Search

Please refer to full text. [ABSTRACT FROM AUTHOR]

Making predictions bounded by uncertainty is a crucial component of modern decision support systems. Knowledge graphs provide a structured, semantic-oriented approach to data integration, storage and retrieval; however, they represent data in an absolute way and do not natively support reasoning under uncertain future conditions. In this paper, we present a novel technique for building a probabilistic model from a knowledge graph using a Bayesian network, which is a step towards enabling probabilistic reasoning under uncertainty within a knowledge graph. Our approach supports mixing of continuously and discretely-distributed variables, which is necessary for jointly processing real-world data, but has not typically been supported in prior work. As an interface to the probabilistic model, we propose an extension of the SPARQL query language called Orion DSL, which is currently a working prototype. We also define a custom probabilistic ontology in order to store outputs of the model directly in the knowledge graph alongside the original data, which we refer to as a Probabilistic Knowledge Graph (PKG). The evaluation shows that: (1) the dependencies and distributions of data in a synthetically-generated knowledge graph were accurately captured by the Bayesian model, and (2) an SPARQL query against the PKG to retrieve computed probability distributions was orders of magnitude more performant than a similarly-intentioned query against the base knowledge graph. We anticipate that the models generated by this system will have applications in the areas of predicting missing data, approximate query processing, and utility-based optimization. Future work will involve more detailed explorations of each of these topics as we work towards a PKG-based decision support system. [ABSTRACT FROM AUTHOR]

The entropy of a graph is an information-theoretic quantity which expresses the complexity of a graph. Entropy functions have been used successfully to capture different aspects of graph complexity. The generalized graph entropies result from applying information measures to a graph using various schemes for defining probability distributions over the elements of the graph. In this paper, we investigate the complexity of a class of composite graphs based on subdivision graphs and corona product evaluating the generalized graph entropies, and we present explicit formulae for the complexity of subdivision-corona type product graphs. [ABSTRACT FROM AUTHOR]

In this paper, continuous-time quantum walk on hypercube is discussed in view of Cartesian product structure. We find that the n -fold Cartesian power of the complete graph K 2 is the n -dimensional hypercube, which give us new ideas for the study of quantum walk on hypercube. Combining the product structure, the spectral distribution of the graph and the quantum decomposition of the adjacency matrix, the probability amplitudes of the continuous-time quantum walker's position at time t are given, and it is discussed that the probability distribution for the continuous-time case is uniform when t = (π ∕ 4) n. The application of this product structure greatly improves the study of quantum walk on complex graphs, which has far-reaching influence and great significance. [ABSTRACT FROM AUTHOR]

Currently, there is no unified criterion to evaluate the failure of single-layer latticed domes, and an accurate nonlinear time-history analysis (NTHA) is generally required; however, this does not consider the uncertainties found in practice. The seismic instability of domes subjected to earthquake ground motions has not been thoroughly investigated. In this paper, a new approach is developed to automatically capture the instability points in the incremental dynamic analysis (IDA) of single-layer lattice domes by integrating different efficient and robust methods. First, a seismic fragility analysis with instability parameters is performed using the bootstrap calibration method for the perfect dome. Second, based on the Sobol sequence, the quasi-Monte Carlo (QMC) sampling method is used to efficiently calculate the failure probability of the dome with uncertain parameters, in which the truncated distributions of random parameters are considered. Third, the maximum entropy principle (MEP) method is used to improve the computational efficiency in the analyses of structures with uncertainties. Last, the uncertain interval of the domes is determined based on the IDA method. The proposed method has been used to investigate the instability of single-layer lattice domes with uncertain parameters. The results show that it can determine the probability of structural failure with high efficiency and reliability. Additionally, the limitations of the proposed method for parallel computation are discussed. [ABSTRACT FROM AUTHOR]

When an earthquake occurs, railway bridges will suffer from different degrees of seismic damage, and it is necessary to assess the seismic risk of bridges. Unfortunately, the majority of studies were done on highway bridges without taking into account railway bridge characteristics; hence they are not applicable to railway bridges. Furthermore, current research methods for risk assessment cannot be performed quickly, and suffer from the problems of subjective personal experience, complicated calculations, and time-consuming. This paper we use machine learning for earthquake damage prediction and empirical vulnerability curves to represent risk assessment results, creating a rapid risk assessment procedure. We gathered and tallied seismic damage data from 335 railway bridges that were damaged in the Tangshan and Menyuan earthquakes, found six variables that had a substantial impact on seismic risk outcomes, and categorized the damage levels into five categories. It is essentially a multi-classification and prediction problem. In order to solve this problem, four algorithms were tested: Random Forest (RF) Back Propagation Artiifcial Neural Network (BP-ANN), PSO-Support Vector Machine (PSO-SVM), and K Nearest Neighbor (KNN). It was found that RF is the most effective method, with an accuracy rate of up to 93.31% for the training set and 89.39% for the test set. Then this study describes the new procedure in detail for rapidly assessing seismic risk to 269 bridges chosen at random from the sample pool. Firstly, the seismic damage data of bridges are collated, then the seismic damage rating is predicted using RF, and finally the empirical vulnerability curve is drawn using a two-parameter normal distribution function for the purpose of seismic damage risk assessment. The study's findings can be used as a guide for choosing a machine learning approach and its inputs to build a rapid assessment model for railway bridges. [ABSTRACT FROM AUTHOR]

