This paper brings a correction to the formulation of the basins of fixed-point states of fully asynchronous discrete-time discrete-state dynamic networks presented in our paper that appeared in the IEEE Transactions on Neural Networks, vol. 17, no. 2, pp. 397-408, March 2006. In our subsequent works on totally asynchronous systems, we have discovered that the formulation given in that previous paper lacks an additional condition. We present in this paper why the previous formulation is incomplete and give the correct formulation.

This paper gives a formulation of the basins of fixed point states of fully asynchronous discrete-time discrete-state dynamic networks. That formulation provides two advantages. The first one is to point out the different behaviors between synchronous and asynchronous modes and the second one is to allow us to easily deduce an algorithm which determines the behavior of a network for a given initialization. In the context of this study, we consider networks of a large number of neurons (or units, processors, etc.), whose dynamic is fully asynchronous with overlapping updates. We suppose that the neurons take a finite number of discrete states and that the updating scheme is discrete in time. We make no hypothesis on the activation functions of the nodes, so that the dynamic of the network may have multiple cycles and/or basins. Our results are illustrated on a simple example of a fully asynchronous Hopfield neural network.

In a previous paper, we have shown the very high power of asynchronism for parallel iterative algorithms in a global context of grid computing. In this article, we study the interest of coupling load balancing with asynchronism in such algorithms. After proposing a noncentralized version of dynamic load balancing which is best suited to asynchronism, we verify its efficiency by some experiments on a general partial differential equation (PDE) problem. Finally, we give some general conditions for the use of load balancing to obtain good results with this kind of algorithm and discuss the choice of the residual as an efficient load estimator.

We introduce a theoretical algorithm and its practical version to perform a decentralized detection of the global convergence of parallel asynchronous iterative algorithms. We prove that, even if the algorithm is completely decentralized, the detection of global convergence is achieved on one processor under the classical conditions. The proposed algorithm is very useful in the context of grid computing in which the processors are distributed and in which detecting the convergence on a master processor may be penalizing or even impossible as in peer to peer computation frameworks. Finally, the efficiency of the practical algorithm is illustrated in a typical experiment.

Summary form only given. AIAC algorithms (Asynchronous Iterations Asynchronous Communications) are a particular class of parallel iterative algorithms. Their asynchronous nature makes them more efficient than their synchronous counterparts in numerous cases as has already been shown in previous works. The first goal is to compare several parallel programming environments in order to see if there is one of them which is best suited to efficiently implement AIAC algorithms. The main criterion for this comparison consists in the performances achieved in a global context of grid computing for two classical scientific problems. Nevertheless, we also take into account two secondary criteria, which are the ease of programming and the ease of deployment. The second goal is to extract from this comparison the important features that a parallel programming environment must have in order to be suited for the implementation of AIAC algorithms.

We consider networks of a large number of neurons (or units, processors, ...), whose dynamics are fully asynchronous with overlapping updating. We suppose that the neurons take a finite number of states (discrete states), and that the updating scheme is discrete in time. We make no hypotheses on the activation function of the neurons; the networks may have multiple cycles and basins. We derive conditions on the initialization of the networks, which ensures convergence to fixed points only. Application to a fully asynchronous Hopfield neural network allows us to validate our study.

This paper introduces and compares three parallel algorithms to compute general geometric image transformations on MIMD machines. We propose three variants of a parallel general scheme. We focus on the load balancing and the data redistributions. Experimental results are reported and compared. The implementation has been done using PPCM library allowing us to run the program over different parallel machines. We compare logical communication schemes for message-passing machines. Since our parallel algorithm needs global communications such as multiscatters, we study the efficiency of two different logical topologies usable with PPCM. These studies allow us to find the best combination of algorithm and virtual topology to use on a given parallel machine.

We propose in this paper, a parallel implementation of a ground visualization algorithm. Our input data consist in a Digital Elevation Model (DEM) covering a rectangular region, together with a raster image of the same area (the texture). The goal of the algorithm is to compute in parallel, images of the DEM from any point of view while mapping the texture onto the surface. The main originality of our approach concerns the distribution of the data, leading to a load-balanced and scalable parallel algorithm. We use a workload estimation to partition the output image, and then redistribute the input data according to this division. Special attention is paid on the data structures used for minimizing the cost of communications.