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Abstract: In this note, we improve some results of Granville and Soundararajan on the distribution of values of the truncated random Euler product , where the are independent random variables, taking the values ±1 with equal probability and 0 with probability . [Copyright &y& Elsevier]

In this paper, a reaction-diffusion population model with Dirichlet boundary condition and a directed movement oriented by a temporally distributed delay is proposed to describe the lasting memory of animals moving over space. The temporal kernel of the memory is taken as Gamma distribution function, among which there are two biologically meaningful cases: one is the weak kernel which implies that animals can immediately acquire knowledge and memory decays over time, the other is the strong kernel by which we assume that animals' memory undergoes learning and memory decay stages. It is shown that the population stabilizes to a positive steady state and aggregates in the interior of the territory when the delay kernel is the weak type. In the strong kernel case, oscillatory patterns can first arise via a Hopf bifurcation with a small memory delay and then vanish when the system undergoes a Hopf bifurcation with a large memory delay, which implies that stability switch occurs and spatial-temporal patterns emerge for intermediate value of delays. [ABSTRACT FROM AUTHOR]

The number of Vehicle Equipment (VE) connected to the Internet is increasing, and these VEs generate tasks that contain large amounts of data. Processing these tasks requires a lot of computing resources. Therefore, it is a promising issue that offloading compute-intensive tasks from resource-limited vehicles to Vehicular Edge Computing (VEC) servers, which involves big data transmission, processing and computation. In a network, multiple providers provide VEC servers. When a vehicle generates a task, our goal is to make an intelligent decision on whether and when to offload this task to VEC servers to minimize the task completion time and total big data processing time. When each vehicle passes VEC servers, the vehicle can decide to offload its task to the VEC server in the current communication range, or continue to drive until it reaches the next server's communication range. This issue can be considered as an asset selling problem. It is a challenging issue to make a smart decision for the vehicle with a location view because the vehicle is not sure when the next VEC server will be available and how much about the available computing capacity of the next VEC server. Firstly, this paper formulates the problem as a Markov Decision Process (MDP), defines and analyzes the state set, action set, reward model, and state transition probability distribution. Then it uses Asynchronous Advantage Actor-Critic (A3C) algorithm to solve this MDP problem, builds the various elements of the A3C algorithm, uses Actor (the strategy function) to generate two actions of the vehicle: offloading and moving without offloading. Thirdly, it uses Critic (the value function) to evaluate Actor's behavior, and guide Actor's actions in subsequent stages. The Actor starts from the initial state in the state space until it enters the termination state, forming a complete decision-making process. It minimizes the completion time of task offloading through learning thereby reducing the delay of big data processing. Compared to the Immediately Offload (IO) scheme and Expect Offload (EO) scheme, the MIDP scheme proposed in this paper reduces the average task offloading delay to 29.93% and 29.99%, close to the EO scheme in terms of task completion rate and up to 66.6% improvement compared to the IO scheme. • A task offloading approach in Internet of Vehicles (IoV) is proposed. • An MDP-based Intelligent Big Data Processing (MIDP) Scheme is proposed. • Simulations demonstrate the better performances of MIDP scheme. [ABSTRACT FROM AUTHOR]

• Novel CRB vibration model considering contact stiffness and natural frequency characteristics. • The outer raceway spalling fault with varying sizes is simulated in this paper, considering spalling defect extents and load distribution. • This paper showed that the effects of contact stiffness variation on natural frequency characteristics by the statistical distribution of fault feature signals. The modeling of early spalling defects in cylindrical roller bearings (CRB) is a challenging problem in fault diagnosis. Due to the absence of prominent "drop-in" excitation, accurately describing the signal characteristics of the early failure mechanism model for CRBs becomes difficult. In this paper, the failure of cylindrical roller bearings due to spalling caused by fatigue is a frequent occurrence. The previous defect models have been centered on sharp-edge impact between the roller and spalling defects. However, they have not provided an adequate depiction of the variation in contact stiffness caused by roller-fault interaction. In this paper, a novel CRB vibration model that takes into account contact stiffness and natural frequency characteristics is proposed. The model considers both the load redistribution and contact stiffness variation caused by spalling defects. This new model provides a spring-damper system based on contact stiffness between the roller and raceway, enabling an estimation of the CRB system's natural frequency characteristics. The outer raceway spalling fault with varying sizes is simulated in this paper, taking into account spalling defect extents and load distribution. The vibration response of the fault signal model is investigated. The simulation results show that the load and contact stiffness will change as the roller passes through the defect zone. Furthermore, the statistical distribution of fault feature signals demonstrates the effects of contact stiffness variation on natural frequency characteristics. The experiments given in this paper have verified the simulation results of the proposed signal model. [ABSTRACT FROM AUTHOR]

This paper builds on Kojima and Pathak (2009) 's result of vanishing manipulability in large stable mechanisms. We show that convergence toward truth-telling in stable mechanisms can be achieved much faster if colleges' preferences are independently drawn from an uniform distribution. Another novelty from our results is that they can be applied to competitive environments in which virtually all vacancies end up being filled. So this paper adds evidence to the fact that, though stable matching mechanisms are not entirely strategy-proof, in practice, when the number of participants in the market is sufficiently large, they can be treated as being effectively strategy-proof. [ABSTRACT FROM AUTHOR]

We consider nonautonomous master equations of finite-state, continuous-time Markovian jump processes with uniformly continuous and bounded transition matrix functions. The Earnshaw–Keener conjecture states that if the omega-limit set of the transition matrix function contains at least one matrix which is neither decomposable nor splitting, then the difference of any two probability distribution solutions tends to zero at infinity. The conjecture has been confirmed under the additional assumption that the transition matrix function is almost-automorphic. In this paper, we prove the conjecture in its full generality. [ABSTRACT FROM AUTHOR]

This paper studies the approximation capacity of ReLU neural networks with norm constraint on the weights. We prove upper and lower bounds on the approximation error of these networks for smooth function classes. The lower bound is derived through the Rademacher complexity of neural networks, which may be of independent interest. We apply these approximation bounds to analyze the convergences of regression using norm constrained neural networks and distribution estimation by GANs. In particular, we obtain convergence rates for over-parameterized neural networks. It is also shown that GANs can achieve optimal rate of learning probability distributions, when the discriminator is a properly chosen norm constrained neural network. [ABSTRACT FROM AUTHOR]

