Accelerating Abelian Random Walks with Hyperbolic Dynamics

Given integers $d \geq 2, n \geq 1$, we consider affine random walks on torii $(\mathbb{Z} / n \mathbb{Z})^{d}$ defined as $X_{t+1} = A X_{t} + B_{t} \mod n$, where $A \in \mathrm{GL}_{d}(\mathbb{Z})$ is an invertible matrix with integer entries and $(B_{t})_{t \geq 0}$ is a sequence of iid random increments on $\mathbb{Z}^{d}$. We show that when $A$ has no eigenvalues of modulus $1$, this random walk mixes in $O(\log n \log \log n)$ steps as $n \rightarrow \infty$, and mixes actually in $O(\log n)$ steps only for almost all $n$. These results generalize those on the so-called Chung-Diaconis-Graham process, which corresponds to the case $d=1$. Our proof is based on the initial arguments of Chung, Diaconis and Graham, and relies extensively on the properties of the dynamical system $x \mapsto A^{\top} x$ on the continuous torus $\mathbb{R}^{d} / \mathbb{Z}^{d}$. Having no eigenvalue of modulus one makes this dynamical system a hyperbolic toral automorphism, a typical example of a chaotic system known to have a rich behaviour. As such our proof sheds new light on the speed-up gained by applying a deterministic map to a Markov chain.Comment: 26 page

Accounting for horizontal gene transfers explains conflicting hypotheses regarding the position of aquificales in the phylogeny of Bacteria

<p>Abstract</p> <p>Background</p> <p>Despite a large agreement between ribosomal RNA and concatenated protein phylogenies, the phylogenetic tree of the bacterial domain remains uncertain in its deepest nodes. For instance, the position of the hyperthermophilic Aquificales is debated, as their commonly observed position close to Thermotogales may proceed from horizontal gene transfers, long branch attraction or compositional biases, and may not represent vertical descent. Indeed, another view, based on the analysis of rare genomic changes, places Aquificales close to epsilon-Proteobacteria.</p> <p>Results</p> <p>To get a whole genome view of <it>Aquifex </it>relationships, all trees containing sequences from <it>Aquifex </it>in the HOGENOM database were surveyed. This study revealed that <it>Aquifex </it>is most often found as a neighbour to Thermotogales. Moreover, informational genes, which appeared to be less often transferred to the <it>Aquifex </it>lineage than non-informational genes, most often placed Aquificales close to Thermotogales. To ensure these results did not come from long branch attraction or compositional artefacts, a subset of carefully chosen proteins from a wide range of bacterial species was selected for further scrutiny. Among these genes, two phylogenetic hypotheses were found to be significantly more likely than the others: the most likely hypothesis placed Aquificales as a neighbour to Thermotogales, and the second one with epsilon-Proteobacteria. We characterized the genes that supported each of these two hypotheses, and found that differences in rates of evolution or in amino-acid compositions could not explain the presence of two incongruent phylogenetic signals in the alignment. Instead, evidence for a large Horizontal Gene Transfer between Aquificales and epsilon-Proteobacteria was found.</p> <p>Conclusion</p> <p>Methods based on concatenated informational proteins and methods based on character cladistics led to different conclusions regarding the position of Aquificales because this lineage has undergone many horizontal gene transfers. However, if a tree of vertical descent can be reconstructed for Bacteria, our results suggest Aquificales should be placed close to Thermotogales.</p

Development of a laser shock adhesion test for the assessment of weak adhesive bonded CFRP structures

Adhesive bondin,g bas a great poœnlial far future ligbtweight bigb-loaded structures in the a.eronautic industiy. A preœquisite for sucb an application is dtat the bond quality of the adhesive joint can be assessed in a non-destructive way. However, the use of da.ssicaJ Non•DesiiUctive Techniques (NDT) does not aUow the evaluation of the adhesion stren,gt:h of an adhesive bond yet This paper pn!sents an investigation made on weak composite bonds in on!er to develop a laser shock wave adhesion test First, the procedure to produce controlled weak bonds is desaibed. CFRP bonded samples are pn!pared in a spedfic way and characterized by ultrasonic techniques to assess the absence of any detectable defect. 1ben, for sorne of the .samples, their bond streDgth is evaluated by mechanical destructive œsts and ether .samples are loaded by v.arious intensity lasers shocks. The obtained results help to understand the behavior of the composite bonds under Jaser shock loading:. thanks to two post-mortem techrùques. 1becorrelation between the laser parameterS and the induced damage is demon.strated, The potential of the laser shock. technique to dl.saiminate different bond quallties is shawn, and the need for the œst optinùzationlsdÛ(

Interface tactile pour la saisie de règles dans un système expert flou

International audienceDans de nombreux logiciels d'intelligence artificielle, comme par exemple les systèmes experts, il est nécessaire qu'un utilisateur saisisse des connaissances sous différentes formes. En particulier, dans les systèmes experts flous, il s'agit de règles de la forme SI...ALORS... manipulant des concepts linguistiques plutôt que des opérateurs mathématiques. Nous présentons dans cet article une interface graphique moderne permettant la saisie des règles dans un système expert flou s'appuyant sur l'usage naturel du glisser-déposer sur des surfaces tactiles comme des tablettes