In this paper, we used the first-principles method to investigate the structural, electronic, mechanical and thermodynamic parameters of the ternary β -Ti–15Nb–xSi alloys with x = 0. 6 , 0. 8 , 1 , 1. 2 , 1. 4 , 1. 6 wt.%. We have carried out theoretical computations inside the density functional theory (DFT) utilizing the generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE) model. The random distribution of Nb atoms in the alloy was described by using both virtual crystal approximation (VCA), special quasirandom structure (SQS) and the coherent potential approximation (CPA) techniques, in combination with first-principles plane-wave pseudopotential (PW-PP) and exact muffin-tin orbital (EMTO) methods. We determined the elastic constants as well as the bulk, shear, Young's modulus and Poisson's ratio. Our structural results are in good agreement with the available experimental and theoretical results for the pure structure of the titanium. In addition, we have estimated the band structure and the density of state (DOS) for the electronic computations. Our findings demonstrate that all of the compounds are metallic, stable and meet the requirements for stability. Young's modulus of Ti–15Nb–0.6Si and Ti–15Nb–1.6Si is 86.5 GPa and 15.11 GPa, respectively, which are similar to Young's moduli of human bone (10–30 GPa). All calculated parameters of the alloys decreased with increasing of Si concentration except for Poisson's ratio, anisotropy and B/G ratio. Furthermore, all of the materials investigated showed ductile nature, and Young's modulus values are needed for further applications. Excitations from the quasi-harmonic Debye approximation's vibrational part were applied to the 0 K free energy calculated via ab-initio calculations. The influence of temperatures up to 800 K on phase stability was investigated. These findings can be utilized to help designers create alternative low-modulus alloys for biomedical applications. [ABSTRACT FROM AUTHOR]

Deep learning has been successfully applied to video anomaly detection. However, the way that deep network learn spatio-temporal features autonomously will ignore the specificity of different pattern features. Therefore, this paper focuses on how to efficiently learn deep appearance feature, introduces the idea of learning appearance information by predicting future frame, and proposes dual stream conditional generative adversarial network fusion for video abnormal behavior detection. The video frame and its corresponding optical flow image are transferred to the conditional generative adversarial network to learn the motion feature representation. In addition, inputting the video frame and its corresponding future frame to the network to generate the appearance representation complementary to motion feature. The model is only trained with normal events, therefore it is not able to generate abnormal events accurately. During the test, for the foreground moving targets, the images generated by the model are compared with the ground truth to obtain a two-stream anomaly probability distribution model based on the mean square error used to achieve the purpose of region anomaly detection. Experiments on the public datasets show that the proposed method can effectively detect and locate abnormal behaviors in the video. [ABSTRACT FROM AUTHOR]

In this paper, we provide a novel generalization of quantum orthogonal polynomials from ℛ (p , q) -deformed quantum algebras introduced in earlier works. We construct related quantum Jacobi polynomials and their probability distribution, factorial moments, recurrence relation, and governing difference equation. Surprisingly, these polynomials obey non-conventional recurrence relations. Particular cases of generalized quantum little Legendre, little Laguerre, Laguerre, Bessel, Rogers–Szegö, Stieltjes–Wigert and Kemp binomial polynomials are derived and discussed. [ABSTRACT FROM AUTHOR]

In this paper, we review some geometrical aspects pertaining to the world of monotone quantum metrics in finite dimensions. Particular emphasis is given to an unfolded perspective for quantum states that is built out of the spectral theorem and is naturally suited to investigate the comparison with the classical case of probability distributions. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the spatiotemporal patterns of solutions to diffusive nonlocal Nicholson’s blowflies equations, wherein a natural death rate of the immature population is included in the distribution function. We first prove the positivity and boundedness of positive solutions in the model by using the minimum principle and the method of lower and upper solutions. Subsequently, we conduct a detailed bifurcation and stability analysis to obtain conditions on all the diffusion coefficients and the death rate coefficient of the immature population required for the emergence of spatiotemporal patterns, including spatially nonhomogeneous time periodic orbits. Our results indicate that the model can undergo Hopf bifurcation when the diffusion rate of the mature population passes through a sequence of critical values. Additionally, we examine the dependence of Hopf bifurcation points and bifurcated oscillations on model parameters, including the diffusion rate and death rate of the immature population. Finally, we report numerical simulations based on the bifurcation analysis to demonstrate the theoretical results, and it will help us better understand the ecological characteristics and behavioral patterns of the blowfly population. [ABSTRACT FROM AUTHOR]

In this paper, we take variable separation method to study Klein–Kramers (KK) equation. By choosing different eigenvalues and noise functions, we can get different probability density functions (PDFs) of KK equation. These PDFs contain not only normal distributions but also other distributions that correspond to anomalous diffusion phenomena. For example, power-law distribution, truncated Cauchy–Lorentz distribution, Weibull distribution, log-logistic distribution, Gamma distribution. We also show the 3D and 2D profiles of these PDFs to analyze the corresponding dynamic properties and illustrate the possible practical applications of these results. In addition, we also find some exact solutions that are not PDFs. They are also listed to ensure the completeness of the results and to illustrate the potential applications of these exact solutions. [ABSTRACT FROM AUTHOR]