By using the work of Frantzikinakis and Wierdl, we can see that for all d ∈ N , α ∈ (d , d + 1) , and integers k ≥ d + 2 and r ≥ 1 , there exist infinitely many n ∈ N such that the sequence (⌊ (n + r j) α ⌋) j = 0 k − 1 is represented as ⌊ (n + r j) α ⌋ = p (j) , j = 0 , 1 , ... , k − 1 , by using some polynomial p (x) ∈ Q [ x ] of degree at most d. In particular, the above sequence is an arithmetic progression when d = 1. In this paper, we show the asymptotic density of such numbers n as above. When d = 1 , the asymptotic density is equal to 1 / (k − 1). Although the common difference r is arbitrarily fixed in the above result, we also examine the case when r is not fixed. Most results in this paper are generalized by using functions belonging to Hardy fields. [ABSTRACT FROM AUTHOR]

This paper studies the matching problem of cross-modality video data from a discrete distribution alignment view. Central to this discussion is the visible-infrared person re-identification (VI-reID), a crucial feature that bolsters surveillance systems' efficacy in monitoring individuals across diverse lighting conditions. Going beyond traditional image-to-image matching paradigms, a recent study shows that temporal information can bring richer cues to encode the pedestrian representation, improving the representation power of deep neural networks. However, this integration further complicates cross-modality data matching due to the joint processing of spatial and temporal information. This paper formulates the video data as a discrete distribution and aligns the cross-modality video representation by reducing the matching cost between the two distributions. To this end, a natural idea for aligning the videos is to reduce the divergence of distributions. Moreover, the powerful optimal transport (OT) scheme, which generates the optimal matching flows and establishes the relevance of two distributions, is also employed as a way to measure the distance of distributions. Nevertheless, we observe that endowing the OT in the advanced VI-reID feature extractor leads to a non-symmetric measurement. To mitigate this, the paper introduces a new metric, namely symmetric optimal transport (SOT), reformulating OT into a symmetric form. Thorough analyses and empirical studies affirm the superiority of the proposed SOT, which significantly outperforms the current state-of-the-art methods according to standard benchmarking evaluations. [Display omitted] • This paper formally formulates the video sequences into a discrete distribution. • This paper further provides a symmetric optimal transport (SOT) scheme. • Thorough experiments are conducted to evaluate the proposed SOT. [ABSTRACT FROM AUTHOR]

In many applications, it is necessary to retrieve the sub-signal building blocks of a multi-component signal, which is usually non-stationary in real-world and real-life applications. Empirical mode decomposition (EMD), synchrosqueezing transform (SST), signal separation operation (SSO), and iterative filtering decomposition (IFD) have been proposed and developed for this purpose. However, these computational methods are restricted by the specification of well-separation of the sub-signal frequency curves for multi-component signals. On the other hand, the chirplet transform-based signal separation scheme (CT3S) that extends SSO from the two-dimensional "time-frequency" plane to the three-dimensional "time-frequency-chirp rate" space was recently proposed in our recent work to remove the frequency-separation specification, and thereby allowing "frequency crossing". The main objective of this present paper is to carry out an in-depth error analysis study of instantaneous frequency estimation and component recovery of the CT3S method. [ABSTRACT FROM AUTHOR]

• MCNs were constructed by applying Jensen-Shannon divergence to regional joint probability distributions derived from different morphological features. • MCNs showed efficient small-word organization and high test-retest reliability, aligned with cortical cytoarchitectonics and symmetry and axonal connectivity, and explained inter-individual variance in behavior and cognition. • MCNs built based on multiple features performed better than those derived from different single features in most aspects mentioned above. Morphological features sourced from structural magnetic resonance imaging can be used to infer human brain connectivity. Although integrating different morphological features may theoretically be beneficial for obtaining more precise morphological connectivity networks (MCNs), the empirical evidence to support this supposition is scarce. Moreover, the incorporation of different morphological features remains an open question. In this study, we proposed a method to construct cortical MCNs based on multiple morphological features. Specifically, we adopted a multi-dimensional kernel density estimation algorithm to fit regional joint probability distributions (PDs) from different combinations of four morphological features, and estimated inter-regional similarity in the joint PDs via Jensen-Shannon divergence. We evaluated the method by comparing the resultant MCNs with those built based on different single morphological features in terms of topological organization, test-retest reliability, biological plausibility, and behavioral and cognitive relevance. We found that, compared to MCNs built based on different single morphological features, MCNs derived from multiple morphological features displayed less segregated, but more integrated network architecture and different hubs, had higher test-retest reliability, encompassed larger proportions of inter-hemispheric edges and edges between brain regions within the same cytoarchitectonic class, and explained more inter-individual variance in behavior and cognition. These findings were largely reproducible when different brain atlases were used for cortical parcellation. Further analysis of macaque MCNs revealed weak, but significant correlations with axonal connectivity from tract-tracing, independent of the number of morphological features. Altogether, this paper proposes a new method for integrating different morphological features, which will be beneficial for constructing MCNs. [ABSTRACT FROM AUTHOR]

• Propose a metal-isolator constitutive model based on parallel spring-slider model. • Friction coefficients of the sliders adhere to a predefined probability distribution. • All parameters of the model can be set from quasi-static compression test data. • This model is capable of high-precision nonlinear dynamic simulation. Metal rubber has been widely applied in the fields of structural vibration reduction and impact protection, due to its excellent mechanical properties. However, an accurate constitutive model of metal rubber to characterize its complex nonlinear mechanical behavior is still lacking. In this paper, a new constitutive model of metal rubber based on the Iwan model (parallel spring-slider model) is proposed, where the friction coefficient of sliders satisfy a given probability distribution. The nonlinear-elasticity and dry friction of metal rubber are considered in this model. The proposed model can characterize the mechanical behavior of metal rubber under the complex loading–unloading-reloading path. Furthermore, the constitutive model is used to simulate random vibration in time domain, and three nonlinear phenomena are simulated, which are consistent with the experiment. Based on the proposed model, a simplified and efficient model is also developed, which can be used for efficient computational. The proposed model would be an effective tool for quasi-static and vibration simulation of metal rubber. [ABSTRACT FROM AUTHOR]

