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We consider a class of scale-free inhomogeneous random graphs, which includes some long-range percolation models. We study the maximum degree in such graphs in a growing observation window and show that its limiting distribution is Frechet. We achieve this by proving convergence of the underlying point process of the degrees to a certain Poisson process. Estimating the index of the power-law tail for the typical degree distribution is an important question in statistics. We prove consistency of the Hill estimator for the inverse of the tail exponent of the typical degree distribution.

We study a Bayesian analysis of the proportional hazards model with time-varying coefficients. We consider two priors for time-varying coefficients – one based on B-spline basis functions and the other based on Gamma processes – and we use a beta process prior for the baseline hazard functions. We show that the two priors provide optimal posterior convergence rates (up to the logn term) and that the Bayes factor is consistent for testing the assumption of the proportional hazards when the two priors are used for an alternative hypothesis. In addition, adaptive priors are considered for theoretical investigation, in which the smoothness of the true function is assumed to be unknown, and prior distributions are assigned based on B-splines.

Traumatic brain injury (TBI) affects millions globally, with a majority of TBI cases being classified as mild, in which diffuse pathologies prevail. Two of the pathological hallmarks of TBI are diffuse axonal injury (DAI) and microglial activation. While progress has been made investigating the breadth of TBI-induced axonal injury and microglial changes in rodents, the neuroinflammatory progression and interaction between microglia and injured axons in humans is less well understood. Our group previously investigated microglial process convergence (MPC), in which processes of non-phagocytic microglia directly contact injured proximal axonal swellings, in rats and micropigs acutely following TBI. These studies demonstrated that MPC occurred on injured axons in the micropig, but not in the rat, following diffuse TBI. While it has been shown that microglia co-exist and interact with injured axons in humans post-TBI, the occurrence of MPC has not been quantitatively measured in the human brain. Therefore, in the current study we sought to validate our pig findings in human postmortem tissue. We investigated MPC onto injured axonal swellings and intact myelinated fibers in cases from individuals with confirmed DAI and control human brain tissue using multiplex immunofluorescent histochemistry. We found an increase in MPC onto injured axonal swellings, consistent with our previous findings in micropigs, indicating that MPC is a clinically relevant phenomenon that warrants further investigation.

