Optimization via Low-rank Approximation for Community Detection in Networks

Community detection is one of the fundamental problems of network analysis, for which a number of methods have been proposed. Most model-based or criteria-based methods have to solve an optimization problem over a discrete set of labels to find communities, which is computationally infeasible. Some fast spectral algorithms have been proposed for specific methods or models, but only on a case-by-case basis. Here we propose a general approach for maximizing a function of a network adjacency matrix over discrete labels by projecting the set of labels onto a subspace approximating the leading eigenvectors of the expected adjacency matrix. This projection onto a low-dimensional space makes the feasible set of labels much smaller and the optimization problem much easier. We prove a general result about this method and show how to apply it to several previously proposed community detection criteria, establishing its consistency for label estimation in each case and demonstrating the fundamental connection between spectral properties of the network and various model-based approaches to community detection. Simulations and applications to real-world data are included to demonstrate our method performs well for multiple problems over a wide range of parameters.Comment: 45 pages, 7 figures; added discussions about computational complexity and extension to more than two communitie

Sparse random graphs: regularization and concentration of the Laplacian

We study random graphs with possibly different edge probabilities in the challenging sparse regime of bounded expected degrees. Unlike in the dense case, neither the graph adjacency matrix nor its Laplacian concentrate around their expectations due to the highly irregular distribution of node degrees. It has been empirically observed that simply adding a constant of order $1/n$ to each entry of the adjacency matrix substantially improves the behavior of Laplacian. Here we prove that this regularization indeed forces Laplacian to concentrate even in sparse graphs. As an immediate consequence in network analysis, we establish the validity of one of the simplest and fastest approaches to community detection -- regularized spectral clustering, under the stochastic block model. Our proof of concentration of regularized Laplacian is based on Grothendieck's inequality and factorization, combined with paving arguments.Comment: Added reference

Alien Registration- Beek, Levina M. (Calais, Washington County)

https://digitalmaine.com/alien_docs/1351/thumbnail.jp

Revisiting digital technologies: envisioning biodigital bodies

In this paper the contemporary practices of human genomics in the 21st century are placed alongside the digital bodies of the 1990s. The primary aim is to provide a trajectory of the biodigital as follows: First, digital bodies and biodigital bodies were both part of the spectacular imaginaries of early cybercultures. Second, these spectacular digital bodies were supplemented in the mid-1990s by digital bodywork practices that have become an important dimension of everyday communication. Third, the spectacle of biodigital bodies is in the process of being supplemented by biodigital bodywork practices, through personal or direct-to-consumer genomics. This shift moves a form of biodigital communication into the everyday. Finally, what can be learned from putting the trajectories of digital and biodigital bodies together is that the degree of this communicative shift may be obscured through the doubled attachment of personal genomics to everyday digital culture and high-tech spectacle.Keywords: genomics, biodigital, bodies, spectacle, everyda

Problems of implementation of GEF in physical education pre-schoolers

Building a culture of preschool children's health is considered as a complex process involving specific components, the formation of which must be comprehensively and consistently with all forms of life through the implementation of health-preschool activitiesФормирование культуры здоровья детей дошкольного возраста рассматривается как сложный процесс, включающий специфические компоненты, формирование которых должно осуществляться комплексно и последовательно при этом во всех формах жизнедеятельности дошкольника через реализацию здоровьесберегающей деятельност

An efficiency upper bound for inverse covariance estimation

We derive an upper bound for the efficiency of estimating entries in the inverse covariance matrix of a high dimensional distribution. We show that in order to approximate an off-diagonal entry of the density matrix of a $d$-dimensional Gaussian random vector, one needs at least a number of samples proportional to $d$. Furthermore, we show that with $n \ll d$ samples, the hypothesis that two given coordinates are fully correlated, when all other coordinates are conditioned to be zero, cannot be told apart from the hypothesis that the two are uncorrelated.Comment: 7 Page

Concentration of random graphs and application to community detection

Random matrix theory has played an important role in recent work on statistical network analysis. In this paper, we review recent results on regimes of concentration of random graphs around their expectation, showing that dense graphs concentrate and sparse graphs concentrate after regularization. We also review relevant network models that may be of interest to probabilists considering directions for new random matrix theory developments, and random matrix theory tools that may be of interest to statisticians looking to prove properties of network algorithms. Applications of concentration results to the problem of community detection in networks are discussed in detail.Comment: Submission for International Congress of Mathematicians, Rio de Janeiro, Brazil 201

