The 1-type of a Waldhausen K-theory spectrum

We give a small functorial algebraic model for the 2-stage Postnikov section of the K-theory spectrum of a Waldhausen category and use our presentation to describe the multiplicative structure with respect to biexact functors.     

Oscillations and concentrations in weak solutions of the incompressible fluid equations

The authors introduce a new concept of measure-valued solution for the 3-D incompressible Euler equations in order to incorporate the complex phenomena present in limits of approximate solutions of these equations. One application of the concepts developed here is the following important result: a sequence of Leray-Hopf weak solutions of the Navier-Stokes equations converges in the high Reynolds number limit to a measure-valued solution of 3-D Euler defined for all positive times. The authors present several explicit examples of solution sequences for 3-D incompressible Euler with uniformly bounded local kinetic energy which exhibit complex phenomena involving both persistence of oscillations and development of concentrations. An extensions of the concept of Young measure is developed to incorporate these complex phenomena in the measure-valued solutions constructed here.Partially supported by N.S.F. GrantPartially supported by N.S.F. Grant 84-0223 and 86-11110     

Current methods for site-directed structure generation

Summary There has been a rapid growth of interest in techniques for site-directed drug design, fuelled by the increasing availability of structural models of proteins of therapeutic importance, and by studies reported in the literature showing that potent chemical leads can be obtained by these techniques. Structure generation programs offer the prospect of discovering highly original lead structures from novel chemical families. Due to the fact that this technique is more-or-less still in its infancy, there are no case studies available that demonstrate the use of structure generation programs for site-directed drug design. Such programs were first proposed in 1986, and became commercially available in early 1992. They have shown their ability to reproduce, or suggest reasonable alternatives for, ligands in well-defined binding sites. This brief review will discuss the recent advances that have been made in the field of site-directed structure generation.     

Performance and analysis of saddle point preconditioners for the discrete steady-state Navier-Stokes equations

Summary. We examine the convergence characteristics of iterative methods based on a new preconditioning operator for solving the linear systems arising from discretization and linearization of the steady-state Navier-Stokes equations. With a combination of analytic and empirical results, we study the effects of fundamental parameters on convergence. We demonstrate that the preconditioned problem has an eigenvalue distribution consisting of a tightly clustered set together with a small number of outliers. The structure of these distributions is independent of the discretization mesh size, but the cardinality of the set of outliers increases slowly as the viscosity becomes smaller. These characteristics are directly correlated with the convergence properties of iterative solvers. Received August 5, 2000 / Published online June 20, 2001     

Optimal Algorithms for Probabilistic Solitude Detection on Anonymous Rings

Probabilistic algorithms are developed for a basic problem in distributed computation, assuming anonymous, asynchronous, unidirectional rings of processors. The problem, known as Solitude Detection, requires that a nonempty subset of the processors, calledcontenders, determine whether or not there is exactly one contender. Monte Carlo algorithms are developed that err with probability bounded by a specified parameter and exhibit either message or processor termination. The algorithms transmit an optimal expected number of bits, to within a constant factor. Their bit complexities display a surprisingly rich dependence on the kind of termination exhibited and on the processors' knowledge of the size of the ring. Two probabilistic tools are isolated and then combined in various ways to achieve all our algorithms.     

A Lie theoretic galois theory for the spectral curves of an integrable system: I

In the study of integrable systems of ODE's arising from a Lax pair with a parameter, the constants of the motion occur as spectral curves. The specific curves depend upon the representation of the Lie algebra. In this paper a Galois theory of spectral curves is given that classifies the spectral curves from an integrable system. The spectral curves correspond to conjugacy classes of certain subgroups of the Weyl group for the Lie algebra. The theory is illustrated with the periodic Toda lattice.Partially supported by a Louisiana Education Quality Support Fund grant LEQSF (87-89)-RD-A-8     

Magnetic resonance imaging (MRI) and pathophysiology of the rat kidney in streptozotocin-induced diabetes.

Proton magnetic resonance imaging was performed on rats before induction of diabetes with streptozotocin (STZ) and at 2 and 12 days postinduction. Images revealed an increase in maximal longitudinal and axial dimensions of the kidneys at 2 days and a further increase at 12 days. Similarly, an increase in the size of the remaining kidney was seen in a rat which underwent uninephrectomy as a positive control. Two major differences were observed between the kidney undergoing compensatory hypertrophy and those developing diabetic nephropathy: (i) Expansion of the renal vasculature was seen only in images of the diabetic rat; (ii) A loss in conspicuity of the normal corticomedullary junction was seen in the T2-weighted images of the diabetic rat but not in the uninephrectomized rat. Histologic examination revealed that the medulla increased to a size greater than the cortex during diabetic nephropathy whereas the medullary volume was less than that of the cortex during compensatory hypertrophy. In vitro T1 relaxation times in cortex, outer medulla and inner medulla of kidneys from control rats were measured and compared with the same respective regions in diabetic rats. When these values were correlated with tissue water content, a linear increase in relaxation rate versus percent water content from cortex to inner medulla was found in the control kidneys, but this correlation was absent in diabetic nephropathy. These studies demonstrate that MRI is an effective noninvasive tool for studying the course of renal hypertrophy and hydration changes in the development of renal disease in STZ-induced diabetes in the rat.     

Traceability issues in measurement

This paper reviews the current state of play of the Mutual Recognition Arrangement created by the International Committee for Weights and Measures in 1999. The aim of the MRA is to provide a framework within which National Metrology Institutes can demonstrate the equivalence of their realisations of the units and quantities of the SI system to which accredited laboratories are traceable. The article offers some views on the need for traceable measurements, their relevance to technical barriers to trade, and the use that is being made of the MRA framework by national and international bodies.