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Several efficient, but non-optimal, solutions to the Selection Problem on coarse grained parallel computers have appeared in the literature. We consider the example of the Saukas-Song algorithm; we analyze it without expressing the running time in terms of communication rounds. This shows that while in the best case the Saukas-Song algorithm runs in asymptotically optimal time, in general it does not. We propose another algorithm for coarse grained selection that has optimal expected running time. [ABSTRACT FROM AUTHOR]

The paper deals with local discrepancies in the problem of the distribution of the sequence , i.e., with the remainder terms in asymptotic formulas for the number of points in this sequence lying in prescribed intervals. A construction of intervals for which local discrepancies tend to infinity slower than any given function is presented. Moreover, it is shown that there exists an uncountable set of such intervals. Previously, similar results were obtained only for irrationalities with bounded partial quotients of their continued fraction expansions. [ABSTRACT FROM AUTHOR]

We review historically the position of Sir R.A. Fisher towards Bayesian inference and, particularly, the classical Bayes–Laplace paradigm. We focus on his Fiducial Argument.

This paper proposes a method to construct a one-dimensional discrete chaotic system. First, we define a generalized distance function to control the boundedness of the one-dimensional discrete system. Based on Marotto’s theorem, one-dimensional discrete systems are proven to be chaotic in the sense of Li–Yorke, and the corresponding chaos criterion theorem is proposed. The system can be distributed uniformly by adjusting the parameters. In this paper, we propose an image encryption scheme based on a uniformly distributed discrete chaotic system and DNA encoding. DNA encoding and decoding rules are determined by plain text. The experimental results demonstrate that our encryption algorithm has a large key space, high key sensitivity, and fast encryption speed and can resist differential and statistical attacks.

In this brief, we study the impact of input data distribution on temporal approximation (TA) in floating point units (FPUs). In TA, rather than performing computations, prior computed results are used as output to introduce approximation. Thus, temporal locality of inputs plays an important role in TA. We show that efficacy of TA is strongly dependent on the input data distribution. While in prior works, uniform random input data distribution is used to perform the worst case analysis in approximate FPUs, it fails to capture the worst case for TA. We show that contrary to conventional idea, input data samples from normal distribution with mean ($\mu $) equal to zero captures the worst case for TA irrespective of the FP operations. We evaluated TA in FP multipliers and FP dividers by studying four different data distributions: a) Normal Distribution ($\mu =0$) b) Normal Distribution ($\mu =1$) c) Uniform Distribution d) Power Law Distribution. The inputs generated by sampling from these distributions were applied to algorithms– dot product, principal component analysis, page rank, vector normalizations, and dot divide. On average, normal distribution ($\mu =0$) is more efficient in capturing the worst case as compared to the widely used uniform distribution by 8% and 12% in for FP multiplier and FP dividers respectively. We also highlight that prior knowledge of input data distribution can be exploited to reduce power delay product. [ABSTRACT FROM AUTHOR]

Chaotic maps are found to be a promising external entropy source for image encryption. However, many existing chaotic systems have relatively narrow parameter space and cannot generate uniformly distributed sequences, which may reduce the reliability of cryptosystem. In this paper, a novel chaotification model named as UCS is proposed to improve the statistical property and expand the parameter range of existing maps. The new chaotic maps generated from UCS exhibit more complex chaotic behaviors than seed maps, and the two independent parameters can take almost any value in R 2 . Moreover, the iterated chaotic sequences are approximately uniformly distributed and thus have better randomness. Based on the improved chaotic maps, a new image encryption algorithm is designed, which encodes digital images by derangement-based confusion, row–column bidirectional diffusion and 2D zigzag diffusion. Experimental results indicate the high performance of the proposed image encryption scheme, since it has obtained excellent results in various tests when compared with several existing methods. [ABSTRACT FROM AUTHOR]

The research objective of this paper is to handle situations where the empirical distribution of multivariate real-valued data is elliptical and with heavy tails. Many statistical models already exist that accommodate these peculiarities. This paper enriches this branch of literature by introducing the multivariate tail-inflated normal (MTIN) distribution, an elliptical heavy tails generalization of the multivariate normal (MN). The MTIN belongs to the family of MN scale mixtures by choosing a convenient continuous uniform as mixing distribution. Moreover, it has a closed-form for the probability density function characterized by only one additional 'inflation' parameter, with respect to the nested MN, governing the tail-weight. The moment generating function, and the first four moments, are also derived; interestingly, the latter always exist and the excess kurtosis can assume any positive value. The method of moments and maximum likelihood (ML) are considered for estimation. As concerns the latter, a direct approach, as well as a variant of the EM algorithm (namely, the ECME algorithm), are illustrated. Furthermore, a way to approximate covariance matrix of the ML estimator is suggested and the existence of the ML estimates is evaluated. Since the inflation parameter is estimated from the data, robust estimates of the mean vector of the nested MN distribution are automatically obtained by down-weighting. Simulations are performed to compare the estimation methods/algorithms, to investigate the ability of AIC and BIC to select among a set of candidate elliptical models, and to evaluate the robustness of these candidate methods when data are skewed. The findings are the following: ML is better than MM, direct ML is suggested for low dimensions, while the ECME algorithm is to be preferred when the number of variables is higher, AIC and BIC work comparably in selecting the true underlying model, and the MTIN outperforms the competing models in terms of robustness toward skew data. For illustrative purposes, the MTIN distribution is finally fitted to multivariate financial data and compared with other well-established multivariate elliptical distributions. The analysis shows how the proposed model represents a valid alternative to the considered competitors in terms of AIC and BIC, but also in reproducing the higher empirical kurtosis which is common in the financial context. [ABSTRACT FROM AUTHOR]

