Scalable Parallel Numerical Constraint Solver Using Global Load Balancing

We present a scalable parallel solver for numerical constraint satisfaction problems (NCSPs). Our parallelization scheme consists of homogeneous worker solvers, each of which runs on an available core and communicates with others via the global load balancing (GLB) method. The parallel solver is implemented with X10 that provides an implementation of GLB as a library. In experiments, several NCSPs from the literature were solved and attained up to 516-fold speedup using 600 cores of the TSUBAME2.5 supercomputer.Comment: To be presented at X10'15 Worksho

On The Complexity and Completeness of Static Constraints for Breaking Row and Column Symmetry

We consider a common type of symmetry where we have a matrix of decision variables with interchangeable rows and columns. A simple and efficient method to deal with such row and column symmetry is to post symmetry breaking constraints like DOUBLELEX and SNAKELEX. We provide a number of positive and negative results on posting such symmetry breaking constraints. On the positive side, we prove that we can compute in polynomial time a unique representative of an equivalence class in a matrix model with row and column symmetry if the number of rows (or of columns) is bounded and in a number of other special cases. On the negative side, we show that whilst DOUBLELEX and SNAKELEX are often effective in practice, they can leave a large number of symmetric solutions in the worst case. In addition, we prove that propagating DOUBLELEX completely is NP-hard. Finally we consider how to break row, column and value symmetry, correcting a result in the literature about the safeness of combining different symmetry breaking constraints. We end with the first experimental study on how much symmetry is left by DOUBLELEX and SNAKELEX on some benchmark problems.Comment: To appear in the Proceedings of the 16th International Conference on Principles and Practice of Constraint Programming (CP 2010

Magic angles and cross-hatching instability in hydrogel fracture

The full 2D analysis of roughness profiles of fracture surfaces resulting from quasi-static crack propagation in gelatin gels reveals an original behavior characterized by (i) strong anisotropy with maximum roughness at $V$-independent symmetry-preserving angles, (ii) a sub-critical instability leading, below a critical velocity, to a cross-hatched regime due to straight macrosteps drifting at the same magic angles and nucleated on crack-pinning network inhomogeneities. Step height values are determined by the width of the strain-hardened zone, governed by the elastic crack blunting characteristic of soft solids with breaking stresses much larger that low strain moduli

Oscillating Fracture in Rubber

We have found an oscillating instability of fast-running cracks in thin rubber sheets. A well-defined transition from straight to oscillating cracks occurs as the amount of biaxial strain increases. Measurements of the amplitude and wavelength of the oscillation near the onset of this instability indicate that the instability is a Hopf bifurcation

Phase transition for cutting-plane approach to vertex-cover problem

We study the vertex-cover problem which is an NP-hard optimization problem and a prototypical model exhibiting phase transitions on random graphs, e.g., Erdoes-Renyi (ER) random graphs. These phase transitions coincide with changes of the solution space structure, e.g, for the ER ensemble at connectivity c=e=2.7183 from replica symmetric to replica-symmetry broken. For the vertex-cover problem, also the typical complexity of exact branch-and-bound algorithms, which proceed by exploring the landscape of feasible configurations, change close to this phase transition from "easy" to "hard". In this work, we consider an algorithm which has a completely different strategy: The problem is mapped onto a linear programming problem augmented by a cutting-plane approach, hence the algorithm operates in a space OUTSIDE the space of feasible configurations until the final step, where a solution is found. Here we show that this type of algorithm also exhibits an "easy-hard" transition around c=e, which strongly indicates that the typical hardness of a problem is fundamental to the problem and not due to a specific representation of the problem.Comment: 4 pages, 3 figure

Introduction

Non peer reviewe

Exponentially hard problems are sometimes polynomial, a large deviation analysis of search algorithms for the random Satisfiability problem, and its application to stop-and-restart resolutions

A large deviation analysis of the solving complexity of random 3-Satisfiability instances slightly below threshold is presented. While finding a solution for such instances demands an exponential effort with high probability, we show that an exponentially small fraction of resolutions require a computation scaling linearly in the size of the instance only. This exponentially small probability of easy resolutions is analytically calculated, and the corresponding exponent shown to be smaller (in absolute value) than the growth exponent of the typical resolution time. Our study therefore gives some theoretical basis to heuristic stop-and-restart solving procedures, and suggests a natural cut-off (the size of the instance) for the restart.Comment: Revtex file, 4 figure

On the photometric variability of blue supergiants in NGC 300 and its impact on the Flux-weighted Gravity-Luminosity Relationship

We present a study of the photometric variability of spectroscopically confirmed supergiants in NGC 300, comprising 28 epochs extending over a period of five months. We find 15 clearly photometrically variable blue supergiants in a sample of nearly 70 such stars, showing maximum light amplitudes ranging from 0.08 to 0.23 magnitudes in the V band, and one variable red supergiant. We show their light curves, and determine semi-periods for two A2 Ia stars. Assuming that the observed changes correspond to similar variations in the bolometric luminosity, we test for the influence of this variability on the Flux-weighted Gravity--Luminosity Relationship and find a negligible effect, showing that the calibration of this relationship, which has the potential to measure extragalactic distances at the Cepheid accuracy level, is not affected by the stellar photometric variability in any significant way.Comment: 9 pages, 3 figures, 3 tables. Accepted for publication in the Astrophysical Journa

Galactose inhibition of the constitutive transport of hexoses in Saccharomyces cerevisiae

The relationship between the pathways of glucose and galactose utilization in Saccharomyces cerevisiae has been studied. Galactose (which is transported and phosphorylated by inducible systems) is a strong inhibitor of the utilization of glucose, fructose and mannose (which have the same constitutive transport and phosphorylation systems). Conversely, all these three hexoses inhibit the utilization of galactose, though with poor efficiency. These cross-inhibitions only occur in yeast adapted to galactose or in galactose-constitutive mutants. The efficiency of galactose as inhibitor is even greater than the efficiencies of each of the other three hexoses to inhibit the utilization of each other. Phosphorylation is not involved in the inhibition and transport of sugars is the affected step. The cross-inhibitions between galactose and either glucose, fructose or mannose do not implicate utilization of one hexose at the expense of the other, as it occurs in the mutual interactions between the latter three sugars. it seems that, by growing the yeast in galactose, a protein component is synthesized, or alternatively modified, that once bound to either galactose or any one of the other three hexoses (glucose, fructose or mannose), cross-interacts respectively with the constitutive or the inducible transport systems, impairing their function.This work was supported by a grant (PB87-0206) from the DGICYT, Promoción General del Conocimiento.Peer Reviewe