesion, friction angle and buoyant unit weight in a non-stationary random field are treated as spatial random variables, where the means of the first two increase linearly with depth. Variation characteristics of the failure probability for various slope angles are analyzed under different scenarios. The outcomes reveal that the safety factor of the slopes at 30% potential for damage is around 1.25 within a given variant characterization. The proposed integrated stability and reliability analysis can effectively provide early warning for collapse of marine hydrate-bearing slopes. [ABSTRACT FROM AUTHOR]

The Poland–Scheraga model, introduced in the 1970s, is a reference model to describe the denaturation transition of DNA. More recently, it has been generalized in order to allow for asymmetry in the strands lengths and in the formation of loops: the mathematical representation is based on a bivariate renewal process, that describes the pairs of bases that bond together. Here, we consider a disordered version of the model, in which the two strands interact via a potential β V (ω ^ i , ω ¯ j) + h when the ith monomer of the first strand and the jth monomer of the second strand meet. Here, h ∈ R is a homogeneous pinning parameter, (ω i ^) i ≥ 1 and ( ω ¯ j) j ≥ 1 are two sequences of i.i.d. random variables attached to each DNA strand, V (· , ·) is an interaction function and β > 0 is the disorder intensity. In our main result, we find some condition on the underlying bivariate renewal so that, if one takes β , h ↓ 0 at some appropriate (explicit) rate as the length of the strands go to infinity, the partition function of the model admits a non-trivial, disordered, scaling limit. This is known as an intermediate disorder regime and is linked to the question of disorder relevance for the denaturation transition. Interestingly, and unlike any other model of our knowledge, the rate at which one has to take β ↓ 0 depends on the interaction function V (· , ·) and on the distribution of (ω i ^) i ≥ 1 , ( ω ¯ j) j ≥ 1 . On the other hand, the intermediate disorder limit of the partition function, when it exists, is universal: it is expressed as a chaos expansion of iterated integrals against a Gaussian process M , which arises as the scaling limit of the field (e β V (ω ^ i , ω ¯ j)) i , j ≥ 0 and exhibits correlations on lines and columns. [ABSTRACT FROM AUTHOR]

In this work, the efficient robust global optimization (ERGO) method is revisited with the aim of enhancing and expanding its existing capabilities. The original objective of ERGO was to address the computational challenges associated with optimization-under-uncertainty through the use of Bayesian optimization (BO). ERGO tackles robust optimization problems which are characterized by sensitivity in the objective function due to stochasticity in the design space. It does this by concurrently minimizing the mean and variance of the objective in a multi-objective setting. To handle the computational complexity arising from the uncertainty propagation, ERGO exploits the analytical expression of the surrogate model underlying BO. In this study, ERGO is extended to accommodate multiple objectives, incorporate an improved predictive error estimation approach, investigate the treatment of failed function evaluations, and explore the handling of stochastic parameters next to stochastic design variables. To evaluate the effectiveness of these improvements, the enhanced ERGO scheme is compared with the original method using an analytical test problem with varying dimensionality. Additionally, the novel optimization technique is applied to an aerodynamic design problem to validate its performance. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the asymptotic form of the joint distribution of maxima and minima of independent observations, when the sample size is a random variable. We also discuss the asymptotic distribution of the Range. [ABSTRACT FROM AUTHOR]