Introduction to Focus Issue: nonlinear and stochastic physics in biology

Frank Moss was a leading figure in the study of nonlinear and stochastic processes in biological systems. His work, particularly in the area of stochastic resonance, has been highly influential to the interdisciplinary scientific community. This Focus Issue pays tribute to Moss with articles that describe the most recent advances in the field he helped to create. In this Introduction, we review Moss's seminal scientific contributions and introduce the articles that make up this Focus Issue.     

Collapse of spatiotemporal chaos

The transient nature of spatiotemporal chaos is examined in reaction-diffusion systems with coexisting stable states. We find the apparent asymptotic spatiotemporal chaos of the Gray-Scott system to be transient, with the average transient lifetime increasing exponentially with medium size. The collapse of spatiotemporal chaos arises when statistical spatial correlations produce a quasihomogeneous medium, and the system obeys its zero-dimensional dynamics to relax to its stable asymptotic state.     

Collective behavior of particle-like chemical waves

Stabilized waves in weakly excitable media propagate with constant velocity and can be directionally controlled with applied excitability gradients. Multiple waves with directional control governed by pairwise interaction potentials form cohesive groups. Processional modes arise in collections of waves with random initial conditions, in which spontaneous alignment plays an essential role. Rotational modes occur with special initial conditions, and highly complex orbits are exhibited in larger groups. The ordered behavior is associated with waves following paths of minimum potential.     

A new approach to variable selection in least squares problems

The title Lasso has been suggested by Tibshirani (1996) as acolourful name for a technique of variable selection which requiresthe minimization of a sum of squares subject to an l₁ bound on the solution. This forces zero components in the minimizingsolution for small values of . Thus this bound can functionas a selection parameter. This paper makes two contributionsto computational problems associated with implementing the Lasso:(1) a compact descent method for solving the constrained problemfor a particular value of is formulated, and (2) a homotopymethod, in which the constraint bound becomes the homotopyparameter, is developed to completely describe the possibleselection regimes. Both algorithms have a finite terminationproperty. It is suggested that modified Gram-Schmidt orthogonalizationapplied to an augmented design matrix provides an effectivebasis for implementing the algorithms.     

A novel synthesis of substituted 3-amino and 3-thio pyrimido[5,4-e]-1,2,4-triazine-5,7(1H,6H)-diones

Fervenulin is a natural product that has been extensively studied due to its molecular features and breadth of biological activities. Published studies have reported the generation of numerous analogues of the bicyclic pyrimidotriazinodione core. One underrepresented subclass are compounds with electron releasing atoms bonded directly to the C-3 position. We report an efficient and straightforward synthesis of compounds with substituted amino and thio functionality attached to the C-3 position. These are derived from a common 3-chloro precursor that is made in six steps in 15.8% overall yield from a starting chlorouracil. Our methodology should be applicable to the synthesis of C-3 ether congeners also, and through previously described chemistry be expandable to incorporating diversity at the N-6 position of the pyrimidotriazinodione core. The chemistry reported herein expands possibilities for the generation of diverse libraries of substituted pyrimidotriazinediones for future studies.     

The sobolev equation,II

Partial differential equations of the form MDtU+LU = f are considered in which M and L denote realizations of regular elliptic linear partial differential operators of respective orders 2 m and 2 l. The abstract existence results of Part I lead to existence of generalized solutions of the equation. Regularity results are obtained by the technique of interpolation theory. The results include the parabolic equation (m = 0) and pseudo-parabolic equations m≧l. The extensive bibliography contains about 36 references to the literature on this class of equations     

Siderophore-Mediated Iron Uptake Promotes Yeast–Bacterial Symbiosis

In the present study, siderophore produced by the marine yeast Aureobasidium pullulans was characterized as hydroxamate by chemical and bioassays. The hydroxamate assignment was supported by the appearance of peaks at 1,647.21?C1,625.99?cm^?1 and at 1,435.04?cm^?1 in the infrared spectrum. The purified siderophore exhibited specific growth-promoting activity under iron-limited conditions for siderophore auxotrophic probiotic bacteria. Cross-utilization of siderophore indicates a symbiotic relationship between the yeast A. pullulans and the selected probiotic bacterial strains. Statistical optimization of medium components for improved siderophore production in A. pullulans was depicted by response surface methodology. The shift in UV?CVis spectroscopy indicates the photoreactive property and subsequent oxidative cleavage of purified siderophore on exposure to sunlight.