In this paper, first we have defined a uniform distribution on the boundary of a regular hexagon and then investigate the optimal sets of n-means and the nth quantization errors for all positive integers n. We give an exact formula to determine them, if n is of the form n = 6 k for some positive integer k. We further calculate the quantization dimension, the quantization coefficient, and show that the quantization dimension is equal to the dimension of the object, and the quantization coefficient exists as a finite positive number. Then, we define a mixture of two uniform distributions on the boundary of a semicircular disc and obtain a sequence and an algorithm, with the help of which we determine the optimal sets of n-means and the nth quantization errors for all positive integers n with respect to the mixed distribution. Finally, for a uniform distribution defined on an elliptical curve, we investigate the optimal sets of n-means and the nth quantization errors for all positive integers n. [ABSTRACT FROM AUTHOR]

To deal with the uncertain relationship between random variables and harmonic spectrum in existing random pulsewidth modulation (PWM), this article links the uniformly distributed random carrier sequence probabilistic parameters with harmonic distributed in the frequency domain, offers an approach to selecting a random carrier sequence. Based on random slope PWM, the formula for 3-dB bandwidth of harmonic power spectrum is deduced. Then, some useful conclusions are also drawn under random carrier sequence obeying uniform distribution. The 3-dB bandwidth formula leads to a method of selecting the main probability statistical parameters. The method has laid a theoretical foundation for the design and selection of random variables in random PWM, provided a scientific reference for the study of random PWM technology, which is used to reduce electromagnetic interference and mechanical vibration. [ABSTRACT FROM AUTHOR]

Aiming at the problems of low efficiency, large error and weak anti-noise ability in point cloud registration, this paper proposed an improved iterative closest point registration algorithm based on t test (test-iterative closest point, T-ICP). In initial registration, this paper used statistical analysis to mark outliers in point cloud and extracted non-outliers. Then, it used principal component analysis (PCA) to calculate the transformation matrix between the non-outlier source point cloud and the non-outlier target point cloud, and the transformation matrix could transform source point cloud to target point cloud. In fine registration, this paper used iterative closest point (ICP) algorithm as the basic framework and introduced t test and uniform distribution. Test could analyze the neighborhood distance distribution of candidate point pairs and eliminate wrong point pairs. Uniform distribution as the strategy of searching point pairs could ensure complete morphological registration of point cloud. Experimental results show that the proposed algorithm improves the efficiency and accuracy by 10% ~ 50% and 4% ~ 40%, respectively, and has better robustness, compared with ICP and some improved registration algorithms in the last two years. [ABSTRACT FROM AUTHOR]

In this paper, we show that for a twice differentiable function g having countable zeros and for Lebesgue almost every β > 1 , the sequence (e 2 π i β n g (β) ) n ∈ N is orthogonal to all topological dynamical systems of zero entropy. To this end, we define the Chowla property and the Sarnak property for numerical sequences taking values 0 or complex numbers of modulus 1. We prove that the Chowla property implies the Sarnak property and show that for Lebesgue almost every β > 1 , the sequence (e 2 π i β n ) n ∈ N shares the Chowla property. It is also discussed whether the samples of a given random sequence have the Chowla property almost surely. Some dependent random sequences having almost surely the Chowla property are constructed. [ABSTRACT FROM AUTHOR]

Intrusion detection is a very sensitive and major concern in wireless sensor networks. In border areas, sensors are installed to discover the presence of enemies or any trace passing in a prohibited area or any vicious moving object in the region of interest. In order to gain access to a region of interest, an intruder can take various paths, i.e., it can move along a straight line, follow a zigzag path or a curved path and move at a particular angle to cross the region without being detected and to improve its attacking ability. This paper formulates and analyzes κ -barrier coverage probability which acts as the intrusion detection probability for an intruder when the intruder follows different paths at different path angles with respect to the shortest path to cross the region of interest in a mobile sensor network. Furthermore, the effect of different network variables such as node density, sensing range, intrusion path angle and the ratio of sensor to intruder velocity on intrusion detection probability are also investigated. It is believed that the proposed model renders an effective tool to incorporate the intruder's movement pattern in the design of an advanced finite wireless sensor network. [ABSTRACT FROM AUTHOR]

