Cech cover of the complement of the discriminant variety. Part I: Goresky--MacPherson stratification

Interest in Conformal Field Theories and Quantum Field Theory lead physicists to consider configuration spaces of marked points on the complex projective line, $Conf_{0,d}(\mathbb{P})$. We investigate the moduli space $\mathcal{M}_{0,[d]}(\mathbb{C})$, of Riemann surfaces of genus 0, with $n$ unordered marked points, in the framework of real geometry. A decomposition of this moduli space, relying on Gauss drawings - objects being reminiscent of Grothendieck's dessin d'enfants, is presented. The main result of the paper is that this decomposition forms a (real) topological stratification, which can be subtly modified so as to form a good Aleksandrov-Cech cover. This approach provides a new very rich and detailed geometric description of this space, and in the panorama of results concerning $\overline{\mathcal{M}}_{0,[d]}(\mathbb{C})$ and $\overline{\mathcal{M}}_{0,[d]}(\mathbb{R})$, this approach fills in the gap between the two different methods employed to study the real and complex part of this moduli space. The results can be extended to calculate explicitly the Aleksandrov-Cech cohomology of braids with values of any sheaf

Enabling sustainable user interaction with domestic heating controls

Copyright @ 2011 University of BathThe way we live greatly effects the carbon emissions of our homes; heating accounts for nearly 60% of domestic energy consumption in the UK. This consumption is directly influenced by occupants through the use of their control systems. Using realworld data from buildings and observational data from users this research proposes guidelines for the design of more inclusive domestic heating controls. Two usercentred studies have been completed to date; one using controls under lab conditions and the other in a low-carbon housing development. In both studies controls were found to exclude users due to the cognitive demands placed on them, therefore creating an unnecessary barrier to reducing heat energy consumption in the home. The design principles proposed aim to help designers consider user needs when designing the interfaces of heating controls and energy management systems. By designing more inclusive and usable controls considerable energy savings could be made in the domestic context.This work is funded by the EPSRC and Buro Happold

An investigation into usability and exclusivity issues of digital programmable thermostats

This is the pre-print version of the Article - Copyright @ 2011 Taylor & FrancisWith nearly 60% of domestic energy consumption relating to space heating, the interaction between users and their heating controls is crucial in reducing consumption. Yet, many heating controls are complex and exclude people due to the demands placed upon their capabilities in terms of vision, reach, dexterity and thinking. This study explores the scale of and reasons for user exclusion in relation to digital programmable thermostats. The Exclusion Calculator was used to estimate the percentage of the population excluded from the use of three products. Full user testing was then conducted to elicit specific usability problems of the devices. The participants were a group of 14 younger users (aged 24–44) and 10 older users (aged 62–75). The exclusion calculations underestimated the actual exclusion significantly for both age ranges (p<0.05). None of the older users were able to complete the programming of the thermostats. Additionally, the cognitive demands of these systems were considered using a subjective workload assessment method, based on the NASA Task Load Index, and were found to be excessive. In conclusion, this study makes recommendations to facilitate the design of more inclusive digital programmable thermostats. It is argued that such changes could result in reductions in domestic heat energy consumption.This work is funded by the ESPRC and Buro Happold

Efficiently Clustering Very Large Attributed Graphs

Attributed graphs model real networks by enriching their nodes with attributes accounting for properties. Several techniques have been proposed for partitioning these graphs into clusters that are homogeneous with respect to both semantic attributes and to the structure of the graph. However, time and space complexities of state of the art algorithms limit their scalability to medium-sized graphs. We propose SToC (for Semantic-Topological Clustering), a fast and scalable algorithm for partitioning large attributed graphs. The approach is robust, being compatible both with categorical and with quantitative attributes, and it is tailorable, allowing the user to weight the semantic and topological components. Further, the approach does not require the user to guess in advance the number of clusters. SToC relies on well known approximation techniques such as bottom-k sketches, traditional graph-theoretic concepts, and a new perspective on the composition of heterogeneous distance measures. Experimental results demonstrate its ability to efficiently compute high-quality partitions of large scale attributed graphs.Comment: This work has been published in ASONAM 2017. This version includes an appendix with validation of our attribute model and distance function, omitted in the converence version for lack of space. Please refer to the published versio

Relaxation kinetics in two-dimensional structures

We have studied the approach to equilibrium of islands and pores in two dimensions. The two-regime scenario observed when islands evolve according to a set of particular rules, namely relaxation by steps at low temperature and smooth at high temperature, is generalized to a wide class of kinetic models and the two kinds of structures. Scaling laws for equilibration times are analytically derived and confirmed by kinetic Monte Carlo simulations.Comment: 6 pages, 7 figures, 1 tabl

