Modular Composition Modulo Triangular Sets and Applications

We generalize Kedlaya and Umans’ modular composition algorithm to the multivariate case. As a main application, we give fast algorithms for many operations involving triangular sets (over a finite field), such as modular multiplication, inversion, or change of order. For the first time, we are able to exhibit running times for these operations that are almost linear, without any overhead exponential in the number of variables. As a further application, we show that, from the complexity viewpoint, Charlap, Coley, and Robbins’ approach to elliptic curve point counting can be competitive with the better known approach due to Elkies.     

Multi-contact vertical ladder climbing with an HRP-2 humanoid

We describe the research and the integration methods we developed to make the HRP-2 humanoid robot climb vertical industrial-norm ladders. We use our multi-contact planner and multi-objective closed-loop control formulated as a QP (quadratic program). First, a set of contacts to climb the ladder is planned off-line (automatically or by the user). These contacts are provided as an input for a finite state machine. The latter builds supplementary tasks that account for geometric uncertainties and specific grasps procedures to be added to the QP controller. The latter provides instant desired states in terms of joint accelerations and contact forces to be tracked by the embedded low-level motor controllers. Our trials revealed that hardware changes are necessary, and parts of software must be made more robust. Yet, we confirmed that HRP-2 has the kinematic and power capabilities to climb real industrial ladders, such as those found in nuclear power plants and large scale manufacturing factories (e.g. aircraft, shipyard) and construction sites.     

Computing monodromy via continuation methods on random Riemann surfaces

We consider a Riemann surface X defined by a polynomial f(x,y) of degree d, whose coefficients are chosen randomly. Hence, we can suppose that X is smooth, that the discriminant δ(x) of f has d(d−1) simple roots, Δ, and that δ(0)≠0, i.e. the corresponding fiber has d distinct points {y₁,…,y_d}. When we lift a loop 0∈γ⊂C−Δ by a continuation method, we get d paths in X connecting {y₁,…,y_d}, hence defining a permutation of that set. This is called monodromy.Here we present experimentations in Maple to get statistics on the distribution of transpositions corresponding to loops around each point of Δ. Multiplying families of “neighbor” transpositions, we construct permutations and the subgroups of the symmetric group they generate. This allows us to establish and study experimentally two conjectures on the distribution of these transpositions and on transitivity of the generated subgroups.Assuming that these two conjectures are true, we develop tools allowing fast probabilistic algorithms for absolute multivariate polynomial factorization, under the hypothesis that the factors behave like random polynomials whose coefficients follow uniform distributions.     

Good reduction of Puiseux series and applications

We have designed a new symbolic-numeric strategy for computing efficiently and accurately floating point Puiseux series defined by a bivariate polynomial over an algebraic number field. In essence, computations modulo a well-chosen prime number p are used to obtain the exact information needed to guide floating point computations. In this paper, we detail the symbolic part of our algorithm. First of all, we study modular reduction of Puiseux series and give a good reduction criterion for ensuring that the information required by the numerical part is preserved. To establish our results, we introduce a simple modification of classical Newton polygons, that we call “generic Newton polygons”, which turns out to be very convenient. Finally, we estimate the size of good primes obtained with deterministic and probabilistic strategies. Some of these results were announced without proof at ISSAC’08.     

Damage quantification in aluminium alloys using in situ tensile tests in X-ray tomography

This paper presents results obtained using in situ tensile experiments allowing the observation of damage nucleation, growth and coalescence. Three different aluminium alloys (2024, 7449 and 5754) exhibiting various mechanical properties were chosen to produce a wide data base. Smooth and notched axisymetric samples were cut out of the raw materials to introduce different levels of initial stress triaxiality using the geometry of the samples. In the different cases, the damage steps (initiation, growth and coalescence) were clearly visualised during interrupted and continuous in situ tensile tests in synchrotron X-ray tomography. The imaging was performed with a voxel size of 1.6 μm. The X-ray tomography method also gives a precise image of the outer shape of the sample and its change during deformation can then be analysed. This allows to calculate precisely the true strain vs true stress curve and also an approximation of the stress triaxiality using the Bridgman formula. The results show that damage can be visualised but also quantified precisely in the different cases in terms of nucleation and growth, coalescence being also evident in the results but still hard to quantify so far. Finally, a previously developed model for damage growth during ductile straining based on the Rice and Tracey approach can be fitted to the results.     

