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.     

A variable rate multipulse speech coder for CDMA cellular systems

Variable Rate (VR) speech coders are classified into: source-controlled VR coders where the rate is selected depending on the local character of the speech, and network-controlled VR coders where an external control signal selects the coding rate. The first category benefits from the variable rate channels used by Code Division Multiple Access (CDMA) mobile communications. The second category is indispensable for the right behaviour of the CDMA systems under conditions as high traffic levels. The VR speech coder presented in this communication exhibits both types of control. The source control is achieved by means of a Voice Activity Detector (VAD) and a phonetic classifier. The network control acts on the selection procedure of the multipulse excitation sequence to the synthesis filter. This is the main advantage of our VR MultiPulse speech coder because by means of an external signal the bit rate can be changed only every 4 msec, without transitions or distortions. Considering one-way communication, six different operating rates can be externally selected ranging from 4.8 to 9.1 kbps for the active frames; an average bit rate of 380 bps is required for the noise frames.This work has been partly funded by the Spanish Research National Plan under grant no. TIC92-0800-C05-02 and by Northern Telecom.     

Sulfonylcarbamimidic azides from sulfonyl chlorides and 5-aminotetrazole

Treatment of o-nitrobenzenesulfonyl chloride ( 3 ) with 5-aminotetrazole (5-AT) gave [(2-nitrophenyl)-sulfonyl]carbamimidic azide ( 6 ), a ring-opened isomer of the expected N-(1H-tetrazol-5-yl)-2-nitrobenzenesulfonamide ( 4 ). Sulfonylcarbamimidic azide 6 was converted to 2-amino-N-(aminoiminomethyl)benzene-sulfonamide ( 7 ) with ethanolic stannous chloride, and to 3-amino-1,2,4-thiadiazine 1,1-dioxide ( 8 ) with sodium dithionite. Methanesulfonyl chloride ( 9 ) and 5-AT gave 2-(methylsulfonyl)carbamimidic azide ( 10 ), which isomerized to 5-[(methylsulfonyl)amino]-1H-tetrazole ( 11 ) in warm ethanol. Attempted cycloaddition of 2-(phenylsulfonyl)carbamimidic azide ( 13 ) and ethyl vinyl ether led only to alkylated tetrazole products. In addition, other tetrazole-alkylating reactions are described. Isomers produced from these alkylations were differentiated with ¹³C nmr spectroscopy.     

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°.     

Positive ion chemistry of esters of carboxylic acids in air plasma at atmospheric pressure

Ionization of esters of carboxylic acids RCOOR' (R = H, alkyl; R' = alkyl) within the air plasma of the Atmospheric Pressure Chemical Ionization (APCI) source occurs largely via H(+)-transfer and, to a minor extent, via NO(+) association. The protonated ester MH(+) is normally observed as M(2)H(+) and as higher aggregates (M(3)H(+), M(3)H(+)(H(2)O)) also at high source temperature. The behavior of M(2)H(+) upon collisional activation is consistent with the reported dissociation of proton-bound dimers to MH(+) species that, in turn, fragment according to the known paths of lowest energy. In addition, other important product ions form within the plasma, some in very high relative abundance, which are attributed to ion-molecule condensation reactions between neutral M and either MH(+) or M(2)H(+) resulting in the elimination of CO, R'OH, alkene from the alkoxy moiety of the ester and HCOOH. A general scheme is proposed to account for the experimental observations, which suggest that the encounter complex formed between MH(+) and M or between M(2)H(+) and M may either collisionally relax to the protonated dimer or trimer, respectively, or react via covalent bond forming and cleaving steps to eliminate stable neutral molecules. The proposed scheme is supported by both the observed concentration dependence and the temperature dependence of the products relative abundances within the plasma. Such reactions can be the dominant process, as in the case of formate esters. A second significant ionization route involves addition of NO(+) to form M(n)NO(+) (n = 1, 2, 3). An additional product corresponding to [M(2)NO(+) - CO(2)] is also observed with iso- and n-butyl formate esters.     

