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Kleinbergs HITS algorithm (Kleinberg 1999), which was originally developed in a Web context, tries to infer the authoritativeness of a Web page in relation to a specific query using the structure of a subgraph of the Web graph, which is obtained considering this specific query. Recent applications of this algorithm in contexts far removed from that of Web searching (Bacchin, Ferro and Melucci 2002, Ng et al. 2001) inspired us to study the algorithm in the abstract, independently of its particular applications, trying to mathematically illuminate its behaviour. In the present paper we detail this theoretical analysis. The original work starts from the definition of a revised and more general version of the algorithm, which includes the classic one as a particular case. We perform an analysis of the structure of two particular matrices, essential to studying the behaviour of the algorithm, and we prove the convergence of the algorithm in the most general case, finding the analytic expression of the vectors to which it converges. Then we study the symmetry of the algorithm and prove the equivalence between the existence of symmetry and the independence from the order of execution of some basic operations on initial vectors. Finally, we expound some interesting consequences of our theoretical results.Supported in part by a grant from the Italian National Research Council (CNR) research project Technologies and Services for Enhanced Content Delivery. 相似文献
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Lauren C. Shuffrey Santiago Morales Melanie H. Jacobson Michelle Bosquet Enlow Akhgar Ghassabian Amy E. Margolis Maristella Lucchini Kecia N. Carroll Rosa M. Crum Dana Dabelea Arielle Deutsch William P. Fifer Brandon Goldson Christine W. Hockett W. Alex Mason Lisette T. Jacobson Thomas G. O'Connor Nicolò Pini Yael Rayport Ayesha Sania Leonardo Trasande Rosalind J. Wright Seonjoo Lee Catherine Monk program collaborators for Environmental influences on Child Health Outcomes 《Child development》2023,94(6):1595-1609
This study examined the association of gestational diabetes mellitus (GDM), prenatal, and postnatal maternal depressive symptoms with externalizing, internalizing, and autism spectrum problems on the Preschool Child Behavior Checklist in 2379 children aged 4.12 ± 0.60 (48% female; 47% White, 32% Black, 15% Mixed Race, 4% Asian, <2% American Indian/Alaskan Native, <2% Native Hawaiian; 23% Hispanic). Data were collected from the NIH Environmental influences on Child Health Outcomes (ECHO) Program from 2009-2021. GDM, prenatal, and postnatal maternal depressive symptoms were each associated with increased child externalizing and internalizing problems. GDM was associated with increased autism behaviors only among children exposed to perinatal maternal depressive symptoms above the median level. Stratified analyses revealed a relation between GDM and child outcomes in males only. 相似文献
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