Introduction. The arrears of buyers for the goods (goods), services rendered or works delivered are the largest component of the receivables at the enterprise, therefore sometimes there are cases of non-repayment by the buyers of their obligations. In order to avoid the negative impact of writing off bad debts of buyers to the financial position of the entity, entities may create a reserve for doubtful debts. Purpose. The purpose of the article is to consider issues related to creating a reserve of doubtful debts and its impact on the formation of costs and financial results of the enterprise. Results. Doubtful debts are current receivables, about which there is uncertainty about its repayment by the debtor. Such an indebtedness can turn into a hopeless one, that is, on which there is confidence in its non-returning to the debtor or beyond which the limitation period expired. There is a need to write off such a bad debt, which will increase the cost of the enterprise. In order to even write down bad debts, there is a need to create a reserve of doubtful debts. Due to such a provision, depreciation of the negative impact of write-off of bad debts on the financial results of the enterprise is carried out. For the purpose of even distribution over time during the reporting year, the amount of the calculated reserve of doubtful debts is expedient for the monthly deduction of 1/12 of the calculated amount of the provision. At the end of the reporting year, that is, in December, the company will receive the necessary amount of the reserve of doubtful debts, which will allow the write-off in his account of bad debts without a negative impact on the expenses of the activity. Conclusions. Since receivables from buyers are a financial asset of an enterprise in accordance with international accounting standards, it should be measured at amortized cost. Creation of amortized cost of accounts receivable should be gradual, which involves the distribution of the calculated amount of the reserve evenly in time through the monthly deduction of it for the costs of activities. The gradual formation of the reserve of doubtful debts minimizes the negative impact of the costs of its creation on the financial performance of the enterprise.

Abstract Background Melanoma is the deadliest type of skin cancer with highest mortality rate. However, the annihilation in its early stage implies a high survival rate therefore, it demands early diagnosis. The accustomed diagnosis methods are costly and cumbersome due to the involvement of experienced experts as well as the requirements for the highly equipped environment. The recent advancements in computerized solutions for this diagnosis are highly promising with improved accuracy and efficiency. Methods In this article, a method for the identification and classification of the lesion based on probabilistic distribution and best features selection is proposed. The probabilistic distribution such as normal distribution and uniform distribution are implemented for segmentation of lesion in the dermoscopic images. Then multi-level features are extracted and parallel strategy is performed for fusion. A novel entropy-based method with the combination of Bhattacharyya distance and variance are calculated for the selection of best features. Only selected features are classified using multi-class support vector machine, which is selected as a base classifier. Results The proposed method is validated on three publicly available datasets such as PH2, ISIC (i.e. ISIC MSK-2 and ISIC UDA), and Combined (ISBI 2016 and ISBI 2017), including multi-resolution RGB images and achieved accuracy of 97.5%, 97.75%, and 93.2%, respectively. Conclusion The base classifier performs significantly better on proposed features fusion and selection method as compared to other methods in terms of sensitivity, specificity, and accuracy. Furthermore, the presented method achieved satisfactory segmentation results on selected datasets.

One of the major issues with pulsewidth modulation (PWM) is that considerable conducted emissions will be generated from power electronics converters. Random modulations are considered one of the viable solutions to reduce conducted electromagnetic interference (EMI) without adding bulky passive filtering components. Literature that investigates the application of such techniques in active front end (AFE) drives is limited. In this article, a novel random switching frequency PWM (RSF-PWM) is proposed for a grid-tied AFE drive to suppress conducted emissions. The statistical behavior of switching frequency is based on uniform distribution. Simulation and experiments are carried out on a 10-hp AFE drive. Results demonstrate that the proposed RSF-PWM can effectively reduce conducted EMI by approximately 20 dB within low-frequency range, compared with conventional constant switching frequency PWM. [ABSTRACT FROM AUTHOR]

We introduce the notion of uniform distribution on a metric compactum. The desired distribution is defined as the limit of a sequence of the classical uniform distributions on finite sets which are uniformly distributed on the compactum in the geometric sense. We show that a uniform distribution exists on the metrically homogeneous compacta and the canonically closed subsets of a Euclidean space whose boundary has Lebesgue measure zero. If a compactum (satisfying some metric constraints) admits a uniform distribution then so does its every canonically closed subset that has zero uniform measure of the boundary. We prove that compacta, admitting a uniform distribution, are dimensionally homogeneous in the sense of box-dimension. [ABSTRACT FROM AUTHOR]

