(Quantum) Space-Time as a Statistical Geometry of Fuzzy Lumps and the Connection with Random Metric Spaces

We develop a kind of pregeometry consisting of a web of overlapping fuzzy lumps which interact with each other. The individual lumps are understood as certain closely entangled subgraphs (cliques) in a dynamically evolving network which, in a certain approximation, can be visualized as a time-dependent random graph. This strand of ideas is merged with another one, deriving from ideas, developed some time ago by Menger et al, that is, the concept of probabilistic- or random metric spaces, representing a natural extension of the metrical continuum into a more microscopic regime. It is our general goal to find a better adapted geometric environment for the description of microphysics. In this sense one may it also view as a dynamical randomisation of the causal-set framework developed by e.g. Sorkin et al. In doing this we incorporate, as a perhaps new aspect, various concepts from fuzzy set theory.Comment: 25 pages, Latex, no figures, some references added, some minor changes added relating to previous wor

Menger Path Systems

https://digitalcommons.memphis.edu/speccoll-faudreerj/1235/thumbnail.jp

The von Neumann Model and the Early Models of General Equilibrium

The paper reconstructs the von Neumann model, comments on its salient features and critically reviews some of its generalisations. The issues related to thetreatment of consumption, decomposability and uniqueness of the rate of growth and interest will be especially scrutinised. The most prominent models of general equilibrium that appeared before or roughly at the same time as von Neumann's model will be also reviewed in the paper and compared with it. It will be demonstrated that none of them had any noticeable influence on von Neumann's model, which is genuinely distinct, ideologically free and methodologically fresh and forward-looking. It will be argued that the model can be viewed as a brilliant mathematical metaphor of some deep-rooted old vision, pertaining to the core issues of commodity production

Analysis of weighted networks

The connections in many networks are not merely binary entities, either present or not, but have associated weights that record their strengths relative to one another. Recent studies of networks have, by and large, steered clear of such weighted networks, which are often perceived as being harder to analyze than their unweighted counterparts. Here we point out that weighted networks can in many cases be analyzed using a simple mapping from a weighted network to an unweighted multigraph, allowing us to apply standard techniques for unweighted graphs to weighted ones as well. We give a number of examples of the method, including an algorithm for detecting community structure in weighted networks and a new and simple proof of the max-flow/min-cut theorem.Comment: 9 pages, 3 figure