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Based on the random finite set (RFS) framework and the probability hypothesis density (PHD) filter, the extended target PHD (ET‐PHD) filter is proposed for multiple extended target tracking. However, the clutter process in the ET‐PHD filter is modelled as Poisson RFS, which is reasonable for only some scenarios in reality. An easily implemented ET‐PHD filter for arbitrary clutter process, has not yet been studied. In this work, another form of the general PHD filter, suitable for arbitrary clutter and target measurement is derived using a probability generating functional (PGFL)‐based RFS framework. The proposed filter is equivalent to the general PHD filter proposed by Clark and Mahler, but it is easily implemented in an arbitrary clutter process because its clutter process is denoted by the probability density function. Then, an arbitrary clutter ET‐PHD (AC‐ET‐PHD) filter is simplified from the general PHD filter derived by us. To reduce the computational complexity of the proposed filter, a variant of the distance partitioning algorithm is put forward. Simulation results show that the AC‐ET‐PHD filter can be applied to the scenarios with the non‐Poisson clutter process, which means that it will be useful for multiple extended targets tracking in a more complicated clutter process. [ABSTRACT FROM AUTHOR]

Review of the probability representation of qubit states and observables is presented as well as the picture of states of two-level systems in terms of Triada of Malevich's squares. A new relation of introduced probability parameters is obtained. Also, it is offered a method to visualize the quantum channel's maps of qubit states. Evolution of the two-level system is considered in terms of Triada of Malevich's squares in case of Rabi and Demkov models. [ABSTRACT FROM AUTHOR]

As the first major step in each object-oriented feature extraction approach, segmentation plays an essential role as a preliminary step towards further and higher levels of image processing. The primary objective of this paper is to illustrate the potential of Polarimetric Synthetic Aperture Radar (PolSAR) features extracted from Compact Polarimetry (CP) SAR data for image segmentation using Markov Random Field (MRF). The proposed method takes advantage of both spectral and spatial information to segment the CP SAR data. In the first step of the proposed method, k-means clustering was applied to over-segment the image using the appropriate features optimally selected using Genetic Algorithm (GA). As a similarity criterion in each cluster, a probabilistic distance was used for an agglomerative hierarchical merging of small clusters into an appropriate number of larger clusters. In the agglomerative clustering approach, the estimation of the appropriate number of clusters using the data log-likelihood algorithm differs depending on the distance criterion used in the algorithm. In particular, the Wishart Chernoff distance which is independent of samples (pixels) tends to provide a higher appropriate number of clusters compared to the Wishart test statistic distance. This is because the Wishart Chernoff distance preserves detailed data information corresponding to small clusters. The probabilistic distance used in this study is Wishart Chernoff distance which evaluates the similarity of clusters by measuring the distance between their complex Wishart probability density functions. The output of this step, as the initial segmentation of the image, is applied to a Markov Random Field model to improve the final segmentation using vicinity information. The method combines Wishart clustering and enhanced initial clusters in order to access the posterior MRF energy function. The contextual image classifier adopts the Iterated Conditional Mode (ICM) approach to converge to a local minimum and represent a good trade-off between segmentation accuracy and computation burden. The results showed that the PolSAR features extracted from CP mode can provide an acceptable overall accuracy in segmentation when compared to the full polarimetry (FP) and Dual Polarimetry (DP) data. Moreover, the results indicated that the proposed algorithm is superior to the existing image segmentation techniques in terms of segmentation accuracy. [ABSTRACT FROM AUTHOR]

Abstract A discrete time quantum walker is considered in one dimension, where at each step, the translation can be more than one unit length chosen randomly. In the simplest case, the probability that the distance travelled is ℓ is taken as P (ℓ) = α δ (ℓ − 1) + (1 − α) δ (ℓ − 2 n) with n > 1. Even the n = 1 case shows a drastic change in the scaling behaviour for any α ≠ 0 , 1. Specifically, 〈 x 2 〉 ∝ t 3 ∕ 2 for 0 < α < 1 implying the walk is slower compared to the usual quantum walk. This scaling behaviour, which is neither conventional quantum nor classical, can be justified using a simple form for the probability density. The decoherence effect is characterised by two parameters which vanish in a power law manner close to α = 0 and 1 with an exponent ≈ 0. 5. It is also shown that randomness is the essential ingredient for the decoherence effect. Highlights • A quantum walk with random step length on a line is considered. • The results show the behaviour 〈 x 2 〉 ∝ t 3 ∕ 2. • Two quantities characterising the decoherence are identified and studied. • Conventional scaling behaviour is noted for periodically varying step lengths. [ABSTRACT FROM AUTHOR]

Abstract This paper considers a class of nonlinear filtering algorithms based on variational Bayesian (VB) theory to settle the unknown measurement noise problem in target tracking system. When the unknown measurement noise is conditionally independent of states, based on the variational idea, estimate of probability density function of state is converted into approximation two probability density functions for both unknown noise and nonlinear states. Then, an iterative algorithm is established to jointly estimate the state and the unknown measurement noise using variational Bayesian inference. Thus, the unknown measurement noise could be estimated as hidden state. The convergence result of the proposed nonlinear probability density function approximation algorithm is also given. The simulation results of typical examples show that the proposed VB based methods have superior performance to these classic algorithms in target tracking problems. [ABSTRACT FROM AUTHOR]

In this article, an analytical moment-based procedure is developed for estimating the first passage probability of stationary non-Gaussian structural responses for practical applications. In the procedure, an improved explicit third-order polynomial transformation (fourth-moment Gaussian transformation) is proposed, and the coefficients of the third-order polynomial transformation are first determined by the first four moments (i.e. mean, standard deviation, skewness, and kurtosis) of the structural response. The inverse transformation (the equivalent Gaussian fractile) of the third-order polynomial transformation is then used to map the marginal distributions of a non-Gaussian response into the standard Gaussian distributions. Finally, the first passage probabilities can be calculated with the consideration of the effects of clumping crossings and initial conditions. The accuracy and efficiency of the proposed transformation are demonstrated through several numerical examples for both the "softening" responses (with wider tails than Gaussian distribution; for example, kurtosis > 3) and "hardening" responses (with narrower tails; for example, kurtosis < 3). It is found that the proposed method has better accuracy for estimating the first passage probabilities than the existing methods, which provides an efficient and rational tool for the first passage probability assessment of stationary non-Gaussian process. [ABSTRACT FROM AUTHOR]