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In simple step-stress models based on exponential distributions, the distributions of the MLEs are commonly obtained using the moment generating function. In this paper, we propose an alternative method, the so-called expected value approach, introduced in Górny (2017) to derive the exact distribution of the MLEs. Moreover, we discuss the benefits of this technique. Further, assuming uniformly distributed lifetimes, we show that the MLEs are also explicitly available and that their distributions are discrete for both the cumulative exposure and the tampered failure rate model. Additionally, we illustrate that confidence regions as well as confidence intervals can be established utilizing a connection to the multinomial distribution. The results are illustrated by an illustrative example as well as simulation results. [ABSTRACT FROM AUTHOR]

In this paper we study hyperuniformity on flat tori. Hyperuniform point sets on the unit sphere have been studied by J. Brauchart, P. Grabner, W. Kusner and J. Ziefle. It is shown that point sets which are hyperuniform for large balls, small balls, or balls of threshold order on the flat tori are uniformly distributed. Moreover, it is also shown that QMC-designs sequences for Sobolev classes, probabilistic point sets (obtained from jittered samplings), and some determinantal point process are hyperuniform. [ABSTRACT FROM AUTHOR]

We consider certain finite sets of circle-valued functions defined on intervals of real numbers and estimate how large the intervals must be for the values of these functions to be uniformly distributed in an approximate way. This is used to establish some general conditions under which a random construction introduced by Katznelson for the integers yields sets that are dense in the Bohr group. We obtain in this way very sparse sets of real numbers (and of integers) on which two different almost periodic functions cannot agree, which makes them amenable to be used in sampling theorems for these functions. These sets can be made as sparse as to have zero asymptotic density or as to be t-sets, i.e., to be sets that intersect any of their translates in a bounded set. Many of these results are proved not only for almost periodic functions but also for classes of functions generated by more general complex exponential functions, including chirps or polynomial phase functions. [ABSTRACT FROM AUTHOR]

Let (f n) n = 1 ∞ be a sequence of polynomials and α > 1. In this paper we study the distribution of the sequence (f n (α)) n = 1 ∞ modulo one. We give sufficient conditions for a sequence (f n) n = 1 ∞ to ensure that for Lebesgue almost every α > 1 the sequence (f n (α)) n = 1 ∞ has Poissonian pair correlations. In particular, this result implies that for Lebesgue almost every α > 1 , for any k ≥ 2 the sequence (α n k ) n = 1 ∞ has Poissonian pair correlations. [ABSTRACT FROM AUTHOR]

A crude Monte Carlo (MC) method allows to calculate integrals over a d-dimensional cube. As the number N of integration nodes becomes large, the rate of probable error of the MC method decreases as O ⁢ (1 / N) {O(1/\sqrt{N})}. The use of quasi-random points instead of random points in the MC algorithm converts it to the quasi-Monte Carlo (QMC) method. The asymptotic error estimate of QMC integration of d-dimensional functions contains a multiplier 1 / N {1/N}. However, the multiplier (ln ⁡ N) d {(\ln N)^{d}} is also a part of the error estimate, which makes it virtually useless. We have proved that, in the general case, the QMC error estimate is not limited to the factor 1 / N {1/N}. However, our numerical experiments show that using quasi-random points of Sobol sequences with N = 2 m {N=2^{m}} with natural m makes the integration error approximately proportional to 1 / N {1/N}. In our numerical experiments, d ≤ 15 {d\leq 15} , and we used N ≤ 2 40 {N\leq 2^{40}} points generated by the SOBOLSEQ16384 code published in 2011. In this code, d ≤ 2 14 {d\leq 2^{14}} and N ≤ 2 63 {N\leq 2^{63}}. [ABSTRACT FROM AUTHOR]

In this paper we consider the problem of estimating the support of a uniform distribution under symmetric additive errors. The maximum likelihood (ML) estimator is of our primary interest, but we also analyze the method of moments (MM) estimator, when it exists. Under some regularity conditions, the ML estimator is consistent and asymptotically efficient. Errors with Student's t-distribution are shown to be a good choice for robustness issues. [ABSTRACT FROM AUTHOR]

A number of practically important imaging problems involve inverting the generalized Radon transform (GRT) R of a function f in ℝ³. On the other hand, not much is known about the spatial resolution of the reconstruction from discretized data. In this paper we study how accurately and with what resolution the singularities of f are reconstructed. The GRT integrates over a fairly general family of surfaces Sy in ℝ³. Here y is the parameter in the data space, which runs over an open set V ⊂ ℝ³. Assume that the data g(y) = (Rf)(y) are known on a regular grid yj with step-sizes O(ε) along each axis, and suppose S = singsupp(f) is a piecewise smooth surface. Let fε denote the result of reconstruction from the discrete data. We obtain explicitly the leading singular behavior of fε in an O(ε)-neighborhood of a generic point x0 ∈ S, where f has a jump discontinuity. We also prove that under some generic conditions on S (which include, e.g., a restriction on the order of tangency of Sy and S), the singularities of f do not lead to nonlocal artifacts. For both computations, a connection with the uniform distribution theory turns out to be important. Finally, we present a numerical experiment, which demonstrates a good match between the theoretically predicted behavior and actual reconstruction. [ABSTRACT FROM AUTHOR]