The performance of electrical connectors can be significantly impacted by periodic variations in contact resistance caused by vibrational stress. Intermittent faults resulting from such stress are characterized by their random and fleeting nature, making it difficult to study and replicate them. This paper proposes a novel method for reproducing intermittent faults in electrical connectors. To implement this method, intermittent fault data are first collected from electrical connectors subjected to different vibration loads. Next, a statistical distribution model is constructed using kernel density estimation (KDE). Based on this model, a fault injector is designed to simulate intermittent faults under varying vibration loads. The simulated faults are then compared to real-world intermittent fault signals in a controlled environment to validate the accuracy of the method. The results demonstrate that the proposed method effectively reproduces intermittent faults in electrical connectors under varying vibration conditions. This approach can be used to better understand the behavior of connectors under vibrational stress and to develop more effective testing and fault diagnosis methods. [ABSTRACT FROM AUTHOR]

In general, dynamic systems of higher dimensions or with more complex nonlinearities exhibit more intricate behaviors. Conversely, it is worthwhile to discuss whether a complex phenomenon persists in simpler systems. This paper investigates a single-degree-of-freedom vibration system with a velocity-dependent stiffness affected by additive noise. Although the underlying deterministic system possesses only one stable equilibrium point, under noise actions, it has the potential for a stochastic P-bifurcation to occur. This bifurcation causes the central peak of the joint probability density function to split into two symmetric peaks. At this stage, the behavior of the system resembles the development of two phantom attractors that deviate from the equilibrium point, causing the system's random states to linger around them for extended periods. The effects of the damping ratio and noise intensity on the phantom attractors are discussed, together with the critical parameter curve associated with the onset of phantom attractors. Moreover, the generation mechanism of phantom attractors is disclosed by investigating the phase trajectories of the underlying conservative system. The distribution law of those critical parameter values is also proven by the stochastic averaging method, which is associated with the most probable amplitude. This study highlights that phantom attractors can manifest in dynamic systems even in the absence of Hopf bifurcation. [ABSTRACT FROM AUTHOR]

Let L be a nonnegative integer and ΓL the power set of the set {0, 1,…,L}. Then there is an adjacency relation in ΓL such that ΓL together with the relation forms a regular graph. In this paper, we propose a model of continuous-time magnetic quantum walk (MQW) on the graph ΓL, and investigate its properties from a viewpoint of probability and quantum information. We first introduce a magnetic Laplacian ΔL(휃) on the graph ΓL and examine its spectrum. And then, with ΔL(휃) as the Hamiltonian, we construct our model of continuous-time MQW on the graph ΓL. We find that the model has probability distributions that are completely independent of the magnetic potential at all times. And we show that it has perfect state transfer at time t = π 2 when the magnetic potential satisfies some mild conditions. Some other interesting results are also obtained. [ABSTRACT FROM AUTHOR]

The set of sampling and reconstruction in trigonometric polynomial spaces will play an important role in signal processing. However, in many applications, the frequencies in trigonometric polynomial spaces are not all integers. In this paper, we consider the problem of weighted random sampling and reconstruction of functions in general multivariate trigonometric polynomial spaces. The sampling set is randomly selected on a bounded cube with a probability distribution. We obtain that with overwhelming probability, the sampling inequality holds and the explicit reconstruction formula succeeds for all functions in the general multivariate trigonometric polynomial spaces when the sampling size is sufficiently large. [ABSTRACT FROM AUTHOR]

In this paper, we implemented a new approach of measuring contagion effect on financial crisis based on the Detrended Multiple Cross-Correlation Coefficient, DMC x 2 , with a statistical test to assess its significance. Our study is restricted to the particular case in which three stock indexes are analyzed at the same time, with the results being divided into simulated and empirical cases. The simulated case was important to present the probability distribution function of DMC x 2 and Δ DMC x 2 , respectively, as well as confidence intervals for Δ DMC x 2 . The empirical case presents DMC x 2 and Δ DMC x 2 for fourteen stock market indexes in the subprime crisis. With these applications, our study defines contagion effect on the financial system where crisis effect was perceived. In general, our results show the statistical significance of Δ DMC x 2 , while measure of contagion effect depends on the size of the series and the time scale evaluated. [ABSTRACT FROM AUTHOR]

Excellent properties of gallium nitride (GaN) make it an ideal material for realizing gas sensors, especially for ammonia (NH 3) detection. Although many researchers have pursued to describe the characteristics of GaN-based NH3 gas sensors by different approaches, few models have been reported. In this paper, with the consideration of the exponential distribution of interfacial states, a model for ammonia concentration detection of GaN gas sensors has been presented. The Poisson equation is applied to model the effect of defect states on the potential. By taking advantage of the current-voltage characteristics, the value of Schottky barrier height can be obtained. The concentration of the adsorbed NH3 gas is derived by exploiting the surface potential. It indicates that densities of acceptor interfacial trap states are in the order of 10 1 1 ∼ 1 0 1 2 cm − 2 eV − 1 . The current increases with the NH3 concentration at the same applied voltage. In addition, detailed investigations of physical mechanisms and the analysis of the sensitivity have been depicted. It shows that the sensitivity followed an approximately exponential dependence on NH3 density. Results compared well with experimental data that verify the proposed model and simulation method. [ABSTRACT FROM AUTHOR]

Among all probability distributions, power law distribution is an intriguing one, which has been studied by many researchers. However, the derivation of power law distribution is still an inconclusive topic. For deriving a distribution, there are various methods, among which maximum entropy principle is a special one. Entropy of random permutation set (RPS), as an uncertainty measure of RPS, is a newly proposed entropy with special features. Deriving power law distribution with maximum entropy of RPS is a promising method. In this paper, certain constraints are given to constrain the entropy of RPS. Power law distribution is able to be finally derived with maximum entropy principle. Numerical experiments are done to show characters of proposed derivation. [ABSTRACT FROM AUTHOR]