This study deals with the stochastic non-linear dynamic response of functionally graded materials (FGMs) plate with uncertain system properties subjected to time-dependent uniformly distributed transverse load in thermal environments. System properties, such as material properties of each constituent's material, volume fraction index, and transverse load, are taken as uncorrelated random input variables. Material properties are assumed as temperature dependent (TD). The formulation is based on higher-order shear deformation theory (HSDT) with von-Karman non-linear strain kinematics using modified C° continuity. A Newton-Raphson-based non-linear finite element method along with a first-order perturbation technique (FOPT) and Monte Carlo sampling (MCS) is outlined to examine the second-order statistics (mean, standard deviation (SD), and probability density function (PDF)) of the non-linear dynamic response of the FGM plate. The governing dynamic equation is solved by Newmark's time integration scheme. The effects of volume fraction index, load parameters, plate thickness ratios, and temperature changes with random system properties are examined through parametric studies. The present outlined approach is validated with the results available in the literature and by MCS. [ABSTRACT FROM AUTHOR]

In this paper, the influence of a zero and a non-zero boresight pointing errors on the performances of free-space optic transmission over the Málaga atmospheric turbulence channel is considered. Closed form expressions for a zero boresight channel model probability density function, non-zero boresight channel model probability density function, as well as a bit-error rate over a binary phase shift keying modulation transmission are provided. Numerical results for zero and non-zero boresight pointing errors are graphically presented. [ABSTRACT FROM AUTHOR]

Abstract A cantilever with an open surface crack excited by the pedestal movement with the form of the Gaussian white noise was modeled in this paper. The open crack was simplified as an elastic hinge and the modal functions of the cracked cantilever were obtained. The dynamical equation governing the transverse motion was gained with the Kane's method after sufficient consideration of the geometrical nonlinearity and the axial inertia. Both quasi-conservative stochastic averaging method and the improved energy envelop stochastic averaging method which is effective on strong nonlinearity were applied to analyze the responses of the cantilever model theoretically. The stationary probability density function (PDF) of the amplitude, as well as the joint stationary PDF of the displacement and velocity, was investigated. For the purpose of exploring the reliability of the cantilever, the reliability function was established to avoid the potential fatigue or damage. Numerical simulations were carried out to vindicate the theoretical analysis. The advantage of the improved energy envelop stochastic averaging method was explicated by the digital results of both the stationary PDF of the amplitude and the joint PDF of displacement and velocity. Furthermore, the accuracy of the prediction on the reliability given by the theoretical analysis was also vindicated by the numerical simulation (Monte Carlo method) of the reliability. [ABSTRACT FROM AUTHOR]

Abstract We investigate the nonlocal dynamics of a single particle placed in an infinite well with moving walls. It is shown that in this situation, the Schrödinger equation (SE) violates local causality by causing instantaneous changes in the probability current everywhere inside the well. This violation is formalized by designing a gedanken faster-than-light communication device which uses an ensemble of long narrow cavities and weak measurements to resolve the weak value of the momentum far away from the movable wall. Our system is free from the usual features causing nonphysical violations of local causality when using the (nonrelativistic) SE, such as instantaneous changes in potentials or states involving arbitrarily high energies or velocities. We explore in detail several possible artifacts that could account for the failure of the SE to respect local causality for systems involving time-dependent boundary conditions. Highlights • We study a quantum particle placed in an infinite well with a moving wall. • We show that the current density is modified instantaneously when the wall moves. • We indicate how this could be experimentally recorded with weak measurements. • By circumventing the measurement noise this effect could give rise to signaling. • We examine the possible artefacts that could account for this unphysical behavior. [ABSTRACT FROM AUTHOR]

Abstract Wavelet estimators for a probability density f enjoy many good properties, however they are not 'shape-preserving' in the sense that the final estimate may not be non-negative or integrate to unity. A solution to negativity issues may be to estimate first the square root of f and then square this estimate up. This paper proposes and investigates such an estimation scheme, generalizing to higher dimensions some previous constructions which are valid only in one dimension. The estimation is mainly based on nearest-neighbor-balls. The theoretical properties of the proposed estimator are obtained, and it is shown to reach the optimal rate of convergence uniformly over large classes of densities under mild conditions. Simulations show that the new estimator performs as well in terms of Mean Integrated Squared Error as the classical wavelet estimator and better than it in terms of Mean Squared Hellinger Distance between the estimator and the truth, while automatically producing estimates which are bona fide densities. [ABSTRACT FROM AUTHOR]

We suggest a method of studying the joint probability density (JPD) of an eigenvalue and the associated ‘non-orthogonality overlap factor’ (also known as the ‘eigenvalue condition number’) of the left and right eigenvectors for non-selfadjoint Gaussian random matrices of size N×N. First we derive the general finite N expression for the JPD of a real eigenvalue λ and the associated non-orthogonality factor in the real Ginibre ensemble, and then analyze its ‘bulk’ and ‘edge’ scaling limits. The ensuing distribution is maximally heavy-tailed, so that all integer moments beyond normalization are divergent. A similar calculation for a complex eigenvalue z and the associated non-orthogonality factor in the complex Ginibre ensemble is presented as well and yields a distribution with the finite first moment. Its ‘bulk’ scaling limit yields a distribution whose first moment reproduces the well-known result of Chalker and Mehlig (Phys Rev Lett 81(16):3367-3370, 1998), and we provide the ‘edge’ scaling distribution for this case as well. Our method involves evaluating the ensemble average of products and ratios of integer and half-integer powers of characteristic polynomials for Ginibre matrices, which we perform in the framework of a supersymmetry approach. Our paper complements recent studies by Bourgade and Dubach (The distribution of overlaps between eigenvectors of Ginibre matrices, 2018. arXiv:1801.01219). [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present a network realization theory for a class of mixed quantum–classical linear stochastic systems. Two forms, the standard form and the general form, of this class of linear mixed quantum–classical systems are proposed. Necessary and sufficient conditions for their physical realizability are derived. Based on these physical realizability conditions, a network synthesis theory for this class of linear mixed quantum–classical systems is developed, which clearly exhibits the quantum component, the classical component, and their interface. An example is used to illustrate the theory presented in this paper. [ABSTRACT FROM AUTHOR]

