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In this work, we explore the Boltzmann equation with Fermi-Dirac statistics (briefly, BFD equation), which models the dilute gases when quantum effects are taking into consideration. Specifically, we firstly establish the uniform energy estimate and construct the global-in-time classical solutions of the scaled BFD equations under small assumption on the initial data. Then we use this uniform estimate to derive the acoustic limit from the scaled BFD equations within the context of classical solutions. Compared with our companion article Jiang and Zhou (2024) [23] , our uniform estimate in Knudsen number in this paper is crucial and hard to be obtained for the compressible Euler scaling and the acoustic limit is global-in-time, rather than almost global-in-time. [ABSTRACT FROM AUTHOR]

Let N k (m , n) denote the number of partitions of n with Garvan k -rank m. It is well-known that Andrews–Garvan–Dyson's crank and Dyson's rank are the k -rank for k = 1 and k = 2 , respectively. In this paper, we prove that the sequences (N k (m , n)) | m | ≤ n − k − 71 are log-concave for all sufficiently large integers n and each integer k. In particular, we partially solve the log-concavity conjecture for Andrews–Garvan–Dyson's crank and Dyson's rank, which was independently proposed by Bringmann–Jennings-Shaffer–Mahlburg and Ji–Zang recently. [ABSTRACT FROM AUTHOR]

In this paper we investigate the following question: if NP is slightly hard on average, is it very hard on average? We give a positive answer: if there is a function in NP which is infinitely often balanced and (1-1/poly(n))-hard for circuits of polynomial size, then there is a function in NP which is infinitely often (1/2+n-1/2+#x03B5;)-hard for circuits of polynomial size. Our proof technique is to generalize the Yao XOR Lemma, allowing us to characterize nearly tightly the hardness of a composite function g( f(x1),…,f(xn)) in terms of: (i) the original hardness of f, and (ii) the expected bias of the function g when subjected to random restrictions. The computational result we prove essentially matches an information-theoretic bound. [Copyright &y& Elsevier]

Wireless-optical broadband access network (WOBAN) or fiber-wireless (FiWi) is a robust and cost-effective solution to provide high bandwidth network connectivity to mobile subscribers. Optical network unit (ONU) placement is a topological optimization problem that plays a vital role in effective deployment of FiWi network. Recently, some artificial intelligence-based approaches for positioning ONUs were proposed and generated promising results. However, the reported performance in the literature is far from the ideal state. This issue emphasizes the necessity of introducing new placement methods or improving the performance of existing methods. This paper presents a hybrid clustering algorithm for finding the optimal position of multiple ONUs. The proposed backtracking K -harmonic means (BKHM) is an integration of K -harmonic means (KHM) and a backtracking search algorithm (BSA). BKHM not only efficiently specifies the optimal positions of ONUs but also significantly decreases the implementation cost. To demonstrate the performance of the BKHM, we evaluate it on well-known placement benchmarks compared with BSA, KHM, whale optimization algorithm (WOA), enhanced backtracking search (EBS), harris hawks optimization (HHO), and chaotic local search-based levy flight distribution (CLF) algorithms. The experimental results and statistical analysis proved that the proposed BKHM algorithm outperformed its counterparts on most benchmarks in terms of cost optimization, convergence accuracy, and solution quality. • Proposing a hybrid clustering algorithm: The proposed not only solves the slow convergence of the BSA algorithm but also helps the KHM to escape from local optimal. • Using the BKHM for solving ONU placement problem: The BSA algorithm is suitable for solving permutation problems, therefore combining it with KHM can work better than other algorithms for the problem of ONU placement. • Improving the performance of the existing ONU placement methods. Simulation results confirm the superiority of the BKHM compared with other methods. [ABSTRACT FROM AUTHOR]

Statistical mediation analysis is commonly used to examine mediation, but it is not the default paradigm; researchers also test for mediation through experimental mediation analysis, such as the two randomized experiments design , the experimental-causal-chain design , the moderation-of-process design , and the parallel design , all of which differ considerably in terms of procedures and requirements. Which requirements are genuinely necessary, and which are not? This paper compares the effectiveness of these research designs in examining mediation. Three constitutive requirements for supporting a mediational hypothesis were identified: (A) a significant interaction effect of the independent variable (X) and the manipulation of the proposed mediating process (M) on the dependent variable (Y); (B) a significant effect of X on the measured M within the control group whose M is not manipulated and can function naturally; and (C) a significant effect of the manipulation on the measured M. Using these criteria, existing designs all have drawbacks, so this paper proposes a manipulation-of-mediation-as-a-moderator (MMM) design to fulfill all three requirements. MMM provides strong evidence for the causal inference M → Y , avoids false alarms in many cases, and provides direct evidence for the relationships between X and M and between manipulated M and measured M. The paper presents a step-by-step example of MMM for interested practitioners. In its discussion of the relationships among X -caused M , manipulated M , and measured M and the distinction between mediation and moderation, this paper enriches the understanding of the nature of mediation analyses in psychology. [Display omitted] [ABSTRACT FROM AUTHOR]

