Grain Buiding Ordering

International audienceGiven a set E, the partitions of E are usually ordered by merging of classes. In segmentation procedures, this ordering often generates small parasite classes. A new ordering, called "grain building ordering", or GBO, is proposed. It requires a connection over E and states that A 4 B, with A,B ⊆ E, when each connected component of B contains a connected component of A. TheGBO applies to sets, partitions, and numerical functions. Thickenings with respect to the GBO are introduced as extensive idempotent operators that do not create connected components. The composition product of a connected opening by a thickening is still a thickening. Moreover, when {i, i ∈ I} is a granulometric family, then the two sequences { i, i ∈ I} and { i , i ∈ I}generate hierarchies, from which semi-groups can be derived. In addition,the approach allows us to combine any set of partitions or of tessellations into a synthetic one

Draw like a builder, build like a writer. And the crack is in the detail

As the inevitable building by numbers ensues, London’s Thames Gateway becomes one of many playgrounds for bar charting enthusiasts. Houses measured by the thousands and little clues as to where it is, that ghost in the machine, what they are, the structures of everyday contemporary life, and who's life it is anyway. Fernand Braudel, Georges Perec, Jorge Luis Borges, amongst others, are employed to examine just how Wittgensteins radiators find their ways into Barratts South East catalogue. They supply the container for Dickensian content with Sinclairesque detail, while late Jan Turnovski's epic lunacy will help to once and for all allay widespread popular fears that Wittgenstein 1 and 2 may add up to one-and-a-half, simple as that. Never has the ideal of treating technology involved with building as an intellectual discipline been further removed from any notion of genius, loci or otherwise; housing policy housing, building policy building. Against the backdrop of mass housing and landmark buildings with little space or time for anything in between, five years of studio work with diploma students at the University of Greenwich, Vienna University of Technology and University Innsbruck, concerned themselves with the structural narrative of the Thames Gateway. This paper, as well as the projects presented through it, is a premature attempt at anchoring buildings on the words they are built on, technology on the sentence structure of its description, assembly instructions written in the most specific of dialects. It describes techniques, suggesting an architecture read backwards, sideways, horizontal and in parallel, free associative sequence, thus discussing issues of site, context, detail and conceptual adhesion. It also poses questions: concerning locality, history, ritual, conceptualisation and intellectual detachment. Above all, in view of the sheer relentlessness of commercially driven urban expansion, questions of soul and character, of design sustainability in terms of creating space to accommodate viable structures social, cultural, narrative. Allowing history to continue, creating place worth telling tales about

A column of grains in the jamming limit: glassy dynamics in the compaction process

We investigate a stochastic model describing a column of grains in the jamming limit, in the presence of a low vibrational intensity. The key control parameter of the model, $\epsilon$, is a representation of granular shape, related to the reduced void space. Regularity and irregularity in grain shapes, respectively corresponding to rational and irrational values of $\epsilon$, are shown to be centrally important in determining the statics and dynamics of the compaction process.Comment: 29 pages, 14 figures, 1 table. Various minor changes and updates. To appear in EPJ

Exploiting Causal Independence in Bayesian Network Inference

A new method is proposed for exploiting causal independencies in exact Bayesian network inference. A Bayesian network can be viewed as representing a factorization of a joint probability into the multiplication of a set of conditional probabilities. We present a notion of causal independence that enables one to further factorize the conditional probabilities into a combination of even smaller factors and consequently obtain a finer-grain factorization of the joint probability. The new formulation of causal independence lets us specify the conditional probability of a variable given its parents in terms of an associative and commutative operator, such as ``or'', ``sum'' or ``max'', on the contribution of each parent. We start with a simple algorithm VE for Bayesian network inference that, given evidence and a query variable, uses the factorization to find the posterior distribution of the query. We show how this algorithm can be extended to exploit causal independence. Empirical studies, based on the CPCS networks for medical diagnosis, show that this method is more efficient than previous methods and allows for inference in larger networks than previous algorithms.Comment: See http://www.jair.org/ for any accompanying file

Growth of a vortex polycrystal in type II superconductors

We discuss the formation of a vortex polycrystal in type II superconductors from the competition between pinning and elastic forces. We compute the elastic energy of a deformed grain boundary, that is strongly non-local, and obtain the depinning stress for weak and strong pinning. Our estimates for the grain size dependence on the magnetic field strength are in good agreement with previous experiments on NbMo. Finally, we discuss the effect of thermal noise on grain growth.Comment: 4 pages, 2 figure

An epitaxial model for heterogeneous nucleation on potent substrates

© The Minerals, Metals & Materials Society and ASM International 2012In this article, we present an epitaxial model for heterogeneous nucleation on potent substrates. It is proposed that heterogeneous nucleation of the solid phase (S) on a potent substrate (N) occurs by epitaxial growth of a pseudomorphic solid (PS) layer on the substrate surface under a critical undercooling (ΔT ). The PS layer with a coherent PS/N interface mimics the atomic arrangement of the substrate, giving rise to a linear increase of misfit strain energy with layer thickness. At a critical thickness (h ), elastic strain energy reaches a critical level, at which point, misfit dislocations are created to release the elastic strain energy in the PS layer. This converts the strained PS layer to a strainless solid (S), and changes the initial coherent PS/N interface into a semicoherent S/N interface. Beyond this critical thickness, further growth will be strainless, and solidification enters the growth stage. It is shown analytically that the lattice misfit (f) between the solid and the substrate has a strong influence on both h and ΔT ; h decreases; and ΔT increases with increasing lattice misfit. This epitaxial nucleation model will be used to explain qualitatively the generally accepted experimental findings on grain refinement in the literature and to analyze the general approaches to effective grain refinement.EPSRC Centre for Innovative Manufacturing in Liquid Metal Engineerin