Flow regime map is often used in choosing constitutive correlations for the two-phase flow model. The related research mainly concentrates on the vertical upward and horizontal flow, while it is not sufficient in the vertical downward flow. Downward flow is very important as it is frequently encountered in the industrial applications. To enrich the downward flow research, an experiment is performed on a piping system with an inner diameter of 0.1524 m. Four different flow patterns (bubbly flow, cap bubbly flow, churn turbulent flow, and annular flow) are classified with the artificial neural network method. The probability density function (PDF) profile of each flow pattern is discussed. The proposed flow regime map is compared with the other experiments and the effect of the pipe size is discussed. The existing downward flow regime boundary criteria are assessed with the experiment results. It is found that these criteria cannot fit the experiment results well. A set of general boundary criteria are still needed. In this paper, the criteria for the boundary of the bubbly flow, the boundary between the cap bubbly flow and the slug flow, and the boundary of the falling film regime are proposed. They are verified with the experiments on different size pipes. A significant inlet effect on the flow regime boundary is found. The falling film boundary criterion proposed cannot be applied when a sparger is used to inject gas into the downward test section. [ABSTRACT FROM AUTHOR]

In this paper, we study the probability density function, P (c , α , β , n) d c , of the center of mass of the finite n Jacobi unitary ensembles with parameters α > −1 and β > −1; that is the probability that trMn ∈ (c, c + dc), where Mn are n × n matrices drawn from the unitary Jacobi ensembles. We compute the exponential moment generating function of the linear statistics ∑ j = 1 n f ( x j ) ≔ ∑ j = 1 n x j , denoted by M f (λ , α , β , n). The weight function associated with the Jacobi unitary ensembles reads xα(1 − x)β, x ∈ [0, 1]. The moment generating function is the n × n Hankel determinant Dn(λ, α, β) generated by the time-evolved Jacobi weight, namely, w (x; λ, α, β) = xα(1 − x)β e−λx, x ∈ [0, 1], α > −1, β > −1. We think of λ as the time variable in the resulting Toda equations. The non-classical polynomials defined by the monomial expansion, Pn(x, λ) = xn + p(n, λ) xn−1 + ⋯ + Pn(0, λ), orthogonal with respect to w (x, λ, α, β) over [0, 1] play an important role. Taking the time evolution problem studied in Basor et al. [J. Phys. A: Math. Theor. 43, 015204 (2010)], with some change of variables, we obtain a certain auxiliary variable rn(λ), defined by integral over [0, 1] of the product of the unconventional orthogonal polynomials of degree n and n − 1 and w (x; λ, α, β)/x. It is shown that rn(2iez) satisfies a Chazy II equation. There is another auxiliary variable, denoted as Rn(λ), defined by an integral over [0, 1] of the product of two polynomials of degree n multiplied by w (x; λ, α, β)/x. Then Yn(−λ) = 1 − λ/Rn(λ) satisfies a particular Painlevé V: PV(α2/2, − β2/2, 2n + α + β + 1, 1/2). The σn function defined in terms of the λp(n, −λ) plus a translation in λ is the Jimbo–Miwa–Okamoto σ-form of Painlevé V. The continuum approximation, treating the collection of eigenvalues as a charged fluid as in the Dyson Coulomb Fluid, gives an approximation for the moment generating function M f (λ , α , β , n) when n is sufficiently large. Furthermore, we deduce a new expression of M f (λ , α , β , n) when n is finite, in terms the σ function of this is a particular case of Painlevé V. An estimate shows that the moment generating function is a function of exponential type and of order n. From the Paley-Wiener theorem, one deduces that P (c , α , β , n) has compact support [0, n]. This result is easily extended to the β ensembles, as long as the weight w is positive and continuous over [0, 1]. [ABSTRACT FROM AUTHOR]

The Horizon Quantum Mechanics is an approach that allows one to analyse the gravitational radius of spherically symmetric systems and compute the probability that a given quantum state is a black hole. We first review the (global) formalism and show how it reproduces a gravitationally inspired GUP relation. This results leads to unacceptably large fluctuations in the horizon size of astrophysical black holes if one insists in describing them as (smeared) central singularities. On the other hand, if they are extended systems, like in the corpuscular models, no such issue arises and one can in fact extend the formalism to include asymptotic mass and angular momentum with the harmonic model of rotating corpuscular black holes. The Horizon Quantum Mechanics then shows that, in simple configurations, the appearance of the inner horizon is suppressed and extremal (macroscopic) geometries seem disfavoured. [ABSTRACT FROM AUTHOR]

Numerical schemes for scalar transport and mixing in turbulent flows must be high-order accurate, and observe conservation and boundedness constraints. Discretization accuracy can be evaluated from the truncation error, and assessed by its dispersion and dissipation properties. Dispersion errors can cause violation of physical scalar bounds, whereas numerical dissipation is key to mitigating those violations. Numerical dissipation primarily alters the energy at small scales that are critical to turbulent mixing. Influence of additional dissipation on scalar mixing in large-eddy simulations (LES) of incompressible temporally evolving shear flow is examined in terms of the resolved passive-scalar field, Z ¯ . Scalar fields in flows with different mixing behavior, exhibiting both uniform and non-uniform mixed-fluid composition across a shear layer, are compared for different grid resolutions, subgrid-scale models, and scalar-convection schemes. Scalar mixing is assessed based on resolved passive scalar probability density function (PDF), variance, and spectra. The numerical-dissipation influence on mixing is found to depend on the nature of the flow. Mixing metrics sensitive to numerical dissipation are applied to examine the performance of limiting methods employed to mitigate unphysical scalar excursions. Two approaches, using a linear-scaling limiter for finite-volume schemes and a monotonicity-preserving limiter for finite-difference schemes, are studied. Their performance with respect to accuracy, conservation, and boundedness is discussed. [ABSTRACT FROM AUTHOR]

