Properties of bounded stochastic processes employed in biophysics

Abstract

Realistic stochastic modeling is increasingly requiring the use of bounded noises. In this work, properties and relationships of commonly employed bounded stochastic processes are investigated within a solid mathematical ground. Four families are object of investigation: the Sine-Wiener (SW), the Doering–Cai–Lin (DCL), the Tsallis–Stariolo–Borland (TSB), and the Kessler–Sørensen (KS) families. We address mathematical questions on existence and uniqueness of the processes defined through Stochastic Differential Equations, which often conceal non-obvious behavior, and we explore the behavior of the solutions near the boundaries of the state space. The expression of the time-dependent probability density of the Sine-Wiener noise is provided in closed form, and a close connection with the Doering–Cai–Lin noise is shown. Further relationships among the different families are explored, pathwise and in distribution. Finally, we illustrate an analogy between the Kessler–Sørensen family and Bessel processes, which allows to relate the respective local times at the boundaries.     

An interior–exterior Schwarz algorithm and its convergenceUn algorithme de Schwarz intérieur–extérieur et sa convergence

In this work we study the solution of Laplace's equation in a domain with holes by an iteration consisting of splitting the problem in an exterior one, around the holes, plus an interior problem in the unholed domain. We show the existence of a decomposition of the solution when the exterior problem is represented by means of a single-layer protential. Also, for the three-dimensional case and with some adjustments for the two-dimensional case, we prove convergence of the method by writing the iteration as a Jacobi iteration for an operator equation and studying the spectrum of the iteration operator. To cite this article: R. Celorrio et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 923–926.     

Asymptotically balanced schemes for non-homogeneous hyperbolic systems – application to the Shallow Water equations

In this work we introduce a class of balanced numerical schemes, up to second order, for the solution of general non-homogeneous hyperbolic systems of conservation laws. We give a general technique to build such schemes. We also prove that they balance up to second order a large class of steady solutions in the whole domain but some subset whose measure tends to zero as the grid size decreases to zero. We finally present an application to Shallow Water equations that exhibit the good performances of some of the schemes introduced. To cite this article: T. Chacón Rebollo et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Growth kinetics and phenolics production inGlycine Max cell suspension cultures

Glycine max was used as a model plant cell suspension culture to establish relationships among growth kinetics, phenolics production, elicitor action, and peroxidase activity. Timing of elictor addition through monitoring of peroxidase provided an excellent means of optimizing yields of phenolics and reduced the time span during which phenolics were formed, negating the need for a secondary production medium. We have also determined that calcium and other cellular effectors like polyamines and organic osmolytes, when used in conjunction with elicitors, enhance phenolics production. Calcium directly enhanced elicitation, whereas polyamines and other osmolytes such as glycerol and proline extended cell viability. The study also demonstrated potential for enhancing secondary metabolite production by a combination of elicitation, cell viability stabilizers, and by addition of nutrients at the time of elicitation.     

Acetoxyphenylketene. Reaction with biacetyl

The generation of acetoxyphenylketene (4) in the cold in the presence of biacetyl yields the single β-lactone $\text{12B}$, which undergoes a novel rearrangement to the tricyclic orthoester lactone $\text{11}$ above 130°.     

Mixtures of sodium dodecyl sulfate/dodecanol at the air/water interface by computer simulations

Molecular dynamics simulations of monolayers of surfactant mixtures at the air/water interface were performed where the binary mixture was composed of sodium dodecyl sulfate (SDS) and dodecanol molecules. At the same ratio of SDS and dodecanol molecules, two monolayer mixtures were prepared. In the first monolayer, all the dodecanol molecules were placed together in the center of the simulation box, whereas in the second monolayer, those molecules were uniformly distributed in the surface area in such a way that they were far from each other. Simulations of both systems indicate that the dodecanol tails in the first monolayer are straighter and more ordered than those in the second monolayer. From the present results, we observed new insights of how the different molecules should array or distribute at the interface in real systems. Finally, studies of the interfacial water around the different surfactants were also analyzed, showing that they are closer to the polar headgroups of dodecanol than to the SDS headgroups.     

LCAO–MO similarity measures and taxonomy

Similarity measures between pairs of molecular wave functions are described. They are based on the geometrical structure of the LCAO–MO framework and upon multivariate analysis ideas. The theoretical framework is presented, and formulae for some integrals needed are given. Two main measures, distance and correlation coefficients, are used. Distance and correlation matrices induce relationships in the whole MO set, which can be depicted through minimal spanning tree techniques. Furthermore, principal component analysis allows a two-dimensional visualization of the Mo manifold geometrical relationships. Various examples are given in order to obtain information on how basis set, environment, excitation, bending, stretching, and electronegativity affect the induced order. For this purpose “ab initio” SCF–LCAO–MO calculations with double- and single-zeta quality basis sets have been used for various simple molecular structures: H₂O, NH₃, CH₄, N₂, O₂, C₂, NO, CN, and CO. The results obtained can open the way to LCAO–MO taxonomy. Using this information, other areas of interest are connected with similarity measures (SCF and CI , localization procedures, etc.), proving in this manner their potential utility.     

Density functional theory study of the mechanism of the proline-catalyzed intermolecular aldol reaction

Transition structures associated with the C-C bond-formation step of the proline-catalyzed intermolecular aldol reaction between acetone and isobutyraldehyde have been studies using density functional theory methods at the B3LYP/6-31G** computational level. A continuum model has been selected to represent solvent effects. For this step, which is the stereocontrolling and rate-determining step, four reactive channels corresponding to the syn and anti arrangement of the active methylene of the enamine relative to the carboxylic acid group of l-proline and the re and si attack modes to both faces of the aldehyde carbonyl group have been analyzed. The B3LYP/6-31G** energies are in good agreement with experiment, allowing us to explain the origin of the catalysis and stereoselectivity for these proline-catalyzed aldol reactions. Received: 2 April 2002 / Accepted: 18 July 2002 / Published online: 11 October 2002 Acknowledgements. This work was supported by research funds provided by the Ministerio de Educación y Cultura of the Spanish Government by DGICYT (project PB98–1429). All the calculations were performed on a Cray–Silicon Graphics Origin 2000 of the Servicio de Informática de la Universidad de Valencia. We are most indebted to this center for providing us with computer capabilities. Correspondence to: L. R. Domingo e-mail: domingo@utopia.uv.es     

Identification of Earth Pigments by Applying Hierarchical Cluster Analysis to Solid State Voltammetry. Application to Severely Damaged Frescoes

Multivariate chemometric methods are applied for identifying earth pigments from square‐wave voltammetric measurements performed at pigment‐modified paraffin‐impregnated graphite electrodes allowing for a separation between hematite‐based earths, French ochres, Spanish ochres, siennas, umbers and green earths. This methodology is applied to the identification of the pigments in samples from the ceiling frescoes of Antonio Palomino (dated 1707) in the vaulted nave of the Sant Joan del Mercat church in Valencia (Spain). These frescoes suffered considerable damage by fire during the Spanish Civil War in 1936, resulting in severe chemical and chromatic alterations. Electrochemical data, supported by scanning electron microscopy/energy dispersive X‐ray microanalysis and Raman spectroscopy, indicate that thermal stress induced the transformation of goethite‐based yellow ochres into hematite and magnetite.