Is protein folding problem really a NP-complete one ? First investigations

To determine the 3D conformation of proteins is a necessity to understand their functions or interactions with other molecules. It is commonly admitted that, when proteins fold from their primary linear structures to their final 3D conformations, they tend to choose the ones that minimize their free energy. To find the 3D conformation of a protein knowing its amino acid sequence, bioinformaticians use various models of different resolutions and artificial intelligence tools, as the protein folding prediction problem is a NP complete one. More precisely, to determine the backbone structure of the protein using the low resolution models (2D HP square and 3D HP cubic), by finding the conformation that minimize free energy, is intractable exactly. Both the proof of NP-completeness and the 2D prediction consider that acceptable conformations have to satisfy a self-avoiding walk (SAW) requirement, as two different amino acids cannot occupy a same position in the lattice. It is shown in this document that the SAW requirement considered when proving NP-completeness is different from the SAW requirement used in various prediction programs, and that they are different from the real biological requirement. Indeed, the proof of NP completeness and the predictions in silico consider conformations that are not possible in practice. Consequences of this fact are investigated in this research work.Comment: Submitted to Journal of Bioinformatics and Computational Biology, under revie

Régulation court terme du trafic aérien et optimisation combinatoire (application de la méthode de génération de colonnes)

On cherche à résoudre un problème combinatoire lié à la régulation court terme du trafic aérien : déterminer pour chaque vol régulable une trajectoire réalisable en 4 dimensions de manière à respecter les contraintes de capacité des secteurs tout en minimisant le coût de la politique choisie. Le problème est modélisé par un programme linéaire mixte et par une représentation ad hoc du système aérien. Un processus de résolution basé sur la génération de colonnes couplée à la technique de branch-and-bound est construit. La génération de colonnes par le sous problème de tarification consiste à construire des chemins à 4 dimensions sur un réseau continu et dynamique. Un algorithme spécifique de plus courts chemins combiné à la programmation dynamique est développé et testé. La méthode est évaluée sur des instances réelles représentant l'espace aérien européen. Les résultats obtenus en un temps de calcul compatible avec le contexte opérationnel valident finalement la méthode développée.ln this work, we address a combinatorial problem arising in the context of dynamic air traffic regulation. ln this problem, four-dimensional trajectories have to be built and assigned to every aircraft in order to suppress any sector overload, while minimizing the cost of the chosen policy. This problem is modelled with a mixed linear program, which is solved through column generation and branch-and-price. Its pricing sub-problem looks for feasible trajectories in a dynamie three dimensional network ; to solve it, we developed a specifie algorithm based on labelling shortest path algorithms and dynamic programming. Each algorithm is tested on real-world data relative to the European air system under the responsibility of the CFMU (Central Flow Management Unit). Results and computing times validate the who le solving processGRENOBLE1-BU Sciences (384212103) / SudocSudocFranceF

Flows, View-Obstructions and the Lonely Runner

We prove the following result. Let G be an undirected graph. If G has a nowhere zero flow with at most k different values, then it also has one with values from the set f1; : : : ; kg. When k 5, this is a trivial consequence of Seymour's "six-flow theorem". When k 4 our proof is based on a lovely number theoretic problem which we call the "Lonely Runner Conjecture". Suppose k runners having nonzero constant speeds run laps on a unit-length circular track. Then there is a time at which all runners are at least 1=(k+1) from their common starting point. This conjecture appears to have been formulated by J. Wills (Montash. Math. 71 (1967)) and independently by T. Cusick (Aequationes Math. 9 (1973)). Fortunately for our purposes, this conjecture has been verified for k 4 by Cusick and Pomerance (J. Number Theory 19 (1984)) in a complicated argument involving exponential sums and electronic case checking. A major part of this paper is an elementary self-contained proof of the case k =..

