The more obvious and well known drawbacks of using refinement as the sole means of progressing from an abstract model to a concrete implementation are reviewed.model to a concrete implementation are reviewed. Retrenchment is presented in a simple partial correctness framework as a more flexible development concept for formally capturing the early and otherwise preformal stages of development, a...

We present maximally fast numerical algorithms for conserved coarsening systems that are stable and accurate with a growing natural time step Deltat=At2/3s. We compare the scaling structure obtained from our maximally fast conserved systems directly against the standard fixed time-step Euler algorithm, and find that the error scales as square root of A--so arbitrary accuracy can be achieved. Fo...

In this paper we propose a Bayesian, information theoretic approach to dimensionality reduction. The approach is formulated as a variational principle on mutual information, and seamlessly addresses the notions of sufficiency, relevance, and representation. Maximally informative statistics are shown to minimize a Kullback-Leibler distance between posterior distributions. Illustrating the approa...

In this research paper, we present a novel frame work for handling $m$-polar information by combining the theory of $m-$polar fuzzy  sets with graphs. We introduce certain types of edge regular $m-$polar fuzzy graphs and edge irregular $m-$polar fuzzy graphs. We describe some useful properties of edge regular, strongly edge irregular and strongly edge totally irregular $m-$polar fuzzy graphs. W...

We characterize the “best” model geometries for the class of virtually free groups, and we show that there is a countable infinity of distinct “best” model geometries in an appropriate sense–these are the maximally symmetric trees. The first theorem gives several equivalent conditions on a bounded valence, cocompact tree T without valence 1 vertices saying that T is maximally symmetric. The sec...

Article history: Received 25 March 2009 Received in revised form 23 September 2009 Available online 23 February 2010

Let G be a connected graph with maximum degree ∆(G). The irregularity index t(G) of G is defined as the number of distinct terms in the degree sequence of G. We say that G is maximally irregular if t(G) = ∆(G). The purpose of this note, apart from pointing out that every highly irregular graph is maximally irregular, is to establish upper bounds on the size of maximally irregular graphs and max...

Kaplansky proved in 1942 that among ail fields with a valuation having a given divisible value group G, a given algebraically closed residue field R, and a given restriction to the minimal subfield (either the trivial valuation on Qor Fp , or the /?-adic valuation on Q), there is one that is maximal in the strong sensé that every other can be embedded in it. In this paper, we construct this fie...

Portfolios are selected in non-Gaussian contexts to maximize a Cherny and Madan index of acceptability. Analytical gradients are developed for the purpose of optimizing portfolio searches on the unit sphere. It is shown that though an acceptability index is not a preference ordering, many utilities will concur with acceptability maximization. A stylized economy illustrates the advantages from t...

We consider 4D weak scale theories arising from 5D supersymmetric (SUSY) theories with maximal Scherk-Schwarz breaking at a Kaluza-Klein scale of several TeV. Many of the problems of conventional SUSY are avoided. Apart from 3rd family sfermions the SUSY spectrum is heavy, with only ∼50% tuning at a gluino mass of ∼2  TeV and a stop mass of ∼650  GeV. A single Higgs doublet acquires a vacuum ex...