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Modeling Sociodynamic Processes Based on the Use of the Differential Diffusion Equation with Fractional Derivatives. INFORMATION 2023. [DOI: 10.3390/info14020121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/16/2023] Open
Abstract
This paper explores the social dynamics of processes in complex systems involving humans by focusing on user activity in online media outlets. The R/S analysis showed that the time series of the processes under consideration are fractal and anti-persistent (they have a short-term memory and a Hurst exponent significantly less than 0.5). Following statistical processing, the observed data showed that there is a small amount of asymmetry in the distribution of user activity change amplitudes in news comments; the amplitude distribution is almost symmetrical, but there is a heavy tail as the probability plots lie above the normal probability plot. The fractality of the time series for the observed processes could be due to the variables describing them (the time and level of a series), which are characterized by fractional variables of measurement. Therefore, when figuring out how to approximate functions to determine the probability density of their parameters, it is advisable to use fractional differential equations, such as those of the diffusion type. This paper describes the development of such a model and uses the observed data to analyze and compare the modeling results.
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Stochastic Diffusion Model for Analysis of Dynamics and Forecasting Events in News Feeds. Symmetry (Basel) 2021. [DOI: 10.3390/sym13020257] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
One of the problems of forecasting events in news feeds, is the development of models which allow for work with semi structured information space of text documents. This article describes a model for forecasting events in news feeds, which is based on the use of stochastic dynamics of changes in the structure of non-stationary time series in news clusters (states of the information space) on the basis of use of diffusion approximation. Forecasting events in a news feed is based on their text description, vectorization, and finding the cosine value of the angle between the given vector and the centroids of various information space semantic clusters. Changes over time in the cosine value of such angles between the above vector and centroids can be represented as a point wandering on the [0, 1] segment. This segment contains a trap at the event occurrence threshold point, which the wandering point may eventually fall into. When creating the model, we have considered probability patterns of transitions between states in the information space. On the basis of this approach, we have derived a nonlinear second-order differential equation; formulated and solved the boundary value problem of forecasting news events, which allowed obtaining theoretical time dependence on the probability density function of the parameter distribution of non-stationary time series, which describe the information space evolution. The results of simulating the events instance probability dependence on time (with sets of parameter values of the developed model, which have been experimentally determined for already occurred events) show that the model is consistent and adequate (all the news events which have been used for the model verification occur with high values of probability (within the order of 80%), or if these are fictitious events, they can only occur over the course of inadmissible long time).
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Lopes AM, Machado JAT. Power Law Behaviour in Complex Systems. ENTROPY (BASEL, SWITZERLAND) 2018; 20:e20090671. [PMID: 33265760 PMCID: PMC7513193 DOI: 10.3390/e20090671] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/31/2018] [Accepted: 09/04/2018] [Indexed: 06/12/2023]
Affiliation(s)
- António M. Lopes
- UISPA–LAETA/INEGI, Faculty of Engineering, University of Porto, R. Dr. Roberto Frias, 4200–465 Porto, Portugal
| | - J. A. Tenreiro Machado
- Institute of Engineering, Polytechnic of Porto, Department of Electrical Engineering, R. Dr. António Bernardino de Almeida, 431, 4249–015 Porto, Portugal
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