The stability of linear operators

In the approximation and solution of both ordinary and partial differential equations by finite difference equations, it is well-known that for different ratios of the time interval to the spatial intervals widely differing solutions are obtained. This problem was first attacked by John von Neumann using Fourier analysis. It has also been studied in the context of the theory of semi-groups of operators. It seemed that the problem could be studied with profit if set in a more abstract structure. The concepts of the stability of a linear operator on a (complex) Banach space and the stability of a Banach sub-algebra of operators were formed in an attempt to generalize the matrix 2 theorems of H.O. Kreiss as applied to the L² stability problem. Chapter 1 deals with the stability and strict stability of linear operators. The equivalence of stability and convergence is discussed in Chapter 2 and special cases of the Equivalence Theorem are considered in Chapters 3 and 4. In Chapter 5 a brief account of the theory of discretizations is given and used to predict instability in non-linear algorithms

Identifying Structural Variation in Haploid Microbial Genomes from Short-Read Resequencing Data Using Breseq

Mutations that alter chromosomal structure play critical roles in evolution and disease, including in the origin of new lifestyles and pathogenic traits in microbes. Large-scale rearrangements in genomes are often mediated by recombination events involving new or existing copies of mobile genetic elements, recently duplicated genes, or other repetitive sequences. Most current software programs for predicting structural variation from short-read DNA resequencing data are intended primarily for use on human genomes. They typically disregard information in reads mapping to repeat sequences, and significant post-processing and manual examination of their output is often required to rule out false-positive predictions and precisely describe mutational events. Results: We have implemented an algorithm for identifying structural variation from DNA resequencing data as part of the breseq computational pipeline for predicting mutations in haploid microbial genomes. Our method evaluates the support for new sequence junctions present in a clonal sample from split-read alignments to a reference genome, including matches to repeat sequences. Then, it uses a statistical model of read coverage evenness to accept or reject these predictions. Finally, breseq combines predictions of new junctions and deleted chromosomal regions to output biologically relevant descriptions of mutations and their effects on genes. We demonstrate the performance of breseq on simulated Escherichia coli genomes with deletions generating unique breakpoint sequences, new insertions of mobile genetic elements, and deletions mediated by mobile elements. Then, we reanalyze data from an E. coli K-12 mutation accumulation evolution experiment in which structural variation was not previously identified. Transposon insertions and large-scale chromosomal changes detected by breseq account for similar to 25% of spontaneous mutations in this strain. In all cases, we find that breseq is able to reliably predict structural variation with modest read-depth coverage of the reference genome (>40-fold). Conclusions: Using breseq to predict structural variation should be useful for studies of microbial epidemiology, experimental evolution, synthetic biology, and genetics when a reference genome for a closely related strain is available. In these cases, breseq can discover mutations that may be responsible for important or unintended changes in genomes that might otherwise go undetected.U.S. National Institutes of Health R00-GM087550U.S. National Science Foundation (NSF) DEB-0515729NSF BEACON Center for the Study of Evolution in Action DBI-0939454Cancer Prevention & Research Institute of Texas (CPRIT) RP130124University of Texas at Austin startup fundsUniversity of Texas at AustinCPRIT Cancer Research TraineeshipMolecular Bioscience

Disruption of axoplasmic transport induces mechanical sensitivity in intact rat C-fibre nociceptor axons

Peripheral nerve inflammation can cause axons conducting through the inflamed site to become mechanically sensitive. Axonal mechanical sensitivity (AMS) of intact axons may explain symptoms in a diverse number of conditions characterized by radiating pain evoked by movements of the affected nerve. Because nerve inflammation also disrupts axoplasmic transport, we hypothesized that the disruption of axoplasmic transport by nerve inflammation could cause the cellular components responsible for mechanical transduction to accumulate and become inserted at the inflamed site, causing AMS. This was tested by examining AMS in C-fibre nociceptors following the application of axoplasmic transport blockers (colchicine and vinblastine) to the sciatic nerve. Both 10 mm colchicine and 0.1 mm vinblastine caused AMS to develop in 30.6% and 33.3% of intact axons, respectively (P < 0.05 compared to sham treatment). Since high doses of colchicine (> 50 mm) can damage axons, and inflammation is involved in the removal of axonal debris, experiments were performed to assess conduction across the treatment site as well as signs of inflammation. Results indicated minimal axonal loss (95% of A- and C-fibres conducting), consistent with the normal microscopic appearance of the colchicine treatment site and absence of ED1-positive (recruited) macrophages. In a separate series of experiments, the block of axoplasmic transport proximal to a localized neuritis significantly reduced inflammation-induced AMS (15.6% compared to 55.6%; P < 0.05), further supporting that the components necessary for AMS are moved by anterograde transport. In summary, nerve inflammation that causes the disruption of axoplasmic transport in patients with painful conditions may result in the accumulation and insertion of mechanosensitive elements at the inflamed site