Each mutation in a population sample of DNA sequences can be classified by the number of sequences that inherit the mutant nucleotide, the resulting frequencies are known as mutations of different sizes or site frequency spectrum. Many summary statistics can be defined as a linear function of these frequencies. A flexible class of such linear summary statistics is explored analytically in this paper which include several well-known quantities, such as the number of segregating sizes and the mean number of nucleotide differences between two sequences. Some asymptotic variances and covariances are obtained while the analytical formulas for the variances and covariances of nine such linear summary statistics are derived, most of which are unknown to date. This study not only provides some theoretical foundations for exploring linear summary statistics, but also provides some newlinear summary statistics that may be utilized for analyzing sample polymorphism. Furthermore it is showed that a newly developed linear summary statistics has a smaller variance almost uniformly than Watterson's estimator, and that a class of linear summary statistics given too heavy weights on mutations of smaller sizes result in asymptotically non-zero variance. [ABSTRACT FROM AUTHOR]

As a natural generalization of permutations, transversals of Young diagrams play an important role in the study of pattern avoiding permutations. Let T λ (τ) and ST λ (τ) denote the set of τ -avoiding transversals and τ -avoiding symmetric transversals of a Young diagram λ , respectively. In this paper, we are mainly concerned with the distribution of the peak set and the valley set on standard Young tableaux and pattern avoiding transversals. In particular, we prove that the peak set and the valley set are equidistributed on the standard Young tableaux of shape λ / μ for any skew diagram λ / μ. The equidistribution enables us to show that the peak set is equidistributed over T λ (12 ⋯ k τ) (resp. ST λ (12 ⋯ k τ)) and T λ (k ⋯ 21 τ) (resp. ST λ (k ⋯ 21 τ)) for any Young diagram λ and any permutation τ of { k + 1 , k + 2 , ... , k + m } with k , m ≥ 1. Our results are refinements of the result of Backelin-West-Xin which states that | T λ (12 ⋯ k τ) | = | T λ (k ⋯ 21 τ) | and the result of Bousquet-Mélou and Steingrímsson which states that | ST λ (12 ⋯ k τ) | = | ST λ (k ⋯ 21 τ) |. As applications, we are able to • confirm a recent conjecture posed by Yan-Wang-Zhou which asserts that the peak set is equidistributed over 12 ⋯ k τ -avoiding involutions and k ⋯ 21 τ -avoiding involutions; • prove that alternating involutions avoiding the pattern 12 ⋯ k τ are equinumerous with alternating involutions avoiding the pattern k ⋯ 21 τ , paralleling the result of Backelin-West-Xin for permutations, the result of Bousquet-Mélou and Steingrímsson for involutions, and the result of Yan for alternating permutations. [ABSTRACT FROM AUTHOR]

Andrews recently provided a q -series proof of congruences for N T (m , k , n) , the total number of parts in the partitions of n with rank congruent to m modulo k. Motivated by Andrews' works, Chern obtain congruences for M ω (m , k , n) which denotes the total number of ones in the partition of n with crank congruent to m modulo k. In this paper, we focus on the modular approach to these new partition statistics. Applying the theory of mock modular forms, we establish equalities and identities for N T (m , 7 , n) and M ω (m , 7 , n). [ABSTRACT FROM AUTHOR]

In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization from a non-Gaussian random vector. The manifold structure is learned using diffusion manifolds and the statistical sample generation is accomplished using a projected Itô stochastic differential equation. This probabilistic learning approach has been extended to polynomial chaos representation of databases on manifolds and to probabilistic nonconvex constrained optimization with a fixed budget of function evaluations. The methodology introduces an isotropic-diffusion kernel with hyperparameter ε. Currently, ε is more or less arbitrarily chosen. In this paper, we propose a selection criterion for identifying an optimal value of ε , based on a maximum entropy argument. The result is a comprehensive, closed, probabilistic model for characterizing data sets with hidden constraints. This entropy argument ensures that out of all possible models, this is the one that is the most uncertain beyond any specified constraints, which is selected. Applications are presented for several databases. • Algebraic closure of hyperparameters for the probabilistic learning on manifolds. • Non-Gaussian statistical model of data from a given dataset of realizations. • Applications to databases generated with advanced computational models. • Computational models using a high computing performance framework. [ABSTRACT FROM AUTHOR]

In this paper we describe the method which we applied to successfully compute the primary decomposition of a certain ideal coming from applications in combinatorial algebra and algebraic statistics regarding conditional independence statements with hidden variables. While our method is based on the algorithm for primary decomposition by Gianni, Trager and Zacharias, we were not able to decompose the ideal using the standard form of that algorithm, nor by any other method known to us. [ABSTRACT FROM AUTHOR]