Abnormal detection of wind turbine converter (WT) is one of the key technologies to ensure long-term stable operation and safe power generation of WT. The number of normal samples in the SCADA data of WT converter operation is much larger than the number of abnormal samples. In order to solve the problem of low abnormal data and low recognition rate of WTs, we propose a sample enhancement method for WT abnormality detection based on an improved conditional Wasserstein generative adversarial network. Since the anomaly samples of WT converters are few and difficult to obtain, the CWGANGP oversampling method is constructed to increase the anomaly samples in the WT converter dataset. The method adds additional category labels to the inputs of the generative and discriminative models of the generative adversarial network, constrains the generative model to generate few types of anomalous samples, and enhances the generative model's ability to generate few types of anomalous samples, enabling data generation in a prescribed direction. The smooth continuous Wasserstein distance is used instead of JS divergence as a distance metric to measure the probability distribution of real and generated data in the conditional generative response network and reduce pattern collapse. The gradient constraint is added to the CWGANGP model to enhance the convergence of the WGAN model, so that the generative model can synthesize minority class anomalous samples more effectively and accurately under the condition of unbalanced sample data categories. The quality of anomalous sample generation is also improved. Finally, the anomaly detection is made on the actual operating variator dataset for the unbalanced dataset and the dataset after reaching Nash equilibrium. The experimental results show that the method used in this paper has lower MAR and FAR in WT converter anomaly detection compared with other oversampling data balance optimization methods such as SMOTE, RandomOverSampler, GAN, etc. The method can be well implemented for anomaly detection of large wind turbines and can be better applied in WT intelligent systems. [ABSTRACT FROM AUTHOR]

In this paper, we propose a robust ABC classification for inventories using a hybrid technique for order of preference by similarity to ideal solution-alternative factor extraction approach (TOPSIS-AFEA) as the cornerstone method to calculate and rank importance scores for each item in stock. This is done to mitigate multicollinearity that may exist among different inventory criteria, which artificially inflates total data variance. Besides, and differently from previous research, information reliability techniques such as information entropy and gray relational analysis (GRA) are used as an auxiliary tool to differentiate alternative ABC methods proposed in the literature in terms of the principle of maximal entropy. This principle states that the probability distribution that best represents the current state of knowledge given prior data is the one with largest entropy. Results suggest that the proposed robust TOPSIS-AFEA provides an adequate representation of score ranks that may be computed on different datasets by using existing alternative ABC inventory classification models. [ABSTRACT FROM AUTHOR]

In this paper, on the basis of constructing a new shift operator S and choosing the Grover coin G as coin operator C , we get the standard evolution operator U on cycles. Using U , we not only got the analytical expression of wavefunction ψ s , j , but also obtained the conclusion that the limit distribution π (ν) of N , which is not uniform distribution, regardless of N is odd or even. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the effects of expansion on large-scale structure formation in our universe. We do that by incorporating a cosmological constant term in the gravitational partition function. This gravitational partition function with a cosmological constant is used for analyzing the thermodynamics of this system. We analyze the virial expansion for this system, and obtain its equation of state. It is observed that the generalization of this equation of state is like the Van der Waals equation. We also analyze a gravitational phase transition in this system using the mean-field theory. We construct the cosmic energy equation for this system of galaxies, and discuss its consequences. We obtain and analyze the distribution function for this system, using the gravitational partition function. We also compare the results obtained in this paper with the observational data. [ABSTRACT FROM AUTHOR]

We continue the study of Confined Vortex Surfaces (CVS) that we introduced in the previous paper. We classify the solutions of the CVS equation and find the analytical formula for the velocity field for arbitrary background strain eigenvalues in the stable region. The vortex surface cross-section has the form of four symmetric hyperbolic sheets with a simple equation | y | | x | μ = const in each quadrant of the tube cross-section (x y plane). We use the dilute gas approximation for the vorticity structures in a turbulent flow, assuming their size is much smaller than the mean distance between them. We vindicate this assumption by the scaling laws for the surface shrinking to zero in the extreme turbulent limit. We introduce the Gaussian random background strain for each vortex surface as an accumulation of a large number of small random contributions coming from other surfaces far away. We compute this self-consistent background strain, relating the variance of the strain to the energy dissipation rate. We find a universal asymmetric distribution for energy dissipation. A new phenomenon is a probability distribution of the shape of the profile of the vortex tube in the x y plane. This phenomenon naturally leads to the "multifractal" scaling of the moments of velocity difference v ( r 1) − v ( r 2). More precisely, these moments have a nontrivial dependence of n , log Δ r , approximating power laws with effective index ζ (n , log Δ r). We derive some general formulas for the moments containing multidimensional integrals. The rough estimate of resulting moments shows the log–log derivative ζ (n , log Δ r) which is approximately linear in n and slowly depends on log Δ r. However, the value of effective index is wrong, which leads us to conclude that some other solution of the CVS equations must be found. We argue that the approximate phenomenological relations for these moments suggested in a recent paper by Sreenivasan and Yakhot are consistent with the CVS theory. We reinterpret their renormalization parameter α ≈ 0. 9 5 in the Bernoulli law p = − 1 2 α v 2 as a probability to find no vortex surface at a random point in space. [ABSTRACT FROM AUTHOR]