Complexity bounds for the rational Newton-Puiseux algorithm over finite fields

We carefully study the number of arithmetic operations required to compute rational Puiseux expansions of a bivariate polynomial F over a finite field. Our approach is based on the rational Newton-Puiseux algorithm introduced by D. Duval. In particular, we prove that coefficients of F may be significantly truncated and that certain complexity upper bounds may be expressed in terms of the output size. These preliminary results lead to a more efficient version of the algorithm with a complexity upper bound that improves previously published results. We also deduce consequences for the complexity of the computation of the genus of an algebraic curve defined over a finite field or an algebraic number field. Our results are practical since they are based on well established subalgorithms, such as fast multiplication of univariate polynomials with coefficients in a finite field.     

Electrical characterization of polyaniline‐based adhesive blends

Preparation and processing of conductive blends based on doped polyaniline (c‐PANI) or tetra‐aniline (c‐TANI) with epoxy resins is described. The dedoping of c‐PANI by the epoxy hardener, in the process of the blend curing, has been investigated by UV–vis–NIR spectroscopy. Classical amine hardeners lead to a quick increase of the blend resistivity during its processing, which can be correlated with the observed spectral features, characteristic of the deprotonation of c‐PANI. For these reasons, for further investigations, BF₃‐amine complexes have been selected as curing agents. Using these hardeners and tuning the curing conditions (temperature and time), it is possible to obtain blends with resistivities down to 10² Ω·cm, depending on the type of the epoxy resin used. In general, resins with higher epoxy network densities give c‐PANI‐based blends of lower percolation thresholds. The effect of the c‐PANI processing solvent on the resistivity of the resulting blend is even more pronounced than the epoxy network density. In particular, blends processed from toluene show much higher resistivities than those processed from tetrahydrofuran (THF) of ethylacetate (EA). Above the percolation threshold, c‐TANI‐based epoxy blends show at least three orders of magnitude higher resistivities than their c‐PANI analogues. They are however technologically interesting, because they are not very sensitive to the processing/curing conditions and show lower percolation thresholds. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

A Herbivore Tag-and-Trace System Reveals Contact- and Density-Dependent Repellence of a Root Toxin

Foraging behavior of root feeding organisms strongly affects plant-environment-interactions and ecosystem processes. However, the impact of plant chemistry on root herbivore movement in the soil is poorly understood. Here, we apply a simple technique to trace the movement of soil-dwelling insects in their habitats without disturbing or restricting their interactions with host plants. We tagged the root feeding larvae of Melolontha melolontha with a copper ring and repeatedly located their position in relation to their preferred host plant, Taraxacum officinale, using a commercial metal detector. This method was validated and used to study the influence of the sesquiterpene lactone taraxinic acid β-D-glucopyranosyl ester (TA-G) on the foraging of M. melolontha. TA-G is stored in the latex of T. officinale and protects the roots from herbivory. Using behavioral arenas with TA-G deficient and control plants, we tested the impact of physical root access and plant distance on the effect of TA-G on M. melolontha. The larvae preferred TA-G deficient plants to control plants, but only when physical root contact was possible and the plants were separated by 5 cm. Melolontha melolontha showed no preference for TA-G deficient plants when the plants were grown 15 cm apart, which may indicate a trade-off between the cost of movement and the benefit of consuming less toxic food. We demonstrate that M. melolontha integrates host plant quality and distance into its foraging patterns and suggest that plant chemistry affects root herbivore behavior in a plant-density dependent manner.