Research departments


“AND” TEAM: Algorithmique Numérique Distribuée (Distributed digital algorithmics)

Team leader




Our AND team started out in the field of distributed digital algorithms and high-performance computing, focusing its investigations on asynchronous iterations. These are used to accelerate convergence towards the solution of a problem formulated as a fixed point.

Subsequently, the team studied how to make asynchronous iterations diverge so as to produce chaos. The chaotic properties of these iterations were studied as a part of dynamic systems, with the results applied to various issues surrounding computer safety. These investigations into asynchronous iterations were also applied to wireless sensor networks for which, in practice, node synchronization is difficult to achieve. Thus, the team was quick to pursue its investigations of these subjects.

Finally, since the spatial and temporal evolution of genomes and proteins can be modeled by dynamic systems, the team has oriented a part of its activities towards biocomputing, which necessitates high-performance computing.

Goals and Research Areas

The AND team’s research is concentrated on the 4 following themes:

› Discrete dynamic systems : a dynamic system is discrete if its global state is measured in discrete times (t=0, 1, 2, ...) and if each of the system’s general states is at values within the product space of a finite domain. Discrete dynamic systems (abbreviated as DDSs) have numerous applications such as in genetic networks, neuronal networks, etc.

Objectives :
- To establish the convergence conditions for certain DDSs, depending on the mode of iterations selected as the pure parallel mode, or the chaotic or asynchronous modes;
- To understand the situations that generate intense disorder, during practical use of these discrete dynamic systems, functioning as chaotic or asynchronous iterations.

› Distributed digital algorithmics : the team studies and designs large-scale iterative parallel algorithms to solve linear or nonlinear problems (for example, modeled by partial differential equations). Much of its work concerns algorithms for which the iterations are desynchronized so as to cover all communications via computing.

› Digital algorithms for sensor networks : a network of wireless sensors/microsensors is a coherent set of sensor nodes using wireless communications within an ad hoc network.

Objectives :
- To model a network of sensors/microsensors able to predict performances (via simulations), but especially to obtain indications concerning the technological production of a sensor node;
- To define algorithms in order to verify the behavior or a network of sensors.

› Biocomputing :
problems of spatial and temporal evolution of nucleotide or protein sequences. Investigations including the writing of algorithms for the study of protein folding models or the description of genome evolution over time.

Implementing our work

The AND team works in collaboration with the majority of the other FEMTO-ST departments : AS2M, OPTICS, TIME FREQUENCY, ENERGY and APPLIED MECHANICS.