Importance sampling of rare events in chaotic systems

The European Physical Journal B - A way to make financial models effective is by letting them to represent the so called “fat tails”, i.e., extreme changes in stock prices that are...     

A sharp inequality for Sobolev functionsUne inégalité dans un espace de Sobolev

Let N?5, a>0, $\text{Ω}$ be a smooth bounded domain in $\text{R}{}^{\mathrm{N}}$, $\text{2}{}^1\text{=}\text{2N}\text{N?2}$, $\text{2}{}^{\mathrm{\#}}\text{=}\text{2(N?1)}\text{N?2}$ and 6u6²=|?u|₂²+a|u|₂². We prove there exists an α₀>0 such that, for all $\text{u∈}\text{H}{}^1\text{(Ω)?{0}}$,

This inequality implies Cherrier's inequality. To cite this article: P.M. Girão, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 105–108     

Reversed-phase high-performance liquid chromatography method for the determination of prolactin in bacterial extracts and in its purified form

Reversed-phase high-performance liquid chromatography methodology for the determination of human prolactin (hPRL) in bacterial periplasmic space or in purified preparations has been developed. The technique, based on the high hydrophobicity of the hPRL molecule, allows its separation from the bulk of bacterial proteins. The precision for periplasmic shock fluid analysis was characterized by relative standard variations of 3-7% for intra-day and of 3-25% for inter-day determinations. Accuracy, evaluated by recovery tests, was of the order of 90%, a calibration curve being constructed with the use of a lyophilized osmotic shock fluid extract, which provided a stable, readily prepared internal reference. Sensitivity was of the order of 0.5 microg of hPRL. The methodology developed also provided a tool for comparing the hydrophobicity of glycosylated and non-glycosylated prolactin molecules obtained from several different species and of different preparations of native or biosynthetic human prolactin.     

Probing the dark energy with quasar clustering

We show through Monte Carlo simulations that the Alcock-Paczyński test, as applied to quasar clustering, is a powerful tool to probe the cosmological density and equation of state parameters Omega(m0), Omega(x0), and w. By taking into account the effect of peculiar velocities upon the correlation function we obtain for the Two-Degree Field QSO Redshift Survey the predicted confidence contours for the cosmological constant (w = -1) and spatially flat (Omega(m0)+Omega(x0) = 1) cases. For w = -1, the test is especially sensitive to the difference Omega(m0)-Omega(Lambda0), thus being ideal to combine with cosmic microwave background results. For the flat case, it is competitive with future supernova and galaxy number count tests, besides being complementary to them.     

Enhanced x-ray phase determination by three-beam diffraction

For decades, solving the phase problem of x-ray scattering has been a goal that, in principle, could be achieved by means of n-beam diffraction (n-BD). However, the phases extracted by the actual n-BD phasing techniques are not very precise, mainly due to systematic errors that are difficult to estimate. We present an innovative theoretical approach and experimental procedure that, combined, eliminate two major sources of error. It is a high precision phasing technique that provides the triplet-phase angle with an error of about 2 degrees.     

Lorentz invariance with an invariant energy scale

We propose a modification of special relativity in which a physical energy, which may be the Planck energy, joins the speed of light as an invariant, in spite of a complete relativity of inertial frames and agreement with Einstein's theory at low energies. This is accomplished by a nonlinear modification of the action of the Lorentz group on momentum space, generated by adding a dilatation to each boost in such a way that the Planck energy remains invariant. The associated algebra has unmodified structure constants. We also discuss the resulting modifications of field theory and suggest a modification of the equivalence principle which determines how the new theory is embedded in general relativity.     

Cholesterol-oleate-doped polymer-dispersed liquid-crystal voltage-controlled ring projector

We report a cholesterol-oleate-doped polymer-dispersed liquid-crystal (PDLC) device that, under laser illumination, exhibits a ring diffraction pattern, the radius of which is controlled by an externally applied voltage. This effect is accurately explained by modeling of the random distribution of spiral cells shown in the microstructure with a voltage-dependent shape variation.     

Description of pulse propagation in a dispersive medium by use of a pulse quality factor

We investigated how the duration of short laser pulses evolves in a dispersive material, using rms widths and a propagation law based on a pulse quality factor. Experiments were carried out with femtosecond pulses (10 to 25fs at the temporal waist) propagating in bulk fused silica. Excellent agreement was found between theory and experiment. This approach does not require complete characterization of laser pulses and eliminates the need for any assumption regarding the interpretation of autocorrelation traces. The method is of general validity, and it can be applied to pulses of arbitrary shape.     

Random surfaces that suppress single scattering

We present a method for numerically generating a one-dimensional random surface, defined by the equation x(3)=zeta(x(1)), that suppresses single-scattering processes in the scattering of light from the surface within a specified range of scattering angles. Rigorous numerical calculations of the scattering of light from surfaces generated by this approach show that the single-scattering contribution to the mean scattered intensity is indeed suppressed within that range of angles.