Fractal Properties of Multiagent News Diffusion Model

📝 Abstract

The paper deals with fractal characteristics (Hurst exponent) and wavelet-scaleograms of the information distribution model, suggested by the authors. The authors have studied the effect of Hurst exponent change depending upon the model parameters, which have semantic meaning. The paper also considers fractal characteristics of real information streams. It is described, how the Hurst exponent dynamics depends on these information streams state in practice

💡 Analysis

The paper deals with fractal characteristics (Hurst exponent) and wavelet-scaleograms of the information distribution model, suggested by the authors. The authors have studied the effect of Hurst exponent change depending upon the model parameters, which have semantic meaning. The paper also considers fractal characteristics of real information streams. It is described, how the Hurst exponent dynamics depends on these information streams state in practice

📄 Content

1 Fractal Properties of Multiagent News Diffusion Model

D.V. Lande, V.A. Dodonov Institute for Information Recording of NAS of Ukraine, Kiev

The paper deals with fractal characteristics (Hurst exponent) and wavelet-scaleograms of the information distribution model, suggested by the authors. The authors have studied the effect of Hurst exponent change depending upon the model parameters, which have semantic meaning. The paper also considers fractal characteristics of real information streams. It is described, how the Hurst exponent dynamics depends on these information streams state in practice

Introduction

Statistical studies of time-series, corresponding to the volume of informative messages streams on some or other topic in the global networks are of great importance in analyzing substantial processes, which are reflected in these networks. However, along with studying common statistic properties of time- series, wavelet-analysis and fractal analysis has been recently used with increased frequency for solving forecasting problems, revealing periodicities, anomalies. This paper will describe a model of topic-based news diffusion. In order to formally define topic-based information streams, let us make some assumptions, common for all further discussion [1]. Information stream Let us consider an interval   ,a  of a real axis (time axis), where a  . Let us assume, that in this time interval in accordance with particular patterns (one of the possible patterns will be suggested later on) some quantity of information documents are published in the network – k . On the time axis we will designate the moments, when separate documents are published, by 1 2 1 2 , ,…, ( … ) k k a             . Let us denote, that information stream is a process ( ) N, the implementation of which is characterized by a number of points (documents), which appeared in the interval   ,a , as a function of the right end of the interval . Thus, the implementation of information stream is a non-decreasing staircase-like, always integer-valued function ( ) N. This definition is true to fact in local time domains, but it does not take into consideration such effect, as ageing of information, which is inconsistent with “accumulating” property of information stream ( ) N in large time spans, which is taken into account in the model, proposed below. In a narrower sense, by topic-based information stream we shall mean a quantity of documents, which in a certain sense (in content) match the specified

2 topic. In the following paragraphs we shall consider a general picture of topic- based information streams dynamics. Different approaches are used to model information streams. Among these approaches one can name nonlinear analytical models, models based upon the cellular automata concept [2-3], multiagent models [4-5]. The complexity of operation processes of informative messages’ interrelation system, their origin and organization of impact upon the society makes it necessary to study the respective mechanisms and, consequently, to develop models or entire simulation complexes. In the following paragraphs we shall turn our attention to multiagent concept of information diffusion. As distinguished from the well-known approaches, where people’s behavior is simulated, in this case the simulation object is the informational space, which is considered as a model environment of information agents. Interconnected substances – informative messages are regarded as these agents. Precisely informative messages are considered as an instrument of information influence. Multiagent model Let us consider a multiagent model with the following performance parameters. Informative messages can be replicated (by way of “reposting”), they can contain links both to informative messages of similar content and to other objects of the real and the virtual world, they can “die” due to ageing etc. [4]. The agent’s evolution will be connected with the events, which happen to such agent. As regards the principal characteristic, let us introduce the “energy” (Е), which reflects the timeliness of the message and the degree of interest to it. It goes without saying, that ageing of information or negative reaction will reduce the message’s energy, and positive reaction or appearance of the link to such message will increase its energy. The agent appears with the initial energy E0 and with each discrete time marking its energy decreases by 1. We shall consider events, which are typical for social networks: “like”, “repost”, “link” (providing the link reference to one agent by another agent). These events make an impact upon the agent’s energy in the following way: “like” increases the energy by 1, “repost” increases the energy by 2, “link” increases the energy by 1. On the other hand, the probability, that one of these events will take place, depends upon th

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