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...     

The Homogeneous Hamilton–Jacobi and Bernoulli Equations Revisited, II

It is shown that the admissible solutions of the continuity and Bernoulli or Burgers' equations of a perfect one-dimensional liquid are conditioned by a relation established in 1949–1950 by Pauli, Morette, and Van Hove, apparently, overlooked so far, which, in our case, stipulates that the mass density is proportional to the second derivative of the velocity potential. Positivity of the density implies convexity of the potential, i.e., smooth solutions, no shock. Non-elementary and symmetric solutions of the above equations are given in analytical and numerical form. Analytically, these solutions are derived from the original Ansatz proposed in Ref. 1 and from the ensuing operations which show that they represent a particular case of the general implicit solutions of Burgers' equation. Numerically and with the help of an ad hoc computer program, these solutions are simulated for a variety of initial conditions called compatible if they satisfy the Morette–Van Hove formula and anti-compatible if the sign of the initial velocity field is reversed. In the latter case, singular behaviour is observed. Part of the theoretical development presented here is rephrased in the context of the Hopf–Lax formula whose domain of applicability for the solution of the Cauchy problem of the homogeneous Hamilton–Jacobi equation has recently been enlarged.     

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.     

Polymer microfluidic chips for electrochemical and biochemical analyses

Our recent developments concerning the fabrication of polymer microchips and their applications for biochemical analyses are reviewed. We first describe two methods of fabrication of polymer microfluidic chips, namely UV-laser photoablation and plasma etching that are well suited for the prototyping and mass fabrication of microchannel networks with integrated microelectrodes. These microanalytical systems can be coupled with various detection means including mass spectrometry, and their applications in capillary electrophoresis are presented here. We also present how UV laser photoablation can be used for the patterning of biomolecules on polymer surfaces for generating two-dimensional arrays of microspots to carry out affinity assays. Finally, the use of the microchips for the development of fast affinity and immunological assays with electrochemical detection is presented, demonstrating the potential of these polymer microchips for medical diagnostics and drug discovery.     

Integration of a membrane-based desalting step in a microfabricated disposable polymer injector for mass spectrometric protein analysis

A simple desalting procedure for the coupling of a polymer microchip injector to mass spectrometry is proposed. The overall process is based on the adsorption of proteins on a poly(vinylidene difluoride) (PVDF) membrane, which are then directly eluted in the spraying solution. This microchip-based approach has been successfully applied to small drugs, peptides and proteins originally diluted in phosphate-buffered saline (PBS). Moreover, when eluting the retained proteins in small volumes, a preconcentration is obtained. The combination of single-use, mass-produceable, low-sample-consumption, easy-to-automate, miniaturized polymer injectors with easy-to-handle solution-exchange membranes makes this system particularly amenable to screening applications.     

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.     

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Entropic rigidity of randomly diluted two- and three-dimensional networks

In recent work, we presented evidence that site-diluted triangular central-force networks, at finite temperatures, have a nonzero shear modulus for all concentrations of particles above the geometric percolation concentration p(c). This is in contrast to the zero-temperature case where the (energetic) shear modulus vanishes at a concentration of particles p(r)>p(c). In the present paper we report on analogous simulations of bond-diluted triangular lattices, site-diluted square lattices, and site-diluted simple-cubic lattices. We again find that these systems are rigid for all p>p(c) and that near p(c) the shear modulus mu approximately (p-p(c))(f), where the exponent f approximately 1.3 for two-dimensional lattices and f approximately 2 for the simple-cubic case. These results support the conjecture of de Gennes that the diluted central-force network is in the same universality class as the random resistor network. We present approximate renormalization group calculations that also lead to this conclusion.