Some effective methods for unconstrained optimization based on the solution of systems of ordinary differential equations

In this paper, we review briefly some methods for minimizing a functionF(x), which proceed by follwoing the solution curve of a system of ordinary differential equations. Such methods have often been thought to be unacceptably expensive; but we show, by means of extensive numerical tests, using a variety of algorithms, that the ODE approach can in fact be implemented in such a way as to be more than competitive with currently available conventional techniques.This work was supported by a SERC research studentship for the first author. Both authors are indebted to Dr. J. J. McKeown and Dr. K. D. Patel of SCICON Ltd, the collaborating establishment, for their advice and encouragement.     

The first total synthesis of (R)-convolutamydine A

The first total synthesis of (R)-convolutamydine A has been achieved by the organocatalytic addition of acetone to 4,6-dibromoisatin. The absolute configuration was determined by single crystal X-ray diffraction. DFT studies were used to model the transition states for the aldol reaction and equilibrium geometries of the post-aldol reaction intermediates. The DFT study revealed that the aldol bond forming reaction was considerably endothermic.     

Using graphs for some discrete tomography problems

Given a rectangular array whose entries represent the pixels of a digitalized image, we consider the problem of reconstructing an image from the number of occurrences of each color in every column and in every row. The complexity of this problem is still open when there are just three colors in the image. We study some special cases where the number of occurrences of each color is limited to small values. Formulations in terms of edge coloring in graphs and as timetabling problems are used; complexity results are derived from the model.     

The effect of linguistic entropy on speech perception in noise in young and elderly listeners.

The rationale for a method to quantify the information content of linguistic stimuli, i.e., the linguistic entropy, is developed. The method is an adapted version of the letter-guessing procedure originally devised by Shannon [Bell Syst. Tech. J. 30, 50-64 (1951)]. It is applied to sentences included in a widely used test to measure speech-reception thresholds and originally selected to be approximately equally redundant. Results of a first experiment reveal that this method enables one to detect subtle differences between sentences and sentence lists with respect to linguistic entropy. Results of a second experiment show that (1) in young listeners and with the sentences employed, manipulating linguistic entropy can result in an effect on SRT of approximately 4 dB in terms of signal-to-noise ratio; (2) the range of this effect is approximately the same in elderly listeners.     

Stochastic Visual Interactive Simulation Models

Many writers and practitioners have mentioned the difficulties that result from randomness in visual interactive simulation or animated simulation modelling. This paper discusses the use of VIS to model transient system behaviour, and proposes some approaches to stochastic VIS modelling which may be helpful in overcoming the difficulties.     

The six-vertex model eigenvectors as critical limit of the eight-vertex model bethe ansatz

The critical limit of the eight-vertex model eigenvectors obtained by means of the generalized Bethe Ansatz is shown to give the six-vertex eigenvectors as constructed in a previous paper by two of the authors. Furthermore, an explicit mapping is established between these eigenvectors and the usual Bethe Ansatz eigenvectors of the six-vertex model. This allows one to show that the indexv labeling the eight-vertex eigenstates becomes exactly the third component of the total spin in the critical limit.     

Limits of parallelism in explicit ODE methods

Numerical methods for ordinary initial value problems that do not depend on special properties of the system are usually found in the class of linear multistage multivalue methods, first formulated by J.C. Butcher. Among these the explicit methods are easiest to implement. For these reasons there has been considerable research activity devoted to generating methods of this class which utilize independent function evaluations that can be performed in parallel. Each such group of concurrent function evaluations can be regarded as a stage of the method. However, it turns out that parallelism affords only limited opportunity for reducing the computing time with such methods. This is most evident for the simple linear homogeneous constant-coefficient test problem, whose solution is essentially a matter of approximating the exponential by an algebraic function. For a given number of stages and a given number of saved values, parallelism offers a somewhat enlarged set of algebraic functions from which to choose. However, there is absolutely no benefit in having the degree of parallelism (number of processors) exceed the number of saved values of the method. Thus, in particular, parallel one-step methods offer no speedup over serial one-step methods for the standard linear test problem. Although the implication of this result for general nonlinear problems is unclear, there are indications that dramatic speedups are not possible in general. Also given are some results relevant to the construction of methods.Work supported in part by National Science Foundation grants DMS 89 11410 and DMS 90 15533 and by US Department of Energy grant DOE DEFG02-87ER25026. Work of the second author was completed while at the University of Illinois.     

FT-EPR and HPLC study of the mechanism of 4-chlorophenol photolysis

The mechanism of 4-chlorophenol (4CP) photolysis was investigated with the aid of Fourier Transform Electron Paramagnetic Resonance (FT-EPR) and pulsed-laser photolysis combined with High Performance Liquid Chromatography (HPLC) detection-of stable (diamagnetic) products. With FT-EPR transient free radicals produced by pulsed-laser excitation of solutions of 4CP in alcohols could be identified. Time profiles of the FT-EPR spectra provided information on reaction kinetics and Chemically Induced Dynamic, Electron Polarization (CIDEP) effects. It was found that 4CP photolysis in alcohols leads to the simultaneous formation of the phenoxyl radical and radicals produced by hydrogen abstraction from the solvent. CIDEP patterns establish that these radicals are formed in a reaction sequence involving a triplet state precursor and radical pair intermediate. Results of earlier transient optical absorption measurements indicate that the triplet precursor must be the carbene 4-oxocyclohexa-2,5-dienylidene. This assignment is supported by the finding that photolysis of quinone diazide in a hydrogen-donating solvent gives the same free radical products as those obtained from 4CP. The formation of the phenoxyl radical intermediate accounts for the finding that photolysis of deoxygenated solutions of 4CP in alcohols gives phenol as stable diamagnetic product. By contrast, photolysis of aerated and deoxygenated aqueous solutions of 4CP produces benzoquinone and hydroquinone as primary products, respectively.     

Quantification of stable minor species in confined flames by cavity ring-down spectroscopy: application to NO

Cavity ring-down spectroscopy (CRDS) is used to measure the NO mole fraction formed in the burnt gases of low-pressure premixed flames. It is shown that the line-of-sight absorption is greatly increased by the contribution of the NO molecules surrounding the burner. This contribution has been quantified by developing a mathematical procedure taking into account the spatial and spectral features of the CRDS measurement. Calculations have been undertaken in the general case of a stable species not consumed in the flame. The most sensitive parameter is the temperature both in the flame and outside the flame. Simulations allow the selection of the best spectroscopic transitions for a given flame (i.e. a given temperature profile), ensuring the weakest influence of the inaccuracy affecting the temperature determination. High quantum states belonging to the A–X (0–1) band of NO have been found to be the most valuable and have led to a NO mole fraction determination with an accuracy of ±13%. NO absorption in the flame was completely masked using the A–X (0–0) band. Finally, the prompt-NO mole fraction formed in a methane/air flame stabilized at 33 Torr is obtained by combining CRDS and laser induced fluorescence techniques. Received: 12 October / Revised version: 1 February 2002 / Published online: 14 March 2002