It is necessary to suppress the emission level of conducted electromagnetic interference (EMI) for the power electronics converters, and the variable switching frequency pulsewidth modulation (VSFPWM) is an alternative approach to reduce conducted EMI without adding bulky passive components. However, the experimental results indicate that many obvious EMI spikes in spectrum remain so that the conducted EMI reduction for VSFPWM is limited. In order to eliminate the EMI spikes in spectrum, this article first investigates the cause of the EMI spikes for VSFPWM, and the analysis results show that the nonuniform distribution of switching frequency is the primary reason. Then, a novel PWM strategy called uniform distribution PWM (UDPWM) is proposed to eliminate the EMI spikes and to further reduce conducted EMI. The design of a UDPWM is based on the uniform distribution of switching frequency and the principle of less switching loss. Moreover, the analytical formula of switching frequency is also deduced in detail, which adopts fixed variation range of switching frequency whatever the modulation index is. Finally, the experiments are carried out to validate the effectiveness of the UDPWM in reducing conducted EMI and switching loss. The UDPWM can approximately reduce conducted EMI by 20 dB compared with the conventional constant switching frequency PWM, and all obvious spikes in the spectrum are eliminated compared with VSFPWM. [ABSTRACT FROM AUTHOR]

Transmission, as a critical part of vehicles, is the hub of power transmission and the core of controlling speed change. Condition monitoring and diagnosis of transmissions have become an effective tool to ensure vehicle safety travelling. The intelligent fault diagnosis strategy using artificial intelligent methods has been studied and applied for gearbox fault diagnosis. However, most algorithms cannot guarantee both accuracy and training efficiency. In this paper, fast convolutional sparse filtering based on convolutional activation and feature normalization is proposed for gearbox fault diagnosis without any time-consuming preprocessing. In fast convolutional sparse filtering, the features of samples are optimized instead of local features, which could obviously reduce the dimension and construction time of the Hessian matrix. In addition, the output features are equally active to guarantee that all features have similar contributions. The l 2-norm of the training features is recorded and used for pseudo-normalization of the test features. The proposed fast convolutional sparse filtering is validated by a bearing fault dataset and a planetary gear fault dataset. Verification results confirm that fast convolutional sparse filtering is a promising tool for fault diagnosis, which has obviously improved the diagnosis accuracy, training efficiency, and robustness and provides the greater advantage of handling large-scale datasets. [ABSTRACT FROM AUTHOR]

In this study, stochastic vehicle routing problem (SVRP), which is one of the most important combinatorial optimization problems studied in the literature, is discussed. As it is known, the capacities of the vehicles and the demands of the customers are known in the classical vehicle routing problem, so the problem is deterministic. Since the problem parameters in real life problems vary according to the different situations, it is rare to know the exact values of the parameters. Therefore, there is a need to formulate the classical vehicle routing problem under uncertainty conditions. In this study, the vehicle routing problem is analyzed, and the demands are stochastically evaluated for the cases where customer demands are uncertain. In order to examine the variable demand conditions, the effects of these distributions on the solutions of the problem are investigated by using three different distributions, which are uniform, exponential, and Poisson. The GAMS software is used for computational results and the results of the stochastic and deterministic models of the problem are compared at the final part of the study. [ABSTRACT FROM AUTHOR]

Recently, A. S. Krishnan, S. M. Sunoj and N. U. Nair [Some reliability properties of extropy for residual and past lifetime random variables, J. Korean Stat. Soc. 2020, 10.1007/s42952-019-00023-x] introduced past extropy for measuring uncertainty contained in past lifetime of random variables. In the present study, we focus on the past extropy of k-records. The motivation for considering past extropy of k-records has been discussed in detail. We have also illustrated the merit of considering past extropy of k-records over past extropy of classical records and past extropy of original random sample using two real life data sets. Some important properties of past extropy of k-records are discussed in this work. We have expressed past extropy of k-records using past extropy of k-records arising from uniform distribution. The work proposes a simple estimator for past extropy of k-records as well. [ABSTRACT FROM AUTHOR]