Multivariate normal/independent (MNI) distributions contain many renowned heavy-tailed distributions such as the multivariate t , multivariate slash, multivariate contaminated normal, multivariate variance-gamma, and multivariate double exponential distributions. A frequent problem encountered in statistical analysis is the occurrence of truncated observations and non-normality such that theoretical moments are required for the estimation of the truncated multivariate normal/independent (TMNI) distributions. This paper is dedicated to deriving explicit expressions for the moments of the TMNI distributions with supports confined within a hyper-rectangle. A Monte Carlo experiment is undertaken to validate to the correctness of the proposed formulae for five selected members of the TMNI distributions. R scripts and data to reproduce the results are available in the GitHub repository. [ABSTRACT FROM AUTHOR]

Gratton and Mundry (2019, Animal Behaviour , 000, 000-000) statistically evaluate an approach I had suggested in an earlier paper that relied merely on verbal arguments (Garamszegi, 2016, Animal Behaviour , 120, 223-234). In particular, their simulation study challenges a methodology I proposed to account for pseudoreplication when the identity of individuals is unknown in conservation studies. Gratton and Mundry (2019) conclude that the random assignment of observations to individuals along the lines of my original idea produces a considerable type I error rate. Here, I suggest that although this evaluation is straightforward, it is still incomplete because it neglects two aspects of my original suggestion. To fill this gap, I have performed additional simulations that show that my proposed approach provides biased estimates even when the random assignment of identity tags is combined with multimodel inference and/or is applied to cases when within-individual correlations exist. These additional results support the conclusions of Gratton and Mundry (2019) with the caveat that the untested aspects of Garamszegi (2016) should not be dismissed. • Gratton & Mundry statistically examined an approach I suggested in an earlier paper. • By not exactly challenging the proposed methodology, the evaluation was incomplete. • I performed new simulations to deal with issues that Gratton & Mundry disregarded. • These additional results supported the conclusions of Gratton & Mundry. [ABSTRACT FROM AUTHOR]

Comparability is a key concept in the evaluation of both manufacturing changes and biosimilars. It constitutes a pragmatic and flexible approach which recognises that biologicals are inherently variable and that minor variations in quality attributes are often clinically irrelevant. In this discussion paper, we argue that comparability exercises rely on a number of pragmatic criteria. These criteria have been remarkably robust for 20 years of comparability exercises; however, the increased scrutiny of biosimilar applications provides an impetus for both codification and improvement of criteria for establishing comparability. Such a more rigorous, methodologically sound, approach towards comparability seems both feasible and beneficial. [ABSTRACT FROM AUTHOR]

In this paper, a statistical analysis of resonance evaluations from the most recent nuclear data libraries is performed with the code TARES. A description of the TARES framework is provided, but also for its use in the production of resonance parameters for the entire TENDL library. Various observables are calculated (e.g. , thermal cross sections, capture integrals but also D 0 and other average resonance quantities) for different libraries and compared to experimental values when available. Finally, for isotopes with no or little information, details are provided for the production of statistical resonances, based on a variety of compound nucleus reaction models. [ABSTRACT FROM AUTHOR]

• A model for synchronous average under keyphasor times uncertainty is developed. • Attenuation bias and variance of the estimates are quantified. • Linear piecewise order tracking is suggested for stationary speed operations. • The model is verified numerically and experimentally using real data. • Possible consequences of the uncertainty on diagnosis are investigated. Time synchronous averaging for the extraction of periodic waveforms is a rather common processing method for rotating machinery diagnosis. By synchronizing the signal to the rotational angle of the component of interest, e.g. by using a keyphasor reference signal, it is possible to perform the averaging in the angular domain, thus obtaining an angle-synchronous signal. Jittering of the reference signal affects the quality of the synchronous averaging process, resulting in attenuation and uncertain estimation of the extracted synchronous signal, especially in the high frequency band. In this paper, the effects of random uncertainty in the pulse arrival times of the reference signal on the synchronous averaging method are studied, with the objective of assessing the relevance of such a jitter error to the extracted waveform and the indicators derived for monitoring purposes. First, a unified framework for the computed order tracking method is presented, and then a model linking the statistics of the random jitter to the statistics of the waveform extracted through synchronous averaging in angle domain is developed. The theoretical model connects the random jitter distribution, the number of averaged periods and the ratio of the period of interest to the reference trigger period, to the distribution of the amplitudes of the synchronous frequency components in the synchronously averaged signal. Approximate analytical solutions are derived for cases of interest, allowing the prediction of the attenuation bias and variability of the extracted components amplitudes. The model is first verified against numerical simulations in order to assess consistency, and then parametric studies are presented. Experimental validation is performed on both an experimental and an operational data sets involving respectively a helicopter gearbox and a helicopter fleet. [ABSTRACT FROM AUTHOR]

Laguerre histories (restricted or not) are certain weighted Motzkin paths with two types of level steps. They are, on one hand, in natural bijection with the set of permutations, and on the other hand, yield combinatorial interpretations for the moments of Laguerre polynomials via Flajolet's combinatorial theory of continued fractions. In this paper, we first introduce a reflection-like involution on restricted Laguerre histories. Then, we demonstrate its power by composing this involution with three bijections due to Françon-Viennot, Foata-Zeilberger, and Yan-Zhou-Lin, respectively. A host of equidistribution results involving various (multiset-valued) permutation statistics follow from these applications. As byproducts, seven apparently new Mahonian statistics present themselves; new interpretations of known Mahonian statistics are discovered as well. Finally, in our effort to show the interconnections between these Mahonian statistics, we are naturally led to a new link between the variant Yan-Zhou-Lin bijection and the Kreweras complement. [ABSTRACT FROM AUTHOR]

