École normale supérieure de Cachan

About: École normale supérieure de Cachan is a education organization based out in Cachan, Île-de-France, France. It is known for research contribution in the topics: Decidability & Finite element method. The organization has 2717 authors who have published 5585 publications receiving 175925 citations.

Angluin-style learning of NFA

Abstract: We introduce NL*, a learning algorithm for inferring non-deterministic finite-state automata using membership and equivalence queries. More specifically, residual finite-state automata (RFSA) are learned similarly as in Angluin's popular L* algorithm, which, however, learns deterministic finite-state automata (DFA). Like in a DFA, the states of an RFSA represent residual languages. Unlike a DFA, an RFSA restricts to prime residual languages, which cannot be described as the union of other residual languages. In doing so, RFSA can be exponentially more succinct than DFA. They are, therefore, the preferable choice for many learning applications. The implementation of our algorithm is applied to a collection of examples and confirms the expected advantage of NL* over L*.

Existence and Uniqueness of Entropy Solution of Scalar Conservation Laws with a Flux Function Involving Discontinuous Coefficients

Abstract: In this paper, the question of existence and uniqueness for entropy solutions of scalar conservation laws with a flux function which is discontinuous with respect to the space variable is investigated. We show that no extra assumption of convexity or genuine non-linearity with respect to the state variable of the flux function is required for the problem to be well-posed and prove it. The proof uses a kinetic formulation of the conservation law.

Synthesis, structures, and physical properties of copper(II)-gadolinium(III) complexes combining ferromagnetic coupling and quadratic nonlinear optical properties.

Abstract: Two copper(II)−gadolinium(III) metal complexes of formula CuIIGdIIILX3 are reported. H2L stands for the Schiff base ligand obtained by condensation of 3,4-dimethoxysalicylaldehyde with ethylenediamine (complex 1) or 1R,2R-(+)-1,2-diphenylethylenediamine (complex 2). While 1 reveals a centrosymmetric crystal structure, 2 crystallizes in the noncentrosymmetric P212121 space group and exhibits an efficiency 0.3 time that of urea in second harmonic generation. Due to a trend for dissociation in solution, the molecular hyperpolarizabilities (β) cannot be determined experimentally for 1 and 2. Nevertheless, the electric field induced second harmonic (EFISH) technique, in connection with spectroscopic data and a ZINDO semiempirical approach, leads to a β value of −6.5 × 10-30 cm5 esu-1, for the related CuIIL monomers, as an indicative range of magnitude in all these Schiff base complexes. In addition, 1 and 2 exhibit a ferromagnetic coupling in solid state with J = 3.3 and 1.3 cm-1, respectively (J being the par...

Photoluminescence of single colour defects in 50 nm diamond nanocrystals

Abstract: We used optical confocal microscopy to study optical properties of diamond 50 nm nanocrystals first irradiated with an electron beam, then dispersed as a colloidal solution and finally deposited on a silica slide. At room temperature, under CW laser excitation at a wavelength of 514.5 nm we observed perfectly photostable single nitrogen-vacancy (NV) colour defects embedded in the nanocrystals. From the zero-phonon line around 575 nm in the spectrum of emitted light, we infer a neutral NV 0 type of defect. Such nanoparticle with intrinsic fluorescence are highly promising for applications in biology where long-term emitting fluorescent bio-compatible nanoprobes are still missing.