12,694 research outputs found
Dual braid monoids, Mikado braids and positivity in Hecke algebras
We study the rational permutation braids, that is the elements of an
Artin-Tits group of spherical type which can be written where
and are prefixes of the Garside element of the braid monoid. We give a
geometric characterization of these braids in type and and then
show that in spherical types different from the simple elements of the
dual braid monoid (for arbitrary choice of Coxeter element) embedded in the
braid group are rational permutation braids (we conjecture this to hold also in
type ).This property implies positivity properties of the polynomials
arising in the linear expansion of their images in the Iwahori-Hecke algebra
when expressed in the Kazhdan-Lusztig basis. In type , it implies
positivity properties of their images in the Temperley-Lieb algebra when
expressed in the diagram basis.Comment: 26 pages, 8 figure
Optimizing the geometrical accuracy of curvilinear meshes
This paper presents a method to generate valid high order meshes with
optimized geometrical accuracy. The high order meshing procedure starts with a
linear mesh, that is subsequently curved without taking care of the validity of
the high order elements. An optimization procedure is then used to both
untangle invalid elements and optimize the geometrical accuracy of the mesh.
Standard measures of the distance between curves are considered to evaluate the
geometrical accuracy in planar two-dimensional meshes, but they prove
computationally too costly for optimization purposes. A fast estimate of the
geometrical accuracy, based on Taylor expansions of the curves, is introduced.
An unconstrained optimization procedure based on this estimate is shown to
yield significant improvements in the geometrical accuracy of high order
meshes, as measured by the standard Haudorff distance between the geometrical
model and the mesh. Several examples illustrate the beneficial impact of this
method on CFD solutions, with a particular role of the enhanced mesh boundary
smoothness.Comment: Submitted to JC
Performance of piezoelectric shunts for vibration reduction
This work addresses passive reduction of structural vibration by means of shunted piezoelectric patches. The two classical resistive and resonant shunt solutions are considered. The main goal of this paper is to give closed-form solutions to systematically estimate the damping performances of the shunts, in the two cases of free and forced vibrations, whatever the elastic host structure is. Then it is carefully demonstrated that the performance of the shunt, in terms of vibration reduction, depends on only one free parameter: the so-called modal electromechanical coupling factor (MEMCF) of the mechanical vibration mode to which the shunts are tuned. Experiments are proposed and an excellent agreement with the model is obtained, thus validating it
Finite element reduced order models for nonlinear vibrations of piezoelectric layered beams with applications to NEMS
This article presents a finite element reduced order model for the nonlinear vibrations of piezoelectric layered beams with application to NEMS. In this model, the geometrical nonlinearities are taken into account through a von Kármán nonlinear strain–displacement relationship. The originality of the finite element electromechanical formulation is that the system electrical state is fully described by only a couple of variables per piezoelectric patches, namely the electric charge contained in the electrodes and the voltage between the electrodes. Due to the geometrical nonlinearity, the piezoelectric actuation introduces an original parametric excitation term in the equilibrium equation. The reduced-order formulation of the discretized problem is obtained by expanding the mechanical displacement unknown vector onto the short-circuit eigenmode basis. A particular attention is paid to the computation of the unknown nonlinear stiffness coefficients of the reduced-order model. Due to the particular form of the von Kármán nonlinearities, these coefficients are computed exactly, once for a given geometry, by prescribing relevant nodal displacements in nonlinear static solutions settings. Finally, the low-order model is computed with an original purely harmonic-based continuation method. Our numerical tool is then validated by computing the nonlinear vibrations of a mechanically excited homogeneous beam supported at both ends referenced in the literature. The more difficult case of the nonlinear oscillations of a layered nanobridge piezoelectrically actuated is also studied. Interesting vibratory phenomena such as parametric amplification or patch length dependence of the frequency output response are highlighted in order to help in the design of these nanodevices.This research is part of the NEMSPIEZO project, under funds from the French National Research Agency (Project ANR-08-NAN O-015-04), for which the authors are grateful
Efficient Learning of Sparse Conditional Random Fields for Supervised Sequence Labelling
Conditional Random Fields (CRFs) constitute a popular and efficient approach
for supervised sequence labelling. CRFs can cope with large description spaces
and can integrate some form of structural dependency between labels. In this
contribution, we address the issue of efficient feature selection for CRFs
based on imposing sparsity through an L1 penalty. We first show how sparsity of
the parameter set can be exploited to significantly speed up training and
labelling. We then introduce coordinate descent parameter update schemes for
CRFs with L1 regularization. We finally provide some empirical comparisons of
the proposed approach with state-of-the-art CRF training strategies. In
particular, it is shown that the proposed approach is able to take profit of
the sparsity to speed up processing and hence potentially handle larger
dimensional models
Properties of selected mutations and genotypic landscapes under Fisher's Geometric Model
The fitness landscape - the mapping between genotypes and fitness -
determines properties of the process of adaptation. Several small genetic
fitness landscapes have recently been built by selecting a handful of
beneficial mutations and measuring fitness of all combinations of these
mutations. Here we generate several testable predictions for the properties of
these landscapes under Fisher's geometric model of adaptation (FGMA). When far
from the fitness optimum, we analytically compute the fitness effect of
beneficial mutations and their epistatic interactions. We show that epistasis
may be negative or positive on average depending on the distance of the
ancestral genotype to the optimum and whether mutations were independently
selected or co-selected in an adaptive walk. Using simulations, we show that
genetic landscapes built from FGMA are very close to an additive landscape when
the ancestral strain is far from the optimum. However, when close to the
optimum, a large diversity of landscape with substantial ruggedness and sign
epistasis emerged. Strikingly, landscapes built from different realizations of
stochastic adaptive walks in the same exact conditions were highly variable,
suggesting that several realizations of small genetic landscapes are needed to
gain information about the underlying architecture of the global adaptive
landscape.Comment: 51 pages, 8 figure
- …