weighted sums
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2022 ◽  
Vol 8 ◽  
Author(s):  
Murilo R. Santos ◽  
Luis C. Dias ◽  
Maria C. Cunha ◽  
João R. Marques

This paper is a systematic review of studies that used multicriteria decision analysis (MCDA) to address plastic waste management. A literature search for scientific articles in online databases (Web of Science and Scopus) enabled us to identify 20 relevant papers from 2008 to 2021, spanning case studies in three continents. These studies focus on: plastics as a resource (material), plastics as a product (reverse logistics), and plastics as a problem (pollution). Content analysis methodology was used, with the focus being on how the authors used MCDA for managing plastic waste, which has relevance for researchers and practitioners. Alternative solutions were found for the selection of disposal methods for almost all types of plastic categorized in this review. The most popular method was AHP, followed by TOPSIS, outranking methods, MAUT/MAVT and simple weighted sums, with some studies including more than one method. The choice of criteria spanned operational (mostly), but also environmental and economic aspects to evaluate the alternatives. Less frequently, one finds criteria related to social, managerial, and political aspects. The weighting of the criteria was performed mainly by consulting experts, followed by decision makers. Representatives of the affected population or other stakeholders have been consulted only on a few occasions. The authors of the studies consider their application of MCDA was successful, highlighting mainly the importance of being able to encompass different dimensions in the evaluation of the alternatives and the transparency of the process. In most cases, a winning alternative emerged clearly, which sometimes was a combination of multiple strategies. We also report other recommendations of these authors concerning marine and terrestrial plastic waste management.


Author(s):  
Nguyen Van Huan ◽  
Nguyen Van Quang

The aim of this study is to provide some strong limit theorems for weighted sums of measurable operators. The almost uniform convergence and the bilateral almost uniform convergence are considered. As a result, we derive the strong law of large numbers for sequences of successively independent identically distributed measurable operators without using the noncommutative version of Kolmogorov’s inequality.


2021 ◽  
Vol 2099 (1) ◽  
pp. 012071
Author(s):  
D A Cherkashin ◽  
A V Voytishek

Abstract This paper presents a computer system for modelling one-dimensional random variables NMPUD, developed in the laboratory of mathematical modelling of Lyceum No. 130 in Novosibirsk. The results of the numerical experiments and the considerations justifying the practicability for using in the NMPUD system: the elementary densities constructed by the technology of sequential (inserted) substitutions, the densities representing weighted sums of elementary densities (which can be simulated using the modified discrete superposition method), the algorithms for a piecewise linear approximation of unknown densities using a given sample, the algorithms of the modified superposition method for computational modelling of random variables with piecewise linear densities, are also presented.


2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Mingzhou Xu ◽  
Kun Cheng

We investigate the complete p th moment convergence for weighted sums of independent, identically distributed random variables under sublinear expectations space. Using moment inequality and truncation methods, we prove the equivalent conditions of complete p th moment convergence of weighted sums of independent, identically distributed random variables under sublinear expectations space, which complement the corresponding results obtained in Guo and Shan (2020).


Author(s):  
A. Hantoute ◽  
M. A. López-Cerdá

AbstractThis paper provides new characterizations for the subdifferential of the pointwise supremum of an arbitrary family of convex functions. The main feature of our approach is that the normal cone to the effective domain of the supremum (or to finite-dimensional sections of it) does not appear in our formulas. Another aspect of our analysis is that it emphasizes the relationship with the subdifferential of the supremum of finite subfamilies, or equivalently, finite weighted sums. Some specific results are given in the setting of reflexive Banach spaces, showing that the subdifferential of the supremum can be reduced to the supremum of a countable family.


2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Yuki Yamagishi ◽  
Kazumi Saito ◽  
Kazuro Hirahara ◽  
Naonori Ueda

AbstractIt is expected that the pronounced decrease in b-value of the Gutenberg–Richter law for some region during some time interval can be a promising precursor in forecasting earthquakes with large magnitudes, and thus we address the problem of automatically identifying such spatio-temporal change points as several clusters consisting of earthquakes whose b-values are substantially smaller than the total one. For this purpose, we propose a new method consisting of two phases: tree construction and tree separation. In the former phase, we employ one of two different declustering algorithms called single-link and correlation-metric developed in the field of seismology, while in the later phase, we employ a variant of the change-point detection algorithm, developed in the field of data mining. In the later phase, we also employ one of two different types of objective functions, i.e., the average magnitude which is inversely proportional to the b-value, and the likelihood function based on the Gutenberg–Richter law. Here note that since the magnitudes of most earthquakes are relatively small, we formulate our problem so as to produce one relatively large cluster and the other small clusters having substantially larger average magnitudes or smaller b-values. In addition, in order to characterize some properties of our proposed methods, we present a method of analyzing magnitude correlation over an earthquake network. In our empirical evaluation using earthquake catalog data covering the whole of Japan, we show that our proposed method employing the single-link strategy can produce more desirable results for our purpose in terms of the improvement of weighted sums of variances, average logarithmic likelihoods, visualization results, and magnitude correlation analyses.


2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mingzhou Xu ◽  
Kun Cheng

AbstractIn this paper, we obtain equivalent conditions of complete moment convergence of the maximum for partial weighted sums of independent identically distributed random variables under sublinear expectations space. The results obtained in the paper are extensions of the equivalent conditions of complete moment convergence of the maximum under classical linear expectation space.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Sridevi Padakanti ◽  
Khong-Loon Tiong ◽  
Yan-Bin Chen ◽  
Chen-Hsiang Yeang

AbstractPrincipal Component Analysis (PCA) projects high-dimensional genotype data into a few components that discern populations. Ancestry Informative Markers (AIMs) are a small subset of SNPs capable of distinguishing populations. We integrate these two approaches by proposing an algorithm to identify necessary informative loci whose removal from the data deteriorates the PCA structure. Unlike classical AIMs, necessary informative loci densely cover the genome, hence can illuminate the evolution and mixing history of populations. We conduct a comprehensive analysis to the genotype data of the 1000 Genomes Project using necessary informative loci. Projections along the top seven principal components demarcate populations at distinct geographic levels. Millions of necessary informative loci along each PC are identified. Population identities along each PC are approximately determined by weighted sums of minor (or major) alleles over the informative loci. Variations of allele frequencies are aligned with the history and direction of population evolution. The population distribution of projections along the top three PCs is recapitulated by a simple demographic model based on several waves of founder population separation and mixing. Informative loci possess locational concentration in the genome and functional enrichment. Genes at two hot spots encompassing dense PC 7 informative loci exhibit differential expressions among European populations. The mosaic of local ancestry in the genome of a mixed descendant from multiple populations can be inferred from partial PCA projections of informative loci. Finally, informative loci derived from the 1000 Genomes data well predict the projections of an independent genotype data of South Asians. These results demonstrate the utility and relevance of informative loci to investigate human evolution.


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