A note on an SOR-like method for augmented systems

Golub et al. (2001, BIT, 41, 71–85) gave a generalizedsuccessive over-relaxation method for the augmented systems.In this paper, the connection between the SOR-like method andthe preconditioned conjugate gradient (PCG) method for the augmentedsystems is investigated. It is shown that the PCG method isat least as accurate (fast) as the SOR-like method. Numericalexamples demonstrate that the PCG method is much faster thanthe SOR-like method.     

A bio-mechanical model for coupling cell contractility with focal adhesion formation

Focal adhesions (FAs) are large, multi-protein complexes that provide a mechanical link between the cytoskeletal contractile machinery and the extracellular matrix. They exhibit mechanosensitive properties; they self-assemble upon application of pulling forces and dissociate when these forces are decreased. We rationalize this mechano-sensitivity from thermodynamic considerations and develop a continuum framework in which the cytoskeletal contractile forces generated by stress fibers drive the assembly of the FA multi-protein complexes. The FA model has three essential features: (i) the low and high affinity integrins co-exist in thermodynamic equilibrium, (ii) the low affinity integrins within the plasma membrane are mobile, and (iii) the contractile forces generated by the stress fibers are in mechanical equilibrium and change the free energies of the integrins. A general two-dimensional framework is presented and the essential features of the model illustrated using one-dimensional examples. Consistent with observations, the coupled stress fiber and FA model predict that (a) the FAs concentrate around the periphery of the cell; (b) the fraction of the cell covered by FAs increases with decreasing cell size while the total FA intensity increases with increasing cell size; and (c) the FA intensity decreases substantially when cell contractility is curtailed.     

The Small Index Property for Free Groups and Relatively Free Groups

1. Some groups with the small index property In this paper we shall use the methods of the paper [6] by Hodges,Hodkinson, Lascar and Shelah to show that the free group ofcountably infinite rank and certain relatively free groups ofcountably infinite rank have the small index property.     

A search for fractional electric charge in sea water

The magnetic levitation technique has been used to test for fractional electric charge in sea water, using steel balls coated with sea water residue by evaporation. The objective was to reach concentration levels below 1 g^?1 which might result from cosmic ray interactions. Four stages of increasing sensitivity are reported: (1) residue from direct evaporation of unprocessed sea water, (2) residue from sea water samples enriched by ion exchangen, (3) residue reduced by high temperature evaporation, and (4) hypothetical enrichment by dilution and separation of soluble residue. Stages 1–3 are based on the generally accepted preferential retention of fractional charge during evaporation, but stage 4 limits are subject to uncertainties in the enrichment process. No evidence for fractional charge was found in a total of about 130 samples tested in these four stages. Samples containing positive and negative ions were tested separately, and concentration limits are reported for each of the stages. Levels in the region 0.01–0.1g^?1 were reached in stage 3, and 0.001 g^?1 in stage 4.     

Selection and Scheduling of Advanced Missions for NASA Using 0-1 Integer Linear Programming

A 0-1 integer linear programme for the selection and scheduling of US National Aeronautics and Space Administration (NASA) missions over a long planning horizon is presented. This model was formulated to allow a higher-level user-interaction with an advanced missions database currently being developed. The model implicitly considers the multi-objective nature of the problem, which results from the desire to maximize benefits in several categories as well as from the desire to minimize cost. In addition, the model allows the planner much flexibility in the selection process. This is accomplished by allowing the planner the ability to specify long- or short-term budget constraints, precursor/follow-on mission requirements, or any number of other idiosyncratic constraints which might be of importance in the decision process. Small example problems are solved in order to illustrate the approach, and areas for further research are discussed.