This paper investigates the shape reconstructions of sub-wavelength objects from near-field measurements in transverse electromagnetic scattering. This geometric inverse problem is notoriously ill-posed and challenging. We develop a novel reconstruction scheme of using plasmon resonances with significantly enhanced sensitivity and resolution. First, by spectral analysis we establish a sharp quantitative relationship between the sensitivity of the reconstruction and the plasmon resonance. It shows that the sensitivity functional blows up when plasmon resonance occurs. Hence, the signal to noise ratio is significantly improved and the robustness and effectiveness of the reconstruction are ensured. Second, a variational regularization method is proposed to overcome the ill-posedness, and an alternating iteration method is introduced to automatically select the regularization parameters. Third, we use Laplace approximation method to capture the statistical information of the target scattering object. Both rigorous theoretical analysis and extensive numerical experiments are conducted to validate the promising features of our method. [ABSTRACT FROM AUTHOR]

The space of discrete copulas admits a representation as a convex polytope, and this has been exploited in entropy-copula methods used in hydrology and climatology. In this paper, we focus on the class of component-wise convex copulas, i.e., ultramodular copulas, which describe the joint behavior of stochastically decreasing random vectors. We show that the family of ultramodular discrete copulas and its generalization to component-wise convex discrete quasi-copulas also admit representations as polytopes. In doing so, we draw connections to the Birkhoff polytope, the alternating sign matrix polytope, and their generalizations, thereby unifying and extending results on these polytopes from both the statistics and the discrete geometry literature. [ABSTRACT FROM AUTHOR]

Abstract Hypothesis testing for the proportionality of covariance matrices is a classical statistical problem and has been widely studied in the literature. However, there have been few treatments of this test in high-dimensional settings, especially for the case where the number of variables is larger than the sample size, despite high-dimensional statistical inference having recently received considerable attention. This paper studies hypothesis testing for the proportionality of two covariance matrices in the high-dimensional setting: m , n ≍ p δ for some δ ∈ (1 ∕ 2 , 1) , where m and n denote the sample sizes and p denotes the number of variables. A test statistic is proposed and its asymptotic distribution is derived under multivariate normality. The non-asymptotic performance of the proposed test procedure is numerically examined. [ABSTRACT FROM AUTHOR]

• Gamut mapping distortions cannot be evaluated effectively by grayscale metrics. • Unlike conventional distortions, gamut mapping also incorporate global distortions. • Quality assessment metrics can be used for benchmarking gamut mapping algorithms. Gamut mapping is a key technology to achieve high-quality cross-media color reproduction. To optimize a gamut mapping algorithm, an important step is to conduct an accurate evaluation of its psycho-visual performance. This paper presents an objective blind image quality assessment (BIQA) metric for gamut-mapped images based on natural scene statistics. Considering both the local and global aspects of distortions in gamut-mapped images, two categories of statistics are analyzed. Specifically, the local statistical features are used to portray structural and color distortions and features extracted from global statistics are utilized to characterize the naturalness of image. The proposed metric does not need ground truth quality scores for training, thus it is "completely" blind. Experimental results on three gamut mapping databases demonstrate that our method outperforms the state-of-the-art general-purpose BIQA models. To further validate its effectiveness, the proposed metric is applied for benchmarking GMAs as an application and achieves encouraging performance. [ABSTRACT FROM AUTHOR]

Highlights • A weighted edge-based level set method is proposed to better segment noisy image. • Introduce a weighted length coefficient by utilizing a normalized local entropy. • Propose a weighted regional coefficient based on local entropy and mean. • Propose a modified edge stop function using local entropy and standard deviation. • Experiments prove the robustness and effectiveness of our method against noise. Abstract Image segmentation plays a fundamental role in image processing. Active contour models have been widely used since they handle topological change easily and provide smooth contours. However, noise presents challenges for edge-based level set methods since it leads contours easily passing through objects or falling into local minima. In this paper, we propose a weighted edge-based level set method based on multi-local statistical information to better segment noisy images. Through analysing the deficiencies of constant length and regional coefficients and traditional edge stop function in noisy image segmentation, weighted length and regional coefficients and modified edge stop function are proposed to overcome their shortcomings, respectively. The weighted edge-based level set method is used to segment synthetic and real images that have added different types and levels of noise. The experiments indicate that our method provides higher segmentation accuracies and more accurate segmentation results, which demonstrate its effectiveness and robustness. [ABSTRACT FROM AUTHOR]

