On two variations of identifying codes

Identifying codes have been introduced in 1998 to model fault detection in multiprocessor systems. In this paper, we introduce two variations of identifying codes: weak codes and light codes. They correspond to fault detection by successive rounds. We give exact bounds for those two definitions for the family of cycles.     

LAD models,trees, and an analog of the fundamental theorem of arithmetic

Motivated by applications of Logical Analysis of Data (LAD) in medical contexts, original discrete optimization problems are proposed. When a patient arrives with a presumption of a disease, he is submitted to a sequence of tests. From one patient to another, the tests allowing to detect the disease may vary. A subset of tests whose results detect the disease in a given part of the population is called a pattern, which has its own prevalence in the population.If there is only a limited number of tests that can be done, which ones must be selected in order to maximize the number of spotted patients? Or, if each test has a cost, in which order the tests have to be done, in order to minimize the cost? It is the kind of questions that are investigated in this paper. For various special cases, polynomial algorithms are proposed, especially when the hypergraph whose vertices are the tests and whose edges are the patterns is a tree graph.One of these questions involves a criterion which is not a number but a sequence of numbers. The objective is then to find the best sequence for the lexicographic order. To solve this question, a new product on finite sequences is defined, namely the maximum shuffle product, which maps two sequences to their shuffle that is maximal for the lexicographic order. Surprisingly, this product leads to a theorem similar to the fundamental theorem of arithmetic: every sequence can be written uniquely as the product of prime sequences, with the suitable definition of prime sequences.     

Paired-Domination in Subdivided Star-Free Graphs

A set S of vertices in a graph G is a paired-dominating set of G if every vertex of G is adjacent to some vertex in S and if the subgraph induced by S contains a perfect matching. The paired-domination number of G, denoted by γ _pr(G), is the minimum cardinality of a paired-dominating set of G. In [Dorbec P, Gravier S, Henning MA, J Comb Optim 14(1):1–7, 2007], the authors gave tight bounds for paired-dominating sets of generalized claw-free graphs. Yet, the critical cases are not claws but subdivided stars. We here give a bound for graphs containing no induced subdivided stars, depending on the size of the star.     

Variations on Tilings in the Manhattan Metric

We investigate tilings of the integer lattice in the Euclidean n-dimensional space. The tiles considered here are the union of spheres defined by the Manhattan metric. We give a necessary condition for the existence of such a tiling for Z ⁿ when n 2. We prove that this condition is sufficient when n=2. Finally, we give some tilings of Z ⁿ when n 3.     

Modelling of particle flows in a scrape-off layer with limiter biasing

The superconducting tokamak Tore Supra will be equipped with an actively cooled toroidal pump limiter (TPL), in the framework of the CIEL (Composants Internes Et Limiteurs) project, dedicated to plasma facing component design for steady state operation. The TPL is equipped with throats, located only on the high field side, for particle collection allowing the control of plasma density which is essential for long plasma discharges. The present design work of the CIEL includes a biasing system in order to enhance the particle pumping. A fluid model, based on the classical fluid equation, is used to estimate the effects of the electric field on the particle flows in the Scrape-Off Layer (SOL). The modifications of the density, the particle flow (toroidal and poloidal) and the position of the stagnation point are discussed as a function of the bias voltage. The model clearly illustrates the different resulting effects on particle pumping for a divertor and a limiter configuration which are designed respectively for poloidal or parallel particle collection. The model is used to interpret the ALT-biasing experiments recently carried out on TEXTOR-94. The pumping capability is shown to be improved by about (15–20)% for positive biasing while the experimental measurements of parallel Mach number are reproduced as a function of the applied voltage. The e-folding length of the edge density in the SOL is also shown to increase from 1.5 to about 2.0 cm for a biased voltage of −400 to 400 V, respectively, in accordance with the model. Finally, the model is used to extrapolate the TEXTOR-94 results to CIEL suggesting that pumping speed enhancement of 25 to 30% may be obtained. Partner in Trilateral Euregio Cluster Partner in Trilateral Euregio Cluster Presented at the Workshop on Role of Electric Fields in Plasma Confinement and Exhaust, Budapest, 18–19 June 2000.     

Dynamical study and control of drift waves in a magnetized laboratory plasma

The various dynamical regimes of collisional drift waves in a magnetized plasma column are experimentally studied. These unstable low-frequency electrostatic waves are related with strong modulations of the ion and electron density. The angular velocity of the rotating plasma column is the control parameter of the dynamics: regular, chaotic and turbulent regimes are obtained. The spatial extension of the system allows for the occurrence of spatiotemporal chaos. The time-delay auto-synchronization method of controlling chaos [K. Pyragas, Phys. Lett. A 170, 421 (1992)] though purely temporal is successfully applied. A numerical study using coupled nonlinear oscillators exhibiting chaos is compared to the experimental results. The control method is tested on this model.     

Spin-dependent transport in cluster-assembled nanostructures: influence of cluster size and matrix material

Spin-dependent transport in granular metallic nanostructures has been investigated by means of a thermoelectric measurement. Cobalt clusters of well-defined size (〈n〉 = 15-600) embedded in copper and silver matrices show magnetic field responses of up to several hundred percent at low temperature. The experimental observations are attributed to spin mixing. The influence of cluster size and matrix are discussed.     

Optimal trajectories between Earth and Mars in their true planetary orbits

The optimal transfers from Earth to Mars and from Mars to Earth, considering the actual planetary orbits, are presented as functions of the corresponding idealized Hohmann transfers. The numerically exact two-impulse optimal trajectories are given in graphical form for all possible Hohmann windows. The two-impulse transfers which are absolute optimals and those for which a third impulse provides the absolute optimal are delineated. These data are designed to provide all the information necessary for quick orbit calculations for preliminary Martian mission analysis. In this form, they are as easy to use as the standard Hohmann transfer approximations and provide much greater accuracy.This research was supported in part by the National Aeronautics and Space Administration through Grant No. NGR-06-003-033.     

Interactions between high-temperature deformation and crystallization in zirconium-based bulk metallic glasses

High-temperature deformation of a ZrTiCuNiBe bulk metallic glass (BMG) is investigated by compression tests in the supercooled liquid region. When the temperature is decreased or strain rate increased, the amorphous alloy exhibits the usual Newtonian/non-Newtonian transition behaviour. Using specific heat treatments, partially crystallized alloys are produced, the associated microstructures characterized and the volume fractions of the crystal measured. The interaction between high-temperature deformation and crystallization is investigated by appropriate mechanical testing. According to these measurements, partial crystallization is responsible for a significant increase in flow stress and the promotion of non-Newtonian behaviour. Deformation does not significantly change the volume fraction, composition or size of the crystal. The flow-stress increase with crystallization is analyzed under different hypotheses. We conclude that the flow-stress increase cannot be interpreted through a compositional change in the residual amorphous matrix, either by reinforcement due to hard crystallites or by connections between crystals. It appears that the effect is due to the nanometric size of the crystals alone.