Unidimensional model of the ad-atom diffusion on a substrate submitted to a standing acoustic wave I. Derivation of the ad-atom motion equation

The effect of a standing acoustic wave on the diffusion of an ad-atom on a crystalline surface is theoretically studied. We used an unidimensional space model to study the ad-atom+substrate system. The dynamic equation of the ad-atom, a Generalized Langevin equation, is analytically derived from the full Hamiltonian of the ad-atom+substrate system submitted to the acoustic wave. A detailed analysis of each term of this equation, as well as of their properties, is presented. Special attention is devoted to the expression of the effective force induced by the wave on the ad-atom. It has essentially the same spatial and time dependences as its parent standing acoustic wave

Low temperature shape relaxation of 2-d islands by edge diffusion

We present a precise microscopic description of the limiting step for low temperature shape relaxation of two dimensional islands in which activated diffusion of particles along the boundary is the only mechanism of transport allowed. In particular, we are able to explain why the system is driven irreversibly towards equilibrium. Based on this description, we present a scheme for calculating the duration of the limiting step at each stage of the relaxation process. Finally, we calculate numerically the total relaxation time as predicted by our results and compare it with simulations of the relaxation process.Comment: 11 pages, 5 figures, to appear in Phys. Rev.

Strain versus stress in a model granular material: a Devil's staircase

The series of equilibrium states reached by disordered packings of rigid, frictionless discs in two dimensions, under gradually varying stress, are studied by numerical simulations. Statistical properties of trajectories in configuration space are found to be independent of specific assumptions ruling granular dynamics, and determined by geometry only. A monotonic increase in some macroscopic loading parameter causes a discrete sequence of rearrangements. For a biaxial compression, we show that, due to the statistical importance of such events of large magnitudes, the dependence of the resulting strain on stress direction is a Levy flight in the thermodynamic limit.Comment: REVTeX, 4 pages, 5 included PostScript figures. New version altered throughout text, very close to published pape

The contamination of the surface of Vesta by impacts and the delivery of the dark material

The Dawn spacecraft observed the presence of dark material, which in turn proved to be associated with OH and H-rich material, on the surface of Vesta. The source of this dark material has been identified with the low albedo asteroids, but it is still a matter of debate whether the delivery of the dark material is associated with a few large impact events, to micrometeorites or to the continuous, secular flux of impactors on Vesta. The continuous flux scenario predicts that a significant fraction of the exogenous material accreted by Vesta should be due to non-dark impactors likely analogous to ordinary chondrites, which instead represent only a minor contaminant in the HED meteorites. We explored the continuous flux scenario and its implications for the composition of the vestan regolith, taking advantage of the data from the Dawn mission and the HED meteorites. We used our model to show that the stochastic events scenario and the micrometeoritic flux scenario are natural consequences of the continuous flux scenario. We then used the model to estimate the amounts of dark and hydroxylate materials delivered on Vesta since the LHB and we showed how our results match well with the values estimated by the Dawn mission. We used our model to assess the amount of Fe and siderophile elements that the continuous flux of impactors would mix in the vestan regolith: concerning the siderophile elements, we focused our attention on the role of Ni. The results are in agreement with the data available on the Fe and Ni content of the HED meteorites and can be used as a reference frame in future studies of the data from the Dawn mission and of the HED meteorites. Our model cannot yet provide an answer to the fate of the missing non-carbonaceous contaminants, but we discuss possible reasons for this discrepancy.Comment: 31 pages, 7 figures, 4 tables. Accepted for publication on the journal ICARUS, "Dark and Bright Materials on Vesta" special issu

On Frobenius structures in symmetric cones

We prove that in any strictly convex symmetric cone Ω there exists a non empty locus where the WDVV equation is satisfied (i.e. there exists a hyperplane being a Frobenius manifold). This result holds over any real division algebra (with a restriction to the rank 3 case if we consider the field O) but also on their linear combinations. This theorem holds as well in the case of pseudo-Riemannian geometry, in particular for a Lorentz symmetric cone of Anti-de-Sitter type. Our statement can be considered as a generalisation of a result by Ferapontov-Kruglikov-Novikov and Mokhov. Our construction is achieved by merging two different approaches: an algebraic/geometric one and the analytic approach given by Calabi in his investigations on the Monge-Ampère equation for the case of affine hyperspheres