Optimizing traditional urban network architectures to increase distributed generation connection

International audienc

Radial Network Reconfiguration Using Genetic Algorithm Based on the Matroid Theory

International audienceThis paper deals with Distribution Network (DN) reconfiguration for loss minimization. To solve this combinatorial problem, a Genetic Algorithm (GA) is considered. In order to enhance its ability to explore the solution space, efficient genetic operators are developed. After a survey of the existing DN topology description methods, a theoretical approach based on the graph and matroid theories (graphic matroid in particular) is considered. These concepts are used in order to propose new intelligent and effective GA operators for efficient mutation and crossover well dedicated to the DN reconfiguration problem. All resulting individuals after GA operators are claimed to be feasible (radial) configurations. Moreover the presented approach is valid for planar or non planar DN graph topologies and avoids tedious mesh checks for the topology constraint validation. The proposed method is finally compared to some previous topology coding techniques used by other authors. The results show smaller or at least equal power losses with considerably less computation effort

Radial Network Reconfiguration Using Genetic Algorithm Based on the Matroid Theory

International audienc

Novel architectures and operation modes of Distribution Network to increase DG integration

International audienceNowadays, distribution networks are facing tremendous challenges. Actually, the opening of the energy market, the wish to preserve the environment and the reduction of fossil energy stocks have lead to use more and more distributed, renewable and local energy resources, such as wind and photovoltaic generators. These generating units are mostly connected to the distribution networks. With the increase of the penetration rate of these generation facilities, the traditional operation as well as planning of the concerned networks may need to evolve. In order to face this situation and offer increased network capabilities to support these new technologies, the distribution network has to switch to a flexible and smart network. To achieve these goals, two research paths are considered: the new architectures and the development of intelligent embedded systems. This paper deals with new architectures and particularly partially meshed distribution networks. It proposes a Monte Carlo algorithm as an efficient tool for analysing and assessing the relationship between grid architecture and DG penetration rate. Simulation results on a real urban French distribution networks have showed the effectiveness of the method with respect to grid planning. Particularly, it has demonstrated that evolving distribution grid architectures towards a partially and adapted meshed structure increases DG penetration level

A Novel Hybrid Network Architecture to Increase DG Insertion in Electrical Distribution systems

International audienceDistribution networks will experience a deep mutation concerning their planning and operation rules due to the expected increase of distributed generation (DG) interconnection to the grid. Indeed, the opening of the electricity market or the growing global concern for environmental issues will lead to a massive development of DGs. Yet, a too large amount of DGs could raise technical problems on distribution networks which have not been planned to operate with bi-directional power flow. The existing solutions to solve marginal DG connections could be no longer relevant. The distribution network definitely has to evolve towards a smarter and more flexible network. Two possible ways to reach this goal are through new architectures and developing intelligent systems. This paper focuses on new architectures and operating modes. The traditional radial distribution network could accept more DGs by introducing appropriately specific loops. A new hybrid structure enabling the coexistence of the radial and meshed operation is proposed. It is equipped with autonomous circuit-breakers and automated switches that improve its reliability. A heuristic algorithm is also proposed to build this new architecture while ensuring the equality of consumers with respect to the continuity of service and while minimizing the global cost

Investigation of new distribution grid architecture for accomodating higher dg penetration rate

International audienceEnvironment considerations combined to regulatory incentives and the opening of the energy markets has fostered the development of distributed generator (DG) in particular renewable ones. However, given the present operating modes and grid structures, a massive introduction of DG could deeply modify the behaviour of distribution networks. The two strategies used in France by the Distribution System Operator to anticipate the problems caused by DG are either reinforcement of the network or a dedicated feeder. The first strategy is acceptable as far as a marginal rate of DG is considered but could become too expensive in presence of a large amount of DG. The dedicated feeders strategy (direct connection of DGs to the HV/MV substation) could face a problem of local constraints. Inspired by the meshed operation of transmission network, a better way to integrate those generating units could be achieved through adding loops in the distribution network at appropriate locations. In order to compare the current architecture and operation mode with a meshed structure for better enabling more DG penetration, a stochastic algorithm based on Monte Carlo method was developed. This method was tested successfully on several networks which are parts of real urban and rural ones