• Summed probability distribution modelling of house and conflict data from the Columbia Plateau of North America. • Gini coefficient of modelling of grave goods as an indicator of wealth inequality. • Application of anarchist theory to ethnographic and archaeological data. • Ethnographic and archaeological records can be seen as complimentary accounts of historic processes. • Identifying future areas of inquiry that are needed within the Columbia Plateau. The Columbia-Fraser Plateau of Northwestern North America was inhabited by complex hunter-gatherer populations throughout the Late Holocene. Archaeological studies have typically characterized these peoples as having corporate households and wealth inequality. Ethnographic accounts emphasize the societies of this region as egalitarian communities and pacifist. In this paper we compare radiocarbon dates for semi-subterranean houses with legacy data for skeletal remains with trauma, mesa-top and island habitations, and storage caves to identify patterns in semi-sedentary settlement and conflict. Additionally, analysis of wealth inequality is conducted using legacy data of burials from throughout the Columbia Plateau. The radiocarbon dataset and legacy data can be reconciled with ethnographic patterns using an anarchist theoretical framework, to provide a potential explanation of the historical changes in socio-economic systems. [ABSTRACT FROM AUTHOR]

Although a generic uniformly distributed sequence has Poissonian pair correlations, only one explicit example has been found up to now. Additionally, it is even known that many classes of uniformly distributed sequences, like van der Corput sequences, Kronecker sequences and LS sequences, do not have Poissonian pair correlations. In this paper, we show that van der Corput sequences and the Kronecker sequence for the golden mean are as close to having Poissonian pair correlations as possible: they both have α -pair correlations for all 0 < α < 1 but not for α = 1 which corresponds to Poissonian pair correlations. [ABSTRACT FROM AUTHOR]

Highlights • This study presents a diurnal and seasonal surface winds characterization applied to the landing site of MSL at Gale Crater, and based on the MSL REMS wind data. • Thus, this paper presents for first time this kind of characterization for the Martian surface winds. • This has been possible due to the large amount of data obtained from the Martian surface by the REMS instrument since 2012, in spite of the trouble that this sensor suffered during the landing stage. • Development of a new methodology for classifying wind measurements in "good wind" and "bad wind" measurements and extracting good wind data from the REMS wind database. • Additional characterization for wind speeds based on probabilistic distribution models, showing periods with high probability of high wind speeds at Gale. Abstract The characterization of Martian surface wind speed as a function of time of day and season at one location can increase our knowledge of Mars surface conditions and assist in planning for future unmanned and manned missions, since the probability of the wind speed exceeding a given value is often required for both engineering and geophysical applications. Wind speeds are also useful for assessing the aeolian impact of the circulation. The Rover Environmental Monitoring Station (REMS) instrument on the Mars Science Laboratory (MSL) rover has been measuring Martian winds since 2012, thus has provided more than two Mars years of wind data in the first Martian landing site with significant topography. Unfortunately, dust debris during the MSL landing stage damaged the sensor, making difficult to extract useful wind data. This paper complements the characterization performed in the companion paper, by producing a wind speed characterization based on probability distribution models. Significant diurnal and seasonal wind speed variability is found, due to complex interactions between the synoptic flow, the regional and local slope winds and microscale flow around MSL. The highest wind speed probabilities are found in general during the midday period, particularly around the equinoxes. In addition, the REMS data suggest strong flows during the summer nighttime, which could be related to the increased aeolian activity detected then by MSL. [ABSTRACT FROM AUTHOR]

Highlights • This study presents a diurnal and seasonal surface winds characterization applied to the landing site of MSL at Gale Crater, and based on the MSL REMS wind data. • Thus, this paper presents for first time this kind of characterization for the Martian surface winds. • This has been possible due to the large amount of data obtained from the Martian surface by the REMS instrument since 2012, in spite of the trouble that this sensor suffered during the landing stage. • Development of a new methodology for classifying wind measurements in "good wind" and "bad wind" measurements and extracting good wind data from the REMS wind database. • Additional characterization for wind speeds based on probabilistic distribution models, showing periods with high probability of high wind speeds at Gale. Abstract The characterization of Martian surface winds as a function of time of day and season at one location can increase our knowledge of Mars surface conditions and assist in planning for future unmanned and manned missions. Martian surface winds vary greatly with location, and even at a particular landing site show a high degree of diurnal, seasonal, and interannual variability. Thus characterizing surface wind speeds and directions requires a long time series, which is rarely obtained on Mars. The Rover Environmental Monitoring Station (REMS) instrument on the Mars Science Laboratory (MSL) rover has been measuring Martian winds since 2012, thus has provided more than two Martian years of wind data at the first Martian landing site to have significant topography, in the trench of Gale Crater. Unfortunately, likely debris impacts during landing damaged the wind sensor, making it difficult to extract useful wind data. The first part of this paper presents a new retrieval that allows "good" wind measurements to be extracted from the raw dataset obtained under such conditions. In addition, a characterization of wind speeds and directions in Gale Crater is presented, after processing the full dataset of wind data in order to obtain the representative winds for different diurnal timeslots and seasons. Results suggest complex wind patterns and great variability depending on local time and season. Also, a significant influence by the synoptic scale circulation in the wind patterns is observed, although the local-scale circulation is suggested to be the major contributor to the observed surface winds in Gale Crater. [ABSTRACT FROM AUTHOR]

Abstract In this paper we study bifurcation solutions from the unique radial solution of a free boundary problem modeling stationary state of tumors with angiogenesis. This model comprises two elliptic equations describing the distribution of the nutrient concentration σ = σ (x) and the inner pressure p = p (x). Unlike similar tumor models that have been intensively studied in the literature where Dirichlet boundary condition for σ is imposed, in this model the boundary condition for σ is a Robin boundary condition. Existence and uniqueness of a radial solution of this model have been successfully proved in a recently published paper [20]. In this paper we study existence of nonradial solutions by using the bifurcation method. Let { γ k } k = 2 ∞ be the sequence of eigenvalues of the linearized problem. We prove that there exists a positive integer k ⁎ ⩾ 2 such that in the two dimension case for any k ⩾ k ⁎ , γ k is a bifurcation point, and in the three dimension case for any even k ⩾ k ⁎ , γ k is also a bifurcation point. [ABSTRACT FROM AUTHOR]