We consider Hermitian random band matrices H in d⩾1 dimensions. The matrix elements Hxy, indexed by x,y∈Λ⊂Zd, are independent, uniformly distributed random variable if |x-y| is less than the band width W,  and zero otherwise. We update the previous results of the converge of quantum diffusion in a random band matrix model from convergence of the expectation to convergence in high probability. The result is uniformly in the size |Λ| of the matrix. [ABSTRACT FROM AUTHOR]

Often it is assumed that a quantum state or a phase-space distribution must be normalizable. Here it is shown that even if it is not normalizable, one may be able to extract normalized observational probabilities from it. [ABSTRACT FROM AUTHOR]

Over the years, combinations of different methods that use multi-satellites and multi-sensors have been developed for estimating global precipitation. Recently, studies that have evaluated Integrated Multi-satellite Retrievals for GPM (IMERG) Final-Run (FR) version V-03D and other precipitation products have indicated better performance for IMERG-FR compared to other similar products in different climate regimes. This study comprehensively evaluates the two GPM-IMERG products, specifically IMERG-FR and IMERG-Real-Time (RT) late-run, against a dense station network (62 stations) in northeast Austria from mid-March 2015 to the end of January 2016 using different time-scales. Both products are examined against station data in capturing the occurrence and statistical characteristics of precipitation intensity. With regard to probability density functions (PDFs), the satellite precipitation estimate (SPE) products have detected more heavy and extreme precipitation events than the ground measurements. Both precipitation products at all time-scales, except for IMERG-RT 12-hourly and daily precipitation, capture less occurrence of precipitation than the station dataset for light precipitation. This partially explains the under-detection of precipitation events. For all time-scales, both IMERG products' CDFs (Cumulative Distribution Function) are well above that of the stations' precipitation. For lower precipitation levels, IMERG-RT is slightly below the IMERG-FR whereas IMERG-RT is above IMERG-FR at higher precipitation levels. Furthermore, for entire spectrum precipitation rates (P ≥ 0.1 mm), 1, 3, 6-hourly, IMERG-FR did not show a clear improvement of the Bias over IMERG-RT, while for 12-hourly and daily precipitation estimates, the bias in IMERG-FR has improved compared to IMERG-RT. In addition, IMERG-FR shows a considerable improvement in RMSE as compared to IMERG-RT. IMERG-FR, however, systematically underestimates moderate to extreme precipitation and overestimates light precipitation for all time scales against rain-gauges in northeast Austria. When comparing the bias, RMSE, and correlation coefficients, IMERG-FR has outperformed IMERG-RT particularly for 6-hourly, 12-hourly, and daily precipitation. Despite the general low probability of detection (POD) and threat score (TS) and the high false alarm ratio (FAR) within specified precipitation thresholds, the contingency table shows relatively acceptable values of the POD, TS and FAR for precipitation without classification. [ABSTRACT FROM AUTHOR]

Among the combustion products, nitrogen oxides are one of the main contributors to a negative impact on the environment, participating in harmful processes such as tropospheric ozone and acid rains production. The main source of emissions of nitrogen oxides is the human combustion of fossil fuels. Their formation models are investigated and implemented with the goal of obtaining a tool for studying the nitrogen-containing pollutant production. In this work, numerical simulation of solid fuel combustion was carried out on a three-dimensional model of a drop tube furnace by using the commercial software FIRE. It was used for simulating turbulent fluid flow and temperature field, concentrations of the reactants and products, as well as the fluid-particles interaction by numerically solving the integro-differential equations describing these processes. Chemical reactions mechanisms for the formation of nitrogen oxides were implemented by the user functions. To achieve reasonable calculation times for running the simulations, as well as efficient coupling with the turbulent mixing process, the nitrogen scheme is limited to sufficiently few homogeneous reactions and species. Turbulent fluctuations that affect the reaction rates of nitrogen oxides' concentration are modelled by probability density function approach. Results of the implemented model for nitrogen oxides' formation from coal and biomass are compared to the experimental data. Temperature, burnout and nitrogen oxides' concentration profiles are compared, showing satisfactory agreement. The new model allows the simulation of pollutant formation in the real-world applications. [ABSTRACT FROM AUTHOR]

This paper develops a hybrid approach of spectral representation and random function for simulating stationary stochastic vector processes. In the proposed approach, the high-dimensional random variables, included in the original spectral representation (OSR) formula, could be effectively reduced to only two elementary random variables by introducing the random functions that serve as random constraints. Based on this, a satisfactory simulation accuracy can be guaranteed by selecting a small representative point set of the elementary random variables. The probability information of the stochastic excitations can be fully emerged through just several hundred of sample functions generated by the proposed approach. Therefore, combined with the probability density evolution method (PDEM), it could be able to implement dynamic response analysis and reliability assessment of engineering structures. For illustrative purposes, a stochastic turbulence wind velocity field acting on a frame-shear-wall structure is simulated by constructing three types of random functions to demonstrate the accuracy and efficiency of the proposed approach. Careful and in-depth studies concerning the probability density evolution analysis of the wind-induced structure have been conducted so as to better illustrate the application prospects of the proposed approach. Numerical examples also show that the proposed approach possesses a good robustness. [ABSTRACT FROM AUTHOR]

We introduce a class of channels called heralded channels, which generalize the quantum erasure channel composed with an arbitrary other quantum channel. We show that monogamy of squashed entanglement limits the superadditivity of Holevo capacity of heralded channels in the regime of rare success (frequent erasure). We prove that in the limit of near-zero success probability, the classical capacity of the heralded channel converges to its Holevo information, which is equal to success probability times the single-letter Holevo information of the channel with which erasure is composed. We also show how entanglement monogamy applies to non-classicality in quantum games, and we consider how faithful monogamous entanglement measures may bound other entanglement-dependent quantities in many-party scenarios. [ABSTRACT FROM AUTHOR]

The fitting of θ/2θ and ω peaks in X-ray diffraction curves is shown to be most accurate in the case of using an inverse fourth-degree polynomial or probability density function with Student’s distribution (Pearson type VII function). These functions describe well both the highest-intensity central part of the experimental peak and its low-intensity broadened base caused by X-ray diffuse scattering. The mean microdeformation ε and mean vertical domain size D are determined by the Williamson-Hall method for layers of GaN (ε ≈ 0.00006, D ≈ 200 nm) and Al0.32Ga0.68N (ε = 0.0032 ± 0.0005, D = 24 ± 7 nm). The D value obtained for the Al0.32Ga0.68N layer is most likely to result from the nominal thickness of this layer, which is 11 nm. [ABSTRACT FROM AUTHOR]

