Observations on the basic (G′/G)-expansion method for finding solutions to nonlinear evolution equations

The extended tanh-function expansion method for finding solutions to nonlinear evolution equations delivers solutions in a straightforward manner and in a neat and helpful form. On the other hand, the more recent but less efficient (G′/G)-expansion method delivers solutions in a rather cumbersome form. It is shown that these solutions are merely disguised forms of the solutions given by the earlier method so that the two methods are entirely equivalent. An unfortunate consequence of this observation is that, in many papers in which the (G′/G)-expansion method has been used, claims that 'new' solutions have been derived are often erroneous; the so-called 'new' solutions are merely disguised versions of previously known solutions

From Regular Expression Matching to Parsing

Given a regular expression $R$ and a string $Q$, the regular expression parsing problem is to determine if $Q$ matches $R$ and if so, determine how it matches, e.g., by a mapping of the characters of $Q$ to the characters in $R$. Regular expression parsing makes finding matches of a regular expression even more useful by allowing us to directly extract subpatterns of the match, e.g., for extracting IP-addresses from internet traffic analysis or extracting subparts of genomes from genetic data bases. We present a new general techniques for efficiently converting a large class of algorithms that determine if a string $Q$ matches regular expression $R$ into algorithms that can construct a corresponding mapping. As a consequence, we obtain the first efficient linear space solutions for regular expression parsing

Gravitational Binding, Virialization and the Peculiar Velocity Distribution of the Galaxies

We examine the peculiar velocity distribution function of galaxies in cosmological many-body gravitational clustering. Our statistical mechanical approach derives a previous basic assumption and generalizes earlier results to galaxies with haloes. Comparison with the observed peculiar velocity distributions indicates that individual massive galaxies are usually surrounded by their own haloes, rather than being embedded in common haloes. We then derive the density of energy states, giving the probability that a randomly chosen configuration of N galaxies in space is bound and virialized. Gravitational clustering is very efficient. The results agree well with the observed probabilities for finding nearby groups containing N galaxies. A consequence is that our local relatively low mass group is quite typical, and the observed small departures from the local Hubble flow beyond our group are highly probable.Comment: Paper in aastex 5.0 format and 9 figures. Replace a new version with figures and typos correcte

The Changing Nature of Pharmaceutical R&D - Opportunities for Asia?

During the 1990''s, the pharmaceutical R&D process has witnessed tremendous technological changes. The emergence of new tools like ''combinatorial chemistry'', ''high throughput screening'' and the in-creasing use of computer-aided in silico experiments has led to significant improvements of research efficiency. This paper discusses the economic impact of this trend. It is argued that the resulting radical improvements in R&D productivity have lowered the minimum efficient scale in pharmeceutical research. As a consequence, the main bottleneck in pharmaceutical research has shifted from the mechanical act of synthesising and screening a sufficient number of active compounds to scientific excellence. Empirical finding indicate that the latter can more easily be achieved in smaller, highly focused firms. Accordingly, the most efficient way to currently conduct pharmaceutical R&D may be a new ''division of labour'' in research between small, highly specialised firms conducting research and large firms focusing on the development, testing, and marketing or new drugs. This reopens a ''window of opportunity'' for Asian pharmaceutical firms who had lost out in the previous race to ever increasing size.economics of technology ;

The Complexity of Three-Way Statistical Tables

Multi-way tables with specified marginals arise in a variety of applications in statistics and operations research. We provide a comprehensive complexity classification of three fundamental computational problems on tables: existence, counting and entry-security. One major outcome of our work is that each of the following problems is intractable already for "slim" 3-tables, with constant and smallest possible number 3 of rows: (1) deciding existence of 3-tables with given consistent 2-marginals; (2) counting all 3-tables with given 2-marginals; (3) finding whether an integer value is attained in entry (i,j,k) by at least one of the 3-tables satisfying given (feasible) 2-marginals. This implies that a characterization of feasible marginals for such slim tables, sought by much recent research, is unlikely to exist. Another important consequence of our study is a systematic efficient way of embedding the set of 3-tables satisfying any given 1-marginals and entry upper bounds in a set of slim 3-tables satisfying suitable 2-marginals with no entry bounds. This provides a valuable tool for studying multi-index transportation problems and multi-index transportation polytopes