Purpose: The aim of the research is to study the various aspects of the circular economy in Bulgaria and the countries of the European Union.   Method: The article evaluates the circular economy by applying different statistical analysis approaches: multivariate statistical methods, convergence analysis and cross-correlation analysis.   Results and conclusion: First, as a result of the conducted dynamic classification of EU countries, it was found that the transition to a circular economy is most advanced in Germany, the Netherlands, Belgium, Spain, Italy and Luxembourg. Second, according to each of the indicators included in the analysis, the absence of a process of general convergence and the presence of club convergence between the EU-27 countries during the period 2012-2019 was established. Convergence among countries in four of the clubs formed is relative, while in the others there is a process of transitional divergence and phase reversal. Third, based on the cross-correlation analysis, we find no relationship between generated and recycled packaging waste in Bulgaria from 2005 to 2019. Between these indicators in the European Union for the same period, there is reason to argue that there is a relationship that occurs within the current year. Fourth, the values of the indicators of waste utilization and rendering waste harmless clearly show that in Bulgaria the waste from economic activities is mainly landfilled, and this is associated with additional costs and leads to environmental pollution. Fifth, the taxonomic analysis shows the existence of minimal differences between the Bulgarian districts in terms of municipal solid waste management. Objetivo: El objetivo de la investigación es estudiar los diversos aspectos de la economía circular en Bulgaria y en los países de la Unión Europea.   Método: El artículo evalúa la economía circular aplicando diferentes enfoques de análisis estadístico: métodos estadísticos multivariantes, análisis de convergencia y análisis de correlación cruzada.   Resultados y conclusión: En primer lugar, como resultado de la clasificación dinámica realizada de los países de la UE, se constató que la transición hacia una economía circular está más avanzada en Alemania, Países Bajos, Bélgica, España, Italia y Luxemburgo. Segundo, conforme a cada uno de los indicadores incluidos en el análisis, se estableció la ausencia de un proceso de convergencia general y la presencia de convergencia de clubes entre los países de la UE-27 durante el periodo 2012-2019. La convergencia entre países en cuatro de los clubes formados es relativa, mientras que en los restantes existe un proceso de divergencia transitoria e inversión de fase. Tercero, a partir del análisis de correlación cruzada, no encontramos relación entre los residuos de envases generados y reciclados en Bulgaria entre 2005 y 2019. Entre estos indicadores en la Unión Europea para el mismo periodo, hay razones para sostener que existe una relación que se produce en el año en curso. En cuarto lugar, los valores de los indicadores de utilización de residuos y de neutralización de residuos muestran claramente que en Bulgaria los residuos procedentes de actividades económicas se depositan principalmente en vertederos, lo que conlleva costes adicionales y provoca la contaminación del medio ambiente. En quinto lugar, el análisis taxonómico muestra la existencia de diferencias mínimas entre los distritos búlgaros en términos de gestión de residuos sólidos urbanos. Objetivo: O objetivo da pesquisa é estudar os vários aspectos da economia circular na Bulgária e nos países da União Europeia.   Método: O artigo avalia a economia circular aplicando diferentes abordagens de análise estatística: métodos estatísticos multivariados, análise de convergência e análise de correlação cruzada.   Resultados e conclusão: Primeiro, como resultado da classificação dinâmica conduzida dos países da UE, constatou-se que a transição para uma economia circular está mais avançada na Alemanha, Países Baixos, Bélgica, Espanha, Itália e Luxemburgo. Segundo, de acordo com cada um dos indicadores incluídos na análise, foi estabelecida a ausência de um processo de convergência geral e a presença de convergência de clube entre os países da UE-27 durante o período de 2012 a 2019. A convergência entre os países em quatro dos clubes formados é relativa, enquanto nos outros há um processo de divergência transitória e inversão de fase. Terceiro, com base na análise de correlação cruzada, não encontramos nenhuma relação entre os resíduos de embalagens gerados e reciclados na Bulgária de 2005 a 2019. Entre esses indicadores na União Europeia para o mesmo período, há motivos para argumentar que existe uma relação que ocorre no ano atual. Quarto, os valores dos indicadores de utilização de resíduos e inofensividade dos resíduos mostram claramente que, na Bulgária, os resíduos de atividades econômicas são principalmente depositados em aterros, o que está associado a custos adicionais e leva à poluição ambiental. Quinto, a análise taxonômica mostra a existência de diferenças mínimas entre os distritos búlgaros em termos de gestão de resíduos sólidos municipais.

We consider first passage percolation on the configuration model with n vertices, and general independent and identically distributed edge weights assumed to have a density. Assuming that the degree distribution satisfies a uniform X2 log X-condition, we analyze the asymptotic distribution for the minimal weight path between a pair of typical vertices, as well the number of edges on this path namely the hopcount. Writing Ln for the weight of the optimal path, we show that Ln – (log n)/αn converges to a limiting random variable, for some sequence αn. Furthermore, the hopcount satisfies a central limit theorem (CLT) with asymptotic mean and variance of order log n. The sequence αn and the norming constants for the CLT are expressible in terms of the parameters of an associated continuous-time branching process that describes the growth of neighborhoods around a uniformly chosen vertex in the random graph. The limit of Ln – (log n)/αn equals the sum of the logarithm of the product of two independent martingale limits, and a Gumbel random variable. So far, for sparse random graph models, such results have only been shown for the special case where the edge weights have an exponential distribution, wherein the Markov property of this distribution plays a crucial role in the technical analysis of the problem. The proofs in the paper rely on a refined coupling between shortest path trees and continuous-time branching processes, and on a Poisson point process limit for the potential closing edges of shortest-weight paths between the source and destination.

