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.     

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.     

Carbon‐Nanotube–PDMS Composite Coatings on Optical Fibers for All‐Optical Ultrasound Imaging

Polymer–carbon nanotube composite coatings have properties that are desirable for a wide range of applications. However, fabrication of these coatings onto submillimeter structures with the efficient use of nanotubes has been challenging. Polydimethylsiloxane (PDMS)–carbon nanotube composite coatings are of particular interest for optical ultrasound transmission, which shows promise for biomedical imaging and therapeutic applications. In this study, methods for fabricating composite coatings comprising PDMS and multiwalled carbon nanotubes (MWCNTs) with submicrometer thickness are developed and used to coat the distal ends of optical fibers. These methods include creating a MWCNT organogel using two solvents, dip coating of this organogel, and subsequent overcoating with PDMS. These coated fibers are used as all‐optical ultrasound transmitters that achieve high ultrasound pressures (up to 21.5 MPa peak‐to‐peak) and broad frequency bandwidths (up to 39.8 MHz). Their clinical potential is demonstrated with all‐optical pulse‐echo ultrasound imaging of an aorta. The fabrication methods in this paper allow for the creation of thin, uniform carbon nanotube composites on miniature or temperature‐sensitive surfaces, to enable a wide range of advanced sensing capabilities.     

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.     

Compound Node–Kayles on paths

In his celebrated book [J.H. Conway, On Numbers and Games, Academic Press, New-York, 1976, Second edition (2001), A.K. Peters, Wellesley, MA], J.H. Conway introduced twelve versions of compound games. We analyze these twelve versions for the Node–Kayles game on paths. For usual disjunctive compound, Node–Kayles has been solved for a long time under normal play, while it is still unsolved under misère play. We thus focus on the ten remaining versions, leaving only one of them unsolved.     

The mini-conical slump flow test: Analysis and numerical study

This paper provides a general study on cement paste flow. Both mini-slump and Marsh cone tests are used to evaluate the workability of fresh paste mixtures derived from self compacting concretes. A numerical approach is used to reproduce global flow behavior and to check the accuracy of the obtained viscosity as well as the validity of expressions available in the literature giving yield stress from the final diameter of slumped paste. The computational modeling allows access to local information in order to analyze different regions and corresponding flow types, i.e. falling solid and flowing fresh cementing material mixtures.The limitation of some empirical models allowing the prediction of yield stress τ₀ and plastic viscosity μ from mini-slump tests is underlined, conditions of validity are expressed and a new expression is proposed.