Electrodynamics with non-linear constitutive laws and memory effects

Maxwell's equations governing the propagation of electro-magnetic fields are considered in conjunction with a class of material relations, which are capable of repre- senting memory effects and time delay

A simple model for heterogeneous flows of yield stress fluids

Various experiments evidence spatial heterogeneities in sheared yield stress fluids. To account for heterogeneities in the velocity gradient direction, we use a simple model corresponding to a non-monotonous local constitutive curve and study a simple shear geometry. Different types of boundary conditions are considered. Under controlled macroscopic shear stress $\Sigma$, we find homogeneous flow in the bulk and a hysteretic macroscopic stress - shear rate curve. Under controlled macroscopic shear rate $\dot{\Gamma}$, shear banding is predicted within a range of values of $\dot{\Gamma}$. For small shear rates, stick slip can also be observed. These qualitative behaviours are robust when changing the boundary conditions.Comment: 13 pages, 13 figure

Gender homophily from spatial behavior in a primary school: a sociometric study

We investigate gender homophily in the spatial proximity of children (6 to 12 years old) in a French primary school, using time-resolved data on face-to-face proximity recorded by means of wearable sensors. For strong ties, i.e., for pairs of children who interact more than a defined threshold, we find statistical evidence of gender preference that increases with grade. For weak ties, conversely, gender homophily is negatively correlated with grade for girls, and positively correlated with grade for boys. This different evolution with grade of weak and strong ties exposes a contrasted picture of gender homophily

Practical quantum realization of the ampere from the electron charge

One major change of the future revision of the International System of Units (SI) is a new definition of the ampere based on the elementary charge \emph{e}. Replacing the former definition based on Amp\`ere's force law will allow one to fully benefit from quantum physics to realize the ampere. However, a quantum realization of the ampere from \emph{e}, accurate to within $10^{-8}$ in relative value and fulfilling traceability needs, is still missing despite many efforts have been spent for the development of single-electron tunneling devices. Starting again with Ohm's law, applied here in a quantum circuit combining the quantum Hall resistance and Josephson voltage standards with a superconducting cryogenic amplifier, we report on a practical and universal programmable quantum current generator. We demonstrate that currents generated in the milliampere range are quantized in terms of $ef_\mathrm{J}$ ($f_\mathrm{J}$ is the Josephson frequency) with a measurement uncertainty of $10^{-8}$. This new quantum current source, able to deliver such accurate currents down to the microampere range, can greatly improve the current measurement traceability, as demonstrated with the calibrations of digital ammeters. Beyond, it opens the way to further developments in metrology and in fundamental physics, such as a quantum multimeter or new accurate comparisons to single electron pumps.Comment: 15 pages, 4 figure

The Hull-Strominger system in complex geometry

In this work, we study the Hull-Strominger system. New solutions are found on hyperkahler fibrations over a Riemann surface. This class of solutions is the first which admits infinitely many topological types. Next, we study the Fu-Yau solutions of the Hull-Strominger system and their generalizations to higher dimensions. We solve the Fu-Yau equation in higher dimensions, and in fact, solve a new class of fully nonlinear elliptic PDE which contains the Fu-Yau equation as a special case. Lastly, we introduce a geometric flow to study the Hull-Strominger system and non-Kahler Calabi-Yau threefolds. Basic properties are established, and we study this flow in the geometric settings of fibrations over a Riemann surface and fibrations over a K3 surface. In both cases, the flow descends to a nonlinear evolution equation for a scalar function on the base, and we study the dynamical behavior of these evolution equations

Non-invasive computer-assisted measurement of knee alignment

The quantification of knee alignment is a routine part of orthopaedic practice and is important for monitoring disease progression, planning interventional strategies, and follow-up of patients. Currently available technologies such as radiographic measurements have a number of drawbacks. The aim of this study was to validate a potentially improved technique for measuring knee alignment under different conditions. An image-free navigation system was adapted for non-invasive use through the development of external infrared tracker mountings. Stability was assessed by comparing the variance (F-test) of repeated mechanical femoro-tibial (MFT) angle measurements for a volunteer and a leg model. MFT angles were then measured supine, standing and with varus-valgus stress in asymptomatic volunteers who each underwent two separate registrations and repeated measurements for each condition. The mean difference and 95% limits of agreement were used to assess intra-registration and inter-registration repeatability. For multiple registrations the range of measurements for the external mountings was 1° larger than for the rigid model with statistically similar variance (p=0.34). Thirty volunteers were assessed (19 males, 11 females) with a mean age of 41 years (range: 20-65) and a mean BMI of 26 (range: 19-34). For intra-registration repeatability, consecutive coronal alignment readings agreed to almost ±1°, with up to ±0.5° loss of repeatability for coronal alignment measured before and after stress maneuvers, and a ±0.2° loss following stance trials. Sagittal alignment measurements were less repeatable overall by an approximate factor of two. Inter-registration agreement limits for coronal and sagittal supine MFT angles were ±1.6° and ±2.3°, respectively. Varus and valgus stress measurements agreed to within ±1.3° and ±1.1°, respectively. Agreement limits for standing MFT angles were ±2.9° (coronal) and ±5.0° (sagittal), which may have reflected a variation in stance between measurements. The system provided repeatable, real-time measurements of coronal and sagittal knee alignment under a number of dynamic, real-time conditions, offering a potential alternative to radiographs

Optimal detection of changepoints with a linear computational cost

We consider the problem of detecting multiple changepoints in large data sets. Our focus is on applications where the number of changepoints will increase as we collect more data: for example in genetics as we analyse larger regions of the genome, or in finance as we observe time-series over longer periods. We consider the common approach of detecting changepoints through minimising a cost function over possible numbers and locations of changepoints. This includes several established procedures for detecting changing points, such as penalised likelihood and minimum description length. We introduce a new method for finding the minimum of such cost functions and hence the optimal number and location of changepoints that has a computational cost which, under mild conditions, is linear in the number of observations. This compares favourably with existing methods for the same problem whose computational cost can be quadratic or even cubic. In simulation studies we show that our new method can be orders of magnitude faster than these alternative exact methods. We also compare with the Binary Segmentation algorithm for identifying changepoints, showing that the exactness of our approach can lead to substantial improvements in the accuracy of the inferred segmentation of the data.Comment: 25 pages, 4 figures, To appear in Journal of the American Statistical Associatio

High Dimensional Classification with combined Adaptive Sparse PLS and Logistic Regression

Motivation: The high dimensionality of genomic data calls for the development of specific classification methodologies, especially to prevent over-optimistic predictions. This challenge can be tackled by compression and variable selection, which combined constitute a powerful framework for classification, as well as data visualization and interpretation. However, current proposed combinations lead to instable and non convergent methods due to inappropriate computational frameworks. We hereby propose a stable and convergent approach for classification in high dimensional based on sparse Partial Least Squares (sparse PLS). Results: We start by proposing a new solution for the sparse PLS problem that is based on proximal operators for the case of univariate responses. Then we develop an adaptive version of the sparse PLS for classification, which combines iterative optimization of logistic regression and sparse PLS to ensure convergence and stability. Our results are confirmed on synthetic and experimental data. In particular we show how crucial convergence and stability can be when cross-validation is involved for calibration purposes. Using gene expression data we explore the prediction of breast cancer relapse. We also propose a multicategorial version of our method on the prediction of cell-types based on single-cell expression data. Availability: Our approach is implemented in the plsgenomics R-package.Comment: 9 pages, 3 figures, 4 tables + Supplementary Materials 8 pages, 3 figures, 10 table