• Single-sensor on-shaft vibration source identification problem is studied. • A dynamic model with resonance frequency random distribution is proposed. • A smart metasurface shaft model is designed with random local resonators. • The frequency response transfer functions are designed to be highly uncorrelated. • Combining compressive sensing algorithm realizes the single-sensor identification. In vibration monitoring of rotating machinery, traditional methods necessarily rely on multiple sensors to locate the vibration sources on the shaft. Reducing the number of sensors is an engineering challenge for on-shaft vibration source identification. This paper proposed a smart metasurface shaft (SMST) to achieve single-sensor identification of vibration sources. For the proposed SMST, a thin metasurface consisting of rubber metal rings is designed to cover the shaft and is capable of smartly on-shaft sensing of vibration sources. For the metasurface, the rubber metal rings with random metal masses are used to construct random local resonator units, which leads to the random modulation of location-different vibration responses. Theoretical derivation and simulations demonstrate the mechanism of random modulation of on-shaft vibrations. By combining the SMST with the compressive sensing algorithm, the vibration source locations can be reconstructed from the measurement of a single sensor. For the proposed SMST, experiments demonstrate that the single-sensor vibration source identification can be achieved with a high correct recognition ratio. The proposed SMST provides a new idea on single-sensor on-shaft vibration sensing, which shows potential applications in rotor dynamics, such as rotating machinery condition monitoring, vibration identification, and fault diagnosis. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of the inhomogeneous wave equation with singular (less than continuous) time dependent coefficients. Particular attention is given to the role of the lower order terms and suitable Levi conditions are formulated in order to obtain a very weak solution as introduced in [15]. Very weak solutions for this kind of equations are also investigated from a numerical point of view in two toy models: the wave equation with a Heaviside function and a delta distribution, respectively, as coefficient in its principal part. [ABSTRACT FROM AUTHOR]

• Utilized Hilbert space-filling curve and serialization for data transfer. • Works with any models including PIC, DSMC and CFD with non-uniform mesh. • Over-decomposition generally reduced the simulation run-time. • Greater benefit in simulations with a highly non-uniform particle distribution. An electric propulsion plasma plume simulation employs the Particle-in-Cell (PIC) model for heavy species (i.e. ions and neutral atoms) and yields a highly non-uniform particle distribution at steady state. For parallel simulations, partitioning the computational domain uniformly and evenly assigning the subdomains to MPI processes would never lead to properly balanced loads across MPI processes. For this reason, a patch-based dynamic load balancing method with over-decomposition and Hilbert space-filling curve has been implemented into the Thermophysics Universal Research Framework (TURF). The data transfer is accomplished by utilizing TURF's serialization and deserialization feature, in which the tree hierarchical object structure is copied into a contiguous memory block of data, and the tree hierarchy is reconstructed after the data transfer. This generalized dynamic load balancing approach allows for the same routine to be used for any models besides the PIC model in TURF (e.g. fluid, continuum kinetic, hybrid models, etc). This paper first introduces individual pieces of TURF that enable dynamic load balancing when they are combined. Then, the dynamic load balancing method is demonstrated in three different particle simulations, showing performance gains when the number of subdomains is larger than that of MPI processes. The benefit is even more notable in simulations with highly non-uniform particle distributions at steady state, commonly seen in plasma plume simulations. [ABSTRACT FROM AUTHOR]

Mutual information can effectively measure the correlation between categorical attributes. However, it is found to be quite computationally intensive and time consuming process for enormous size and different distribution data sets. It involves steps for computation of marginal entropies, probability distribution and so on. Spark is a fast, general-purpose parallel framework designed specifically for large-scale data processing. Main motivation of this paper is to provide an intelligent method for parallel mutual information calculation based on Spark computing environment with maintaining the synchronization between different computing nodes. Proposed method named MiCS-P has been able to execute with different number of computing nodes, and gives significant speedup working with different dimensions and sizes of data sets. The MiCS-P algorithm adopts column-wise transformation scheme, which is conducive to the calculation of mutual information between a large number of feature pairs. And to alleviate imbalanced load causing long execution times, we implement a two-phase virtual partitioning scheme running on Spark. • A Spark-based parallel mutual-information computing system is proposed for categorical data. • A column-wise transformation is designed and implemented on Spark. • A virtual partitioning scheme is utilized on Spark to mitigate the data skewness issue. • Extensive experiments are carried out to evaluate MiCS-P. [ABSTRACT FROM AUTHOR]

We consider different kinds of densities on natural numbers and investigate the problems on densities stated in the paper “Open problems on densities II” by Giuliano, Grekos and Mišík. We find answers to several of those problems and obtain new results related to the notions mentioned in that paper like distribution functions and density sets. [ABSTRACT FROM AUTHOR]

One of the most powerful and versatile system identification frameworks of the last three decades is the NARMAX/NARX 1 Nonlinear Auto-Regressive Moving Average with eXogenous inputs; NARX if the moving average noise model is omitted. 1 approach, which is based on a nonlinear discrete-time representation. Recent advances in machine learning have motivated new functional forms for the NARX model, including one based on Gaussian processes (GPs), which is the focus of this paper. Because of their nonparametric form, NARX models can only provide physical insight through their frequency-domain connection to Higher-order Frequency Response Functions (HFRFS). Because of the desirable properties of the GP-NARX form (no structure detection needed, natural confidence intervals), the analytical derivation of the HFRFs for the model is presented here for the first time. Furthermore, an algorithm for propagating uncertainty from the GP into the HFRF estimates is presented. A valuable by-product of the latter algorithm is a new test for nonlinearity, capable of detecting the presence of odd and even system nonlinearities. The new results are illustrated via two case studies; the first is based on simulation of an asymmetric Duffing oscillator. The second case study presents a validation of the new theory in the area of wave force prediction on offshore structures. This problem is one that has been considered by some of the authors before; the current paper takes the opportunity to highlight and correct a number of weaknesses of the original study in the light of modern best practice in machine learning. [ABSTRACT FROM AUTHOR]