This paper proposes a novel and efficient clustering algorithm for probability density functions based on k-medoids. Further, a scheme used for selecting the powerful initial medoids is suggested, which speeds up the computational time significantly. Also, a general proof for convergence of the proposed algorithm is presented. The effectiveness and feasibility of the proposed algorithm are verified and compared with various existing algorithms through both artificial and real datasets in terms of adjusted Rand index, computational time, and iteration number. The numerical results reveal an outstanding performance of the proposed algorithm as well as its potential applications in real life. [ABSTRACT FROM AUTHOR]

Probability interpretation is the cornerstone of standard quantum mechanics. To ensure the validity of the probability interpretation, wavefunctions have to satisfy the square-integrable (SI) condition, which gives rise to the well-known phenomenon of energy quantization in confined quantum systems. On the other hand, nonsquare-integrable (NSI) solutions to the Schrödinger equation are usually ruled out and have long been believed to be irrelevant to energy quantization. This paper proposes a quantum-trajectory approach to energy quantization by releasing the SI condition and considering both SI and NSI solutions to the Schrödinger equation. Contrary to our common belief, we find that both SI and NSI wavefunctions contribute to energy quantization. SI wavefunctions help to locate the bifurcation points at which energy has a step jump, while NSI wavefunctions form the flat parts of the stair-like distribution of the quantized energies. The consideration of NSI wavefunctions furthermore reveals a new quantum phenomenon regarding the synchronicity between the energy quantization process and the center-saddle bifurcation process. [ABSTRACT FROM AUTHOR]

As the key requirement of the power system, the power transformer's running state of security is directly related to the safety and stability of entire power system. Since condition‐based maintenance for a power transformer cannot directly determine the best maintenance cycle, from a better engineering application perspective, this paper proposes a novel maintenance strategy based on failure probability analysis. First, the power transformer's basic fault probability curve is fitted using the nonlinear least‐squares method. Second, comprehensively considering the long‐term evolution factors and the short‐term sudden factors, the transformer's actual fault probability model is established through amending its basic fault probability model. Third, in accordance with the periodic maintenance experience and the transformer's actual fault probability model, the best maintenance cycle is suggested using the threshold constraint. Finally, the simulation results testify that the proposed maintenance strategy can provide a more accurate maintenance cycle than the existing condition‐based maintenance and can better meet the requirement of engineering applications. © 2018 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [ABSTRACT FROM AUTHOR]

Quantum Lovász number is a quantum generalization of the Lovász number in graph theory. It is the best known efficiently computable upper bound of the entanglement-assisted zero-error classical capacity of a quantum channel. However, it remains an intriguing open problem whether quantum entanglement can always enhance the zero-error capacity to achieve the quantum Lovász number. In this paper, by constructing a particular class of qutrit-to-qutrit channels, we show that there exists a strict gap between the entanglement-assisted zero-error capacity and the quantum Lovász number. Interestingly, for this class of quantum channels, the quantum generalization of fractional packing number is strictly larger than the zero-error capacity assisted with feedback or no-signaling correlations, which differs from the case of classical channels. [ABSTRACT FROM PUBLISHER]

Maps on a parameter space for expressing distribution functions are exactly derived from the Perron-Frobenius equations for a generalized Boole transform family. Here the generalized Boole transform family is a one-parameter family of maps, where it is defined on a subset of the real line and its probability distribution function is the Cauchy distribution with some parameters. With this reduction, some relations between the statistical picture and the orbital one are shown. From the viewpoint of information geometry, the parameter space can be identified with a statistical manifold, and then it is shown that the derived maps can be characterized. Also, with an induced symplectic structure from a statistical structure, symplectic and information geometric aspects of the derived maps are discussed. [ABSTRACT FROM AUTHOR]

Developing effective monitoring methods for elusive, rare, or patchily distributed species requires extra considerations, such as imperfect detection. Although detection is frequently modeled, the opportunity to assess it empirically is rare, particularly for imperiled species. We used Pecos assiminea (Assiminea pecos), an endangered semiaquatic snail, as a case study to test detection and accuracy issues surrounding quadrat searches. Quadrats (9 × 20 cm; n = 12) were placed in suitable Pecos assiminea habitat and randomly assigned a treatment, defined as the number of empty snail shells (0, 3, 6, or 9). Ten observers rotated through each quadrat, conducting 5-min visual searches for shells. The probability of detecting a shell when present was 67.4 ± 3.0%, but it decreased with the increasing litter depth and fewer number of shells present. The mean (± SE) observer accuracy was 25.5 ± 4.3%. Accuracy was positively correlated to the number of shells in the quadrat and negatively correlated to the number of times a quadrat was searched. The results indicate quadrat surveys likely underrepresent true abundance, but accurately determine the presence or absence. Understanding detection and accuracy of elusive, rare, or imperiled species improves density estimates and aids in monitoring and conservation efforts. [ABSTRACT FROM AUTHOR]

Current degradation modeling and remaining useful life prediction studies share a common assumption that the degrading systems are not maintained or maintained perfectly (i.e., to an as-good-as new state). This paper concerns the issues of how to model the degradation process and predict the remaining useful life of degrading systems subjected to imperfect maintenance activities, which can restore the health condition of a degrading system to any degradation level between as-good-as new and as-bad-as old. Toward this end, a nonlinear model driven by Wiener process is first proposed to characterize the degradation trajectory of the degrading system subjected to imperfect maintenance, where negative jumps are incorporated to quantify the influence of imperfect maintenance activities on the system’s degradation. Then, the probability density function of the remaining useful life is derived analytically by a space-scale transformation, i.e., transforming the constructed degradation model with negative jumps crossing a constant threshold level to a Wiener process model crossing a random threshold level. To implement the proposed method, unknown parameters in the degradation model are estimated by the maximum likelihood estimation method. Finally, the proposed degradation modeling and remaining useful life prediction method are applied to a practical case of draught fans belonging to a kind of mechanical systems from steel mills. The results reveal that, for a degrading system subjected to imperfect maintenance, our proposed method can obtain more accurate remaining useful life predictions than those of the benchmark model in literature. [ABSTRACT FROM AUTHOR]

