Volume 14 - 2011 - Special issue CARI'10

1. A transmission model of Bilharzia : A mathematical analysis of an heterogeneous model

Riveau Gilles ; Sallet Gauthier ; Tendeng Lena.
We consider an heterogeneous model of transmission of bilharzia. We compute the basic reproduction ratio R 0. We prove that if R 0 < 1, then the disease free equilibrium is globally asymptotically stable. If R 0 > 1 then there exists an unique endemic equilibrium, which is globally asymptotically stable. We will then consider possible applications to real data

2. Sur un modèle de compétition et de coexistence dans le chémostat

Radhouane Fekih Salem ; Tewfik Sari ; Nahla Abdellatif.
In this paper, we consider the mathematical model of two microbial species competition on a single resource in a chemostat. We take into account the interspecific interactions between the two populations of micro-organisms and intraspecific interactions between individuals themselves. The growth functions are monotonic and the dilution ratios are distinct. We determine the equilibrium points, and their local stability.

3. Segmentation d’Images Texturées Couleur à l’aide de modèles paramétriques pour approche la distribution des erreurs de prédiction linéaires

Imtnan-Ul-Haque Qazi ; O. Alata ; J.-C. Burie ; A. Moussa ; Christine Fernandez-Maloigne.
We propose novel a priori parametric models to approximate the distribution of the two dimensional multichannel linear prediction error in order to improve the performance of color texture segmentation algorithms. Two dimensional linear prediction models are used to characterize the spatial structures in color images. The multivariate linear prediction error of these texture models is approximated with Wishart distribution and multivariate Gaussian mixture models. A novel color texture segmentation framework based on these models and a spatial regularization model of initial class label fields is presented. For the proposed method and with different color spaces, experimental results show better performances in terms of percentage segmentation error, in comparison with the use of a multivariate Gaussian law.

4. Evaluation objective des méthodes de segmentation des maillages polygonaux 3D basée sur la classification de régions

Amira Zguira ; Narjes Doggaz ; Ezzeddine Zagoubra.
In this paper, we propose an objective evaluation approach of polygonal 3D mesh segmentation algorithms. Our approach is based on region classification. For that, we classify first manual segmented mesh into convex, concave and planar regions. Secondly, we present three quality measures that quantify the similarity of each type of region of the ground-truth relatively to the segmentation obtained by an automatic algorithm. We apply this approach on eight wellselected existing algorithms on heterogeneous images. This provides better understanding as to the strengths and weaknesses of each technique in function of each mesh-regions type in the aim to make the better choice concerning the segmentation algorithms for different applications.

5. Multigrid methods and data assimilation ― Convergence study and first experiments on non-linear equations

Emilie Neveu ; Laurent Debreu ; François-Xavier Le Dimet.
In order to limit the computational cost of the variational data assimilation process, we investigate the use of multigrid methods to solve the associated optimal control system. On a linear advection equation, we study the impact of the regularization term and the discretization errors on the efficiency of the coarse grid correction step introduced by the multigrid method. We show that even if for a perfect numerical model the optimal control problem leads to the solution of an elliptic system, discretization errors introduce implicit diffusion that can alter the success of the multigrid methods. Then we test the multigrids configuration and the influence of the algorithmic parameters on a non-linear Burgers equation to show that the algorithm is robust and converges much faster than the monogrid one.

6. Parallel GMRES with a multiplicative Schwarz preconditioner

Désiré Nuentsa Wakam ; Guy-Antoine Atenekeng-Kahou.
This paper presents a robust hybrid solver for linear systems that combines a Krylov subspace method as accelerator with a Schwarz-based preconditioner. This preconditioner uses an explicit formulation associated to one iteration of the multiplicative Schwarz method. The Newtonbasis GMRES, which aim at expressing a good data parallelism between subdomains is used as accelerator. In the first part of this paper, we present the pipeline parallelism that is obtained when the multiplicative Schwarz preconditioner is used to build the Krylov basis for the GMRES method. This is referred as the first level of parallelism. In the second part, we introduce a second level of parallelism inside the subdomains. For Schwarz-based preconditioners, the number of subdomains are keeped small to provide a robust solver. Therefore, the linear systems associated to subdomains are solved efficiently with this approach. Numerical experiments are performed on several problems to demonstrate the benefits of using these two levels of parallelism in the solver, mainly in terms of numerical robustness and global efficiency.

