A sketch for the KS test for Big Data

Motivated by the challenges of Big Data, this paper presents an approximative algorithm to assess the Kolmogorov-Smirnov test. This goodness of fit statistical test is extensively used because it is non-parametric. This work focuses on the one-sample test, which considers the hypothesis that a given univariate sample follows some reference distribution. The method allows to evaluate the departure from such a distribution of a input stream, being space and time efficient. We show the accuracy of our algorithm by making several experiments in different scenarios: varying reference distribution and its parameters, sample size, and available memory. The performance of rival methods, some of which are considered the state-of-the-art, were compared. It is demonstrated that our algorithm is superior in most of the cases, considering the absolute error of the test statistic.

Novel assessment of numerical forecasting model relative humidity with satellite probabilistic estimates

A novel method of comparison between an atmospheric model and satellite probabilistic estimates of relative humidity (RH) in the tropical atmosphere is presented. The method is developed to assess the Météo-France numerical weather forecasting model ARPEGE using probability density functions (PDF) of RH estimated from the SAPHIR microwave sounder. The satellite RH reference is derived by aggregating footprint-scale probabilistic RH to match the spatial and temporal resolution of ARPEGE over the April-May-June 2018 period. The probabilistic comparison is discussed with respect to a classical deterministic comparison confronting each model RH value to the reference average and using a set confidence interval. The study first documents the significant spatial and temporal variability of the reference distribution spread and shape. It warrants the need for a finer assessment at the individual case level to characterise specific situations beyond the classical bulk comparison using determinist “best” reference estimates. The probabilistic comparison allows for a more contrasted assessment than the deterministic one. Specifically, it reveals cases where the ARPEGE simulated values falling within the deterministic confidence range actually correspond to extreme departures in the reference distribution.

Statistical assessment of A-weighted sound power level for printer with electrophotographic engine

Statistical distribution and statistical upper limit (the value which 93.5 % of the batch of new equipment are expected to lie) of A-weighted sound power level for one office printer were experimentally estimated from 10 new samples picked up from market. The printer is capable of A4-size printing with electrophotographic engine which corresponds Annex C.16 Page printers in ECMA74 17th (2019). A-weighted sound power level for continuous printing mode was determined in accordance with noise test code for ITTE (Information Technology and Telecommunications Equipment such as printers and personal computers), ISO 7779:2018 and ECMA-74 Annex C. Sample standard distribution of production of overall A-weighted sound power level (determined from 100-10000 Hz one-third-octave band) is 0.25 dB, whereas individual one-third-octave band has larger distribution. The value obtained is better than reference distribution 1.32 dB set in ISO 9296:2017 which states estimation of statistical upper limit value of the batch of equipment for ITTE.

A Model of Income Evaluation: Income Comparison on Subjective Reference Income Distribution

People's evaluation of the relative position of their income is not as accurate as the relative income hypothesis assumes. It is observed from empirical survey data that income evaluation is concentrated in the middle. We develop a model that assumes income comparison on a subjective income reference distribution to explain the centralization phenomenon of income evaluation. We conduct theoretical analysis and empirical parameter estimation using Bayesian statistical modeling. The theoretical analysis shows that the centralization of income evaluation distribution occurs when the subjective reference distribution is more dispersed than the objective distribution. Empirical analysis using Japanese data from 2015 shows that the relationship between subjective and objective distributions differed depending on social categories with different social experiences. Women had a more ambiguous distribution than men. Among men, those aged 45--54 had a subjective distribution closest to the objective distribution. Thus, the subjective reference income distributions that potentially define people's evaluation of their income and their differences based on social category were only clarified by constructing the model.

Real-time finite element analysis allows homogenization of tissue scale strains and reduces variance in a mouse defect healing model

Mechanical loading allows both investigation into the mechano-regulation of fracture healing as well as interventions to improve fracture-healing outcomes such as delayed healing or non-unions. However, loading is seldom individualised or even targeted to an effective mechanical stimulus level within the bone tissue. In this study, we use micro-finite element analysis to demonstrate the result of using a constant loading assumption for all mouse femurs in a given group. We then contrast this with the application of an adaptive loading approach, denoted real time Finite Element adaptation, in which micro-computed tomography images provide the basis for micro-FE based simulations and the resulting strains are manipulated and targeted to a reference distribution. Using this approach, we demonstrate that individualised femoral loading leads to a better-specified strain distribution and lower variance in tissue mechanical stimulus across all mice, both longitudinally and cross-sectionally, while making sure that no overloading is occurring leading to refracture of the femur bones.