Abstract The threshold-free cluster enhancement (TFCE) approach integrates cluster information into voxel-wise statistical inference to enhance detectability of neuroimaging signal. Despite the significantly increased sensitivity, the application of TFCE is limited by several factors: (i) generalisation to data structures, like brain network connectivity data is not trivial, (ii) TFCE values are in an arbitrary unit, therefore, P-values can only be obtained by a computationally demanding permutation-test. Here, we introduce a probabilistic approach for TFCE (pTFCE), that gives a simple general framework for topology-based belief boosting. The core of pTFCE is a conditional probability, calculated based on Bayes' rule, from the probability of voxel intensity and the threshold-wise likelihood function of the measured cluster size. In this paper, we provide an estimation of these distributions based on Gaussian Random Field theory. The conditional probabilities are then aggregated across cluster-forming thresholds by a novel incremental aggregation method. pTFCE is validated on simulated and real fMRI data. The results suggest that pTFCE is more robust to various ground truth shapes and provides a stricter control over cluster "leaking" than TFCE and, in many realistic cases, further improves its sensitivity. Correction for multiple comparisons can be trivially performed on the enhanced P-values, without the need for permutation testing, thus pTFCE is well-suitable for the improvement of statistical inference in any neuroimaging workflow. Implementation of pTFCE is available at https://spisakt.github.io/pTFCE. Graphical abstract Image 1 Highlights • PTFCE is a generalized probabilistic approach for threshold-free cluster enhancement (TFCE). • PTFCE overcomes the limitations of cluster inference. • The method is robust to the cluster topology and provides a strict control over false positives. • Enhanced p-values can trivially be corrected for multiple comparisons, without permutation test. • easy to integrate into any neuroimaging analysis workflow. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we consider the rotating charged Gödel black hole and study the effect of the higher order corrections of the entropy on the thermodynamics and statistics quantities of the Kerr–Newman–Gödel black hole. The leading order correction is logarithmic while higher-order terms are proportional to the inverse of the area of the black hole. We obtain modified thermodynamics and statistics and find that correction terms are important in the stability of the black hole. [ABSTRACT FROM AUTHOR]

Classification of crop species is an actively studied topic in remote sensing using multispectral image sensors. Unfortunately, the spectral bands available in the multispectral imagery are broad and limited in number to classify the crop species. In this paper, we propose optimal spectral bands to classify Allium (garlic and onion) and Brassicaceae (Chinese cabbage and radish) by using higher-dimensional data from hyperspectral imagery. A decision-tree classifier was used to determine the optimal method to use the high-dimensional data. The high-dimensional data were analysed for all growth stages and considering bandwidths with different full width at half maximum (FWHM) values at 25, 40, 50 and 80 nm. The spectral bands selected for Allium were differentiated into green, blue, and NIR bands for each growth stage. The results show that Allium can be classified clearly as overall accuracy (OA) 1 and kappa coefficient 1 for all FWHM based on March 22 data. For each April 19 and May 12 data, the decision-tree classifier with each 80 nm FWHM and 50 nm FWHM yielded a better classification accuracy of more than OA 0.921 and kappa coefficient 0.839 than other FWHM. The spectral bands selected for Brassicaceae were found to be similar to blue band for all growth stages. Brassicaceae was classified clearly for all FWHM based on October 27 data. Also, Brassicaceae was classified clearly for 25 nm FWHM based on November 25 data and OA, kappa coefficient for 40 nm FWHM and 50 nm FWHM are high as 0.974, 0.947 respectively. Highlights • We propose commercial band pass filters to identify Allium and Brassicaceae. • Decision-tree classifier based on hyperspectral data selects the spectral filters. • Hyperspectral data analysed depending on growth stages and different filter bandwidth. • Allium is efficiently classified in Green, Blue and NIR bands for each growth stage. • Brassicaceae is classified in Blue bands throughout all growth stages. [ABSTRACT FROM AUTHOR]

The partially linear model (PLM) is a useful semiparametric extension of the linear model that has been well studied in the statistical literature. This paper proposes a variable selection procedure for the PLM with ultrahigh dimensional predictors. The proposed method is different from the existing penalized least squares procedure in that it relies on partial correlation between the partial residuals of the response and the predictors. We systematically study the theoretical properties of the proposed procedure and prove its model consistency property. We further establish the root- n convergence of the estimator of the regression coefficients and the asymptotic normality of the estimate of the baseline function. We conduct Monte Carlo simulations to examine the finite-sample performance of the proposed procedure and illustrate the proposed method with a real data example. [ABSTRACT FROM AUTHOR]

This paper examines the secondary data requirements for multilevel small area synthetic estimation (ML-SASE). This research method uses secondary survey data sets as source data for statistical models. The parameters of these models are used to generate data for small areas. The paper assesses the impact of knowing the geographical location of survey respondents on the accuracy of estimates, moving beyond debating the generic merits of geocoded social survey datasets to examine quantitatively the hypothesis that knowing the approximate location of respondents can improve the accuracy of the resultant estimates. Four sets of synthetic estimates are generated to predict expected levels of limiting long term illnesses using different levels of knowledge about respondent location. The estimates were compared to comprehensive census data on limiting long term illness (LLTI). Estimates based on fully geocoded data were more accurate than estimates based on data that did not include geocodes. [ABSTRACT FROM AUTHOR]

