Micro-domes based on a combination of metallic and dielectric multilayer mirrors are studied using a fully vectorial numerical basis-expansion method that accurately accounts for the effects of an arbitrary Bragg stack and can efficiently cover a large range of dome shapes and sizes. Results are examined from three different viewpoints: (i) the ray-optics limit, (ii) the (semi-) confocal limit ...

In this paper, we propose the Kernel Laplacian Eigenmaps for nonlinear dimensionality reduction. This method can be extended to any structured input beyond the usual vectorial data, enabling the visualization of a wider range of data in low dimension once suitable kernels are defined. Comparison with related methods based on MNIST handwritten digits data set supported the claim of our approach....

The generalized optical theorem is an integral relation for the angle-dependent scattering amplitude of an inhomogeneous scattering object embedded in a homogeneous background. It has been derived separately for several scalar and vectorial wave phenomena. Here a unified optical theorem is derived that encompasses the separate versions for scalar and vectorial waves. Moreover, this unified theo...

By using a Danes̆’ drop theorem in locally convex spaces we obtain a vectorial form of Ekelandtype variational principle in locally convex spaces. From this theorem, we derive some versions of vectorial Caristi-Kirk’s fixed-point theorem, Takahashi’s nonconvex minimization theorem, and Oettli-Théra’s theorem. Furthermore, we show that these results are equivalent to each other. Also, the existen...

Abstract. The notion of o-polynomial comes from finite projective geometry. In 2011 and later, it has been shown that those objects play an important role in symmetric cryptography and coding theory to design bent Boolean functions, bent vectorial Boolean functions, semi-bent functions and to construct good linear codes. In this note, we characterize o-polynomials by the Walsh transform of the ...

Criteria based on the analysis of the properties of vectorial Boolean functions for selection of substitutions (S-boxes) for symmetric cryptographic primitives are given. We propose an improved gradient descent method for increasing performance of nonlinear vectorial Boolean functions generation with optimal cryptographic properties. Substitutions are generated by proposed method for the most c...

Due to the variety of shapes and sizes that present both living organisms and static objects, the necessity to look for automated systems of identification, both in industry and scientific research has arisen. During the 1960s, the scientific community in the field of optics has used the Fourier transform and other types of mathematical transformations for pattern recognition, taking advantage ...

We present a new vectorial total variation (VTV) method that addresses the problem of color consistent image filtering. Our approach combines insights based on the double-opponent cell representation in the visual cortex with state-of-the-art variational modelling using VTV regularization. Existing methods of vectorial total variation regularizers have insufficient (even no) coupling between th...

Many neurons of the central nervous system are broadly tuned to some sensory or motor variables. This property allows one to assign to each neuron a preferred attribute (PA). The width of tuning curves and the distribution of PAs in a population of neurons tuned to a given variable define the collective behavior of the population. In this article, we study the relationship of the nature of the ...

This paper deals with optimal coding for vectorial signals by means of a decorrelating transform such as DPCM. We show that the optimal causal transform corresponds to a (Lower-Diagonal-Upper) triangular factorization of the autocorrelation matrix of the signal : the transformation matrix is triangular and unit diagonal. Each one of its rows is the optimal prediction filter for the correspondin...