Maternal Nutrition Status and Human Milk Composition of DHA and AA Fatty Acids in Breastfeeding Honduran Women

Dietary habits and maternal nutrition status are the most important modifiable factors that will determine the concentration of certain essential components and nutrients in Breast Milk (BM).The objectives were to estimate the nutritional status of Breastfeeding (BF) women in rural Honduras, identifying the main food sources that contribute to the consumption of EFA and its content in BM. The Honduran study was part of an international study with a sample (n=25) with children between 26 and 64 days of age. The consumption of food sources of Essential Fatty Acids (EFA) was evaluated with a frequency questionnaire. BMcomposition was analyzed using the dry drop method with Guthrie cards. 56% of mothers provided exclusive BF, 27% of mothers were overweightand 68% had excess body fat. The average monthly consumptionof marine foods was 1.44, 0.60 and 0.68 servings of fish, sardines and tuna, respectively. The average consumption of Docosahexaenoic Acid (DHA) and Arachidonic Acid (AA) was 0.05 g / day. The content of DHA, EPA and AA fatty acids in BM was 0.14, 0.01 and 0.4% respectively. The amount of DHA and AA in the BF women is well below the median values of a global reference distribution.

Bayesian Bandwidths in Semiparametric Modelling for Nonnegative Orthant Data with Diagnostics

Multivariate nonnegative orthant data are real vectors bounded to the left by the null vector, and they can be continuous, discrete or mixed. We first review the recent relative variability indexes for multivariate nonnegative continuous and count distributions. As a prelude, the classification of two comparable distributions having the same mean vector is done through under-, equi- and over-variability with respect to the reference distribution. Multivariate associated kernel estimators are then reviewed with new proposals that can accommodate any nonnegative orthant dataset. We focus on bandwidth matrix selections by adaptive and local Bayesian methods for semicontinuous and counting supports, respectively. We finally introduce a flexible semiparametric approach for estimating all these distributions on nonnegative supports. The corresponding estimator is directed by a given parametric part, and a nonparametric part which is a weight function to be estimated through multivariate associated kernels. A diagnostic model is also discussed to make an appropriate choice between the parametric, semiparametric and nonparametric approaches. The retention of pure nonparametric means the inconvenience of parametric part used in the modelization. Multivariate real data examples in semicontinuous setup as reliability are gradually considered to illustrate the proposed approach. Concluding remarks are made for extension to other multiple functions.

Relative entropy of freely cooling granular gases. A molecular dynamics study

Whereas the original Boltzmann’s H-theorem applies to elastic collisions, its rigorous generalization to the inelastic case is still lacking. Nonetheless, it has been conjectured in the literature that the relative entropy of the velocity distribution function with respect to the homogeneous cooling state (HCS) represents an adequate nonequilibrium entropy-like functional for an isolated freely cooling granular gas. In this work, we present molecular dynamics results reinforcing this conjecture and rejecting the choice of the Maxwellian over the HCS as a reference distribution. These results are qualitatively predicted by a simplified theoretical toy model. Additionally, a Maxwell-demon-like velocity-inversion simulation experiment highlights the microscopic irreversibility of the granular gas dynamics, monitored by the relative entropy, where a short “anti-kinetic” transient regime appears for nearly elastic collisions only.

Developing the Logistics Strategy by «MOHITO» Retailer in Siberia and the Far East

The strategic development of retail is taking place in a fiercely competitive environment. In the context of the coronavirus pandemic and the weakening of the ruble, the development of the strategy has become particularly important for retailers. The apparel market has a number of specific features that significantly affect the formation of the development strategy. One of the most important directions in achieving competitive stability is to optimize logistics costs through the development of the distribution network. The article presents the results of a study of the competitive position of the apparel brand "MOHITO". The study proved the logistics strategy of the retailer in Siberia and the Far East as well-founded. This strategy is based on the organization of a distribution centre in Irkutsk which leads to reorganization of the supply chain of the LPP holding including the retailer "MOHITO". We also provided supporting rationale of the capacity of the potential market of the retailer in Siberia and the Far East in the case of the opening of a reference distribution centre in Irkutsk.

Kullback–Leibler Divergence of a Freely Cooling Granular Gas

Finding the proper entropy-like Lyapunov functional associated with the inelastic Boltzmann equation for an isolated freely cooling granular gas is a still unsolved challenge. The original H-theorem hypotheses do not fit here and the H-functional presents some additional measure problems that are solved by the Kullback–Leibler divergence (KLD) of a reference velocity distribution function from the actual distribution. The right choice of the reference distribution in the KLD is crucial for the latter to qualify or not as a Lyapunov functional, the asymptotic “homogeneous cooling state” (HCS) distribution being a potential candidate. Due to the lack of a formal proof far from the quasielastic limit, the aim of this work is to support this conjecture aided by molecular dynamics simulations of inelastic hard disks and spheres in a wide range of values for the coefficient of restitution (α) and for different initial conditions. Our results reject the Maxwellian distribution as a possible reference, whereas they reinforce the HCS one. Moreover, the KLD is used to measure the amount of information lost on using the former rather than the latter, revealing a non-monotonic dependence with α.