Graph Theory Methods in Analysis of Model Structures

The present paper consists of an introduction, in two parts and an appendix. The Introduction is devoted to the definition of the problem and describes, as a whole, the methods used. The close connection between choosing the set of indicators and constructing the structural scheme of the model is discussed here. The possibility for using graph theory methods for analyzing and evaluating the given set of indicators is shown. Part I deals with the formal definition of the problem and describes graph theory algorithms employed in model structure analysis. In Part II, brief characteristics of the models under investigation and analysis of their graph models are given. The methods suggested in the present work appeared in the analysis of three global models: World 3, Mesarovic and Pestel model and MOIRA. In the Appendix, the sets of indicators of the graph models and the graph models themselves are given

Discussion quality diffuses in the digital public square

Studies of online social influence have demonstrated that friends have important effects on many types of behavior in a wide variety of settings. However, we know much less about how influence works among relative strangers in digital public squares, despite important conversations happening in such spaces. We present the results of a study on large public Facebook pages where we randomly used two different methods--most recent and social feedback--to order comments on posts. We find that the social feedback condition results in higher quality viewed comments and response comments. After measuring the average quality of comments written by users before the study, we find that social feedback has a positive effect on response quality for both low and high quality commenters. We draw on a theoretical framework of social norms to explain this empirical result. In order to examine the influence mechanism further, we measure the similarity between comments viewed and written during the study, finding that similarity increases for the highest quality contributors under the social feedback condition. This suggests that, in addition to norms, some individuals may respond with increased relevance to high-quality comments.Comment: 10 pages, 6 figures, 2 table

Algorithmic statistics revisited

The mission of statistics is to provide adequate statistical hypotheses (models) for observed data. But what is an "adequate" model? To answer this question, one needs to use the notions of algorithmic information theory. It turns out that for every data string $x$ one can naturally define "stochasticity profile", a curve that represents a trade-off between complexity of a model and its adequacy. This curve has four different equivalent definitions in terms of (1)~randomness deficiency, (2)~minimal description length, (3)~position in the lists of simple strings and (4)~Kolmogorov complexity with decompression time bounded by busy beaver function. We present a survey of the corresponding definitions and results relating them to each other

Improving the presentation of search results by multipartite graph clustering of multiple reformulated queries and a novel document representation

The goal of clustering web search results is to reveal the semantics of the retrieved documents. The main challenge is to make clustering partition relevant to a user’s query. In this paper, we describe a method of clustering search results using a similarity measure between documents retrieved by multiple reformulated queries. The method produces clusters of documents that are most relevant to the original query and, at the same time, represent a more diverse set of semantically related queries. In order to cluster thousands of documents in real time, we designed a novel multipartite graph clustering algorithm that has low polynomial complexity and no manually adjusted hyper–parameters. The loss of semantics resulting from the stem–based document representation is a common problem in information retrieval. To address this problem, we propose an alternative novel document representation, under which words are represented by their synonymy groups.This work was supported by Yandex grant 110104

Two-dimensional ranking of Wikipedia articles

The Library of Babel, described by Jorge Luis Borges, stores an enormous amount of information. The Library exists {\it ab aeterno}. Wikipedia, a free online encyclopaedia, becomes a modern analogue of such a Library. Information retrieval and ranking of Wikipedia articles become the challenge of modern society. While PageRank highlights very well known nodes with many ingoing links, CheiRank highlights very communicative nodes with many outgoing links. In this way the ranking becomes two-dimensional. Using CheiRank and PageRank we analyze the properties of two-dimensional ranking of all Wikipedia English articles and show that it gives their reliable classification with rich and nontrivial features. Detailed studies are done for countries, universities, personalities, physicists, chess players, Dow-Jones companies and other categories.Comment: RevTex 9 pages, data, discussion added, more data at http://www.quantware.ups-tlse.fr/QWLIB/2drankwikipedia

Worldwide spreading of economic crisis

We model the spreading of a crisis by constructing a global economic network and applying the Susceptible-Infected-Recovered (SIR) epidemic model with a variable probability of infection. The probability of infection depends on the strength of economic relations between the pair of countries, and the strength of the target country. It is expected that a crisis which originates in a large country, such as the USA, has the potential to spread globally, like the recent crisis. Surprisingly we show that also countries with much lower GDP, such as Belgium, are able to initiate a global crisis. Using the {\it k}-shell decomposition method to quantify the spreading power (of a node), we obtain a measure of ``centrality'' as a spreader of each country in the economic network. We thus rank the different countries according to the shell they belong to, and find the 12 most central countries. These countries are the most likely to spread a crisis globally. Of these 12 only six are large economies, while the other six are medium/small ones, a result that could not have been otherwise anticipated. Furthermore, we use our model to predict the crisis spreading potential of countries belonging to different shells according to the crisis magnitude.Comment: 13 pages, 4 figures and Supplementary Materia

Sequences close to periodic

The paper is a survey of notions and results related to classical and new generalizations of the notion of a periodic sequence. The topics related to almost periodicity in combinatorics on words, symbolic dynamics, expressibility in logical theories, algorithmic computability, Kolmogorov complexity, number theory, are discussed.Comment: In Russian. 76 pages, 6 figure

An output-sensitive algorithm for the minimization of 2-dimensional String Covers

String covers are a powerful tool for analyzing the quasi-periodicity of 1-dimensional data and find applications in automata theory, computational biology, coding and the analysis of transactional data. A \emph{cover} of a string $T$ is a string $C$ for which every letter of $T$ lies within some occurrence of $C$. String covers have been generalized in many ways, leading to \emph{k-covers}, \emph{$\lambda$-covers}, \emph{approximate covers} and were studied in different contexts such as \emph{indeterminate strings}. In this paper we generalize string covers to the context of 2-dimensional data, such as images. We show how they can be used for the extraction of textures from images and identification of primitive cells in lattice data. This has interesting applications in image compression, procedural terrain generation and crystallography

Line graphs as social networks

The line graphs are clustered and assortative. They share these topological features with some social networks. We argue that this similarity reveals the cliquey character of the social networks. In the model proposed here, a social network is the line graph of an initial network of families, communities, interest groups, school classes and small companies. These groups play the role of nodes, and individuals are represented by links between these nodes. The picture is supported by the data on the LiveJournal network of about 8 x 10^6 people. In particular, sharp maxima of the observed data of the degree dependence of the clustering coefficient C(k) are associated with cliques in the social network.Comment: 11 pages, 4 figure