A Generalized Inverse Iteration for Computing Simple Eigenvalues of Nonsymmetric Matrices

. A Newton type method for approximating eigenpairs of nonnormal matrices is proposed. It takes full advantage of known approximations and circumvents shortcomings of Newton's method applied to the nonlinear system Ax \Gamma x = 0; (x T x \Gamma 1)=2 = 0 caused by a possibly ill-conditioned Jacobian. Instead, the eigenvalue problem is considered as a nonlinear parameter dependent system of equations F (x; ) = Ax \Gamma x = 0 without a normalization condition. If is an eigenvalue of A then (0; ) is a bifurcation point on the solution manifold of the system. In the paper, a bifurcation point algorithm proposed by Griewank/Reddien and modified by Allgower/Schwetlick is adapted to the case of computing a simple eigenvalue and the corresponding right and left eigenvector of a nonnormal matrix. The extended algorithm with updated bordering vectors can be viewed as generalized Rayleigh quotient iteration. Surprisingly it turns out that these algorithms which come from nonlinear analysis, u..

Selective Cell Death of Hyperploid Neurons in Alzheimer’s Disease

Aneuploidy, an abnormal number of copies of a genomic region, might be a significant source for neuronal complexity, intercellular diversity, and evolution. Genomic instability associated with aneuploidy, however, can also lead to developmental abnormalities and decreased cellular fitness. Here we show that neurons with a more-than-diploid content of DNA are increased in preclinical stages of Alzheimer’s disease (AD) and are selectively affected by cell death during progression of the disease. Present findings show that neuronal hyperploidy in AD is associated with a decreased viability. Hyperploidy of neurons thus represents a direct molecular signature of cells prone to death in AD and indicates that a failure of neuronal differentiation is a critical pathogenetic event in AD

Quantifying the effects of prior acetyl-salicylic acid on sepsis-related deaths: An individual patient data meta-analysis using propensity matching

Objective: The primary objective was to conduct a meta-analysis on published observational cohort data describing the association between acetyl-salicylic acid (aspirin) use prior to the onset of sepsis and mortality in hospitalized patients. Study Selection: Studies that reported mortality in patients on aspirin with sepsis with a comparison group of patients with sepsis not on prior aspirin therapy were included. Data Sources: Fifteen studies described hospital-based cohorts (n = 17,065), whereas one was a large insurance-based database (n = 683,421). Individual-level patient data were incorporated from all selected studies. Data Extraction: Propensity analyses with 1:1 propensity score matching at the study level were performed, using the most consistently available covariates judged to be associated with aspirin. Meta-analyses were performed to estimate the pooled average treatment effect of aspirin on sepsis-related mortality. Data Synthesis: Use of aspirin was associated with a 7% (95% CI, 2-12%; p = 0.005) reduction in the risk of death as shown by meta-analysis with considerable statistical heterogeneity (I-2 = 61.6%). Conclusions: These results are consistent with effects ranging from a 2% to 12% reduction in mortality risk in patients taking aspirin prior to sepsis onset. This association anticipates results of definitive studies of the use of low-dose aspirin as a strategy for reduction of deaths in patients with sepsi