Unconventional Secondary Structure Mimics: Ladder‐Rungs

Secondary structures tend to be recognizable because they have repeating structural motifs, but mimicry of these does not have to follow such well‐defined patterns. Bioinformatics studies to match side‐chain orientations of a novel hydantoin triazole chemotype ( 1 ) to protein‐protein interfaces revealed it tends to align well across parallel and antiparallel sheets, like rungs on a ladder. One set of these overlays was observed for the protein‐protein interaction uPA?uPAR. Consequently, chemotype 1 was made with appropriate side‐chains to mimic uPA at this interface. Biophysical assays indicate these compounds did in fact bind uPAR, and elicit cellular responses that affected invasion, migration, and wound healing.     

Expectations and fairness in a simple bargaining experiment

We evaluate two competing hypotheses that try to account for robust violations of the predictions of game theory in Ultimatum bargaining experiments. One popular hypothesis is that the subjects are motivated by considerations of fairness that are not modelled by traditional theory. The alternative hypothesis is that the subjects do not have common knowledge of the rationality, beliefs and motives of other players. Each hypothesis can explain existing data. We design several experiments to discriminate between these two hypotheses. The results provide strong support for the alternative hypothesis.     

A Discrete Wavelet Transform without edge effects using wavelet extrapolation

The Discrete Wavelet Transform (DWT) is of considerable practical use in image and signal processing applications. For example, significant compression can be achieved through the use of the DWT. A fundamental problem with the DWT, however, is the treatment of finite length data sequences. Commonly used techniques such as circular convolution and symmetric extension can produce undesirable edge effects which propagate into the interior of the transformed data as the number of DWT iterations increases. In this paper, we develop a DWT applicable to Daubechies’ orthogonal wavelets which does not exhibit edge effects. The underlying idea is to extrapolate the data at the boundaries by determining the coefficients of a best fit polynomial through data points in the vicinity of the boundary. This approach can be regarded as a solution to the problem of orthogonal wavelets on an interval. However, it has the advantage that it does not involve the explicit construction of boundary wavelets. The extrapolated DWT is designed to be well conditioned and to produce a critically sampled output. The methods we describe are equally applicable to biorthogonal wavelet bases.     

Constrained peptidomimetics: building bicyclic analogs of pyrazoline derivatives

A synthetic route has been developed for incorporating pyrazoline derivatives as proline surrogates in constrained X-Pro peptidomimetics. The route allows for the synthesis of dipeptide building blocks having either a six or seven-membered-ring annulated onto the pyrazoline moiety, as well as for the asymmetric synthesis of analogs having substituents on N-terminal side of the building block.     

Effective tuning of the arene and alkanesulfinamides for highly enantioselective synthesis of (S)-4-chlorophenylphenylmethylamine, a key intermediate for antihistamic (S)-cetirizine

High diastereoselectivity (>94%) has been achieved in the phenylMgBr addition process to chlorophenyl aldimine derived from the new and sterically hindered triisopropylbenzene sulfinamide (TIPBSA) in the synthesis of a key intermediate of (S)-Cetirizine. Surprisingly, under the same reaction conditions, toluenesulfinamide derived chlorophenyl aldimine provided only 10% ee.     

Efficient Computation of Analytic Bases in Evans Function Analysis of Large Systems

In Evans function computations of the spectra of asymptotically constant-coefficient linearized operators of large systems, a problem that becomes important is the efficient computation of global analytically varying bases for invariant subspaces of the limiting coefficient matrices. In the case that the invariant subspace is spectrally separated from its complementary invariant subspace, we propose an efficient numerical implementation of a standard projection-based algorithm of Kato, for which the key step is the solution of an associated Sylvester problem. This may be recognized as the analytic cousin of a C ^k algorithm developed by Dieci and collaborators based on orthogonal projection rather than eigenprojection as in our case. For a one-dimensional subspace, it reduces essentially to an algorithm of Bridges, Derks and Gottwald based on path-finding and continuation methods.     

Phase structure function of random wave fields

The phase properties of a complex Gaussian field, which can arise following scattering from random phase screens and through extended random media, are investigated. It is shown that the unwrapped phase of a complex Gaussian field constitutes a non-stationary process, such that the phase autocorrelation function does not exist. However, the phase structure function remains finite, allowing analytical results to be obtained for various field correlations. Methods for numerical simulation are discussed and their results found to be in excellent agreement with analytical predictions. More general considerations reveal that the phase structure function of a complex Gaussian field increases linearly with large separation distance. The results are relevant to phase-sensitive detection in fields undergoing strong intensity fluctuations.     

On closed boundary value problems for equations of mixed elliptic‐hyperbolic type

For partial differential equations of mixed elliptic‐hyperbolic type we prove results on existence and existence with uniqueness of weak solutions for closed boundary value problems of Dirichlet and mixed Dirichlet‐conormal types. Such problems are of interest for applications to transonic flow and are overdetermined for solutions with classical regularity. The method employed consists in variants of the a ? b ? c integral method of Friedrichs in Sobolev spaces with suitable weights. Particular attention is paid to the problem of attaining results with a minimum of restrictions on the boundary geometry and the form of the type change function. In addition, interior regularity results are also given in the important special case of the Tricomi equation. © 2006 Wiley Periodicals, Inc.     

A generalization of Ryser's theorem on term rank

In his work on classes of (0, 1)-matrices with given row and column sum vectors, Herbert Ryser proved that the maximum term rank possible in a normalized class, ρ, can be realized by a matrix having ρ (independent) 1's in positions (1, ρ), (2, ρ − 1), … , (ρ, 1). We study the positions occupied by sets of t ρ independent 1's.