Aubry sets vs Mather sets in two degrees of freedom

We study autonomous Tonelli Lagrangians on closed surfaces. We aim to clarify the relationship between the Aubry set and the Mather set, when the latter consists of periodic orbits which are not fixed points. Our main result says that in that case the Aubry set and the Mather set almost always coincide.Comment: Revised and expanded version. New proof of Lemma 2.3 (formerly Lemma 14

Level set based eXtended finite element modelling of the response of fibrous networks under hygroscopic swelling

Materials like paper, consisting of a network of natural fibres, exposed to variations in moisture, undergo changes in geometrical and mechanical properties. This behaviour is particularly important for understanding the hygro-mechanical response of sheets of paper in applications like digital printing. A two-dimensional microstructural model of a fibrous network is therefore developed to upscale the hygro-expansion of individual fibres, through their interaction, to the resulting overall expansion of the network. The fibres are modelled with rectangular shapes and are assumed to be perfectly bonded where they overlap. For realistic networks the number of bonds is large and the network is geometrically so complex that discretizing it by conventional, geometry-conforming, finite elements is cumbersome. The combination of a level-set and XFEM formalism enables the use of regular, structured grids in order to model the complex microstructural geometry. In this approach, the fibres are described implicitly by a level-set function. In order to represent the fibre boundaries in the fibrous network, an XFEM discretization is used together with a Heaviside enrichment function. Numerical results demonstrate that the proposed approach successfully captures the hygro-expansive properties of the network with fewer degrees of freedom compared to classical FEM, preserving desired accuracy.Comment: 27 pages, 22 figures, 4 tables, J. Appl. Mech. June 19, 202

Chronological age, somatic maturation and anthropometric measures: Association with physical performance of young male judo athletes

© 2021 by the authors. Licensee MDPI, Basel, Switzerland.Sport for children and adolescents must consider growth and maturation to ensure suitable training and competition, and anthropometric variables could be used as bio-banding strategies in youth sport. This investigation aimed to analyze the association between chronological age, biologic maturation, and anthropometric characteristics to explain physical performance of young judo athletes. Sixty-seven judokas (11.0–14.7 years) were assessed for anthropometric and physical performance. Predicted adult stature was used as a somatic maturation indicator. A Pearson’s bivariate correlation was performed to define which anthropometric variables were associated with each physical test. A multiple linear hierarchical regression was conducted to verify the effects of age, maturity, and anthropometry on physical performance. The regression models were built with age, predicted adult stature, and the three most significantly correlated anthropometric variables for each physical test. Older judokas performed better in most of the physical tests. However, maturation attenuated the age effect in most variables and significantly affected upper body and handgrip strength. Anthropometric variables attenuated age and maturity and those associated with body composition significantly affected the performance in most tests, suggesting a potential as bio-banding strategies. Future studies should investigate the role of anthropometric variables on the maturity effect in young judokas

Adaptive estimation in circular functional linear models

We consider the problem of estimating the slope parameter in circular functional linear regression, where scalar responses Y1,...,Yn are modeled in dependence of 1-periodic, second order stationary random functions X1,...,Xn. We consider an orthogonal series estimator of the slope function, by replacing the first m theoretical coefficients of its development in the trigonometric basis by adequate estimators. Wepropose a model selection procedure for m in a set of admissible values, by defining a contrast function minimized by our estimator and a theoretical penalty function; this first step assumes the degree of ill posedness to be known. Then we generalize the procedure to a random set of admissible m's and a random penalty function. The resulting estimator is completely data driven and reaches automatically what is known to be the optimal minimax rate of convergence, in term of a general weighted L2-risk. This means that we provide adaptive estimators of both the slope function and its derivatives

Sparsity and Incoherence in Compressive Sampling

We consider the problem of reconstructing a sparse signal $x^0\in\R^n$ from a limited number of linear measurements. Given $m$ randomly selected samples of $U x^0$, where $U$ is an orthonormal matrix, we show that $\ell_1$ minimization recovers $x^0$ exactly when the number of measurements exceeds $$m\geq \mathrm{Const}\cdot\mu^2(U)\cdot S\cdot\log n,$$ where $S$ is the number of nonzero components in $x^0$, and $\mu$ is the largest entry in $U$ properly normalized: $\mu(U) = \sqrt{n} \cdot \max_{k,j} |U_{k,j}|$. The smaller $\mu$, the fewer samples needed. The result holds for ``most'' sparse signals $x^0$ supported on a fixed (but arbitrary) set $T$. Given $T$, if the sign of $x^0$ for each nonzero entry on $T$ and the observed values of $Ux^0$ are drawn at random, the signal is recovered with overwhelming probability. Moreover, there is a sense in which this is nearly optimal since any method succeeding with the same probability would require just about this many samples

Adaptive density estimation for stationary processes

We propose an algorithm to estimate the common density $s$ of a stationary process $X_1,...,X_n$. We suppose that the process is either $\beta$ or $\tau$-mixing. We provide a model selection procedure based on a generalization of Mallows' $C_p$ and we prove oracle inequalities for the selected estimator under a few prior assumptions on the collection of models and on the mixing coefficients. We prove that our estimator is adaptive over a class of Besov spaces, namely, we prove that it achieves the same rates of convergence as in the i.i.d framework

Impact of diet in shaping gut microbiota revealed by a comparative study in children from Europe and Rural Africa

peer reviewe

A tomographic imagery segmentation methodology for three-phase geomaterials based on simultaneous region growing

peer reviewedX-Ray Computed Tomography (X-Ray CT) is a powerful non-destructive technique used in many domains to obtain the three-dimensional representation of objects, starting from the reconstitution of two-dimensional images of radiographic scanning. This technique is now able to analyze objects within a few microns resolution. Consequently, X-Ray micro-computed tomography (X-Ray μCT) opens perspectivesfor the analysis of the fabric of multi-phase geomaterials such as soils, concretes, rocks or ceramics. To be able to characterize the spatial distribution of the different phases in such complex and disordered materials, automated phase recognition has to be implemented through image segmentation. A crucial difficulty in segmenting images lies in the presence of noise in the obtained tomographic representation, making it difficult to assign a specific phase to each voxel (vx) of the image. In the present study, simultaneous region growing is used to reconstitute the three-dimensional segmented image of granular materials. First, based on a set of expected phases in the image, regions where specific phases are sure to be present are identified, leaving uncertain regions of the image unidentified. Subsequently, the identified regions are grown until growing phases meet each other with vanishing unidentified regions. The methodrequires a limited number of manual parameters that are easily determined. The developed method is illustrated based on three applications on granular materials, comparing the phase volume fractions obtained by segmentation with macroscopic data. It is demonstrated that the algorithm rapidly converges and fills the image after a few iterations