Accurate identification of moving load is one of the main tasks in the field of bridge health monitoring. Due to the uncertainty in practical bridge, moving load identified via deterministic method is bound to be inconsistent with reality. As statistical information on the uncertain parameters is usually limited for actual bridges, this paper proposes a time-domain moving load identification method considering the uncertainty in the finite element model. Firstly, the moving load identification is divided into nominal value and interval radius identification. Then the deterministic methods based on shape function and second-order interval analysis are presented to identify the nominal value and interval radius, respectively. Finally, the effectiveness and superiority of the proposed method are verified through numerical and experimental examples, and the influence of the measurement point number, measurement noise, and vehicle velocity is investigated. The outcomes indicate that the results obtained by the deterministic method may deviate seriously from the actual one, and the calculation efficiency can be enhanced markedly compared with the probability method. The identification accuracy of the proposed method is higher than that of the first-order method at the same computational cost. [ABSTRACT FROM AUTHOR]

Let N T (m , k , n) denote the total number of parts in the partitions of n with rank congruent to m modulo k. Andrews recently provided a q -series proof of congruences for N T (m , k , n) modulo 5 and 7. In this paper, we establish congruences for N T (m , k , n) modulo powers of primes ℓ ≥ 7. Our proof utilizes the Hecke operators. [ABSTRACT FROM AUTHOR]

This paper aims to present the various contributions to the Special Issue of the Journal of Multivariate Analysis on Functional Data Analysis and some related topics including High-Dimensional Statistics and Multivariate Analysis of complex data. The presentation is made by emphasizing on how the contributions are behaving among recent trends in the fields, in such a way that this paper can also be viewed as a selected bibliographical discussion about recent advances in these topics. [ABSTRACT FROM AUTHOR]

Since the early work of Richard Stanley, it has been observed that several permutation statistics have a remarkable property with respect to shuffles of permutations. We formalize this notion of a shuffle-compatible permutation statistic and introduce the shuffle algebra of a shuffle-compatible permutation statistic, which encodes the distribution of the statistic over shuffles of permutations. This paper develops a theory of shuffle-compatibility for descent statistics—statistics that depend only on the descent set and length—which has close connections to the theory of P -partitions, quasisymmetric functions, and noncommutative symmetric functions. We use our framework to prove that many descent statistics are shuffle-compatible and to give explicit descriptions of their shuffle algebras, thus unifying past results of Stanley, Gessel, Stembridge, Aguiar–Bergeron–Nyman, and Petersen. [ABSTRACT FROM AUTHOR]

In this paper, we study common fixed point properties for a family of mappings. We present the extensions of Caristi's fixed point theorem and Markov–Kakutani fixed point theorem for a family of set-valued mappings. [ABSTRACT FROM AUTHOR]

Perspective functions arise explicitly or implicitly in various forms in applied mathematics and in statistical data analysis. To date, no systematic strategy is available to solve the associated, typically nonsmooth, optimization problems. In this paper, we fill this gap by showing that proximal methods provide an efficient framework to model and solve problems involving perspective functions. We study the construction of the proximity operator of a perspective function under general assumptions and present important instances in which the proximity operator can be computed explicitly or via straightforward numerical operations. These results constitute central building blocks in the design of proximal optimization algorithms. We showcase the versatility of the framework by designing novel proximal algorithms for state-of-the-art regression and variable selection schemes in high-dimensional statistics. [ABSTRACT FROM AUTHOR]

• A Bayesian Maximum Entropy (BME) framework is developed for imprecise probabilistic model with both measurement data and statistic information. • Heterogeneous datasets are integrated in a comprehensive framework for stochastic model updating. • The approximate Bayesian computation is employed to expedite the updating process. • A novel Wasserstein distance-based uncertainty quantification metric is developed to effectively capture higher order moment information. The presence of summarized statistical information, such as some statistics of the system response, is not rare in practical engineering as the acquisition of precisely measured point data is expensive and may not be always accessible. In this paper, we integrate the Bayesian framework with the maximum entropy theory and develop a Bayesian Maximum Entropy (BME) approach for model updating in a scenario where measurement data and statistical information are simultaneously available. Within the scope of this contribution, it is assumed that measurement data denote direct observations, e.g. point data, representing system response measurements while statistical information involves summarized information, e.g. moment and/or reliability information, of the system response. The basic principle of our approach is to convert point data and various statistical information into constraints under the BME framework and use the method of Lagrange multipliers to find the optimal posterior distributions. We then extend this approach to imprecise probabilistic models which have not been addressed so far. The approximate Bayesian computation is employed to facilitate the estimation of cumbersome likelihood functions which results from the involvement of entropy terms accounting for statistical information. Furthermore, a Wasserstein distance-based metric is proposed and embedded into the framework to capture the divergence information in an effective and efficient way. The effectiveness of the proposed approach is verified by a numerical case of simply supported beam and an engineering problem of fatigue crack growth. It shows some promising aspects of this research as better calibration results are produced with less uncertainty, and hence potential of our approach for engineering applications. [ABSTRACT FROM AUTHOR]

