Testing Independence Based on Bernstein Empirical Copula and Copula Density

In this paper we provide three nonparametric tests of independence between continuous random variables based on the Bernstein copula distribution function and the Bernstein copula density function. The first test is constructed based on a Cramér-von Mises divergence-type functional based on the empirical Bernstein copula process. The two other tests are based on the Bernstein copula density and use Cramér-von Mises and Kullback–Leibler divergence-type functionals, respectively. Furthermore, we study the asymptotic null distribution of each of these test statistics. Finally, we consider a Monte Carlo experiment to investigate the performance of our tests. In particular we examine their size and power which we compare with those of the classical nonparametric tests that are based on the empirical distribution function

Cholesteric liquid crystals with a helical pitch gradient: Spatial distribution of the concentration of chiral groups by Raman mapping in relation with the optical response and the microstructure

International audienceCholesteric liquid crystals (CLC) selectively reflect light when the helical pitch is of the order of the wavelength of the incident beam propagating along the helix axis. The wavelength bandwidth, related to the optical anisotropy, is typically limited to a few tens of nanometers in the visible part of the spectrum, which is insufficient for applications such as white-or-black polarizer-free reflective displays and smart windows for the control of the solar light and heat. A way to make cholesteric films reflecting in a broad wavelength band consists in associating various cholesteric pitches in the same film. In this work, it is shown how a study by confocal micro Raman spectrometry mapping makes it possible to have access to information accounting for the local organization of CLCs in the case of graded pitch materials. These investigations will be correlated to the optical response and the transverse microstructure of the CLC material as investigated by transmission electron microscopy. An accurate analysis of the vibrational behavior evolution of the CO can be correlated to the evolution of the populations of the chiral and achiral groups in the case of the interdiffusion of two CLC substances with various stoechiometries. Besides an easy measurement of the Raman spectrum gives the opportunity to quantify the relative ratio of the mesogenic species and thus to go up by a simple way to the pitch of the helical structure

Image retrieval based on effective feature extraction and diffusion process

Feature extraction and its matching are two critical tasks in image retrieval. This paper presents a new methodology for content-based image retrieval by integrating three features, and then optimizing feature metric by diffusion process. To boost the discriminative power, the color histogram, local directional pattern, and dense SIFT features based on bag of features (BoF) are selected. Then diffusion process is applied to seek a global optimization for image matching based on fused multi-features. The diffusion process can capture the intrinsic manifold structure on a dataset, and thus enhance the overall retrieval performance significantly. Finally, a new search strategy is explored to make the diffusion process work even better when the number of retrieval images is small. In order to validate our proposed approach, four benchmark databases are used, and the results of experiments show that the proposed approach outperforms all other existing approaches