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

Koponen, Ismo T.; Pehkonen, Maija

doi:10.3390/e12071653

Cited by 7 publications

(3 citation statements)

References 44 publications

(116 reference statements)

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“…That is, those properties that characterizes the network as a whole. There have been several works analyzing the role of communicability and self-communicability at these three different scales (Bradonjić et al, 2011;Crofts and Higham, 2009;Crofts et al, 2011;da Fontoura Costa et al, 2008;Došlić, 2005;Estrada 2007a;2010b;Estrada and Bodin, 2008;Estrada and Hatano, 2009a;Estrada et al, 2009;Jungsbluth et al, 2007;Koponen and Pehkonen, 2010;Li et al, 2010;MacArthur et al, 2010;Malliaros and Megalooikonomou, 2011;Ren et al, 2011;Tordesillas et al, 2010;Shang, 2011b;Wang and Qin, 2010;Walker and Tordesillas, 2010;Ying and Wu, 2008). We present here some illustrative examples to give a flavor of the relevance of these approaches.…”

Section: Communicability and The Analysis Of Networkmentioning

confidence: 98%

The physics of communicability in complex networks

2012

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a b s t r a c tA fundamental problem in the study of complex networks is to provide quantitative measures of correlation and information flow between different parts of a system. To this end, several notions of communicability have been introduced and applied to a wide variety of real-world networks in recent years. Several such communicability functions are reviewed in this paper. It is emphasized that communication and correlation in networks can take place through many more routes than the shortest paths, a fact that may not have been sufficiently appreciated in previously proposed correlation measures. In contrast to these, the communicability measures reviewed in this paper are defined by taking into account all possible routes between two nodes, assigning smaller weights to longer ones. This point of view naturally leads to the definition of communicability in terms of matrix functions, such as the exponential, resolvent, and hyperbolic functions, in which the matrix argument is either the adjacency matrix or the graph Laplacian associated with the network.Considerable insight on communicability can be gained by modeling a network as a system of oscillators and deriving physical interpretations, both classical and quantummechanical, of various communicability functions. Applications of communicability measures to the analysis of complex systems are illustrated on a variety of biological, physical and social networks. The last part of the paper is devoted to a review of the notion of locality in complex networks and to computational aspects that by exploiting sparsity can greatly reduce the computational efforts for the calculation of communicability functions for large networks.

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Section: Communicability and The Analysis Of Networkmentioning

confidence: 98%

The physics of communicability in complex networks

2012

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“…us, the concept maps are network representations of the organization of the concepts. e advantage of such representations emphasizes the relational structure of knowledge, where the concepts and principles are interconnected and where the principles of making the connections can be explicated [39]. Concept mapping is exceptionally efficient, in comparison to other techniques such as outlining or defining knowledge elements [5].…”

Section: Related Work On Conceptual and Cognitive Complexmentioning

confidence: 99%

“…e semantic relatedness metric generated glosses that correlate very well with human judgments of semantic relatedness. In [39], the authors state that, in practice, successful instruction and learning, which set its goals on the holistic understanding, require a deeper understanding of the knowledge as a coherent and connected structure. Consequently, the coherence and connectivity of such a knowledge representation are known to be closely related to knowledge production, acquisition, and processing.…”

Section: Related Work On Conceptual and Cognitive Complexmentioning

confidence: 99%

Structural Analysis of Factual, Conceptual, Procedural, and Metacognitive Knowledge in a Multidimensional Knowledge Network

2020

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Discovering the most suitable network structure of the learning domain represents one of the main challenges of knowledge delivery and acquisition. We propose a multidimensional knowledge network (MKN) consisting of three components: multilayer network and its two projections. Each network layer constitutes factual, conceptual, procedural, or metacognitive knowledge within the domain of databases as a standard course of computer science study. In the MKN layer, nodes are concepts or knowledge units and the edges are weighted with regard to Bloom's cognitive learning level. The projected network layers are contrasted with a monolayer network by comparing characterizations of the centrality measures: degree centrality, closeness centrality, betweenness centrality, and eccentricity. The study revealed indications of how concepts, supported with the higher number of previously introduced concepts, have a dominant role in knowledge acquisition, from a view of knowledge structure and content. The analysis of communities, assortativity coefficient, and overlap between MKN layers contributes to better structuring of knowledge. MKN enables systematic insights into the efficiency of knowledge integration across metacognitive layers, as well as the detection of crucial cognitive concepts that reduce/increase the cognitive load during learning.

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Modelling Students’ Thematically Associated Knowledge: Networked Knowledge from Affinity Statistics

Koponen

2019

Complex Networks X

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

Cited by 7 publications

References 44 publications

The physics of communicability in complex networks

The physics of communicability in complex networks

Structural Analysis of Factual, Conceptual, Procedural, and Metacognitive Knowledge in a Multidimensional Knowledge Network

Modelling Students’ Thematically Associated Knowledge: Networked Knowledge from Affinity Statistics

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