The convergence of a sequence of point processes with dependent points, defined by a symmetric function of iid high-dimensional random vectors, to a Poisson random measure is proved. This also implies the convergence of the joint distribution of a fixed number of upper order statistics. As applications of the result a generalization of maximum convergence to point process convergence is given for simple linear rank statistics, rank-type U-statistics and the entries of sample covariance matrices.

We consider the estimation of the marginal excess moment (MEM), which is defined for a random vector (X, Y) and a parameter β>0 as E[(X-QX(1-p))+β|Y>QY(1-p)] provided E|X|β<∞, and where y+:=max(0,y), QX and QY are the quantile functions of X and Y respectively, and p∈(0,1). Our interest is in the situation where the random variable X is of Weibull-type while the distribution of Y is kept general, the extreme dependence structure of (X, Y) converges to that of a bivariate extreme value distribution, and we let p↓0 as the sample size n→∞. By using extreme value arguments we introduce an estimator for the marginal excess moment and we derive its limiting distribution. The finite sample properties of the proposed estimator are evaluated with a simulation study and the practical applicability is illustrated on a dataset of wave heights and wind speeds.

In this paper, we develop technology to improve the stability and quality of boat equipment manufacturing through vacuum injection process fusion to increase the safety of boats. Safe mold design and fabrication are carried out to determine the resin flow rate and water flow rate of a boat, and the performance of vacuum maintenance work is guaranteed through the tensile and compressive strength of the manufactured hull and deck. When manufacturing the boat air mechanism (Aerostat), the adhesion between equipment materials and the deformation of the joints are very important factors for safety. Due to the nature of equipment manufacturing, process fusion to minimize manual process minimizes deformation after manufacturing through accurate manufacturing ratio. Accordingly, it is possible to accurately control the mixing ratio of resin and hardener as optimal conditions for boat drying and securing safety, and to convert optimal information into a database by analyzing working conditions over time such as resin flow rate and flow rate, thereby improving durability and quality. Through this, it is expected that production efficiency and safety design will be improved by enabling efficient production process management with a small number of personnel.

This book contains the proceedings of the 14th International Conference on p-adic Functional Analysis, held from June 30-July 4, 2016, at the Universit d'Auvergne, Aurillac, France. Articles included in this book feature recent developments in various areas of non-Archimedean analysis: summation of p-adic series, rational maps on the projective line over \\mathbb{Q}p, non-Archimedean Hahn-Banach theorems, ultrametric Calkin algebras, G-modules with a convex base, non-compact Trace class operators and Schatten-class operators in p-adic Hilbert spaces, algebras of strictly differentiable functions, inverse function theorem and mean value theorem in Levi-Civita fields, ultrametric spectra of commutative non-unital Banach rings, classes of non-Archimedean K the spaces, p-adic Nevanlinna theory and applications, and sub-coordinate representation of p-adic functions. Moreover, a paper on the history of p-adic analysis with a comparative summary of non-Archimedean fields is presented. Through a combination of new research articles and a survey paper, this book provides the reader with an overview of current developments and techniques in non-Archimedean analysis as well as a broad knowledge of some of the sub-areas of this exciting and fast-developing research area.

Europe's growth will have to be golden in yet another sense. Economic prosperity has brought to Europeans the gift of longer lives, and the continent's population has aged a lot over the last five decades. Over the next five, it will age even more by 2060; almost a third of Europeans will be older than 65 years. Europe will have to rebuild its structures to make fuller use of the energies and experience of its more mature population's people in their golden years. These desires and developments already make the European growth model distinct. Keeping to the discipline of the golden rule would make it distinguished. This report shows how Europeans have organized the six principal economic activities trade, finance, enterprise, innovation, labor, and government in unique ways. But policies in parts of Europe do not recognize the imperatives of demographic maturity and clash with growth's golden rule. Conforming growth across the continent to Europe's ideals and the iron laws of economics will require difficult decisions. This report was written to inform them. Its findings the changes needed to make trade and finance will not be as hard as those to improve enterprise and innovation; these in turn are not as arduous and urgent as the changes needed to restructure labor and government. Its message the remedies are not out of reach for a part of the world that has proven itself both intrepid and inclusive.