In this paper, we present our QCD analysis of the Nucleon Form Factors presented by JLab to extract a new parameterization for the valence Generalized Parton Distributions (GPDs), H v q (x , ξ = 0 , t) and E v q (x , ξ = 0 , t). We choose simple parameterizations for x − and t − dependence of GPDs at zero skewness. These free parameters of the model are then obtained using old and new data of nucleon's elastic electromagnetic form factors (FFs) from JLAB. We have also used the "Hessian method" to perform a careful estimation of the uncertainties for the nucleon GPDs and corresponding observables originate from experimental errors. We also calculate the parton distribution functions (PDFs) in Impact parameter space to show the 3D structure of the Nucleon. We also calculated the proton and the neutron charge densities ρ ch (p , n) . We show that there is a highly localized negative charge near the center of the neutron and it is because of the negatively charged down quarks dominating the high momentum quarks in the neutron. Finally using the obtained Dirac's FF, we had an estimation for the proton charge radius. The predictions based on the obtained nucleon GPDs are in good agreement with all available experimental data and other phenomenological models. [ABSTRACT FROM AUTHOR]

In this paper, we establish a stochastic dynamical grazing ecosystem with time delays and fluctuations. The effects of time delay, Gaussian noise and Lévy noise on the stationary probability distribution (SPD), the mean first passage time (MFPT) and stochastic resonance (SR) are analyzed. Our research results show the following: (i) For small time delay, the increasing Gaussian noise intensity leads to catastrophic regime shift (CRS) from high vegetation state to low vegetation state, while the increasing Lévy noise intensity contributes to the recovery of these shifts. For large time delay, the increasing Gaussian noise intensity or Lévy noise intensity causes the CRS phenomenon, the larger the time delay, the more frequent the CRS phenomenon. (ii) The increasing Gaussian noise intensity can diminish the stability of the high vegetation state and low vegetation state, the increasing Lévy noise intensity and Lévy stability index can enhance the stability of the high vegetation state and diminish the stability of the low vegetation state. The increasing Lévy noise intensity can lead to noise-enhanced stability (NES) of the high vegetation state, and the larger the time delay, the more pronounced the NES phenomenon. (iii) The increase of time delay can weaken SR phenomenon when signal-to-noise ratio (SNR) is a function of Gaussian noise intensity and Lévy noise intensity. [ABSTRACT FROM AUTHOR]

This paper develops a model to assess the number of nurses needed to ensure both healthy patients and caregivers. We propose a model with random arrivals and exits of patients who may be of a single type (or several), and calculate the average care time they can receive. We show that the mean care time does not depend only on the mean number of patients in the unit. Actually, the probability distribution of the new patients per time step plays a central role. In the Poissonian case, we obtain totally explicit results, prove that the mean care time converges to a constant and give numerical examples. We also propose an analysis of the impact of working conditions on the average time that can be devoted to a patient. Four scenarios are proposed with numerical applications. Our analysis provides insights into current discussions on the introduction of caregiver ratios in hospitals to improve both the quality of care and caregivers' working conditions. [ABSTRACT FROM AUTHOR]

An advanced shrink–expand–shrink method is proposed in this paper for efficiently modeling concrete-like particle-reinforced composites with ultrahigh volume fraction of aggregates. The gradation of the aggregates can be pre-given and the aggregate spatial distribution can be nonuniform. By this method, the shrunk aggregates are first generated in the model space, and then expanded to jostle each other, afterwards they are shrunk again to normal size to obtain the final mesostructure models. Any high volume fractions of particles even more than 90% can be easily achieved by adjusting the shrinkage level during this process. Besides, a gradient distribution algorithm is established to conform to the aggregate segregation during the actual pouring process, and the corresponding periodic boundaries can also be generated to quickly create large specimens. Finally, the compression processes of polymer concrete with different aggregate packing densities are calculated via a finite element method. The shrink–expand–shrink method and the corresponding numerical models have memorable importance in the performance analysis and material design of particle-reinforced composites. [ABSTRACT FROM AUTHOR]

In this paper, we construct a hierarchical network generated from the Thue–Morse sequence. First, we deduce that the degree distribution of the Thue–Morse hierarchical network follows an exponential distribution. Then, we compute the degree correlations by calculating the average degree of all neighbors of nodes which have degree k, denoted k n n (k). By getting an accurate range of k n n (k) , we show that k n n (k) ∼ 1 2 k and the Thue–Morse hierarchical network is assortative. Finally, we conclude that the hierarchical networks generated from substitution sequences still have the same properties as deterministic hierarchical networks. [ABSTRACT FROM AUTHOR]

In this paper, we consider a phased mission system consisting of k phases (subsystems) wherein the control flows sequentially. The mission is successful if tasks associated with every phase are successful. Density and reliability functions of the lifetime of such a system are worked out when the lifetimes of components of the subsystems follow exponential distribution. It is assumed that components in different subsystems are in series configuration and function independently. The subsystems are assumed to operate independently. A simulation study is conducted to find bias of the estimates of the parameters and the reliability function. The Root Mean Square Error (RMSE) of the estimates is also calculated. [ABSTRACT FROM AUTHOR]