This paper outlines a novel approach for solution of the Boltzmann–BGK equation describing molecular gas dynamics applied to the challenging problem of drag prediction of a 2D circular nano-particle at transitional Knudsen number (0.0214) and low Reynolds number (0.25–2.0). The numerical scheme utilises a discontinuous-Galerkin finite element discretisation for the physical space representing the problem particle geometry and a high order discretisation for molecular velocity space describing the molecular distribution function. The paper shows that this method produces drag predictions that are aligned well with the range of drag predictions for this problem generated from the alternative numerical approaches of molecular dynamics codes and a modified continuum scheme. It also demonstrates the sensitivity of flow-field solutions and therefore drag predictions to the wall absorption parameter used to construct the solid wall boundary condition used in the solver algorithm. The results from this work has applications in fields ranging from diagnostics and therapeutics in medicine to the fields of semiconductors and xerographics. [ABSTRACT FROM AUTHOR]

Two-dimensional distributions whose marginal distributions are uniform are called bivariate copulas. Among them, the one that satisfies given constraints on expectation and is closest to being an independent distribution in the sense of Kullback–Leibler divergence is called the minimum information bivariate copula. The density function of the minimum information copula contains a set of functions called the normalizing functions, which are often difficult to compute. Although a number of proper scoring rules for probability distributions having normalizing constants such as exponential families have been proposed, these scores are not applicable to the minimum information copulas due to the normalizing functions. In this paper, we propose the conditional Kullback–Leibler score, which avoids computation of the normalizing functions. The main idea of its construction is to use pairs of observations. We show that the proposed score is strictly proper in the space of copula density functions and therefore the estimator derived from it has asymptotic consistency. Furthermore, the score is convex with respect to the parameters and can be easily optimized by the gradient methods. [ABSTRACT FROM AUTHOR]

Studying the multivariate extension of copula correlation yields a dimension reduction principle, which turns out to be strongly related with the 'simple measure of conditional dependence' T recently introduced by Azadkia and Chatterjee (2021). In the present paper, we identify and investigate the dependence structure underlying this dimension reduction principle, provide a strongly consistent estimator for it, and demonstrate its broad applicability. For that purpose, we define a bivariate copula capturing the scale-invariant extent of dependence of an endogenous random variable Y on a set of d ≥ 1 exogenous random variables X = (X 1 , ... , X d) , and containing the information whether Y is completely dependent on X , and whether Y and X are independent. The dimension reduction principle becomes apparent insofar as the introduced bivariate copula can be viewed as the distribution function of two random variables Y and Y ′ sharing the same conditional distribution and being conditionally independent given X. Evaluating this copula uniformly along the diagonal, i.e., calculating Spearman's footrule, leads to an unconditional version of Azadkia and Chatterjee's 'simple measure of conditional dependence' T. On the other hand, evaluating this copula uniformly over the unit square, i.e., calculating Spearman's rho, leads to a distribution-free coefficient of determination (also known as 'copula correlation'). Several real data examples illustrate the importance of the introduced methodology. [ABSTRACT FROM AUTHOR]

The recently-developed general synthetic iterative scheme (GSIS) is efficient in simulating multiscale rarefied gas flows due to the coupling of mesoscopic kinetic equation and macroscopic synthetic equation: for linearized Poiseuille flow where the boundary flux is fixed at each iterative step, the steady-state solutions are found within dozens of iterations in solving the gas kinetic equations, while for general nonlinear flows the iteration number is increased by about one order of magnitude, caused by the incompatible treatment of the boundary flux for the macroscopic synthetic equation. In this paper, we propose a generalized boundary treatment (GBT) to further accelerate the convergence of GSIS. The main idea is, the truncated velocity distribution function at the boundary, similar to that used in the Grad 13-moment equation, is reconstructed by the macroscopic conserved quantities from the synthetic equation, as well as the high-order correction of non-equilibrium stress and heat flux from the kinetic equation; therefore, in each inner iteration solving the synthetic equation, the explicit constitutive relations facilitate real-time updates of the macroscopic boundary flux, driving faster information exchange in the flow field, and consequently achieving faster convergence. Moreover, the high-order correction derived from the kinetic equation can compensate the approximation by the truncation and ensure the boundary accuracy. The one-dimensional Fourier flow, two-dimensional hypersonic flow around a cylinder, three-dimensional pressure-driven pipe flow and the flow around the hypersonic technology vehicle are simulated. The accuracy of GSIS-GBT is validated by the direct simulation Monte Carlo method, the previous versions of GSIS, and the unified gas-kinetic wave-particle method. For the efficiency, in the near-continuum flow regime and slip regime, GSIS-GBT can be faster than the conventional iteration scheme in the discrete velocity method and the previous versions of GSIS by two- and one-order of magnitude, respectively. • The generalized boundary treatment (GBT) is proposed to further accelerate the general synthetic iterative scheme (GSIS). • In both low-speed internal flows and hypersonic flows, GSIS-GBT can achieve convergence within 100 iterations. • GSIS-GBT is respectively faster than previous version of GSIS/conventional iterative scheme by one/two orders of magnitude. [ABSTRACT FROM AUTHOR]

It is increasingly realized that taking stochastic effects into account is important in order to study biological cells. However, the corresponding mathematical formulation, the chemical master equation (CME), suffers from the curse of dimensionality and thus solving it directly is not feasible for most realistic problems. In this paper we propose a dynamical low-rank algorithm for the CME that reduces the dimensionality of the problem by dividing the reaction network into partitions. Only reactions that cross partitions are subject to an approximation error (everything else is computed exactly). This approach, compared to the commonly used stochastic simulation algorithm (SSA, a Monte Carlo method), has the advantage that it is completely noise-free. This is particularly important if one is interested in resolving the tails of the probability distribution. We show that in some cases (e.g. for the lambda phage) the proposed method can drastically reduce memory consumption and run time and provide better accuracy than SSA. • We propose a low-rank algorithm that does not rely on single orbital basis functions. • The proposed approach is better suited for biological/chemical reaction networks. • We demonstrate better accuracy and improved efficiency compared to SSA for some problems. • The proposed complexity reduction algorithm is noise free (in contrast to SSA). • We demonstrate that our algorithm accurately resolves the tails of the distribution (in contrast to SSA). [ABSTRACT FROM AUTHOR]