Controllable synthesis of atomically ordered intermetallic nanoparticles (NPs) is crucial to obtain superior electrocatalytic performance for fuel cell reactions, but still remains arduous. Herein, we demonstrate a novel and general hydrogel‐freeze drying strategy for the synthesis of reduced graphene oxide (rGO) supported Pt3M (M=Mn, Cr, Fe, Co, etc.) intermetallic NPs (Pt3M/rGO‐HF) with ultrasmall particle size (about 3 nm) and dramatic monodispersity. The formation of hydrogel prevents the aggregation of graphene oxide and significantly promotes their excellent dispersion, while a freeze‐drying can retain the hydrogel derived three‐dimensionally (3D) porous structure and immobilize the metal precursors with defined atomic ratio on GO support during solvent sublimation, which is not afforded by traditional oven drying. The subsequent annealing process produces rGO supported ultrasmall ordered Pt3M intermetallic NPs (≈3 nm) due to confinement effect of 3D porous structure. Such Pt3M intermetallic NPs exhibit the smallest particle size among the reported ordered Pt‐based intermetallic catalysts. A detailed study of the synthesis of ordered intermetallic Pt3Mn/rGO catalyst is provided as an example of a generally applicable method. This study provides an economical and scalable route for the controlled synthesis of Pt‐based intermetallic catalysts, which can pave a way for the commercialization of fuel cell technologies. [ABSTRACT FROM AUTHOR]

We consider a special type of interval catch digraph (ICD) for one-dimensional data in a randomized setting and propose its use for testing uniformity. These ICDs are defined with expansion and centrality parameters, hence are called parameterized ICDs (PICDs). We derive the exact (and asymptotic) distribution of the domination number of this PICD when its vertices are from a uniform (and non-uniform) distribution in one dimension for the entire parameter ranges; thereby determine the parameters for which the asymptotic distribution is non-degenerate. We use the domination number for testing uniformity of one-dimensional data, prove its consistency against certain alternatives, and compare it with commonly used and recently proposed tests in literature and also arc density of two ICD families in terms of size and power. Based on our Monte Carlo simulations, we demonstrate that PICD domination number has higher power for certain types of alternatives compared to other tests. [ABSTRACT FROM AUTHOR]

A nonuniform vertical phase distribution and thick insulating barrier can decrease the energy transfer between slices in layered perovskite solar cells (PSCs). Herein, an interlayer cross‐linked Dion–Jacobson (DJ)‐type 2D PSC with 1,4‐butanediamine (BDA) as a short‐chain insulating spacer [formula: (BDA)MAn −1PbnI3n + 1] is reported and demonstrates the vertical phase becoming uniform with enhanced exciton coupling, leading to reduced nonradiative recombination. For n = 1 pure phase perovskite, an exciton binding energy of the DJ phase (BDA)PbI4 is ≈142 meV, much smaller than ≈435 meV of Ruddlesden–Popper (RP) phase (BA)2PbI4 (n = 1) perovskite, indicative of exciton‐coupling‐induced efficient energy transfer. Therefore, the high energy emission peaks for the (BDA)MA3Pb4I13 film are not observed even in liquid nitrogen temperature (78 K), which can be distinguished from that of the (BA)2MA3Pb4I13 film. Energy transfer between 2D slices of (BDA)MA3Pb4I13 is 100 times faster than that of (BA)2MA3Pb4I13. The uniform vertical distribution and exciton coupling mitigate nonradiative energy loss and significantly improve Voc in inverted structures (PEDOT:PSS/(BDA)MA3Pb4I13/PCBM/bathocuproine/Ag) to ≈1.15 V and the control n‐butylammonium‐based device demonstrates only a Voc = ≈1 V. It is believed that the results would provide a deep understanding of exciton coupling in hybrid multicomponent quantum wells. [ABSTRACT FROM AUTHOR]

Let (x n) n = 1 ∞ be a sequence on the torus T (normalized to length 1). A sequence (x n) is said to have Poissonian pair correlation if, for all s > 0 , lim N → ∞ ⁡ 1 N # { 1 ≤ m ≠ n ≤ N : | x m − x n | ≤ s N } = 2 s. It is known that this implies uniform distribution of the sequence (x n). Hinrichs, Kaltenböck, Larcher, Stockinger & Ullrich extended this result to higher dimensions and showed that sequences (x n) in [ 0 , 1 ] d that satisfy, for all s > 0 , lim N → ∞ ⁡ 1 N # { 1 ≤ m ≠ n ≤ N : ‖ x m − x n ‖ ∞ ≤ s N 1 / d } = (2 s) d are also uniformly distributed. We prove the same result for the extension by the Euclidean norm: if a sequence (x n) in T d satisfies, for all s > 0 , lim N → ∞ ⁡ 1 N # { 1 ≤ m ≠ n ≤ N : ‖ x m − x n ‖ 2 ≤ s N 1 / d } = ω d s d , where ω d is the volume of the unit ball, then (x n) is uniformly distributed. Our approach shows that Poissonian Pair Correlation implies an exponential sum estimate that resembles and implies the Weyl criterion. [ABSTRACT FROM AUTHOR]

