Complexity of Networks (reprise)

Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as species enter an ecosystem via migration or speciation, and leave via extinction. In a previous paper, a complexity measure of networks was proposed based on the {\em complexity is information content} paradigm. To apply this paradigm to any object, one must fix two things: a representation language, in which strings of symbols from some alphabet describe, or stand for the objects being considered; and a means of determining when two such descriptions refer to the same object. With these two things set, the information content of an object can be computed in principle from the number of equivalent descriptions describing a particular object. The previously proposed representation language had the deficiency that the fully connected and empty networks were the most complex for a given number of nodes. A variation of this measure, called zcomplexity, applied a compression algorithm to the resulting bitstring representation, to solve this problem. Unfortunately, zcomplexity proved too computationally expensive to be practical. In this paper, I propose a new representation language that encodes the number of links along with the number of nodes and a representation of the linklist. This, like zcomplexity, exhibits minimal complexity for fully connected and empty networks, but is as tractable as the original measure. ...Comment: Accepted in Complexit

Europe, Continental Philosophy and the Philosophy of Education

On what might a comparative discussion of philosophy of education that takes Europe as one of its terms be based? This paper begins by addressing the complexity that attaches to the name ‘Europe’ in this context in order to lay the way for a more detailed consideration of so-called ‘Continental’ philosophy—specifically of poststructuralism. It makes reference to the ways in which the work of poststructuralist thinkers has often been interpreted in ‘postmodern’ educational theory and seeks to reveal certain errors in this regard. Distinctions are drawn between postmodernity, postmodernism and poststructuralism, illustrating the last of these in terms of two influential strands of thought drawn from Levinas and Nietzsche, and indicating their value for education. In conclusion, some brief remarks are offered regarding the institutionalization of philosophy of education in Europe

Towards an Economy of Higher Education

This paper draws a distinction between ways thinking and acting, and hence of policy and practice in higher education, in terms of different kinds of economy: economies of exchange and economies of excess. Crucial features of economies of exchange are outlined and their presence in prevailing conceptions of teaching and learning is illustrated. These are contrasted with other possible forms of practice, which in turn bring to light the nature of an economy of excess. In more philosophical terms, and to expand on the picture, economies of excess are elaborated with reference, first, to the understanding of alterity in the work of Emmanuel Levinas and, second, to the idea of Dionysian intensity that is to be found in Nietzsche. In the light of critical comment on some current directions in policy and practice, the implications of these ways of thinking for the administrator, the teacher and the student in higher education are explored

Mechanical generation of networks with surplus complexity

In previous work I examined an information based complexity measure of networks with weighted links. The measure was compared with that obtained from by randomly shuffling the original network, forming an Erdos-Renyi random network preserving the original link weight distribution. It was found that real world networks almost invariably had higher complexity than their shuffled counterparts, whereas networks mechanically generated via preferential attachment did not. The same experiment was performed on foodwebs generated by an artificial life system, Tierra, and a couple of evolutionary ecology systems, EcoLab and WebWorld. These latter systems often exhibited the same complexity excess shown by real world networks, suggesting that the complexity surplus indicates the presence of evolutionary dynamics. In this paper, I report on a mechanical network generation system that does produce this complexity surplus. The heart of the idea is to construct the network of state transitions of a chaotic dynamical system, such as the Lorenz equation. This indicates that complexity surplus is a more fundamental trait than that of being an evolutionary system.Comment: Accepted for ACALCI 2015 Newcastle, Australi