A modified steepest descent method with applications to maximizing likelihood functions

In maximizing a non-linear function G(), it is well known that the steepest descent method has a slow convergence rate. Here we propose a systematic procedure to obtain a 1–1 transformation on the variables , so that in the space of the transformed variables, the steepest descent method produces the solution faster. The final solution in the original space is obtained by taking the inverse transformation. We apply the procedure in maximizing the likelihood functions of some generalized distributions which are widely used in modeling count data. It was shown that for these distributions, the steepest descent method via transformations produced the solutions very fast. It is also observed that the proposed procedure can be used to expedite the convergence rate of the first derivative based algorithms, such as Polak-Ribiere, Fletcher and Reeves conjugate gradient methods as well.     

Grouped coordinate minimization using Newton's method for inexact minimization in one vector coordinate

Letf(x,y) be a function of the vector variablesx R ⁿ andy R ^m. The grouped (variable) coordinate minimization (GCM) method for minimizingf consists of alternating exact minimizations in either of the two vector variables, while holding the other fixed at the most recent value. This scheme is known to be locally,q-linearly convergent, and is most useful in certain types of statistical and pattern recognition problems where the necessary coordinate minimizers are available explicitly. In some important cases, the exact minimizer in one of the vector variables is not explicitly available, so that an iterative technique such as Newton's method must be employed. The main result proved here shows that a single iteration of Newton's method solves the coordinate minimization problem sufficiently well to preserve the overall rate of convergence of the GCM sequence.The authors are indebted to Professor R. A. Tapia for his help in improving this paper.     

Some identities for products and degree raising of splines

In this paper it is shown how the algebraic product of two spline functions, each represented in terms of B-splines, can again be represented as a linear combination of suitable B-splines. As a corollary to this result we obtain an explicit representation of a given B-spline function in terms of B-splines of some arbitrary higher degree. This generalizes some known results for raising the degree by one. Recurrence relations for both products and degree raising are established that may be useful for computation.Communicated by Larry L. Schumaker.     

Thermal decomposition of sodium nitrite and sodium nitrate pre-adsorbed on TiO2 surfaces

The thermal decomposition of sodium nitrite or nitrate pre-adsorbed upon TiO₂ surfaces has been investigated by employing several techniques as infrared spectroscopy (IR) and temperature programmed desorption in conjunction with mass spectrometry analysis (TPD-MS) to study the features observed during these thermal decompositions. Differential thermal analysis (DTA) in combination with X-ray diffraction analysis (XRD) were used to investigate the possibility of a solid state chemical reaction between the solid products originated from the thermal decomposition of the pre-adsorbed species and the TiO₂. On the basis of our results, various characteristic features of these thermal decomposition reactions will be discussed.This work was supported by JUNTA DE ANDALUCIA (financial support for research groups/1990).     

New Methods for the Synthesis of Glycosides and Oligosaccharides—Are There Alternatives to the Koenigs-Knorr Method? [New Synthetic Methods (56)]

Glycoproteins, glycolipids, and glycophospholipids (glycoconjugates) are components of membranes. The oligosaccharide residue is responsible for intercellular recognition and interaction; it acts as a receptor for proteins, hormones, and viruses and governs immune reactions. These significant activities have stimulated interest in oligosaccharides and glycoconjugates. With their help it should be possible to clarify the molecular basis of these phenomena and to derive new principles of physiological activity. Major advances in the synthesis of oligosaccharides have been made by the use of the Koenigs-Knorr method, in which glycosyl halides in the presence of heavy-metal salts are employed to transfer the glycosyl group to nucleophiles. The disadvantages of this procedure have led to an intensive search for new methods. Such methods will be discussed in this article. Emphasis is placed on glycoside and saccharide formation by 1-O-alkylation, on the trichloroacetimidate method, and on activation through the formation of glycosylsulfonium salts and glycosyl fluorides.     

Time-resolved fluorescence analysis of the mobile flavin cofactor in p -hydroxybenzoate hydroxylase

Conformational heterogeneity of the FAD cofactor in p-hydroxybenzoate hydroxylase (PHBH) was investigated with time-resolved polarized flavin fluorescence. For binary enzyme/substrate (analogue) complexes of wild-type PHBH and Tyr222 mutants, crystallographic studies have revealed two distinct flavin conformations; the ‘in’ conformation with the isoalloxazine ring located in the active site, and the ‘out’ conformation with the isoalloxazine ring disposed towards the protein surface. Fluorescence-lifetime analysis of these complexes revealed similar lifetime distributions for the ‘in’ and ‘out’ conformations. The reason for this is twofold. First, the active site of PHBH contains various potential fluorescence-quenching sites close to the flavin. Fluorescence analysis of uncomplexed PHBH Y222V and Y222A showed that Tyr222 is responsible for picosecond fluorescence quenching free enzyme. In addition, other potential quenching sites, including a tryptophan and two tyrosines involved in substrate binding, are located nearby. Since the shortest distance between these quenching sites and the isoalloxazine ring differs only little on average, these aromatic residues are likely to contribute to fluorescence quenching. Second, the effect of flavin conformation on the fluorescence lifetime distribution is blurred by binding of the aromatic substrates: saturation with aromatic substrates induces highly efficient fluorescence quenching. The flavin conformation is therefore only reflected in the small relative contributions of the longer lifetimes.     