We report a non-perturbative study of the effects of shear flows on turbulence reduction in a decaying turbulence in two dimensions. By considering different initial power spectra and shear flows (zonal flows, streamers and zonal flows and streamers combined), we demonstrate how shear flows rapidly generate small scales, leading to a fast damping of turbulence amplitude. In particular, a double exponential decrease in the turbulence amplitude is shown to occur due to an exponential increase in wavenumber. The scaling of the effective dissipation time scale τe, previously taken to be a hybrid time scale τe ∝ τ2/3 Ω τη, is shown to depend on types of shear flow as well as the initial power spectrum. Here, τΩ and τη are shearing and molecular diffusion times, respectively. Furthermore, we present time-dependent Probability Density Functions (PDFs) and discuss the effect of enhanced dissipation on PDFs and a dynamical time scale τ(t), which represents the time scale over which a system passes through statistically different states. [ABSTRACT FROM AUTHOR]

Motivated by high filtration efficiency (mass- and number-based) and low pressure drop requirements for gasoline particulate filters (GPFs), a previously developed heterogeneous multiscale filtration (HMF) model is extended to simulate dynamic filtration characteristics of GPFs. This dynamic HMF model is based on a probability density function (PDF) description of the pore size distribution and classical filtration theory. The microstructure of the porous substrate in a GPF is resolved and included in the model. Fundamental particulate filtration experiments were conducted using an exhaust filtration analysis (EFA) system for model validation. The particulate in the filtration experiments was sampled from a spark-ignition direct-injection (SIDI) gasoline engine. With the dynamic HMF model, evolution of the microscopic characteristics of the substrate (pore size distribution, porosity, permeability, and deposited particulate inside the porous substrate) during filtration can be probed. Also, predicted macroscopic filtration characteristics including particle number concentration and normalized pressure drop show good agreement with the experimental data. The resulting dynamic HMF model can be used to study the dynamic particulate filtration process in GPFs with distinct microstructures, serving as a powerful tool for GPF design and optimization. [ABSTRACT FROM AUTHOR]

Nearest-neighbor queries, which ask for returning the nearest neighbor of a query point in a set of points, are important and widely studied in many fields because of a wide range of applications. In many of these applications, such as sensor databases, location based services, face recognition, and mobile data, the location of data is imprecise. We therefore study nearest-neighbor queries in a probabilistic framework in which the location of each input point and/or query point is specified as a probability density function and the goal is to return the point that minimizes the expected distance, which we refer to as the expected nearest neighbor ( $$\mathop {\mathrm {ENN}}$$ ). We present methods for computing an exact $$\mathop {\mathrm {ENN}}$$ or an $$\varepsilon $$ -approximate $$\mathop {\mathrm {ENN}}$$ , for a given error parameter $$0<\varepsilon < 1$$ , under different distance functions. These methods build a data structure of near-linear size and answer $$\mathop {\mathrm {ENN}}$$ queries in polylogarithmic or sublinear time, depending on the underlying function. As far as we know, these are the first nontrivial methods for answering exact or $$\varepsilon $$ -approximate $$\mathop {\mathrm {ENN}}$$ queries with provable performance guarantees. Moreover, we extend our results to answer exact or $$\varepsilon $$ -approximate k- $$\mathop {\mathrm {ENN}}$$ queries. [ABSTRACT FROM AUTHOR]

We discuss several features of the classical quantum potential appearing in Covariant Quantum Mechanics. In particular, we compare the “observed potential” A [ K , G , o ] of the joined spacetime connection K with the potential A ↑ of the cosymplectic phase 2-form Ω [ K , G ] and with the potential A ↑ of the upper quantum connection Ч ↑ . Moreover, we discuss the distinguished observer o [ Ψ ] and the distinguished timelike potential A [ Ψ ] associated with a non-vanishing quantum section Ψ. We show that the above objects play a natural role in the context of the kinetic quantum momentum Q [ Ψ ] , of the quantum probability current J [ Ψ ] , of the Schrödinger operator S [ Ψ ] and of the classical fluid associated with a non-vanishing quantum section Ψ. [ABSTRACT FROM AUTHOR]

This paper investigates the force transmission modes, mainly described by probability density distributions, in non-cohesive dry and cohesive wet granular materials by discrete element modeling. The critical state force transmission patterns are focused on with the contact model effect being analyzed. By shearing relatively dense and loose dry specimens to the critical state in the conventional triaxial loading path, it is observed that there is a unique critical state force transmission mode. There is a universe critical state force distribution pattern for both the normal contact forces and tangential contact forces. Furthermore, it is found that using either the linear Hooke or the non-linear Hertz model does not affect the universe force transmission mode, and it is only related to the grain size distribution. Wet granular materials are also simulated by incorporating a water bridge model. Dense and loose wet granular materials are tested, and the critical state behavior for the wet material is also observed. The critical state strength and void ratio of wet granular materials are higher than those of a non-cohesive material. The critical state inter-particle distribution is altered from that of a non-cohesive material with higher probability in relatively weak forces. Grains in non-cohesive materials are under compressive stresses, and their principal directions are mainly in the axial loading direction. However, for cohesive wet granular materials, some particles are in tension, and the tensile stresses are in the horizontal direction on which the confinement is applied. The additional confinement by the tensile stress explains the macro strength and dilatancy increase in wet samples. [ABSTRACT FROM AUTHOR]

