Mathematical Evolution in Discrete Networks

Pfaltz, John F.

doi:10.13164/ma.2013.12

Cited by 3 publications

(1 citation statement)

References 37 publications

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“…In all cases, the organizational structure of the network was markedly increased, as shown by a significantly greater number of embedded triangles, a traditional measure of network structure [13,35], and a decrease in the length of embedded chordless cycles. The details of these experiments can be found in [26].…”

Section: Continuous Evolutionmentioning

confidence: 99%

The Role of Continuous Processes in Cognitive Development

Pfaltz¹

2015

Math. Appl.

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Abstract. Many scientists observing the cognitive development in children have noted distinct phases in the way they learn. One phase appears to be a gradual accumulation of experience. Another phase appears to be a reorganization of those experiences to make them more useful. In this paper we show how mathematical closure concepts can be used to abstractly model these cognitive processes.Closed sets, which we will call knowledge units, represent tight collections of experience, facts, or skills, etc. Associated with each knowledge unit is the notion of its generators consisting of those attributes which characterize it.Finally, we provide a rigorous mathematical model of these different kinds of learning in terms of continuous and discontinuous transformations. There are illustrations of both kinds of transformation, together with necessary and sufficient criteria for certain kinds of transformation to be continuous. By using a rigorous definition, one can derive necessary alternative properties which may be more easily observed in experimental situations.The formal mathematics is illustrated with reference to Lev Vygotsky's view of cognitive psychology, but it is not a verification of his model. We believe that this concept of "continuity" can be refined to test, and possibly verify, his and other models of cognitive behavior.

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Section: Continuous Evolutionmentioning

confidence: 99%