This paper proposes a novel hybrid physics-data-driven framework for system modelling by integrating a physical model and an online learning data model to improve model accuracy, interpretability, and generalization. Taking an in-wheel Motor Driven Vehicle (IMDV) as an example, two hybrid representations, i.e. the Dynamic Linearization Data Model (DLDM) and Recurrent High-Order Neural Network (RHONN) are introduced for the planar dynamics modelling of the electric vehicle. However, it is difficult to obtain the statistical information of the operation process and measurement noise when the weight vectors of the data-driven model is updated online. To address this issue, a H ∞ -based learning algorithm is adopted. The stability and convergence rate are elaborated and compared with an existing Extended Kalman Filter (EKF)-based method. Finally, we compare four methods, including the physics-based, data-based and two hybrid models, to evaluate their performances of modelling the IMDV's dynamics. The feasibility test and comparison studies are conducted in simulations and on a Hardware-in-the-Loop (HiL) test rig. The results demonstrated that the proposed H ∞ -based hybrid method, which does not make any assumption on measurement noise, has better generalization ability and robustness in practical implementations, compared to other baseline methods. • A novel hybrid physics-data-driven framework for system online modelling is proposed. • The data-driven online modelling can adapt to the fast dynamics of vehicle systems. • H ∞ -based learning shows fast convergency and robustness for parameter identification. [ABSTRACT FROM AUTHOR]

Abstract: Recently Lao and Mayer (2008) considered -max-statistics, where the maximum of kernels over the set of indices is studied instead of the usual sums. Such statistics emerge frequently in stochastic geometry. The examples include the largest distance between random points in a ball, the maximal diameter of a random polygon, the largest scalar product within a sample of points, etc. Their limit distributions are related to the distributions of extreme values. Among the results obtained by Lao and Mayer, the limit theorems for the maximal perimeter and the maximal area of random triangles inscribed in a circumference are of great interest. In the present paper, we generalize these theorems to the case of convex -polygons, , with random vertices on the circumference. In addition, a similar problem for the minimal perimeter and the minimal area of circumscribed -polygons is solved in this paper. This problem has not been studied in the literature so far. [Copyright &y& Elsevier]

Abstract: This paper develops a novel full analytic model for vibration analysis of solid-state electronic components. The model is just as accurate as finite element models and numerically light enough to permit for quick design trade-offs and statistical analysis. The paper shows the development of the model, comparison to finite elements and an application to a common engineering problem. A gull-wing flat pack component was selected as the benchmark test case, although the presented methodology is applicable to a wide range of component packages. Results showed very good agreement between the presented method and finite elements and demonstrated the usefulness of the method in how to use standard test data for a general application. [Copyright &y& Elsevier]

Permutation statistics w m ¯ and rlm are both arising from permutation tableaux. w m ¯ was introduced by Chen and Zhou, which was proved equally distributed with the number of unrestricted rows of a permutation tableau. While rlm is shown by Nadeau equally distributed with the number of 1's in the first row of a permutation tableau. In this paper, we investigate the joint distribution of w m ¯ and rlm. Statistic (rlm, w m ¯ , rlmin, des, (321)) is shown equally distributed with (rlm, rlmin, w m ¯ , des, (321)) on S n. Then the generating function of (rlm, w m ¯) follows. An involution is constructed to explain the symmetric property of the generating function. Also, we study the triple statistic (w m ¯ , rlm, asc), which is shown to be equally distributed with (rlmax − 1, rlmin, asc) as studied by Josuat-Vergès. The main method we adopt throughout the paper is constructing bijections based on a block decomposition of permutations. [ABSTRACT FROM AUTHOR]

Time series data are popular in environmental epidemiology as they make use of the natural experiment of how changes in exposure over time might impact on disease. Many published time series papers have used parameter-heavy models that fully explained the second order patterns in disease to give residuals that have no short-term autocorrelation or seasonality. This is often achieved by including predictors of past disease counts (autoregression) or seasonal splines with many degrees of freedom. These approaches give great residuals, but add little to our understanding of cause and effect. We argue that modelling approaches should rely more on good epidemiology and less on statistical tests. This includes thinking about causal pathways, making potential confounders explicit, fitting a limited number of models, and not over-fitting at the cost of under-estimating the true association between exposure and disease. [ABSTRACT FROM AUTHOR]

Abstract: Text: One of the most important statistics in studying the zeros of L-functions is the 1-level density, which measures the concentration of zeros near the central point. Fouvry and Iwaniec (2003) proved that the 1-level density for L-functions attached to imaginary quadratic fields agrees with results predicted by random matrix theory. In this paper, we show a similar agreement with random matrix theory occurring in more general sequences of number fields. We first show that the main term agrees with random matrix theory, and similar to all other families studied to date, is independent of the arithmetic of the fields. We then derive the first lower order term of the 1-level density, and see the arithmetic enter. Video: For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=zpb-gu3G8i0. [Copyright &y& Elsevier]