Multivariate count distributions are crucial for the inference of ecological processes underpinning biodiversity. In particular, neutral theory provides useful null distributions allowing the evaluation of adaptation or natural selection. In this paper, we build a broader family of multivariate distributions: the Polya-splitting distributions. We show that they emerge naturally as stationary distributions of a multivariate birth–death process. This family of distributions is a consistent extension of non-zero sum neutral models based on a master equation approach. It allows considering both total abundance of the community and relative abundances of species. We emphasize that this family is large enough to encompass various dependence structures among species. We also introduce the strong closure under addition property that can be useful to generate nested multi-level dependence structures. Although all Pólya splitting distributions do not share this property, we provide numerous example verifying it. They include the previously known example with independent species, and also new ones with alternative dependence structures. Overall, we advocate that Polya-splitting distribution should become a part of the classic toolbox for the analysis of multivariate count data in ecology, providing alternative approaches to joint species distribution framework. Comparatively, our approach allows to model dependencies between species at the observation level, while the classical JSDM's model dependencies at the latent process strata. [ABSTRACT FROM AUTHOR]

This study proposes a novel filtering method for unbiased minimum variance state estimation. A key challenge in the development of digital twinning and system identification of operational civil infrastructure is the difficulties associated with measurement of the often nonstationary, and stochastic unknown input to the system, e.g. traffic, earthquake, and wind loads. Herein a novel algorithm is presented for an unbiased output-only state estimation for linear state space systems with direct feedthrough. In this paper, the problem of state estimation for discrete time systems with unknown input, where no previous assumption is made regarding the probability distribution of the input, is addressed. In this regard, a two-stage output-only filter is proposed. The unbiasedness of the estimation is demonstrated, and the error covariance propagation over time is derived. It is shown that the unknown input of the system can be subsequently reconstructed via the system matrices, the measured responses, and the estimated state vector. A closed-form solution is provided for the parameters associated with pseudo-inverse in gain calculations to ensure the numerical stability of the filter. Three case studies including simulated and laboratory experiments for verification, validation, and cross comparison of the proposed method are presented. The first case study corresponds to a simulated shear building subjected to two different load time histories, a parametric sinusoidal load, and an earthquake ground acceleration. The second case study shows the results for a simulated experiment on a steel railway bridge subjected to a concentrated load. The third case study corresponds to a laboratory shear building subjected to ground motion and observed through accelerometers. The results of the experiments show a good agreement between the "true response" and the filter state estimation. Moreover, the proposed method is compared against a state-of-the-art algorithm. [ABSTRACT FROM AUTHOR]

Photoelectrons are an integral part of the sunlit lunar plasma environment. This paper formulates the characteristic velocity distribution of the emitted photoelectrons over the sunlit Moon. As an advancement, Fowler's photoemission theory has been coupled with observed solar spectra, photoelectric quantum yield, and latitude-dependent surface temperature in deriving the velocity distribution function (VDF) of the photoelectrons. It is noticed that the dominant contribution in the photoelectron VDF comes from extreme ultraviolet photons of the solar spectra and it significantly deviates from the Maxwellian nature. Moreover, within a photoelectron sheath which refers to finite surface potential, the velocity distributions significantly differ from that of the uncharged surface — VDF has been evaluated in terms of free and trapped photoelectron population densities. The derived VDF is found in close agreement with the measured photoelectron velocity distribution. • Photoelectron velocity distribution over sunlit Moon is formulated. • Fowler's theory is coupled with observed solar/lunar parameters to characterize photoelectrons. • Trapped and free photoelectron populations coexist with different mean energies. • Derived photoelectron distribution closely matches the measured distribution. [ABSTRACT FROM AUTHOR]

• A nonlinear compensation scheme for FMF MDM-WDM using PNN is proposed for the first time. • This scheme has a good benefit to fiber nonlinear compensation and device nonlinear compensation. • Its effectiveness is verified by simulation system. • The complexity of this scheme is lower than that of DBP under comparable performance. In this paper, we propose for the first time to apply probabilistic neural network (PNN) to fiber nonlinear compensation (NLC) in a high-speed coherent optical communication system that combines few-mode fiber (FMF) mode division multiplexing (MDM) with wavelength division multiplexing (WDM). By training on a small number of symbols, the PNN equalizer can compute the statistical distribution of the signal nonlinearity, make decisions on test symbols, and thereby compensate for the nonlinear impairments of the signals. To verify the effectiveness of the proposed scheme, we construct a MDM-WDM simulation system with 28 GBaud polarization division multiplexing (PDM) 16-quadrature amplitude modulation(QAM) and 64 GBaud PDM-64QAM, 6 spatial mode signals are transmitted over 11 wavelength channels with link lengths of 1500 km and 400 km, respectively. The results show that the PNN equalizer can make nonlinear judgments on received signals and effectively compensate the signal impairments caused by Kerr nonlinearity and device nonlinearity in a large launch power range after undergoing carrier phase recovery (CPR). Meanwhile, this scheme exhibits strong robustness against residual linear mode coupling (LMC), differential mode group delay (DMGD), and amplified spontaneous emission (ASE) noise. Finally, by the computational complexity comparison, it is proved that the complexity of the probabilistic neural network nonlinear compensation (PNN NLC) scheme is lower than that of digital back propagation (DBP) with comparable performance, which is on the order O(N). [ABSTRACT FROM AUTHOR]

Boundary effects are crucial for dynamics of dilute charged gases governed by the Vlasov-Poisson-Boltzmann (VPB) system. In this paper, we study the existence and regularity of solutions to the VPB system with soft potential in a bounded convex domain with in-flow boundary condition. We establish the existence of strong solutions in the time interval [ 0 , T ] for an arbitrary given T > 0 when the initial distribution function is near an absolute Maxwellian. Our contribution is based on a new weighted energy estimate in some W 1 , p space and L x 3 L v 1 + space for soft potential. By using the classical L 2 – L ∞ method and bootstrap argument, we extend the local solutions from small time scale to large time scale. [ABSTRACT FROM AUTHOR]