We study the problem of constructing sequences (x n) n = 1 ∞ on [0, 1] in such a way that D N ∗ = sup 0 ≤ x ≤ 1 # 1 ≤ i ≤ N : x i ≤ x N - x is small. A result of Schmidt shows that for all sequences sequences (x n) n = 1 ∞ on [0, 1] we have D N ∗ ≳ (log N) N - 1 for infinitely many N, several classical constructions attain this growth. We describe a type of uniformly distributed sequence that seems to be completely novel: given x 1 , ⋯ , x N - 1 , we construct x N in a greedy manner x N = arg min min k | x - x k | ≥ N - 10 ∑ k = 1 N - 1 1 - log (2 sin (π | x - x k |)). We prove that D N ∗ ≲ (log N) N - 1 / 2 and conjecture that D N ∗ ≲ (log N) N - 1 . Numerical examples illustrate this conjecture in a very impressive manner. We also establish a discrepancy bound D N ∗ ≲ (log N) d N - 1 / 2 for an analogous construction in higher dimensions and conjecture it to be D N ∗ ≲ (log N) d N - 1 . [ABSTRACT FROM AUTHOR]

There is a probability charge on the power set of the integers that gives probability 1 / p to every residue class modulo a prime p. There exists such a charge that gives probability w to the set of prime numbers iff w ∈ [ 0 , 1 / 2 ] . Similarly, there is such a charge that gives probability x to a residue class modulo c, where c is composite, iff x ∈ [ 0 , 1 / y ] , where y is the largest prime factor of c. [ABSTRACT FROM AUTHOR]

Uncertainty is an inseparable part of all types of measurement. Recently, the International Organization for Standardization (ISO) released a new standard (ISO 20914) on how to calculate measurement uncertainty (MU) in laboratory medicine. This standard can be regarded as the beginning of a new era in laboratory medicine. Measurement uncertainty comprises various components and is used to calculate the total uncertainty. All components must be expressed in standard deviation (SD) and then combined. However, the characteristics of these components are not the same; some are expressed as SD, while others are expressed as a ± b, such as the purity of the reagents. All non-SD variables must be transformed into SD, which requires a detailed knowledge of common statistical distributions used in the calculation of MU. Here, the main statistical distributions used in MU calculation are briefly summarized. [ABSTRACT FROM AUTHOR]

Bloom Filter is a space-efficient probabilistic data structure for checking the membership of elements in a set. Given multiple sets, a standard Bloom Filter is not sufficient when looking for the items to which an element or a set of input elements belong. An example case is searching for documents with keywords in a large text corpus, which is essentially a multiple set matching problem where the input is single or multiple keywords, and the result is a set of possible candidate documents. This article solves the multiple set matching problem by proposing two efficient Bloom Multifilters called Bloom Matrix and Bloom Vector, which generalize the standard Bloom Filter. Both structures are space-efficient and answer queries with a set of identifiers for multiple set matching problems. The space efficiency can be optimized according to the distribution of labels among multiple sets: Uniform and Zipf. Bloom Vector efficiently exploits the Zipf distribution of data for further space reduction. Indeed, both structures are much more space-efficient compared with the state-of-the-art, Bloofi. The results also highlight that a Lookup operation on Bloom Matrix is significantly faster than on Bloom Vector and Bloofi. [ABSTRACT FROM AUTHOR]

We prove that, for given positive numbers α and h, the Riemann zeta-function ζ can approximate any nonvanishing analytic function on a simply connected compact subset of the right open half of the critical strip by shifts of type ζ(s + ih⌊αn⌋). [ABSTRACT FROM AUTHOR]

We consider a characteristic simultaneously reflecting certain properties of Riemann integrable functions f on the closed interval [0, 1] and properties of some sequence X = {xn} points on [0, 1]. The properties of functions are expressed by characteristics similar to the modulus of continuity, mean oscillation modulus, and the modulus of variation, while the properties of sequences are characterized by notions of maximal deviation and deviation in Lp. This characteristic is used to estimate the error RN(f, X) of the quadrature formula ∫ 0 1 f (x) d x = 1 N ∑ n = 1 N f (x n) − R N (f , X) and to formulate condition for the uniform distribution of number sequences and the Riemann integrability of functions. All of the obtained main estimates are extremal. [ABSTRACT FROM AUTHOR]

This article addresses a job-shop problem with limited output buffers (JS-LOB) with the objective of minimizing the process makespan. An integer nonlinear mathematical programming model is proposed to describe this problem. Based on the model, a two-stage algorithm consisting of obtaining feasible solutions and a local search is proposed to solve the JS-LOB problem. The local search has two operators: the first is a neighbourhood structure based on a disjunctive graph model, and the second is similar to crossover in the genetic algorithm to avoid falling into local optima. Computational results are presented for a set of benchmark tests. The results show the effectiveness of the proposed algorithm and indicate whether the processing time of the job conforms to a uniform distribution. When the proportion between the capacity of the buffer and the number of jobs is larger than 20%, the influence of the buffer becomes very small. [ABSTRACT FROM AUTHOR]