Significance of Non-isothermal Kinetic Data. A statistical study

Arrhenius parameters values, in non-isothermal kinetic vaporisation processes for a series of compounds with related structures, have been calculated. This was made using a method of calculation that allows to find the most probable vaporisation mechanisms. According to this method DTG curves were compared with some theoretical ones reported in literature, whose shape results to be only a function of the mechanisms. In this way the choice of the mathematical functions which can be inserted in the kinetic equations, was influenced by the shape of the DTG plots and other thermal analysis signals thus allowing to choose the most probable mechanisms. The kinetic parameters derived from these mechanisms were compared, using statistical analysis, with those obtained from another method of calculation based on ‘a priori’ vaporisation mechanism chosen for the investigated liquid–gas transition. The standard deviations of the slope and of the intercept, together with the standard deviation and the square correlation coefficient (r ²) of the linear regression equations related to the mechanisms of the two methods were calculated. Student t-test, Fisher F-test, confidence intervals (c.i.) and residuals valueswere also given. Statistical analysis shows that the mechanisms obtained with the former method (diffusive and geometrical models) and the related Arrhenius parameters result to be more significant (in terms of probability) than the corresponding quantities of the latter for which a first-order model was chosen. This revised version was published online in August 2006 with corrections to the Cover Date.     

Complexation of 6-Deoxy-6-(aminoethyl)amino-β-cyclodextrin with Sodium Cholate and Sodium Deoxycholate

In order to study its guest binding and the inclusion phenomena, 6-deoxy-6-(aminoethyl)amino--cyclodextrin (CDN) was synthesised and its binding properties examined. The complexation phenomena of sodium cholate (NaC) and sodium deoxycholate (NaDC) with CDN has been monitored by the NMR method using ¹³C chemical shift data. The method of continuous variation Job's method has been used to determine the stoichiometry of these supramolecular complexes. The Job's plot confirms the 1 : 1 supramolecular complex for NaC: CDN and the 1 : 2 supramolecular complex for NaDC: CDN. The interaction of NaC and NaDC with CDN has been obtained through two-dimensional Rotational Nuclear Overhauser Effect Spectroscopy (ROESY) NMR. Equilibrium constants were also obtained from ¹³C chemical shift data (C-1, C-3 & C-4) at different pH values (7, 9, & 11).     

Functionality map analysis of the active site cleft of human thrombin

Summary The Multiple Copy Simultaneous Search methodology has been used to construct functionality maps for an extended region of human thrombin, including the active site. This method allows the determination of energetically favorable positions and orientations for functional groups defined by the user on the three-dimensional surface of a protein. The positions of 10 functional group sites are compared with those of corresponding groups of four thrombin-inhibitor complexes. Many, but not all features, of known thrombin inhibitors are reproduced by the method. The results indicate that certain aspects of the binding modes of these inhibitors are not optimal. In addition, suggestions are made for improving binding by interaction with functional group sites on the thrombin surface that are not used by the thrombin inhibitors. Abbreviations: MCSS, multiple copy simultaneous search; PPACK, d-phenylalanyl-l-propyl-l-arginine chloromethane; NAPAP, N -(2-naphthylsulfonylglycyl)-d-para-amidinophenylalanylpiperidine; argatroban, (2R,4R)-4-methyl-1-[N -(3-methyl-1,2,3,4-tetrahydro-8-quinolinylsulfonyl)-l-arginyl]-2-piperidine carboxylic acid; rms, root mean square. The thrombin residues are numbered according to the chymotrypsin-based numbering by Bode et al. [8]. P1, P2, P3, etc., denote the peptide inhibitor residues on the amino-terminal side of the scissile peptide bond, and S1, S2, S3, etc., the corresponding subsites of thrombin     

FRICTIONAL DISSIPATION AND NONLINEAR BAROTROPIC INSTABILITY

Based on the nonlinear quasi-geostrophic barotropic vorticity equation with Ekman friction, the criteria for nonlinear barotropic stability of the zonal basic flows are derived using Serrin-Joseph energy approach and through total energy, total enstrophy and their linear combination, separately, in terms of variational principle. Since the new transformation for Euler equation is utilized, the estimation of eigenvalue is more accurate, and the previous results of the author are improved very well.