• The EasyPAP environment allows students to really focus on parallelism while developing OpenMP, OpenCL or MPI kernels. • Interactive display of increasingly optimized variants of a 2D kernel help to popularize HPC. • Linking CPUs and image tiles in monitoring windows allow to better understand scheduling policies. • Linking tasks and image tiles when visualizing port mortem execution traces help to diagnose parallel efficiency issues. This paper presents EasyPAP , an easy-to-use programming environment designed to help students to learn parallel programming. EasyPAP features a wide range of 2D computation kernels that the students are invited to parallelize using Pthreads, OpenMP, OpenCL or MPI. Execution of kernels can be interactively visualized, and powerful monitoring tools allow students to observe both the scheduling of computations and the assignment of 2D tiles to threads/processes. By focusing on algorithms and data distribution, students can experiment with diverse code variants and tune multiple parameters, resulting in richer problem exploration and faster progress towards efficient solutions. We present selected lab assignments which illustrate how EasyPAP improves the way students explore parallel programming. [ABSTRACT FROM AUTHOR]

In 1972 Delange [9] observed in analogy of the classical Erdős-Wintner theorem that q -additive functions f (n) has a distribution function if and only if the two series ∑ f (d q j) , ∑ f (d q j) 2 converge. The purpose of this paper is to provide quantitative versions of this theorem as well as generalizations to other kinds of digital expansions. In addition to the q -ary and Cantor case we focus on the Zeckendorf expansion that is based on the Fibonacci sequence, where we provide a sufficient and necessary condition for the existence of a distribution function, namely that the two series ∑ f (F j) , ∑ f (F j) 2 converge (previously only a sufficient condition was known [2]). [ABSTRACT FROM AUTHOR]

• An intelligent taxi dispatch system for big cities validated by real-world dataset. • Taxi demand and destination prediction based on historical data. • Realtime taxi assignment and reallocation strategy to optimize multiple goals. • Performance comparison with several popular prediction and optimization strategies. In this paper we describe an intelligent taxi dispatch system that has the goal of reducing the waiting time of the passengers and the idle driving distance of the taxis. The system relies on two separate models that predict the probability distributions of the taxi demand and destinations respectively. The models are learned from historical data and use a combination of long short term memory cells and mixture density networks. Using these predictors, taxi dispatch is formulated as a mixed integer programming problem. We validate the performance of the predictors and the overall system on a real world dataset of taxi trips in New York City. [ABSTRACT FROM AUTHOR]

In this paper, we consider (random) sampling of signals concentrated on a bounded Corkscrew domain Ω of a metric measure space, and reconstructing concentrated signals approximately from their (un)corrupted sampling data taken on a sampling set contained in Ω. We establish a weighted stability of bi-Lipschitz type for a (random) sampling scheme on the set of concentrated signals in a reproducing kernel space. The weighted stability of bi-Lipschitz type provides a weak robustness to the sampling scheme, however due to the nonconvexity of the set of concentrated signals, it does not imply the unique signal reconstruction. From (un)corrupted samples taken on a finite sampling set contained in Ω, we propose an algorithm to find approximations to signals concentrated on a bounded Corkscrew domain Ω. Random sampling is a sampling scheme where sampling positions are randomly taken according to a probability distribution. Next we show that, with high probability, signals concentrated on a bounded Corkscrew domain Ω can be reconstructed approximately from their uncorrupted (or randomly corrupted) samples taken at i.i.d. random positions drawn on Ω, provided that the sampling size is at least of the order μ (Ω) ln ⁡ (μ (Ω)) , where μ (Ω) is the measure of the concentrated domain Ω. Finally, we demonstrate the performance of proposed approximations to the original concentrated signals when the sampling procedure is taken either with large density or randomly with large size. [ABSTRACT FROM AUTHOR]

Some recent papers deal with smooth nonparametric estimators for copula functions and copula derivatives. These papers contain results on copula-based Bernstein estimators for conditional distribution functions and related functionals such as regression and quantile functions. The focus in the present paper is on new copula-based smooth Bernstein estimators for the conditional density. Our approach avoids going through separate density estimation of numerator and denominator. Our estimator is defined as a smoother of the copula-based Bernstein estimator of the conditional distribution function. We establish asymptotic properties of bias and variance and discuss the asymptotic mean squared error in terms of the smoothing parameters. We also obtain the asymptotic normality of the new estimator. In a simulation study we show the good performance of the new estimator in comparison with other estimators proposed in the literature. [ABSTRACT FROM AUTHOR]

In both quantum optics and cold atom physics, the behaviour of bosonic photons and atoms is often treated using phase space methods, where mode annihilation and creation operators are represented by c-number phase space variables, with the density operator equivalent to a distribution function of these variables. The anti-commutation rules for fermion annihilation, creation operators suggests the possibility of using anti-commuting Grassmann variables to represent these operators. However, in spite of the seminal work by Cahill and Glauber and a few applications, the use of Grassmann phase space methods in quantum-atom optics to treat fermionic systems is rather rare, though fermion coherent states using Grassmann variables are widely used in particle physics. This paper presents a phase space theory for fermion systems based on distribution functionals, which replace the density operator and involve Grassmann fields representing anti-commuting fermion field annihilation, creation operators. It is an extension of a previous phase space theory paper for fermions (Paper I) based on separate modes, in which the density operator is replaced by a distribution function depending on Grassmann phase space variables which represent the mode annihilation and creation operators. This further development of the theory is important for the situation when large numbers of fermions are involved, resulting in too many modes to treat separately. Here Grassmann fields, distribution functionals, functional Fokker–Planck equations and Ito stochastic field equations are involved. Typical applications to a trapped Fermi gas of interacting spin 1/2 fermionic atoms and to multi-component Fermi gases with non-zero range interactions are presented, showing that the Ito stochastic field equations are local in these cases. For the spin 1/2 case we also show how simple solutions can be obtained both for the untrapped case and for an optical lattice trapping potential. [ABSTRACT FROM AUTHOR]

This paper presents preliminary developments of entropy-stable residual distribution methods for scalar problems. Controlling entropy generation is achieved by formulating an entropy conserved signals distribution coupled with an entropy-stable signals distribution. Numerical results of the entropy-stable residual distribution methods are accurate and comparable with the classic residual distribution methods for steady-state problems. High order accurate extensions for the new method on steady-state problems are also demonstrated. Moreover, the new method preserves second order accuracy on unsteady problems using an explicit time integration scheme. The idea of the multi-dimensional entropy-stable residual distribution method is generic enough to be extended to the system of hyperbolic equations, which will be presented in the sequel of this paper. [ABSTRACT FROM AUTHOR]