Identification of complex network topologies through delayed mutual information

The definitions of delayed mutual information and multi-information are recalled. It is shown how the delayed mutual information may be used to reconstruct the interaction topology resulting from some unknown scale-free graph with its associated local dynamics. Delayed mutual information is also used to solve the community detection problem. A probabilistic voter model defined on a scale-free graph is used throughout the paper as an illustrative example.Comment: 6 pages, 9 figures. arXiv admin note: text overlap with arXiv:1911.0654

A study of composite material damage induced by laser shock waves

A laser shock wave technique has been used to study the damage tolerance of T800/M21 CFRP (Carbon Fiber Reinforced Polymer) composite material with different lay_ups. Different levels of damage have been created according to various laser irradiation conditions. Several characterization methods such as Optical Microscopy, X-ray Radiography, or Interferometric Confocal Microscopy have been used to quantify these defects. The nature of the defects induced by the shock wave propagation has been studied. The sensitivity of the composite material damage to the shock conditions has been shown and quantified. Moreover, the experimental results gathered with each technique have been compared to each other and it leads to a better understanding of the CFRP behavior under high dynamic loading. These original results have enabled the definition of a specific damage criterion for CFRP under dynamic loading

A Lattice Boltzmann Model to Study Sedimentation Phenomena in Irrigation Canals

Fresh water is one of the most significant resources for human activities and survival, and irrigation is among the most important uses of water. The sustainibility and performance of irrigation canals can be greatly affected by sediment transport and deposition. In our previous works, we proposed a Lattice Boltzmann model for simulating a free surface flow in an irrigation canal, as an alternative to more traditional models mainly based on shallow water equations. Here we introduce the sedimentation phenomenon into our model by adding a new algorithm, based on the earlier work by B. Chopard, A. Dupuis and A. Masselot [9,11,12,27]. Transport, erosion, deposition and toppling of sediments are taken into account and enable the global sedimentation algorithm to simulate different transport modes such as bed load and suspended load. In the present work, we study both the behaviour of a sediment deposit located at an underflow submerged gate (depending on the gate opening and the flow discharge) and the influence of the presence of such a deposit on the flow. Both numerical and experimental validations have been performed. The experiments were realized on the micro-canal of the LCIS laboratory at Valence, France. The comparisons between simulations and experiments give good qualitative agreemen

Linear Sampling Method applied to Non Destructive Testing of an elastic waveguide: theory, numerics and experiments

International audienceThis paper presents an application of the Linear Sampling Method to ultrasonic Non Destructive Testing of an elastic waveguide. In particular, the NDT context implies that both the solicitations and the measurements are located on the surface of the waveguide and are given in the time domain. Our strategy consists in using a modal formulation of the Linear Sampling Method at multiple frequencies, such modal formulation being justified theoretically in [1] for rigid obstacles and in [2] for cracks. Our strategy requires the inversion of some emission and reception matrices which deserve some special attention due to potential ill-conditioning. The feasibility of our method is proved with the help of artificial data as well as real data

Extensive collection of femtoliter pad secretion droplets in beetle Leptinotarsa decemlineata allows nanoliter microrheology

Pads of beetles are covered with long, deformable setae, each ending in a micrometric terminal plate coated with secretory fluid. It was recently shown that the layer of the pad secretion covering the terminal plates is responsible for the generation of strong attractive forces. However, less is known about the fluid itself because it is produced in extremely small quantity. We here present a first experimental investigation of the rheological properties of the pad secretion in the Colorado potato beetle {\it Leptinotarsa decemlineata}. Because the secretion is produced in an extremely small amount at the level of the terminal plate, we first develop a procedure based on capillary effects to collect the secretion. We then manage to incorporate micrometric beads, initially in the form of a dry powder, and record their thermal motion to determine the mechanical properties of the surrounding medium. We achieve such a quantitative measurement within the collected volume, much smaller than the $1 {\rm \mu}$l sample volume usually required for this technique. Surprisingly, the beetle secretion was found to behave as a purely viscous liquid, of high viscosity. This suggests that no specific complex fluid behaviour is needed during beetle locomotion. We build a scenario for the contact formation between the spatula at the setal tip and a substrate, during the insect walk. We show that the attachment dynamics of the insect pad computed from the high measured viscosity is in good agreement with observed insect pace. We finally discuss the consequences of the secretion viscosity on the insect adhesion

Derivation via Hamilton's principle of a new shallow-water model using a color function for the macroscopic description of partial wetting phenomena

This paper presents a new shallow-water type model suitable for the simulation of partially wetting liquid films without the need for very fine resolution of the contact line phenomena, which is particularly suitable for industrial applications. This model is based on the introduction of a color function, propagated at the averaged velocity of the bulk flow, and equal to one where there is a liquid film and zero in the dry zone, which implies a non zero gradient only at the interface. This approach has the advantage of easily locating the interface, allowing to model macroscopically the forces acting at the contact line, which is essential for the simulation of partial wetting phenomena. The formal derivation of this model is based on the principle of least action known as Hamilton's principle. Here this principle is applied in a full Eulerian form to derive the complete system of equations with the color function. This method proves to be particularly suitable for this type of development and as an illustration it is also applied to recover another model proposed by Lallement et al. [39, 73]. Finally, both models are compared from a theoretical point of view and the advantages of the new color function based model are discussed