Systemic States of Spreading Activation in Describing Associative Knowledge Networks II : Generalisations with Fractional Graph Laplacians and q-Adjacency Kernels

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Koponen , I 2021 , ' Systemic States of Spreading Activation in Describing Associative Knowledge Networks II : Generalisations with Fractional Graph Laplacians and q-Adjacency Kernels ' , Systems , vol. 9 , no. 2 , 22 . https://doi.org/10.3390/systems9020022

Title: Systemic States of Spreading Activation in Describing Associative Knowledge Networks II : Generalisations with Fractional Graph Laplacians and q-Adjacency Kernels
Author: Koponen, Ismo
Contributor organization: Department of Physics
Date: 2021-06
Language: eng
Number of pages: 18
Belongs to series: Systems
ISSN: 2079-8954
DOI: https://doi.org/10.3390/systems9020022
URI: http://hdl.handle.net/10138/328983
Abstract: Associative knowledge networks are often explored by using the so-called spreading activation model to find their key items and their rankings. The spreading activation model is based on the idea of diffusion- or random walk -like spreading of activation in the network. Here, we propose a generalisation, which relaxes an assumption of simple Brownian-like random walk (or equally, ordinary diffusion process) and takes into account nonlocal jump processes, typical for superdiffusive processes, by using fractional graph Laplacian. In addition, the model allows a nonlinearity of the diffusion process. These generalizations provide a dynamic equation that is analogous to fractional porous medium diffusion equation in a continuum case. A solution of the generalized equation is obtained in the form of a recently proposed q-generalized matrix transformation, the so-called q-adjacency kernel, which can be adopted as a systemic state describing spreading activation. Based on the systemic state, a new centrality measure called activity centrality is introduced for ranking the importance of items (nodes) in spreading activation. To demonstrate the viability of analysis based on systemic states, we use empirical data from a recently reported case of a university students' associative knowledge network about the history of science. It is shown that, while a choice of model does not alter rankings of the items with the highest rank, rankings of nodes with lower ranks depend essentially on the diffusion model.
Subject: 114 Physical sciences
systemic states
spreading activation
fractional graph Laplacian
nonlinear diffusion
associative knowledge networks
ANOMALOUS DIFFUSION
SCIENCE-EDUCATION
SEMANTIC NETWORKS
QUANTUM WALKS
DYNAMICS
MODEL
MAPS
Peer reviewed: Yes
Rights: cc_by
Usage restriction: openAccess
Self-archived version: publishedVersion


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