Nested error regression models are useful tools for the analysis of grouped data, especially in the context of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in each area is expressed as a mixture of a normal distribution and a positive mass at 0. For the estimation of the model parameters and prediction of the random effects, an objective Bayesian inference is proposed by setting non-informative prior distributions on the model parameters. Under mild sufficient conditions, it is shown that the posterior distribution is proper and the posterior variances are finite, confirming the validity of posterior inference. To generate samples from the posterior distribution, a Gibbs sampling method is provided with familiar forms for all the full conditional distributions. This paper also addresses the problem of predicting finite population means, and a sampling-based method is suggested to tackle this issue. Finally, the proposed model is compared with the conventional nested error regression model through simulation and empirical studies. [ABSTRACT FROM AUTHOR]

• A novel VSSTFrFT method is proposed to improve the concentration of time-frequency distribution. • Using the idea of optimal rotation order in FrFT to adaptively set the number of modal decomposition in VMD. • SET is utilized to extract the coefficient of ridgeline position, improving the time-frequency concentration. • The robustness and concentration performance of the proposed method are verified by simulation signals with different components. • The effectiveness of the VSSTFrFT method is verified by the data from the cantilever hammering modal signal, bat echolocation chirp signal and bearing fault signals. To improve the time–frequency (TF) concentration performance of the short-time fractional Fourier transform (STFrFT), and solve the multi-order matching problem of multi-component signals, this paper introduces a new algorithm that is referred to as the Variational mode decomposition-short-time fractional Fourier transform- Synchroextracting transform (VSSTFrFT). This work employs the Variational mode decomposition (VMD) algorithm to decompose multi-component signals into single-component sets, then the STFrFT algorithm matches the optimal rotation order of each component separately to solve the multi-order matching problem. Finally, this paper utilizes the Synchroextracting transform (SET) to extract the TF coefficient of ridgeline position in STFrFT distribution, improving the concentration performance. For different types of signals, the VSSTFrFT algorithm can get a higher TF concentration than the traditional TFA methods. In the application of engineering measured data, the VSSTFrFT algorithm can extract the modalities of the signals and display the frequency curve clearly, which can be used for structural complexity and time-varying characteristics analysis in practical engineering applications. [ABSTRACT FROM AUTHOR]

To characterize the regularity of distribution-path dependent SDEs in the initial distribution which varies as probability measure on the path space, we introduce the intrinsic and Lions derivatives for probability measures on Banach spaces, and prove the chain rule of the Lions derivative for the distribution of Banach-valued random variables. By using Malliavin calculus, we establish the Bismut type formula for the Lions derivatives of functional solutions to SDEs with distribution-path dependent drifts. When the noise term is also path dependent so that the Bismut formula is invalid, we establish the asymptotic Bismut formula. Both non-degenerate and degenerate noises are considered. The main results of this paper generalize and improve the corresponding ones derived recently in the literature for the classical SDEs with memory and McKean-Vlasov SDEs without memory. [ABSTRACT FROM AUTHOR]

Though numerous studies have investigated optimal locations for biorefineries given the availability of feedstock supplies, few have considered that these supplies could vary over time, thereby potentially failing to meet feedstock requirements. In this paper, we develop a process for identifying a shortlist of five potentially viable biorefinery sites in Alberta, and then consider the stochastic nature of these supplies, and what that variation could mean for supplying a biorefinery. A shortlist of sites was selected based on agricultural residues within a distance of 80 km of the site. Across all sites, a total amount of 16.7 million t [oven dried] y−1 is found to be economically accessible in the province. However, this shortlist is based only on a summation of one-year crop yields surrounding the sites. When crop yield variability (estimated from data over 40 years between 1978 and 2017) is also considered, substantially different results were found. For example, if supply was required to exceed 1.59 million t [oven dried] y−1, 95% of the time, then two selected sites, which were chosen based on one-year crop yields, must be excluded. Under these circumstances the total amount available across sites falls to 12.4 million t [oven dried] y−1. Overall, when variability in supply is included as a criterion, site selection and rankings change, suggesting that site selection using only an average or point estimate is not sufficient. Instead, more sophisticated techniques to investigate feedstock supply variability would be useful. • Economic accessibility of agricultural residues can vary substantially over time. • Selecting biorefinery locations based on one year of data is misleading. • Modelling stochastic feedstock supplies can improve biorefinery siting decisions. [ABSTRACT FROM AUTHOR]

Protein nanoparticles have attracted increased interest due to their broad applications ranging from drug delivery and vaccines to biocatalysts and biosensors. The morphology and the size of the nanoparticles play a crucial role in determining their suitability for different applications. Yet, effectively controlling the size of the nanoparticles is still a significant challenge in their manufacture. The hypothesis of this paper is that the assembly conditions and size of protein particles can be tuned via a mechanical route by simply modifying the mixing time and strength, while keeping the chemical parameters constant. We use an acoustically actuated, high throughput, ultrafast, microfluidic mixer for the assembly of protein particles with tuneable sizes. The performance of the acoustic micro-mixer is characterized via Laser Doppler Vibrometry and image processing. The assembly of protein nanoparticles is monitored by dynamic light scattering (DLS) and transmission electron microscopy (TEM). By changing actuation parameters, the turbulence and mixing in the microchannel can be precisely varied to control the initiation of protein particle assembly while the solution conditions of assembly (pH and ionic strength) are kept constant. Importantly, mixing times as low as 6 ms can be achieved for triggering protein assembly in the microfluidic channel. In comparison to the conventional batch process of assembly, the acoustic microfluidic mixer approach produces smaller particles with a more uniform size distribution, promising a new way to manufacture protein particles with controllable quality. [ABSTRACT FROM AUTHOR]

This paper studies the optimal contract for a risk-neutral agency with limited liability. We introduce a novel formulation of the model, in which the contract design problem reduces to a problem of constructing the distribution function of a random variable. This formulation directly balances the principal's tradeoff between incentivizing the agent to exert proper effort and minimizing the cost of the agent's compensation. We show that the optimal contract may involve one or two tiers of performance-based bonuses. We obtain new sufficient conditions for the optimality of bonus contracts and provide new insights into the choice of contract parameters. [ABSTRACT FROM AUTHOR]