The rise of Performance Based Design methodologies for fire safety engineering has increased the interest of the fire safety community in the concepts of risk and reliability. Practical applications have however been severely hampered by the lack of an efficient unbiased calculation methodology. This is because on the one hand, the distribution types of model output variables in fire safety engineering are not known and traditional distribution types as for example the normal and lognormal distribution may result in unsafe approximations. Therefore unbiased methods must be applied which make no (implicit) assumptions on the PDF type. Traditionally these unbiased methods are based on Monte Carlo simulations. On the other hand, Monte Carlo simulations require a large number of model evaluations and are therefore too computationally expensive when large and nonlinear calculation models are applied, as is common in fire safety engineering. The methodology presented in this paper avoids this deadlock by making an unbiased estimate of the PDF based on only a very limited number of model evaluations. The methodology is known as the Maximum Entropy Multiplicative Dimensional Reduction Method (ME-MDRM) and results in a mathematical formula for the probability density function (PDF) describing the uncertain output variable. The method can be applied with existing models and calculation tools and allows for a parallelization of model evaluations. The example applications given in the paper stem from the field of structural fire safety and illustrate the excellent performance of the method for probabilistic structural fire safety engineering. The ME-MDRM can however be considered applicable to other types of engineering models as well. [ABSTRACT FROM AUTHOR]

In this paper, we give possible suggestions for a classroom lesson about an application of probability using basic mathematical notions. We will approach to some combinatoric results without using ‘induction’, ‘polynomial identities’ nor ‘generating functions’, and will give a proof of the ‘Vandermonde Identity’ using elementary notions of probability. [ABSTRACT FROM AUTHOR]

Based on the random theory of the probability density evolution method (PDEM), a refined random wheel/rail contact model for train-track-bridge systems is proposed. The trace line method with the law of equal slopes is developed to determine the wheel/rail contact locations, which are described by probability density functions on the wheel/rail surface. The number theoretic method (NTM) and stochastic harmonic functions (SHFs) are employed to generate the representative random track irregularities. Considering the excitation of random track irregularities and the wheel/rail contact geometry, the wheel/rail normal contact force and the tangential creep force are accurately calculated and analyzed using the proposed wheel/rail contact model. A high-speed railway case study is presented to reveal the random dynamic characteristics of a train-track-bridge system and the wheel/rail interaction. The results show that the time-varying probability density evolution functions of the wheel/rail contact points can effectively indicate both the phenomenon of wear on the rail surface and its distribution characteristics. Additionally, some significant conclusions are obtained. [ABSTRACT FROM AUTHOR]

Motivated by that the quartic potential can confined Lévy flights, we investigate the escape rate of an inertial Lévy particle from a truncated quartic potential well via Langevin simulation. The escape rate still depends on the noise intensity in a power-law form in low noise intensity, but the exponent and the inverse coefficient vary significantly for different Lévy indexes compared with previous works. Trimodal structure of the probability density function was found in simulations. The probability density function in a quasi-stable state exhibits transition among unimodal, bimodal, and trimodal structures. A metastable state by stable state approach is developed to calculate the escape rate analytically, which may be applied to extensive escape problems. The theoretical approach is confirmed by Langevin simulation for the Cauchy case of Lévy flight in the applied potential. [ABSTRACT FROM AUTHOR]

The probability density evolution method (PDEM) provides a feasible approach for the dynamic response analysis of nonlinear stochastic structures. The key step in this regard is to solve a generalized density evolution equation (GDEE) in order to establish the probability density function (PDF). Previously, a finite difference method (FDM) has often been resorted to solve the GDEE. However, one may encounter the problem of mesh sensitivity in the application of FDM to the PDEM. To this end, a novel difference-wavelet method that can improve the finite difference result by means of a nonlinear wavelet density estimation method is proposed in the present paper. By exploiting the multi-resolution property of wavelet functions and by choosing the optimal scale at each instant, it is expected that the bothering mesh sensitivity issue in finite difference method can be overcome to some extent and a better probability density result can be obtained. In order to verify the proposed method, a single-degree-of-freedom (SDOF) oscillator and an 8-story frame structure are investigated in detail. The results show the notable superiority of the proposed method to finite difference method. [ABSTRACT FROM AUTHOR]

In an elementary variational treatment of the electronic structure of H2+, Eyring, Walter, and Kimball (EWK) serendipitously discovered charge migration (CM) in 1944. Using an analytic expression for the electronic probability density (EPD), they found that if the electron is initially localized on one of the protons (by taking the initial state to be a superposition of the ground and first excited electronic energy eigenstates), then it oscillates adiabatically between fixed protons with a period T inversely proportional to the energy gap between the eigenstates. At the equilibrium internuclear separation, T = 550.9 as. As shown here, the EWK model also yields an analytic formula for the electronic flux density (EFD). While the EPD indicates where the electron is at any instant, the EFD reveals the pathways the electron follows during its migration. Thus, the EFD complements the EPD, providing valuable new insight into the mechanism of CM. The formula for the EFD is a simple product of a time factor and a spatial factor. This factoring exposes a plethora of spatial-temporal symmetry relations which imply novel and surprising properties. An especially significant finding is that, in contrast to multielectron systems, where electron correlation may play a role in CM, in the EWK model of H2+, CM is due strictly to quantum interference between the ground and first excited electronic states. [ABSTRACT FROM AUTHOR]

Subjects observing many samples from a Bernoulli distribution are able to perceive an estimate of the generating parameter. A question of fundamental importance is how the current percept-what we think the probability now is-depends on the sequence of observed samples. Answers to this question are strongly constrained by the manner in which the current percept changes in response to changes in the hidden parameter. Subjects do not update their percept trial-by-trial when the hidden probability undergoes unpredictable and unsignaled step changes; instead, they update it only intermittently in a step-hold pattern. It could be that the step-hold pattern is not essential to the perception of probability and is only an artifact of step changes in the hidden parameter. However, we now report that the step-hold pattern obtains even when the parameter varies slowly and smoothly. It obtains even when the smooth variation is periodic (sinusoidal) and perceived as such. We elaborate on a previously published theory that accounts for: (i) the quantitative properties of the step-hold update pattern; (ii) subjects' quick and accurate reporting of changes; (iii) subjects' second thoughts about previously reported changes; (iv) subjects' detection of higher-order structure in patterns of change. We also call attention to the challenges these results pose for trial-by-trial updating theories. [ABSTRACT FROM AUTHOR]