In Part I of this study, some new theorems, corollaries and lemmas on circularly-symmetric complex normal ratio distribution have been mathematically proved. This part II paper is dedicated to providing a rigorous treatment of statistical properties of raw scalar transmissibility functions at an arbitrary frequency line. On the basis of statistics of raw FFT coefficients and circularly-symmetric complex normal ratio distribution, explicit closed-form probabilistic models are established for both multivariate and univariate scalar transmissibility functions. Also, remarks on the independence of transmissibility functions at different frequency lines and the shape of the probability density function (PDF) of univariate case are presented. The statistical structures of probabilistic models are concise, compact and easy-implemented with a low computational effort. They hold for general stationary vector processes, either Gaussian stochastic processes or non-Gaussian stochastic processes. The accuracy of proposed models is verified using numerical example as well as field test data of a high-rise building and a long-span cable-stayed bridge. This study yields new insights into the qualitative analysis of the uncertainty of scalar transmissibility functions, which paves the way for developing new statistical methodologies for modal analysis, model updating or damage detection using responses only without input information. [ABSTRACT FROM AUTHOR]

In this paper, we draw attention to one unique and valuable source of big data, genomic data, by demonstrating the opportunities they provide to social scientists. We discuss different types of large-scale genomic data and recent advances in statistical methods and computational infrastructure used to address challenges in managing and analyzing such data. We highlight how these data and methods can be used to benefit social science research. [ABSTRACT FROM AUTHOR]

The reliability of a phylogenetic inference method from genomic sequence data is ensured by its statistical consistency. Bayesian inference methods produce a sample of phylogenetic trees from the posterior distribution given sequence data. Hence the question of statistical consistency of such methods is equivalent to the consistency of the summary of the sample. More generally, statistical consistency is ensured by the tree space used to analyse the sample. In this paper, we consider two standard parameterisations of phylogenetic time-trees used in evolutionary models: inter-coalescent interval lengths and absolute times of divergence events. For each of these parameterisations we introduce a natural metric space on ultrametric phylogenetic trees. We compare the introduced spaces with existing models of tree space and formulate several formal requirements that a metric space on phylogenetic trees must possess in order to be a satisfactory space for statistical analysis, and justify them. We show that only a few known constructions of the space of phylogenetic trees satisfy these requirements. However, our results suggest that these basic requirements are not enough to distinguish between the two metric spaces we introduce and that the choice between metric spaces requires additional properties to be considered. Particularly, that the summary tree minimising the square distance to the trees from the sample might be different for different parameterisations. This suggests that further fundamental insight is needed into the problem of statistical consistency of phylogenetic inference methods. [ABSTRACT FROM AUTHOR]

This study is designed to develop an acceleration response spectrum that can be used in vibration serviceability assessment of civil engineering structures, such as floors and grandstands those are dynamically excited by individual bouncing. The spectrum is derived from numerical simulations and statistical analysis of acceleration responses of a single degree of freedom system with variable natural frequency and damping under a large number of experimentally measured individual bouncing loads. Its mathematical representation is fit for fast yet reliable application in design practice and is comprised of three equations that describe three distinct frequency regions observed in the actual data: the first resonant plateau (2–3.5 Hz), the second resonant plateau (4–7 Hz) and a descension region (7–15 Hz). Finally, this paper verifies the proposed response spectrum approach to predict structural vibration by direct comparison against numerical simulations and experimental results. [ABSTRACT FROM AUTHOR]

A combined analysis method is developed in the present paper for studying the dynamic properties of a type of geometrically nonlinear vibration isolator, which is composed of push–pull configuration rings. This method combines the geometrically nonlinear theory of curved beams and the Harmonic Balance Method to overcome the difficulty in calculating the vibration and vibration transmissibility under large deformations of the ring structure. Using the proposed method, nonlinear dynamic behaviors of this isolator, such as the lock situation due to the coulomb damping and the usual jump resulting from the nonlinear stiffness, can be investigated. Numerical solutions based on the primary harmonic balance are first verified by direct integration results. Then, the whole procedure of this combined analysis method is demonstrated and validated by slowly sinusoidal sweeping experiments with different amplitudes of the base excitation. Both numerical and experimental results indicate that this type of isolator behaves as a hardening spring with increasing amplitude of the base excitation, which makes it suitable for isolating both steady-state vibrations and transient shocks. [ABSTRACT FROM AUTHOR]

It is well known that, in the presence of outliers, the single linkage algorithm generally fails to identify clusters. In this paper, we construct a new version of this algorithm, less sensitive to outliers, and study both its theoretical properties and its practical behavior. In particular, we provide an oracle-type inequality which guarantees that our procedure recovers clusters with high probability under mild assumptions on the distribution of the outliers. Using this inequality, we prove the consistency of our method and exhibit rates of convergence in various situations. The performance of this approach is also assessed through simulation studies. A thorough comparison with several classical clustering algorithms on simulated data is presented. [ABSTRACT FROM AUTHOR]