Efficient periodic band diagram computation using a finite element method, Arnoldi eigensolver and sparse linear system solver

We present here a Finite Element Method devoted to the simulation of 3D periodic structures of arbitrary geometry. The numerical method based on ARPACK and PARDISO libraries, is discussed with the aim of extracting the eigenmodes of periodical structures and thus establishing their frequency band gaps. Simulation parameters and the computational optimization are the focus. Resolution will be used to characterize EBG (Electromagnetic Band Gap) structures, such as plasma rods and metallic cubes

Currency Total Return Swaps: Valuation and Risk Factor Analysis

Currency total return swaps (CTRS) are hybrid derivatives instruments that allow to simultaneously hedge against credit and currency risks. We develop a structural credit risk model to evaluate CTRS premia. Empirical test on a sample of 23,005 price observations from 59 underlying issuers yields an average percentage error of around 10%. This indicates that, beyond interest rate risk, firm-specific factors are major drivers of the variations in the valuation of these instruments. Regression analysis of residuals shows that exchange rate determinants account for up to 40% of model pricing errors – indicating that a currency risk premium affects the CTRS price significantly but only marginally, which confirms the prevalence of credit risk in the pricing of CTRS.Credit derivative, credit risk, currency risk

On the convergence of Maronna's MM-estimators of scatter

In this paper, {we propose an alternative proof for the uniqueness} of Maronna's $M$-estimator of scatter (Maronna, 1976) for $N$ vector observations $\mathbf y_1,...,\mathbf y_N\in\mathbb R^m$ under a mild constraint of linear independence of any subset of $m$ of these vectors. This entails in particular almost sure uniqueness for random vectors $\mathbf y_i$ with a density as long as $N>m$. {This approach allows to establish further relations that demonstrate that a properly normalized Tyler's $M$-estimator of scatter (Tyler, 1987) can be considered as a limit of Maronna's $M$-estimator. More precisely, the contribution is to show that each $M$-estimator converges towards a particular Tyler's $M$-estimator.} These results find important implications in recent works on the large dimensional (random matrix) regime of robust $M$-estimation

Convergence and Fluctuations of Regularized Tyler Estimators

This article studies the behavior of regularized Tyler estimators (RTEs) of scatter matrices. The key advantages of these estimators are twofold. First, they guarantee by construction a good conditioning of the estimate and second, being a derivative of robust Tyler estimators, they inherit their robustness properties, notably their resilience to the presence of outliers. Nevertheless, one major problem that poses the use of RTEs in practice is represented by the question of setting the regularization parameter $\rho$. While a high value of $\rho$ is likely to push all the eigenvalues away from zero, it comes at the cost of a larger bias with respect to the population covariance matrix. A deep understanding of the statistics of RTEs is essential to come up with appropriate choices for the regularization parameter. This is not an easy task and might be out of reach, unless one considers asymptotic regimes wherein the number of observations $n$ and/or their size $N$ increase together. First asymptotic results have recently been obtained under the assumption that $N$ and $n$ are large and commensurable. Interestingly, no results concerning the regime of $n$ going to infinity with $N$ fixed exist, even though the investigation of this assumption has usually predated the analysis of the most difficult $N$ and $n$ large case. This motivates our work. In particular, we prove in the present paper that the RTEs converge to a deterministic matrix when $n\to\infty$ with $N$ fixed, which is expressed as a function of the theoretical covariance matrix. We also derive the fluctuations of the RTEs around this deterministic matrix and establish that these fluctuations converge in distribution to a multivariate Gaussian distribution with zero mean and a covariance depending on the population covariance and the parameter $\rho$

Intra-session absolute and relative reliability of pressure pain thresholds in the low back region of vine-workers:effect of the number of trials