In this paper, we study the hydrodynamic limit for the fluid–particle model, which consists of the inhomogeneous incompressible Navier–Stokes equations coupled with the Vlasov equation through a drag force in a bounded domain of ℝ 2 with a homogeneous Dirichlet boundary condition on the fluid velocity field and Maxwell boundary condition on the kinetic distribution function. The proof relies on the relative entropy argument, which extends the work of El Ghani [Asymptotic analysis for a Vlasov–Navier–Stokes system in a bounded domain, J. Hyperbolic Differ. Equ. 7 (2010) 191–210] to inhomogeneous incompressible Navier–Stokes–Vlasov equations. [ABSTRACT FROM AUTHOR]

In reliability studies, the data is often truncated and hence the residual random variable plays a vital role in the modelling and analysis of lifetime data. Like various reliability measures such as hazard rate, mean residual life function, variance residual life function, the residual coefficient of variation is also an important tool considered by many. In this paper, we study a quantile version of coefficient of variation of residual life, an alternative to the traditional distribution function measure. We study various properties of it and obtain characterizations based on some well-known probability models. We introduce a class of distributions with linear quantile-based residual coefficient of variation and study their basic reliability properties. We also obtain some stochastic comparison and aging properties using quantile-based residual coefficient of variation. The L-moment method of estimation for the class of distributions with linear quantile-based residual coefficient of variation has also been illustrated using two real data sets. [ABSTRACT FROM AUTHOR]

This paper is a probabilistic performance study of a repairable complex system with three subsystems coupled in a series configuration. All three subsystems have been differently configured and also have different operational schemes. The first subsystem has n units and works under the k -out-of- n :G scheme, the second subsystem has four identical units and associates with a defined work scheme 2-out-of-4:G, however, the third subsystem has two indistinguishable units and works under the 1-out-of-2:G policy. The units' failure rates of the subsystems are different but constant and follow an exponential distribution, however, there are two types of repair facilities available for repair general and copula repair. Under the consideration of the system with the operational duration, the failed unit was replaced with a new one and it was assigned for repair. In the complete shutdown condition, a copula repair has been employed to repair the system. Traditional reliability measures have been studied for different values of failure and repair through supplementary variable and copula approaches. The numerical computations for securing different values of k and n have been exhibited and tables and graphs predict the future behavior of the system performance. In the conclusion section, the effect of reliability measures has been highlighted. [ABSTRACT FROM AUTHOR]

In this paper, we present an abstract model of continuous-time quantum walk (CTQW) based on Bernoulli functionals and show that the model has perfect state transfer (PST), among others. Let be the space of square integrable complex-valued Bernoulli functionals, which is infinitely dimensional. First, we construct on a given subspace L ⊂ a self-adjoint operator Δ L via the canonical unitary involutions on , and by analyzing its spectral structure we find out all its eigenvalues. Then, we introduce an abstract model of CTQW with L as its state space, which is governed by the Schrödinger equation with Δ L as the Hamiltonian. We define the time-average probability distribution of the model, obtain an explicit expression of the distribution, and, especially, we find the distribution admits a symmetry property. We also justify the model by offering a graph-theoretic interpretation to the operator Δ L as well as to the model itself. Finally, we prove that the model has PST at time t = π 2 . Some other interesting results about the model are also proved. [ABSTRACT FROM AUTHOR]

Duration and convexity are important measures in fixed-income portfolio management. In this paper, we analyze this measure of the bonds by applying the beta model. The general usefulness of the beta probability distribution enhances its applicability in a wide range of reliability analyses, especially in the theory and practice of reliability management. We estimate the beta density function of the duration/convexity. This estimate is based on two important and simple models of short rates, namely, Vasicek and CIR (Cox, Ingersoll, and Ross CIR). The models are described and then their sensitivity of the models with respect to changes in the parameters is studied. We generate the stochastic interest rate on the duration and convexity model. The main results show that the beta probability distribution can be applied to model each phase of the risk function. This distribution approved its effectiveness, simplicity and flexibility. In this paper, we are interested in providing a decision-making tool for the manager in order to minimize the portfolio risk. It is helpful to have a model that is reasonably simple and suitable to different maturity of bonds. Also, it is widely used by investors for choosing bond portfolio immunization through the investment strategy. The finding also shows that the probability of risk measured by the reliability function is to highlight the relationship between duration/convexity and different risk levels. With these new results, this paper offers several implications for investors and risk management purposes. [ABSTRACT FROM AUTHOR]

Cloud providers face the challenge of managing large amounts of heterogeneous resources in real time. It is usually very costly to conduct experiments with real cloud systems. Therefore, tools to analyze and evaluate cloud scenarios and experimental studies are very useful for them. In this paper, we model cloud systems and the user interactions with the cloud provider using the UML2Cloud profile. In general, users request virtual machines according to their needs, but they can also subscribe to the cloud provider and wait to be notified when the requested resources are not available. In this case, users indicate a maximum subscription time, so once this time elapses without being notified, users leave the system unattended. Thus, we present an exhaustive experimental study to measure how the user subscription times affect the overall system responsiveness. To this end, four different cloud configurations are analyzed, and the workloads for these studies are produced by using three distribution functions for the user arrivals, namely, a uniform, a normal, and a cyclic normal distribution. Furthermore, we also analyze the cloud performance with a workload obtained from a real trace. The purpose of this study is to find out the inflection point for the waiting time of the users, from which the cloud responsiveness and its performance do not improve. The obtained information is, therefore, useful for the cloud provider to improve the configuration of the cloud. [ABSTRACT FROM AUTHOR]

