On the role of autocorrelations in texts

The task of finding a criterion allowing to distinguish a text from an arbitrary set of words is rather relevant in itself, for instance, in the aspect of development of means for internet-content indexing or separating signals and noise in communication channels. The Zipf law is currently considered to be the most reliable criterion of this kind [3]. At any rate, conventional stochastic word sets do not meet this law. The present paper deals with one of possible criteria based on the determination of the degree of data compression.Comment: 5 pages, 4 figures, 5 reference

Diagram of measurement series elements deviation from local linear approximations

Method for detection and visualization of trends, periodicities, local peculiarities in measurement series (dL-method) based on DFA technology (Detrended fluctuation analysis) is proposed. The essence of the method lies in reflecting the values of absolute deviation of measurement accumulation series points from the respective values of linear approximation. It is shown that dL-method in some cases allows better determination of local peculiarities than wavelet-analysis. Easy-to-realize approach that is proposed can be used in the analysis of time series in such fields as economics and sociology.Comment: 4 pages, 6 figure

Self-similarity properties in a queuing network model

In this paper a model of subscriber telephone network based on the concept of cellular automata is elaborated. Some fractal properties inherent in the model are revealed that vary depending on parameters assigning its operation rules. The main advantage of the model in question is its compatibility with algorithmic methods - a finite set of formal rules, assigned on a finite set of elements (cells), allows precise realization in the form of algorithms.Comment: 5 pages, 5 figure

Compactified Horizontal Visibility Graph for the Language Network

A compactified horizontal visibility graph for the language network is proposed. It was found that the networks constructed in such way are scale free, and have a property that among the nodes with largest degrees there are words that determine not only a text structure communication, but also its informational structure.Comment: 9 pages, 3 figures, 2 appendix table

Power law in website ratings

In the practical work of websites popularization, analysis of their efficiency and downloading it is of key importance to take into account web-ratings data. The main indicators of website traffic include the number of unique hosts from which the analyzed website was addressed and the number of granted web pages (hits) per unit time (for example, day, month or year). Of certain interest is the ratio between the number of hits (S) and hosts (H). In practice there is even used such a concept as "average number of viewed pages" (S/H), which on default supposes a linear dependence of S on H. What actually happens is that linear dependence is observed only as a partial case of power dependence, and not always. Another new power law has been discovered on the Internet, in particular, on the WWW.Comment: 4 pages, 5 figure

Ranking of nodes of networks taking into account the power function of its weight of connections

To rank nodes in quasi-hierarchical networks of social nature, it is necessary to carry out a detailed analysis of the network and evaluate the results obtained according to all the given criteria and identify the most influential nodes. Existing ranking algorithms in the overwhelming majority estimate such networks in general, which does not allow to clearly determine the influence of nodes among themselves. In the course of the study, an analysis of the results of known algorithms for ranking the nodes of HITS, PageRank and compares the obtained data with the expert evaluation of the network. For the effective analysis of quasi-hierarchical networks, the basic algorithm of HITS is modified, which allows to evaluate and rank nodes according to the given criteria (the number of input and output links among themselves), which corresponds to the results of expert evaluation. It is shown that the received method in some cases provides results that correspond to the real social relation, and the indexes of the authorship of the nodes - pre-assigned social roles.Comment: 11 pages, 2 fi

Decomposing an information stream into the principal components

We propose an approach to decomposing a thematic information stream into principal components. Each principal component is related to a narrow topic extracted from the information stream. The essence of the approach arises from analogy with the Fourier transform. We examine methods for analyzing the principal components and propose using multifractal analysis for identifying similar topics. The decomposition technique is applied to the information stream dedicated to Brexit. We provide a comparison between the principal components obtained by applying the decomposition to Brexit stream and the related topics extracted by Google Trends.Comment: 14 pages; 4 figures; 4 table

On the fractal nature of mutual relevance sequences in the Internet news message flows

In the task of information retrieval the term relevance is taken to mean formal conformity of a document given by the retrieval system to user's information query. As a rule, the documents found by the retrieval system should be submitted to the user in a certain order. Therefore, a retrieval perceived as a selection of documents formally solving the user's query, should be supplemented with a certain procedure of processing a relevant set. It would be natural to introduce a quantitative measure of document conformity to query, i.e. the relevance measure. Since no single rule exists for the determination of the relevance measure, we shall consider two of them which are the simplest in our opinion. The proposed approach does not suppose any restrictions and can be applied to other relevance measures.Comment: 6 pages, 56 figure

Detection Implicit Links and G-betweenness

A concept of implicit links for Complex Networks has been defined and a new value - cohesion factor, which allows to evaluate numerically the presence of such connection between any two nodes, has been introduced. We introduce a generalization of such characteristics as the betweenness, which allows to rank network nodes in more details. The effectiveness of the proposed concepts is shown by the numerical examples.Comment: 11 pages, 3 figure

"Conjectural" links in complex networks

This paper introduces the concept of Conjectural Link for Complex Networks, in particular, social networks. Conjectural Link we understand as an implicit link, not available in the network, but supposed to be present, based on the characteristics of its topology. It is possible, for example, when in the formal description of the network some connections are skipped due to errors, deliberately hidden or withdrawn (e.g. in the case of partial destruction of the network). Introduced a parameter that allows ranking the Conjectural Link. The more this parameter - the more likely that this connection should be present in the network. This paper presents a method of recovery of partially destroyed Complex Networks using Conjectural Links finding. Presented two methods of finding the node pairs that are not linked directly to one another, but have a great possibility of Conjectural Link communication among themselves: a method based on the determination of the resistance between two nodes, and method based on the computation of the lengths of routes between two nodes. Several examples of real networks are reviewed and performed a comparison to know network links prediction methods, not intended to find the missing links in already formed networks.Comment: 12 pages, 3 figure