BACKGROUND: Pressure pain thresholds (PPT) are commonly used to quantify mechanical pain sensitivity of deep structures. Excellent PPT reliability has been previously reported among the low back of healthy subjects. However, there is a lack of studies assessing PPT over the low back of workers exposed to biomechanical risk factors of low back pain. Thus, the purpose of this study was threefold: (1) to evaluate the intra-session absolute and relative reliability as well as minimal detectable change (MDC) values of PPT within 14 locations covering the low back region of vine-workers and (2) to determine the number of trial required to ensure reliable PPT assessments and (3) to assess the effect of modifier factors such as gender, age, body mass index (BMI) and pain intensity on PPT reliability. METHODS: Twenty-nine vine-workers voluntarily participated in this study. Twenty-two reported low intensity of low-back pain while seven were pain-free. PPTs were assessed among 14 anatomical locations in the lower back region. Three trials were performed on each location with an interval time of at least one minute. Reliability was assessed computing intraclass correlation coefficients (ICC), standard error of measurement (SEM) for all possible combinations between trials. Bland-Altman plots were also generated to assess potential bias in the dataset. Finally, a repeated measure analysis of variance (RM-ANOVA) with the number of trials used as within subject factor was performed on (1) PPT, (2) ICC and (3) SEM values. RESULTS: ICC ranged from 0.86 to 0.99 for all anatomical locations and for all possible combinations between trials. SEM for comparison between trial 1–2, 2–3, 1–3 and, 1-2-3 ranged from respectively, 36.7–77.5, 27.8–77.7, 50–95.2 and, 39.3–80.8 kPa. ICC and SEM remained similar to the ones obtained for the entire population when taking modifier factors in consideration. The visual analysis of Bland-Altman plots suggested small measurement errors for all anatomical locations and for all possible combinations between trials. CONCLUSIONS: The assessment of PPTs of the lower back among vine-workers was found to have excellent relative and absolute reliability. Moreover, reliable measurements can be equally achieved when using the mean of three PPT measurement or with the first one

Second order statistics of robust estimators of scatter. Application to GLRT detection for elliptical signals

International audienceA central limit theorem for bilinear forms of the type a * ˆ C N (ρ) −1 b, where a, b ∈ C N are unit norm deterministic vectors and C N (ρ) a robust-shrinkage estima-tor of scatter parametrized by ρ and built upon n independent elliptical vector observations, is presented. The fluctuations of a * ˆ C N (ρ) −1 b are found to be of order N − 1 2 and to be the same as those of a * ˆ S N (ρ) −1 b for S N (ρ) a matrix of a theoretical tractable form. This result is exploited in a classical signal detection problem to provide an improved detector which is both robust to elliptical data observations (e.g., impulsive noise) and optimized across the shrinkage parameter ρ

Hippocampal sclerosis affects fMR-adaptation of lyrics and melodies in songs

Songs constitute a natural combination of lyrics and melodies, but it is unclear whether and how these two song components are integrated during the emergence of a memory trace. Network theories of memory suggest a prominent role of the hippocampus, together with unimodal sensory areas, in the build-up of conjunctive representations. The present study tested the modulatory influence of the hippocampus on neural adaptation to songs in lateral temporal areas. Patients with unilateral hippocampal sclerosis and healthy matched controls were presented with blocks of short songs in which lyrics and/or melodies were varied or repeated in a crossed factorial design. Neural adaptation effects were taken as correlates of incidental emergent memory traces. We hypothesized that hippocampal lesions, particularly in the left hemisphere, would weaken adaptation effects, especially the integration of lyrics and melodies. Results revealed that lateral temporal lobe regions showed weaker adaptation to repeated lyrics as well as a reduced interaction of the adaptation effects for lyrics and melodies in patients with left hippocampal sclerosis. This suggests a deficient build-up of a sensory memory trace for lyrics and a reduced integration of lyrics with melodies, compared to healthy controls. Patients with right hippocampal sclerosis showed a similar profile of results although the effects did not reach significance in this population. We highlight the finding that the integrated representation of lyrics and melodies typically shown in healthy participants is likely tied to the integrity of the left medial temporal lobe. This novel finding provides the first neuroimaging evidence for the role of the hippocampus during repetitive exposure to lyrics and melodies and their integration into a song