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     

Positive and negative ion chemistry of the anesthetic halothane (1-bromo-1-chloro-2,2,2-trifluoroethane) in air plasma at atmospheric pressure

The ion chemistry of 1-bromo-1-chloro-2,2,2-trifluoroethane (the common anesthetic halothane) in air plasma at atmospheric pressure was investigated by atmospheric pressure chemical ionization mass spectrometry (APCI-MS). The major positive ion observed at low declustering (API interface) energies is the ionized dimer, M(+.)M, an unexpectedly abundant species which possibly is stabilized by two H-bonding interactions. At higher energies [M--HF](+.) and [M--Br](+) prevail; the former, corresponding to ionized olefin [ClBrC=CF(2)](+.), appears to originate from M(+.)M and is quite stable towards fragmentation. The latter fragment ion ([M--Br](+)) and its analogue, [M--Cl](+), which is also observed though at much lower abundance, are originally ethyl cations (+)CHX--CF(3) (X = Br, Cl) which, upon collisional activation, rearrange and fragment to CHFX(+) via elimination of CF(2). All of the above described ions are also observed in humid air: in addition, the oxygenated ion [ClBrC=CFOH](+.) also forms in humid air via water addition to [ClBrC=CF(2)](+.) and HF elimination, as observed earlier for ionized trichloroethene. In contrast with similar chloro- and fluoro-substituted ethanes, halothane does not react with H(3)O(+) in the APCI plasma, a result confirmed by selected ion APCI triple-quadrupole (TQ) experiments. Major negative ions formed from halothane in the air plasma are Br(-) and, to a lesser extent, Cl(-), and their complexes with neutral halothane. APCI-TQ experiments indicated that Br(-) and Cl(-) are formed via reaction of halothane with O(2) (-.), O(2) (-.)(H(2)O) and O(3) (-.), possibly via dissociative electron transfer or nucleophilic substitution. Competing proton transfer was also observed in the reaction with O(2) (-.) and, at high halothane pressure, also with O(2) (-.)(H(2)O); at lower pressures the molecular anion M(-.) was observed instead. The other minor anions of the air plasma, NO(2) (-), N(2)O(2) (-.) and NO(3) (-), were found to be unreactive towards halothane.     

Novel CFCs-substitutes recommended by EPA (hydrofluorocarbon-245fa and hydrofluoroether-7100): Ion chemistry in air plasma and reactions with atmospheric ions

The ion chemistry of the title compounds, a nonafluorobutyl methyl ether and a hydrofluoropropane, is elucidated by a combination of studies using atmospheric pressure ionization mass spectrometry and triple quadrupole mass spectrometry. In the positive ion mode, the hydrofluoroether readily forms an [M - F]+ ion, attributable to hydronium ion induced dehydrofluorination, the product of which can be further hydrated to give a protonated hydrofluoroester. By contrast, the hydrofluoropropane does not react with the hydronium ion but rather gives hydrofluoroalkenylium cations via H atom and F atom abstraction by the dioxygen radical cation. In the negative ion mode, the fluorobutyl methyl ether undergoes dissociative electron capture with O2-*, O2-*(H2O), O3-*, and NO2- to generate the fluorobutoxy anion, which can dissociate by CF2[doublebond]O loss to give the perfluorocarbanion when the precursor ions are internally excited. The hydrofluoropropane reacts readily with common atmospheric anions to form molecular complexes with F-, O2-*, and O3-* and the strongly H-bonded species, O2-*(HF) and F-(HF). Interestingly, isomeric pentafluoropropanes form in the reaction with O2-*, either O2-*(HF) or F-(HF), depending on the specific pattern of the fluoro substitution.     

Monocyclopentadienylhydride derivatives of ruthenium: stereoselective proton transfer and proton-hydride exchange in an extremely short dihydrogen bond

Diastereomerically pure complexes of formula CpRuCl(PP) and CpRuH(PP) with chiral ferrocenyl diphosphines were prepared and the selectivity of proton-transfer processes over the monohydride compounds with different acids was studied. With 1 equiv of HBF(4) the cis-dihydrogen and trans-dihydride complexes were formed while with 3 equiv of CF(3)CO(2)H the trans-dihydride derivative was the only product. However, the use of 1 equiv of CF(3)CO(2)H led to a dihydrogen bonded complex with an extremely short RuH...HO(2)CF(3) interaction that exhibits proton-hydride exchange. Using the labeled acid CF(3)CO(2)D, a stereoselective transference of the deuteron was demonstrated that implies the previous epimerization of the monohydride and the subsequent attack of the acid in the position previously occupied by the hydride.