Value Chain Structure Analysis as A Starting Point for Bamboo Enterprise Development: Lessons from Gunungkidul, Indonesia

The economic contributions of rural enterprises in Indonesia are significant to support local people's livelihoods, although it remains at micro to medium levels. One small-scale enterprise, which remains understudied and receives little policy attention, is the bamboo enterprise. Gunungkidul Regency in Yogyakarta Special Province, a central region in Java Island, Indonesia, have many bamboo enterprises, creating various products that support some 6,500 jobs. This research is conducted as a case study of the Gunungkidul Regency. A value chain perspective was used to study three bamboo-based enterprises' value chain structure: kitchen utensils, bamboo toy handicraft, and chemically treated bamboo. The snowball concept was used until the data was saturated. In total, 86 respondents were interviewed. The traditional chain was dominant. The longest value chain and the highest number of actor levels were bamboo toy handicrafts, and the shortest and smallest actor level was the chemically treated bamboo. Most channels were in the toy handicraft chain in the production flow, then kitchen utensils, and chemically treated bamboo. The credit payment method is prevalent in financial flow, and trust has been widely established between actors. The information flow related to price was imbalanced. In each chain, collaboration in the raw material segment was weak. The lack of willingness of artisans to be more productive and the weak cooperation among artisans, coupled with the lack of support from the government seems to be obstacles to the development of bamboo as a small to medium enterprise in Gunungkidu

A Textbook Evaluation On English Textbook Entitled “Grow With English” Used By Students Of MI Nurul Huda Bengkulu City

Based on the perception of the teacher and students in Madrasah Ibtidaiyyah (MI) Nurul Huda Bengkulu City when the researchers conducted an observation, the textbook is suitable for use in the teaching and learning process. Based on those perceptions, this study was intended to evaluate the quality on English textbooks Grow with English published by Erlangga Publisher used by students grade V and IV of MI Nurul Huda Bengkulu city with how much it meets the requirement of good EFL textbook considered four criteria, namely: (1) Subjects  and Contents; (2) Skills and Sub-skills; (3) Layout and Physical Make-up; and (4) Practical Consideration viewed by teacher and see students perception about these textbooks. This study used a quantitative research approach. Total population of this study were 114 students and 1 english teacher. Samples of this research were 25% of the population or 29 students which divided into 2 grades. 15 students from 5th grade and 14 students taken from 4th grade. In collecting data, researchers used checklist as the instrument which adapted from Demir and Ertas. Both textbooks was qualified based on the score ranges which divided into very bad (0-20), bad (21-40), fairly good (41-60), good (61-80), very good (81-100). The result of this study was first, Grow with English for grade five was categorized as good toward the four criteria of good EFL textbook requirements. It reached 79,78% of total score while 80,48% by students’ perception and 79,08% viewed by teachers’s perspective. Second, Grow with English for grade four was categorized  as  good  because  the  total  score  toward  the  four  criteria  is 77,77%. The total score was gained from 80,9% based on students’ perception and 74,65% viewed by teacher’s perspective. So based on the result of this study, it can concluded that both of textbooks met the criteria in fulfilling the requirements of good EFL textbook criteria covering the availability of materials based on Subjects and Contents, Skills and Sub-skills, Layout and Physical Make-up, and the Practical

Biodigital publics: personal genomes as digital media artifacts

The recent proliferation of personal genomics and direct-to-consumer (DTC) genomics has attracted much attention and publicity. Concern around these developments has mainly focused on issues of biomedical regulation and hinged on questions of how people understand genomic information as biomedical and what meaning they make of it. However, this publicity amplifies genome sequences which are also made as internet texts and, as such, they generate new reading publics. The practices around the generation, circulation and reading of genome scans do not just raise questions about biomedical regulation, they also provide the focus for an exploration of how contemporary public participation in genomics works. These issues around the public features of DTC genomic testing can be pursued through a close examination of the modes of one of the best known providers—23andMe. In fact, genome sequences circulate as digital artefacts and, hence, people are addressed by them. They are read as texts, annotated and written about in browsers, blogs and wikis. This activity also yields content for media coverage which addresses an indefinite public in line with Michael Warner’s conceptualisation of publics. Digital genomic texts promise empowerment, personalisation and community, but this promise may obscure the compliance and proscription associated with these forms. The kinds of interaction here can be compared to those analysed by Andrew Barry. Direct-to-consumer genetics companies are part of a network providing an infrastructure for genomic reading publics and this network can be mapped and examined to demonstrate the ways in which this formation both exacerbates inequalities and offers possibilities for participation in biodigital culture