In this paper, we study the concomitants of m -dual generalized order statistics (m -DGOS) from Bairamov–Kotz–Becki Farlie–Gumbel–Morgenstern bivariate distributions as an extension of several recent papers. This study can also be applied to the model of m -generalized order statistics (m -GOS) as a parallel model of m -DGOS. Furthermore, the joint distribution of m -DGOS of concomitants for this family is studied. Some useful recurrence relations between single and product moments of concomitants are obtained. Moreover, most of the paper results are extended to any arbitrary distribution. Finally, an application of these results is given for bivariate generalized exponential distribution. [ABSTRACT FROM AUTHOR]

In this paper, we describe the gluon parton distribution function (PDF) in the proton, deduced by data from the ATLAS and HERA experiments, in the framework of the parton statistical model. The best fit parameters involved in the Planck formula that describes the gluon distribution are consistent with the results obtained from analysis of LHC deep inelastic proton–proton scattering processes. Remarkably, the agreement between the statistical model and the experimental gluon distributions is obtained with the same value of the "temperature" parameter x ̄ found by fitting the valence parton distributions from deep inelastic scattering. This result corroborates the validity of the statistical approach in the gluon sector. [ABSTRACT FROM AUTHOR]

Standby spare systems are particularly important because of their high reliability over other competing systems. A great deal of research has been done in the literature on these systems under various assumptions. Obtaining explicit reliability equations for such systems is achieved only when the failure behavior of their components follows the exponential distribution due to its ease of use. However, in practice, there are many components that their failure behavior does not follow the exponential distribution. In this paper, a closed-form equation is derived for the reliability of the 1-out-of- n cold standby spare system under conditions that the failure of the active component follows the Weibull distribution. The solution method for the system is based on the Maclaurin series and multinomial expansion. [ABSTRACT FROM AUTHOR]

In this paper, in order to study the dynamic behavior of the three-body interaction, the generalized Kuramoto model with bimodal frequency distribution under the joint interaction of two-body and three-body is proposed. The comparative numerical results of the phase synchronization paths of the three-body interaction under different coupling strengths show that the three-body interaction can transform the continuous transition process into the first-order transition process. Interestingly, the change from continuous to discontinuous transition due to the variation of the coupling strength of the three-body interaction is similar to the shape of the bimodal distribution of the natural frequency. The critical coupling strength of the two-body interaction of synchronous transition is derived from the Ott–Antonsen–Ansatz method. The numerical results are consistent with the theoretical ones. The findings help our understanding of the transformation process from being continuous to discontinuous. [ABSTRACT FROM AUTHOR]

In the present paper, we construct QMCs (Quantum Markov Chains) associated with Open Quantum Random Walks such that the transition operator of the chain is defined by OQRW and the restriction of QMC to the commutative subalgebra coincides with the distribution ℙ ρ of OQRW. This sheds new light on some properties of the measure ℙ ρ . As an example, we simply mention that the measure can be considered as a distribution of some functions of certain Markov processes. Furthermore, we study several properties of QMC and associated measures. A new notion of φ -recurrence of QMC is studied, and the relations between the concepts of recurrence introduced in this paper and the existing ones are established. [ABSTRACT FROM AUTHOR]

The distribution of the primes of the forms ⌊ n α ⌋ and ⌊ n α + β ⌋ are studied extensively, where ⌊ x ⌋ denotes the largest integer not exceeding x. In this paper, we will consider several new type problems on the distribution of the primes involving the ceiling (floor) function. For any real number 𝜃 with 0 < 𝜃 ≤ 1 , let π 𝜃 ′ (n) be the number of integers k with 1 ≤ k ≤ n 𝜃 such that ⌈ n / k ⌉ is prime and let π 𝜃 ′ ′ (n) be the number of primes p for which there exists an integer k with 1 ≤ k ≤ n 𝜃 such that p = ⌈ n / k ⌉ , where ⌈ x ⌉ denotes the least integer not less than x. These are closely related to the number of the prime factors of the denominator of the Bernoulli polynomial B n (x) − B n . In this paper, we study asymptotic properties of π 𝜃 ′ (n) and π 𝜃 ′ ′ (n). The methods in this paper are also effective for corresponding distribution functions of the primes involving the floor function. [ABSTRACT FROM AUTHOR]

The paper presents a computationally efficient method for modeling and simulating distributed systems with lossy transmission line (TL) including multiconductor ones, by a less conventional method. The method is devised based on 1D and 2D Laplace transforms, which facilitates the possibility of incorporating fractional-order elements and frequency-dependent parameters. This process is made possible due to the development of effective numerical inverse Laplace transforms (NILTs) of one and two variables, 1D NILT and 2D NILT. In the paper, it is shown that in high frequency operating systems, the frequency dependencies of the system ought to be included in the model. Additionally, it is shown that incorporating fractional-order elements in the modeling of the distributed parameter systems compensates for losses along the wires, provides higher degrees of flexibility for optimization and produces more accurate and authentic modelling of such systems. The simulations are performed in the Matlab environment and are effectively algorithmized. [ABSTRACT FROM AUTHOR]

