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.     

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°.     

Determination of dopamine in synthetic cerebrospinal fluid by SWV with a graphite–polyurethane composite electrode

This work describes an electroanalytical investigation of dopamine using cyclic voltammetry (CV) and the graphite–polyurethane composite electrode (GPU). In CV studies, well-defined redox peaks characterize the oxidation process at the GPU electrode, which is indicative of electrocatalytic effects associated with active sites on the GPU electrode surface. A new analytical methodology was developed using the GPU electrode and square wave voltammetry (SWV) in BR buffer solution (0.1 mol L^–1; pH 7.4). Analytical curves were constructed under optimized conditions (f=60s^–1, E_a=50 mV, E_I=2 mV) and detection and quantification limits of 6.4×10^–8 mol L^–1 (12.1 g L^–1) and 5.2×10^–6 mol L^–1 (0.9 mg L^–1), respectively, were achieved. The precision of the method was checked by performing ten successive measurements for a 9.9×10^–6 mol L^–1 dopamine solution. For intra-assay and inter-assay precisions, the relative standard deviations were 1.9 and 2.3%, respectively. In order to evaluate the developed methodology, the determination of dopamine was performed with good sensitivity and selectivity, without the interference of ascorbic acid in synthetic cerebrospinal fluid, which indicates that the new methodology enables reliable analysis of dopamine.     

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     

Synthesis and Characterization of a [Mn12O12(O2CR)16(H2O)4] Complex Bearing Paramagnetic Carboxylate Ligands. Use of a Modified Acid Replacement Synthetic Approach

Summary.  A new modified approach for the synthesis of Mn₁₂ clusters, based on the use of complex [Mn₁₂O₁₂(O₂C ^t Bu)₁₆(H₂O)₄] (2) as starting material to promote the acidic ligand replacement, is presented here. This new synthetic approach allowed us to obtain complex [Mn₁₂O₁₂(O₂CC₆H₄N(O^•) ^t Bu)₁₆(H₂O)₄] (3), whose preparation remained elusive by direct replacement of the acetate groups of Mn₁₂Ac (1). Complex 3 bearing open-shell radical units, was prepared to increase the total spin number of its ground state, and consequently, to increase T _B , with the expectation that the radical ligands may couple ferromagnetically with the Mn₁₂ core. Unfortunately, magnetic measurements of complex 3 revealed that the sixteen radical carboxylate ligands interact antiferromagnetically with the Mn₁₂ core to yield a S = 2 magnetic ground state. Corresponding author. E-mail: vecianaj@icmab.es Received March 27, 2002; accepted May 2, 2002     

Recent results from the TCV tokamak

During the first two years of operation, the TCV tokamak has produced a large variety of plasma shapes and magnetic configurations, with 1.0B _tor1.46T,I _p800kA,k2.05, –0.71. A new shape control algorithm, based on a finite element reconstruction of the plasma current in real time, has been implemented. Vertical growth rates up to 1000s^–1 have been stabilized using the external coil system. Ohmic H-modes with Troyon factors ( _tor aB/I _p) up to two and densities up to 2.25×10²⁰m^–3, corresponding to the Greenwald limit, have been obtained in diverted discharges. Limiter H-modes with line averaged electron densities up to 1.7×10²⁰m^–3 have been obtained in elongated D-shaped plasmas with 360 kAI _P600 kA.Presented at 17^th Symposium Plasma Physics and Technology, Prague, June 13–16, 1995.This work was partly supported by the Fonds National Suisse de la Recherche Scientifique.     

Rigidity of harmonic maps of maximum rank

Thehomotopical rank of a mapf:M →N is, by definition, min{dimg(M) ¦g homotopic tof}. We give upper bounds for this invariant whenM is compact Kähler andN is a compact discrete quotient of a classical symmetric space, e.g., the space of positive definite matrices. In many cases the upper bound is sharp and is attained by geodesic immersions of locally hermitian symmetric spaces. An example is constructed (Section 9) to show that there do, in addition, exist harmonic maps of quite a different character. A byproduct is construction of an algebraic surface with large and interesting fundamental group. Finally, a criterion for lifting harmonic maps to holomorphic ones is given, as is a factorization theorem for representations of the fundamental group of a compact Kähler manifold. The technique for the main result is a combination of harmonic map theory, algebra, and combinatorics; it follows the path pioneered by Siu in his ridigity theorem and later extended by Sampson.