We consider bipartite matching algorithms for computing permutations of a sparse matrix so that the diagonal of the permuted matrix has entries of large absolute value. We discuss various strategies for this and consider their implementation as computer codes. We also consider scaling techniques to further increase the relative values of the diagonal entries. Numerical experiments show the effect of the reorderings and the scaling on the solution of sparse equations by a direct method and by preconditioned iterative techniques.

We consider techniques for permuting a sparse matrix so that the diagonal of the permuted matrix has entries of large absolute value. We discuss various criteria for this and consider their implementation as computer codes. We then indicate several cases where such a permutation can be useful. These include the solution of sparse equations by a direct method and by an iterative technique. We also consider its use in generating a preconditioner for an iterative method. We see that the effect of these reorderings can be dramatic although the best a priori strategy is by no means clear.

The phenomenon of ischemic preconditioning was initially observed over 20 years ago. The basic tenant is that if stimuli are applied at a subtoxic level, cells upregulate endogenous protective mechanisms to block injury induced by subsequent stress. Since this discovery, many conserved signaling mechanisms that contribute to activation of this potent protective program have been identified in the brain. A clinical correlate of this basic research finding can be found in patients with a history of transient ischemic attack (TIA), who have a decreased morbidity after stroke. In spite of multidisciplinary efforts to design safer, more effective stroke therapies, we have thus far failed to translate our understanding of endogenous protective pathways to treatments for neurodegeneration. This review is designed to provide clinicians and basic scientists with an overview of stress biology after TIA and preconditioning, discuss new therapeutic strategies to target the protein dysfunction that follows ischemic injury, and propose enhanced biochemical profiling to identify individuals at risk of stroke after TIA. We pay particular attention to the unanticipated consequences of overly aggressive intervention after TIA in which we have found that traditional cytotoxic agents such as free radicals and apoptosis associated proteases is essential for neuroprotection and communication in the stressed brain. These data emphasize the importance of understanding the complex interplay between chaperones, apoptotic proteases including caspases, and the proteolytic degradation machinery in adaptation to neurological injury.

42% pre ischemia

SHOCK March 2005, Volume 23, Issue 3, p. 258