Large amounts of research efforts have been focused on learning gene regulatory networks (GRNs) based on gene expression data to understand the functional basis of a living organism. Under the assumption that the joint distribution of the gene expressions of interest is a multivariate normal distribution, such networks can be constructed by assessing the nonzero elements of the inverse covariance matrix, the so-called precision matrix or concentration matrix. This may not reflect the true connectivity between genes by considering just pairwise linear correlations. To relax this limitative constraint, we employ Gaussian process (GP) model which is well known as computationally efficient non-parametric Bayesian machine learning technique. GPs are among a class of methods known as kernel machines which can be used to approximate complex problems by tuning their hyperparameters. In fact, GP creates the ability to use the capacity and potential of different kernels in constructing precision matrix and GRNs. In this paper, in the first step, we choose the GP with appropriate kernel to learn the considered GRNs from the observed genetic data, and then we estimate kernel hyperparameters using rule-of-thumb technique. Using these hyperparameters, we can also control the degree of sparseness in the precision matrix. Then we obtain kernel-based precision matrix similar to GLASSO to construct kernel-based GRN. The findings of our research are used to construct GRNs with high performance, for different species of Drosophila fly rather than simply using the assumption of multivariate normal distribution, and the GPs, despite the use of the kernels capacity, have a much better performance than the multivariate Gaussian distribution assumption. [ABSTRACT FROM AUTHOR]

It has been argued that the existence of a zero-point length is the hallmark of quantum gravity. In this paper, we suggest a thermal mechanism whereby this quantum of length arises in flat, Euclidean spacetime ℝ d . For this, we consider the infinite sequence of all flat, Euclidean spacetimes ℝ d ′ with d ′ ≥ d , and postulate a probability distribution for each d ′ to occur. The distribution considered is that of a canonical ensemble at temperature T , the energy levels those of a 1-dimensional harmonic oscillator. Since both the harmonic energy levels and the spacetime dimensions are evenly spaced, one can identify the canonical distribution of harmonic-oscillator eigenvalues with that of dimensions d ′ . The state describing this statistical ensemble has a mean square deviation in the position operator, that can be interpreted as a quantum of length. Thus, placing an oscillator in thermal equilibrium with a bath provides a thermal mechanism whereby a zero-point length is generated. The quantum-gravitational implications of this construction are then discussed. In particular, a model is presented that realizes a conjectured duality between a weakly gravitational, strongly quantum system and a weakly quantum, strongly gravitational system. [ABSTRACT FROM AUTHOR]

Asymmetrical models like the generalized and q-generalized extreme value distributions have been widely used to describe a variety of random events observed in studies including survival, finance, and dependability. The q-analogues, with the extra parameter q, provide for more modelling freedom. In this paper, Shannon entropy, Varentropy and Varexentropy measures are computed in closed form in cases of generalized and q-generalized extreme value distributions. Maximum likelihood estimation method is applied for computing the values of Shannon entropy, Varentropy and Varexentropy measures. [ABSTRACT FROM AUTHOR]

In this paper, the phase space representation for a semiconfined harmonic oscillator model with a position-dependent effective mass is constructed. We have found the Husimi distribution function for the stationary states of the oscillator model under consideration for both cases without and with the applied external homogeneous field. The obtained function is expressed through the double sum of the parabolic cylinder function. Different special cases and the limit relations are discussed, too. [ABSTRACT FROM AUTHOR]

Construction of future Muon Collier (or dedicated μ -ring) tangential to the energy frontier h h colliders will give opportunity to realize μ p and μ A collisions at multi-TeV center-of-mass energies with sufficiently high luminosities. Obviously, such colliders will essentially enlarge the physics search potential of corresponding muon and hadron colliders for both the SM (especially for clarifying QCD basics and confinement hypothesis) and BSM phenomena. In addition, they will provide parton distribution functions for adequate interpretation of energy frontier h h colliders' and cosmic ray experiments data. This paper is devoted to review of main parameters of μ h colliders proposed until now. [ABSTRACT FROM AUTHOR]

In this paper, a next-to-next-to-leading order (NNLO) quantum chromodynamics (QCD) calculation of gluon distribution function at small- x is presented. The gluon distribution function is explored analytically in the Dokshitzer–Gribov–Lipatov–Altarelli–Parisi approach by a Taylor expansion at small- x as two first-order partial differential equations in two variables: Bjorken x and t (t = ln ( Q 2 Λ 2 )). We have solved the system of equations at LO, NLO and NNLO, respectively, by Lagrange's method. The resulting analytical expressions are compared with the available global parton distribution function fits as well as with the results of the Block–Durand–McKay model. We have further performed an χ 2 test to check the compatibility of our predictions and observed that our results can be consistently described in the context of perturbative QCD. A comparative analysis of the obtained results at LO, NLO and NNLO reveals that the NNLO approximation has a significant contribution to the gluon distribution function particularly in the small- x region. [ABSTRACT FROM AUTHOR]

In recent years, the interaction of electrons with the electromagnetic field in plasma at low pressure has received significant attention because of its high application. In low-pressure plasma, electrons can move long distances without any collisions in physical dimensions of the problem. This causes nonlocal dynamics, which leads to strong time and space dependence on and anisotropy of the distribution function. In this paper, a hybrid Particle-in-Cell (PIC) method with Direct Monte Carlo Simulation (DSMC) was proposed to investigate electron interactions with the electrostatic field. A capacitively coupled plasma (CCP) reactor at low pressure (0.01–10Pa) was also investigated. The effect of electric field was studied on electrons and field distribution in the computational domain at different times. Also, the amplitude current was investigated in a complete radio frequency (RF) cycle. As a result, this work proposed tools to examine the discharge flow for accurate knowledge of CCP discharge for optimization of reactors and its related processes. [ABSTRACT FROM AUTHOR]