7. Two-Aircraft Acoustic Optimal Control Problem: SQP algorithms

F. Nahayo ; S. Khardi ; J. Ndimubandi ; M. Haddou ; M. Hamadiche.
This contribution aims to develop an acoustic optimization model of flight paths minimizing two-aircraft perceived noise on the ground. It is about minimizing the noise taking into account all the constraints of flight without conflict. The flight dynamics associated with a cost function generate a non-linear optimal control problem governed by ordinary non-linear differential equations. To solve this problem, the theory of necessary conditions for optimal control problems with instantaneous constraints is well used. This characterizes the optimal solution as a local one when the newtonian approach has been used alongside the optimality conditions of Karush-Kuhn-Tucker and the trust region sequential quadratic programming. The SQP methods are suggested as an option by commercial KNITRO solver under AMPL programming language. Among several possible solution, it was shown that there is an optimal trajectory (for each aircraft) leading to a reduction of noise levels on the ground.

8. Instrumentation des activités des tuteurs à l’aide d’un système multi-agents d’analyse automatique des interactions

Ilham Oumaira ; Rochdi Messoussi ; Raja TOUAHNI.
Research presented in this article is dedicated to the tutor instrumentation in distance collaborative learning situations. We are particularly interested in the reuse of interaction analysis indicators. In this paper, we present our system SYSAT; a multi-agent system for monitoring the activities of learners. The aim of SYSAT is to reuse indicators (social, cognitive, emotional ...) reported in the literature, in an open and adaptive system. We tested our system on the interaction data from two experiments conducted with two master students of the Ibn Tofail University. The article presents the results and discusses the prospects for Research.

9. Schéma DHT hiérarchique pour la tolérance aux pannes dans les réseaux P2P-SIP

Ibrahima Diané ; Ibrahima Niang.
This paper focuses on fault tolerance of super-nodes in P2P-SIP systems. These systems are characterized by high volatility of super-nodes. Most fault-tolerant proposed solutions are only for physical defects. They do not take into consideration the timing faults that are very important for multimedia applications such as telephony. This paper proposes a timing and physical fault tolerant mechanism based on P2P overlay with two levels for P2P-SIP systems. The simulation results show that our proposition reduces mostly the nodes location latency and increases the probability to find the called nodes.

10. Collision-resistant hash function based on composition of functions

René Ndoundam ; Juvet Karnel Sadie.
A cryptographic hash function is a deterministic procedure that compresses an arbitrary block of numerical data and returns a fixed-size bit string. There exists many hash functions: MD5, HAVAL, SHA, ... It was reported that these hash functions are no longer secure. Our work is focused on the construction of a new hash function based on composition of functions. The construction used the NP-completeness of Three-dimensional contingency tables and the relaxation of the constraint that a hash function should also be a compression function.

11. Dépliage des réseaux de Petri temporels à modèle sous-jacent non sauf

M. Sogbohossou ; D. Delfieu.
For the formal verification of the concurrent or communicating dynamic systems modeled with Petri nets, the method of the unfolding is used to cope with the well-known problem of the state explosion. An extension of the method to the non safe time Petri nets is presented. The obtained unfolding is simply a prefix of that from the underlying ordinary Petri net to the time Petri net. For a certain class of time Petri nets, a finite prefix capturing the state space and the timed language ensues from the calculation of a finite set of finite processes with valid timings. The quantitative temporal constraints associated with these processes can serve to validate more effectively the temporal specifications of a hard real-time system.

12. Cohérence de vues dans la spécification des Architectures Logicielles

Georges-Edouard Kouamou.
Cet article s’intéresse à la spécification des architectures logicielles. Il présente une symbiose entre l’approche conceptuelle basée sur les profils UML et la vision opérationnelle prônée par ArchJava. Actuellement, chaque langage de description se situe à une extrémité du processus, engendrant ainsi un découplage entre la spécification des Architectures Logicielles et leur implémentation et un risque d’incohérence. Nous décrivons une démarche basée sur un profil UML pour la description structurale des architectures logicielles et des règles de transformation pour générer le code source. Les expérimentations actuelles sont probantes et nous espérons poursuivre la réflexion sur les configurations et l’aspect dynamique.

13. Un protocole de fertilisation croisée d’un langage fonctionnel et d’un langage objet: application à la mise en oeuvre d’un prototype d’éditeur coopératif asynchrone

Maurice Tchoupé Tchendji.
The cross-fertilization is a technique to pool expertise and resources of at least two sectors in order to make the best of each. In this paper, we present a protocol of programming based on cross-fertilization of two programming languages (Haskell and Java) under two different programming paradigms: the functional paradigm and the object paradigm. This pooling of the strengths of each type of language permit to develop more secure applications in a shorter time, with functional code concise, easily understandable and thus, easily maintainable by one third. We present the meta-architecture of applications developed following this approach and an instantiation of it for the implementation of a prototype of an asynchronous collaborative editor.