We present 21 new radio-continuum detections at catalogued planetary nebula (PN) positions in the Large Magellanic Cloud (LMC) using all presently available data from the Australia Telescope Online Archive at 3, 6, 13 and 20 cm. Additionally, 11 previously detected LMC radio PNe are re-examined with seven detections confirmed and reported here. An additional three PNe from our previous surveys are also studied. The last of the 11 previous detections is now classified as a compact H ii region that makes for a total sample of 31 radio PNe in the LMC. The radio-surface-brightness-to-diameter (&#931--D) relation is parametrized as Σ ∝ D-β. With the available 6 cm Σ–D data, we construct Σ–D samples from 28 LMC PNe and nine Small Magellanic Cloud (SMC) radio-detected PNe. The results of our sampled PNe in the MCs are comparable to previous measurements of the Galactic PNe. We obtain β = 2.9 ± 0.4 for the MC PNe compared to β = 3.1 ± 0.4 for the Galaxy. For a better insight into sample completeness and evolutionary features, we reconstruct the &#931--D data probability density function (PDF). The PDF analysis implies that PNe are not likely to follow linear evolutionary paths. To estimate the significance of sensitivity selection effects, we perform a Monte Carlo sensitivity simulation on the &#931--D data. The results suggest that selection effects are significant for values larger than β ~ 2.6 and that a measured slope of β = 2.9 should correspond to a sensitivity-free value of ~3.4. [ABSTRACT FROM AUTHOR]

Stochastic distribution control (SDC) systems are a group of systems where the outputs considered is the measured probability density function (PDF) of the system output whilst subjected to a normal crisp input. The purpose of the active fault tolerant control of such systems is to use the fault estimation information and other measured information to make the output PDF still track the given distribution when the objective PDF is known. However, if the target PDF is unavailable, the PDF tracking operation will be impossible. Minimum entropy control of the system output can be considered as an alternative strategy. The mean represents the center location of the stochastic variable, and it is reasonable that the minimum entropy fault tolerant controller can be designed subjected to mean constraint. In this paper, using the rational square-root B-spline model for the shape control of the system output probability density function (PDF), a nonlinear adaptive observer based fault diagnosis algorithm is proposed to diagnose the fault. Through the controller reconfiguration, the system entropy subjected to mean restriction can still be minimized when fault occurs. An illustrative example is utilized to demonstrate the use of the minimum entropy fault tolerant control algorithms. [ABSTRACT FROM AUTHOR]

At low densities, the standard ionization history of the intergalactic medium (IGM) predicts a decreasing temperature of the IGM with decreasing density once hydrogen (and helium) reionization is complete. Heating the high-redshift, low-density IGM above the temperature expected from photoheating is difficult, and previous claims of high/rising temperatures in lowdensity regions of the Universe based on the probability density function (PDF) of the opacity in Ly α forest data at 2 < z < 4 have been met with considerable scepticism, particularly since they appear to be in tension with other constraints on the temperature-density relation (TDR). We utilize here an ultrahigh signal-to-noise spectrum of the Quasi-stellar object HE0940-1050 and a novel technique to study the low opacity part of the PDF. We show that there is indeed evidence (at 90 per cent confidence level) that a significant volume fraction of the underdense regions at z ~ 3 has temperatures as high or higher than those at densities comparable to the mean and above. We further demonstrate that this conclusion is nevertheless consistent with measurements of a slope of the TDR in overdense regions that imply a decreasing temperature with decreasing density, as expected if photoheating of ionized hydrogen is the dominant heating process.We briefly discuss implications of our findings for the need to invoke either spatial temperature fluctuations, as expected during helium reionization, or additional processes that heat a significant volume fraction of the low-density IGM. [ABSTRACT FROM AUTHOR]

A parameterization scheme is proposed for the subgrid-scale transport of hydrometeors in an assumed probability density function (PDF) scheme. Joint distributions of vertical velocity and hydrometeor mixing ratios are typically unknown, but marginal (1D) PDFs of these variables are available. The parameterization is developed using high-resolution simulations of continental and tropical deep convection. A 3D cloudresolving model (CRM) providing benchmark solutions has a horizontal grid spacing of 250m and employs the Morrison microphysics scheme, which treats prognostically mass and number mixing ratios for four types of precipitating hydrometeors (rain, graupel, snow, and ice) as well as cloud droplet number mixing ratio. The subgrid-scale hydrometeor transport scheme assumes input given in the form of marginal PDFs of vertical velocity and hydrometeor mixing ratios; in this study, these marginal distributions are provided by the cloudresolving model. Conditional sampling and scaling are then applied to the marginal distributions to account for subplume correlations. The parameterized fluxes tested for four episodes of deep convection show good agreement with benchmark fluxes computed directly from the CRM output. The results demonstrate the potential use of the subgrid-scale hydrometeor transport scheme in an assumed PDF scheme to parameterize the covariances of vertical velocity and hydrometeor mixing ratios. [ABSTRACT FROM AUTHOR]

There are relatively few publications that assess capacity decline in enough commercial cells to quantify cell-to-cell variation, but those that do show a surprisingly wide variability. Capacity curves cross each other often, a challenge for efforts to measure the state of health and predict the remaining useful life (RUL) of individual cells. We analyze capacity fade statistics for 24 commercial pouch cells, providing an estimate for the time to 5% failure. Our data indicate that RUL predictions based on remaining capacity or internal resistance are accurate only once the cells have already sorted themselves into “better” and “worse” ones. Analysis of our failure data, using maximum likelihood techniques, provide uniformly good fits for a variety of definitions of failure with normal and with 2- and 3-parameter Weibull probability density functions, but we argue against using a 3-parameter Weibull function for our data. pdf fitting parameters appear to converge after about 15 failures, although business objectives should ultimately determine whether data from a given number of batteries provides sufficient confidence to end lifecycle testing. Increased efforts to make batteries with more consistent lifetimes should lead to improvements in battery cost and safety. [ABSTRACT FROM AUTHOR]

We clarify the significance of quasiprobability (QP) in quantum mechanics that is relevant in describing physical quantities associated with a transition process. Our basic quantity is Aharonov's weak value, from which the QP can be defined up to a certain ambiguity parameterized by a complex number. Unlike the conventional probability, the QP allows us to treat two noncommuting observables consistently, and this is utilized to embed the QP in Bohmian mechanics such that its equivalence to quantum mechanics becomes more transparent. We also show that, with the help of the QP, Bohmian mechanics can be recognized as an ontological model with a certain type of contextuality. [ABSTRACT FROM AUTHOR]