Paul Albuquerque

Coupling a Lattice Boltzmann and a Finite Difference Scheme

We show how a lattice Boltzmann (LB) scheme can be spatially coupled with a finite difference (FD) scheme in order to solve the same problem. The typical situation we consider is a computational domain which is partitioned in two regions. The same spatio-temporal physical process extends over the full domain but a different numerical method is used over each region. At the interface of the subdomains, the LB and FD must be connected so as to ensure a perfect continuity of the physical quantities. We derive the theoretical concepts, which allow us to link both methods in the case of a diffusion process, and validate them with numerical simulations on a 2D domain.

A Parallel Cellular Ant Colony Algorithm for Clustering and Sorting

Some ant species are known to gather and sort corpses in an auto-organized way. In this contribution, we propose a new cellular ant colony algorithm for sorting and clustering. This algorithm mimics the behavior of real ants. The cellular automata nature of our algorithm implies a straightforward parallelization. The rule consists of a pick-up, a deposition and a diffusion. Our probabilistic pick-up rule is based on some spatial neighborhood information. We observe that probabilistic pick-up yields compact clusters and also speeds up the clustering process. In the long run, a single cluster emerges. Moreover, in the presence of several corpse species, our algorithm sorts the corpses into distinct clusters. Thus our model reproduces realistic results, but however we do not observe any collective effect.

Mutation-Selection Algorithm: A Large Deviation Approach.

Abstract We consider a two-operator mutation–selection algorithm designed to optimize a fitness function on the space of fixed length binary strings. Mutation acts as in classical genetic algorithms, while the fitness-based selection operates through a Gibbs measure (Boltzmann selection). The selective pressure is controlled by a temperature parameter. We provide a mathematical analysis of the convergence of the algorithm, based on the probabilistic theory of large deviations. In particular, we obtain convergence to optimum fitness by resorting to an annealing process, which makes the algorithm asymptotically equivalent to simulated annealing.

A Branch-and-Bound algorithm using multiple GPU-based LP solvers

The Branch-and-Bound (B&B) method is a well-known optimization algorithm for solving integer linear programming (ILP) models in the field of operations research. It is part of software often employed by businesses for finding solutions to problems such as airline scheduling problems. It operates according to a divide-and-conquer principle by building a tree-like structure with nodes that represent linear programming (LP) problems. A LP solver commonly used to process the nodes is the simplex method. Nowadays its sequential implementation can be found in almost all commercial ILP solvers. In this paper, we present a hybrid CPU-GPU implementation of the B&B algorithm. The B&B tree is managed by the CPU, while the revised simplex method is mainly a GPU implementation, relying on the CUDA technology of NVIDIA. The CPU manages concurrently multiple instances of the LP solver. The principal difference with a sequential implementation of the B&B algorithm pertains to the LP solver, provided that the B&B tree is managed with the same strategy. We thus compared our GPU-based implementation of the revised simplex to a well-known open-source sequential solver, named CLP, of the COIN-OR project. For given problem densities, we measured a size threshhold beyond which our GPU implementation outperformed its sequential counterpart.

On the Impact of the Representation on Fitness Landscapes

In this paper we study the role of program representation on the properties of a type of Genetic Programming (GP) algorithm. In a specific case, which we believe to be generic of standard GP, we show that the way individuals are coded is an essential concept which impacts the fitness landscape. We give evidence that the ruggedness of the landscape affects the behavior of the algorithm and we find that, below a critical population, whose size is representation-dependent, premature convergence occurs.

Parallel simulation of particle transport in an advection field applied to volcanic explosive eruptions

Volcanic ash transport and dispersal models typically describe particle motion via a turbulent velocity field. Particles are advected inside this field from the moment they leave the vent of the volcano until they deposit on the ground. Several techniques exist to simulate particles in an advection field such as finite difference Eulerian, Lagrangian-puff or pure Lagrangian techniques. In this paper, we present a new flexible simulation tool called TETRAS (TEphra TRAnsport Simulator) based on a hybrid Eulerian-Lagrangian model. This scheme offers the advantages of being numerically stable with no numerical diffusion and easily parallelizable. It also allows us to output particle atmospheric concentration or ground mass load at any given time. The model is validated using the advection-diffusion analytical equation. We also obtained a good agreement with field observations of the tephra deposit associated with the 2450 BP Pululagua (Ecuador) and the 1996 Ruapehu (New Zealand) eruptions. As this kind of model can lead to computationally intensive simulations, a parallelization on a distributed memory architecture was developed. A related performance model, taking into account load imbalance, is proposed and its accuracy tested. HighlightsA new 3D Eulerian-Lagrangian TEphra TRAnsport Simulator (TETRAS) is presented.TETRAS describes dispersal and transport of volcanic particles in a wind field.TETRAS takes advantage of an efficient parallelization and describes wind advection.TETRAS has been validated with field observations of two explosive eruptions.TETRAS has a modular architecture designed to accommodate further extensions.

A framework for probabilistic numerical evaluation of sensor networks: a case study of a localization protocol

In this paper we show how to use stochastic estimation methods to investigate the topological properties of sensor networks as well as the behaviour of dynamical processes on these networks. The framework is particularly important to study problems for which no theoretical results are known, or can not be directly applied in practice, for instance, when only asymptotic results are available. We also interpret Russos formula in the context of sensor networks and thus obtain practical information on their reliability. As a case study, we analyse a localization protocol for wireless sensor networks and validate our approach by numerical experiments. Finally, we mention three applications of our approach: estimating the number of pivotal sensors in a real network, minimizing the number of such sensors for robustness purposes during the network design and estimating the distance between successive localized positions for mobile sensor networks.

A Minimal Model for the Formation of an Ant Cemetery

Several species of ants are known to build a cemetery, apparently without any individual planning. A simple cellular automaton like model has been proposed by Deneubourg in 1991 to explain this phenomenon. Here we show that Deneubourg’s hypotheses are not necessary and that a simpler dynamics also produces the observed clustering of corpses. In our approach the global task can be explained by a fluctuation-threshold effect. We argue that the cemetery formation is not a collective phenomenon since a single ant would also produce it, yet slowly. Finally our model naturally accounts for the observed fact that the clustering of corpses takes place around the inhomogeneities of the ants’ environment.

Mesures de Patterson-Sullivan dans les espaces symétriques

Abstract Let X = G/K be a symmetric space of noncompact type, Γ a Zariski-dense subgroup of G with critical exponent δ(Γ). We show that all Γ-invariant conformal densities of dimension δ(Γ) (e.g. Patterson-Sullivan densities) have their support contained in a same and single G-orbit on the geometric boundary of X. In the lattice case, we explicitly determine δ(Γ) and this G-orbit, and we establish the uniqueness of such densities.

A framework for probabilistic numerical evaluation of sensor networks: A case study of a localization protocol

In this paper we show how to use stochastic estimation methods to investigate topological properties of sensor networks as well as the behavior of dynamical processes on these networks. The framework is particularly important to study problems for which no theoretical results are known, or cannot be directly applied in practice, for instance, when only asymptotic results are available. We also interpret Russos formula in the context of sensor networks and thus obtain practical information on their reliability. As a case study, we analyze a localization protocol for wireless sensor networks and validate our approach by numerical experiments. Finally, we mention three applications of our approach: estimating the number of pivotal sensors in a real network, minimizing the number of such sensors for robustness purposes during the network design and estimating the distance between successive localized positions for mobile sensor networks.