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

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.

Beyond two modes of thought: A quantum model of how three cognitive variables yield conceptual change

“…By exploring more of the space of possible modes of thought, child j may have more opportunity than child i to acquire mental dexterity and become adept at fine-tuning thought processes to match current task demands. Mental dexterity could be due to enhanced access to remote associates (Mednick, 1962 ), robustness to network percolation (Kenett et al, 2018 ), or individual differences in global, systemic-level properties of the network over the course of spreading activation (Koponen, 2021 ). Thus, even if the two children possess roughly the same knowledge, child j may be better able to make use of that knowledge.…”