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

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.Peer reviewe

Systemic States of Spreading Activation in Describing Associative Knowledge Networks : From Key Items to Relative Entropy Based Comparisons

Associative knowledge networks are central in many areas of learning and teaching. One key problem in evaluating and exploring such networks is to find out its key items (nodes), substructures (connected set of nodes), and how the roles of sub-structures can be compared. In this study, we suggest an approach for analyzing associative networks, so that analysis is based on spreading activation and systemic states that correpond to the state of spreading. The method is based on the construction of diffusion-propagators as generalized systemic states of the network, for an exploration of the connectivity of a network and, subsequently, on generalized Jensen-Shannon-Tsallis relative entropy (based on Tsallis-entropy) in order to compare the states. It is shown that the constructed systemic states provide a robust way to compare roles of sub-networks in spreading activation. The viability of the method is demonstrated by applying it to recently published network representations of students' associative knowledge regarding the history of science.Non peer reviewe

Usage of Terms “Science” and “Scientific Knowledge” in Nature of Science (NOS): Do Their Lexicons in Different Accounts Indicate Shared Conceptions?

Nature of science (NOS) has been a central theme in science education and research on it for nearly three decades, but there is still debate on its proper focus and underpinnings. The focal points of these debates revolve around different ways of understanding the terms “science” and “scientific knowledge”. It is suggested here that the lack of agreement is at least partially related to and reflected as a lack of common vocabulary and terminology that would provide a shared basis for finding consensus. Consequently, the present study seeks motivation from the notions of centrality of lexicons in recognizing the identity of disciplinary communities and different schools of thought within NOS. Here, by using a network approach, we investigate how lexicons used by different authors to discuss NOS are confluent or divergent. The lexicons used in these texts are investigated on the basis of a network analysis. The results of the analysis reveal clear differences in the lexicons that are partially related to differences in views, as evident from the debates surrounding the consensus NOS. The most divergent views are related to epistemology, while regarding the practices and social embeddedness of science the lexicons overlap significantly. This suggests that, in consensus NOS, one can find much basis for converging views, with common understanding, where constructive communication may be possible. The basic vocabulary, in the form of a lexicon, can reveal much about the different stances and the differences and similarities between various disciplinary schools. The advantage of such an approach is its neutrality and how it keeps a distance from preferred epistemological positions and views of nature of knowledge

Agent-Based Modeling of Consensus Group Formation with Complex Webs of Beliefs

Formation of consensus groups with shared opinions or views is a common feature of human social life and also a well-known phenomenon in cases when views are complex, as in the case of the formation of scholarly disciplines. In such cases, shared views are not simple sets of opinions but rather complex webs of beliefs (WoBs). Here, we approach such consensus group formation through the agent-based model (ABM). Agents’ views are described as complex, extensive web-like structures resembling semantic networks, i.e., webs of beliefs. In the ABM introduced here, the agents’ interactions and participation in sharing their views are dependent on the similarity of the agents’ webs of beliefs; the greater the similarity, the more likely the interaction and sharing of elements of WoBs. In interactions, the WoBs are altered when agents seek consensus and consensus groups are formed. The consensus group formation depends on the agents’ sensitivity to the similarity of their WoBs. If their sensitivity is low, only one large and diffuse group is formed, while with high sensitivity, many separated and segregated consensus groups emerge. To conclude, we discuss how such results resemble the formation of disciplinary, scholarly consensus groups

Usage of Terms “Science” and “Scientific Knowledge” in Nature of Science (NOS): Do Their Lexicons in Different Accounts Indicate Shared Conceptions?

Nature of science (NOS) has been a central theme in science education and research on it for nearly three decades, but there is still debate on its proper focus and underpinnings. The focal points of these debates revolve around different ways of understanding the terms “science” and “scientific knowledge”. It is suggested here that the lack of agreement is at least partially related to and reflected as a lack of common vocabulary and terminology that would provide a shared basis for finding consensus. Consequently, the present study seeks motivation from the notions of centrality of lexicons in recognizing the identity of disciplinary communities and different schools of thought within NOS. Here, by using a network approach, we investigate how lexicons used by different authors to discuss NOS are confluent or divergent. The lexicons used in these texts are investigated on the basis of a network analysis. The results of the analysis reveal clear differences in the lexicons that are partially related to differences in views, as evident from the debates surrounding the consensus NOS. The most divergent views are related to epistemology, while regarding the practices and social embeddedness of science the lexicons overlap significantly. This suggests that, in consensus NOS, one can find much basis for converging views, with common understanding, where constructive communication may be possible. The basic vocabulary, in the form of a lexicon, can reveal much about the different stances and the differences and similarities between various disciplinary schools. The advantage of such an approach is its neutrality and how it keeps a distance from preferred epistemological positions and views of nature of knowledge

Systemic States of Spreading Activation in Describing Associative Knowledge Networks: From Key Items to Relative Entropy Based Comparisons

Associative knowledge networks are central in many areas of learning and teaching. One key problem in evaluating and exploring such networks is to find out its key items (nodes), sub-structures (connected set of nodes), and how the roles of sub-structures can be compared. In this study, we suggest an approach for analyzing associative networks, so that analysis is based on spreading activation and systemic states that correpond to the state of spreading. The method is based on the construction of diffusion-propagators as generalized systemic states of the network, for an exploration of the connectivity of a network and, subsequently, on generalized Jensen–Shannon–Tsallis relative entropy (based on Tsallis-entropy) in order to compare the states. It is shown that the constructed systemic states provide a robust way to compare roles of sub-networks in spreading activation. The viability of the method is demonstrated by applying it to recently published network representations of students’ associative knowledge regarding the history of science

Entropy and Energy in Characterizing the Organization of Concept Maps in Learning Science

The coherence and connectivity of such knowledge representations is known to be closely related to knowledge production, acquisition and processing. In this study we use network theory in making the clustering and cohesion of concept maps measurable, and show how the distribution of these properties can be interpreted through the Maximum Entropy (MaxEnt) method. This approach allows to introduce new concepts of the “energy of cognitive load” and the “entropy of knowledge organization” to describe the organization of knowledge in the concept mapsPeer reviewe

Lexicons of Key Terms in Scholarly Texts and Their Disciplinary Differences: From Quantum Semantics Construction to Relative-Entropy-Based Comparisons

Complex networks are often used to analyze written text and reports by rendering texts in the form of a semantic network, forming a lexicon of words or key terms. Many existing methods to construct lexicons are based on counting word co-occurrences, having the advantage of simplicity and ease of applicability. Here, we use a quantum semantics approach to generalize such methods, allowing us to model the entanglement of terms and words. We show how quantum semantics can be applied to reveal disciplinary differences in the use of key terms by analyzing 12 scholarly texts that represent the different positions of various disciplinary schools (of conceptual change research) on the same topic (conceptual change). In addition, attention is paid to how closely the lexicons corresponding to different positions can be brought into agreement by suitable tuning of the entanglement factors. In comparing the lexicons, we invoke complex network-based analysis based on exponential matrix transformation and use information theoretic relative entropy (Jensen–Shannon divergence) as the operationalization of differences between lexicons. The results suggest that quantum semantics is a viable way to model the disciplinary differences of lexicons and how they can be tuned for a better agreement