Superquantiles at Work: Machine Learning Applications and Efficient Subgradient Computation

Set-Valued and Variational Analysis - R. Tyrell Rockafellar and his collaborators introduced, in a series of works, new regression modeling methods based on the notion of superquantile (or...     

Generation of achromatic and propagation-invariant spot arrays by use of continuously self-imaging gratings

A particular class of Montgomery's self-imaging objects that we call continuously self-imaging gratings (CSIG's) is introduced. When they are illuminated by a plane wave, these objects produce a field whose intensity profile is a propagation- and wavelength-invariant biperiodic array of bright spots. The mathematical construction of these objects and their intrinsic properties are described. On a practical level, CSIG's are compact and achromatic nondiffracting array generators. We show that a good CSIG approximation can be realized by a two-level phase grating that is experimentally tested.     

Inversion de la transformation de Pompeiu locale dans les espaces hyperboliques reel et complexe: Cas des deux boules

In this paper we extend the result we have established for the hyperbolic disk in [8] to the real and complex hyperbolic spaces. This includes the reconstruction of a function defined in a fixed ball from its averages on balls of radiir ₁,r ₂ lying inB(0,R).      

Self-consistent Shaw optimized model potential: Application to the determination of structural and atomic transport properties of liquid alkali metals by molecular dynamics simulations

The ‘first-principles’ fully non-local and energy-dependent optimized model potential (OMP) derived by Shaw is developed further. In contrast to Shaw's original paper, OMP parameters are derived in a self-consistent manner that does not rely on knowledge of experimental values of the ionization and cohesive energies. To our knowledge, this is the first time that this method has been used for effective potential calculations. In an application to liquid Li, Na, and K alkali metals, we used OMP pseudopotential-based interactions between ions to carry out standard molecular dynamics simulations. In the calculations, the ionic structure for the liquid state was first checked at a temperature near the melting point. Similar accurate calculations, but for atomic transport properties, predict the temperature dependence of the self-diffusion coefficients. The theoretical results obtained are in overall agreement with available experimental measurements. Thus, one can have some confidence in the ability of the optimized model potential to give a good representation of the physical properties of these alkali ions in the liquid environment.     

Talbot experiment re-examined: demonstration of an achromatic and continuous self-imaging regime

In the original Talbot experiment, a grating made of thin slits was illuminated in polychromatic light. Reconstituting this simple experiment, we have observed that at a certain distance from the grating, achromatic lines are formed whose transverse-resolution remains unaffected over a wide propagation-distance range. To our knowledge, this phenomenon has never been reported before. A theoretical explanation of this achromatic and continuous self-imaging regime is given and experimental results are reported.