The Three Gap Theorem states that there are at most three distinct lengths of gaps if one places n points on a circle, at angles of z; 2z; : : : nz from the starting point. The theorem was first proven in 1958 by Sós and many proofs have been found since then. In this note we show how the Three Gap Theorem can easily be deduced by using Rauzy-Veech induction. [ABSTRACT FROM AUTHOR]

Given any minimal ring extension k ⊂ L of finite fields, several families of examples are constructed of a finite local (commutative unital) ring A which is not a field, with a (necessarily finite) inert (minimal ring) extension A ⊂ B (so that B is a separable A -algebra), such that A ⊂ B is not a Galois extension and the residue field of A (respectively, B) is k (respectively, L). These results refute an assertion of G. Ganske and McDonald stating that if R ⊆ S are finite local rings such that S is a separable R -algebra, then R ⊆ S is a Galois ring extension. We identify the homological error in the published proof of that assertion. Let (A , M) be a finite special principal ideal ring (SPIR), but not a field, such that M has index of nilpotency α (≥ 2). Impose the uniform distribution on the (finite) set of (A -algebra) isomorphism classes of the minimal ring extensions of A. If 2 ∈ M (for instance, if A ≅ ℤ / 2 α ℤ), the probability that a random isomorphism class consists of ramified extensions of A is at least 2 / 3 ; if 2 ∉ M (for instance, if A ≅ ℤ / p α ℤ for some odd prime p), the corresponding probability is at least 3 / 4. Additional applications, examples and historical remarks are given. [ABSTRACT FROM AUTHOR]

The purpose of this work is to develop a method for the hydraulic calculation of a heat exchange panel of a solar tube collector of a tube type with a given nonuniform distribution of fluid flow under conditions of forced circulation. On the basis of previously obtained design dependencies, a method of hydraulic calculation of a heat exchange panel of a solar thermal collector of a flat-plate type with a given uneven distribution of fluid flow under conditions of forced circulation has been developed. An example of calculation using the developed method is given. [ABSTRACT FROM AUTHOR]

This article considers a circular regression model for clustered data, where both the cluster effects and the regression errors have von Mises distributions. It involves β, a vector of parameters for the fixed effects, and two concentration parameters for the error distribution. A measure of intra‐cluster circular correlation and a predictor for an unobserved cluster random effect are studied. Preliminary estimators for the vector β and the two concentration parameters are proposed, and their performance is compared with that of the maximum likelihood estimators in a simulation study. A numerical example investigating the factors impacting the orientation taken by a sand hopper when released is presented. The Canadian Journal of Statistics 47: 712–728; 2019 © 2019 Statistical Society of Canada [ABSTRACT FROM AUTHOR]

It is known that discrete sets of uniformly distributed points on the hypersphere S d ⊂ ℝ d + 1 can be obtained from minimizing the energy functional corresponding to Riesz s-kernels k s (x , y) = ∥ x − y ∥ − s (s > 0) or the logarithmic kernel k log (x , y) = − log ∥ x − y ∥ + log 2 . We prove the same for the kernel k log (x , y) = ∥ x − y ∥ (log ∥ x − y ∥ 2 − 1) + 2 which is a front-extension of the sequence of derivatives k log , k 1 , k 2 , k 3 , ... , up to sign and constants. The boundedness of the kernel simplifies the classical potential-theoretical proof of the asymptotic uniformity of the point distributions. Still, the property of a singular derivative for x → y is preserved, with the physical interpretation of infinite repulsive forces for touching particles. The quality of the resulting point distributions is exemplary compared with that of Riesz- and classical logarithmic point sets, and found to be competitive. Originally motivated by problems of high-dimensional data, the applicability of log -optimal point sets with a novel concentric interpolation and differentiation scheme is demonstrated. The method is significantly optimized by the introduction of symmetrized kernels for both the generation of the minimum energy points and the spherical basis functions. Both the point generation and the Concentric Interpolation software are available as Open Source software and selected point sets are provided. [ABSTRACT FROM AUTHOR]

Recently a second directional derivative-based Hessian updating formula was used for Hessian approximation in mesh adaptive direct search (MADS). The approach combined with a quadratic program solver significantly improves the performance of MADS. Unfortunately it imposes some strict requirements on the position of points and the order in which they are evaluated. The subject of this paper is the introduction of a Hessian update formula that utilizes the points from the neighborhood of the incumbent solution without imposing such strict restrictions. The obtained approximate Hessian can then be used for constructing a quadratic model of the objective and the constraints. The proposed algorithm was compared to the reference implementation of MADS (NOMAD) on four sets of test problems. On all but one of them it outperformed NOMAD. The biggest performance difference was observed on constrained problems. To validate the algorithm further the approach was tested on several real-world optimization problems arising from yield approximation and worst case analysis in integrated circuit design. On all tested problems the proposed approach outperformed NOMAD. [ABSTRACT FROM AUTHOR]