K-Theory for group C^*-algebras

These notes are based on a lecture course given by the first author in the Sedano Winter School on K-theory held in Sedano, Spain, on January 22-27th of 2007. They aim at introducing K-theory of C^*-algebras, equivariant K-homology and KK-theory in the context of the Baum-Connes conjecture.Comment: 22 pages, 2 figures, to be published in Springer Lecture Note

Nambu-Jona-Lasinio Model in Curved Spacetime with Magnetic Field

We discuss the phase structure of the NJL model in curved spacetime with magnetic field using $1/N$-expansion and linear curvature approximation. The effective potential for composite fields $\bar\psi \psi$ is calculated using the proper-time cut-off in the following cases: a) at non-zero curvature, b) at non-zero curvature and non-zero magnetic field, and c) at non-zero curvature and non-zero covariantly constant gauge field. Chiral symmetry breaking is studied numerically. We show that the gravitational field may compensate the effect of the magnetic field what leads to restoration of chiral symmetry.Comment: LaTex file, 11 pages, 5 figures (not included) avaliable by request from first or third autho

Small-angle x-ray-scattering study of phase separation and crystallization in the bulk amorphous Mg62Cu25Y10Li3 alloy

We report on a small-angle x-ray-scattering (SAXS) and differential scanning calorimetry study of phase separation and crystallization in rapidly quenched amorphous Mg62Cu25Y10Li3 alloy samples. Differential scanning calorimetry demonstrates the occurrence of crystallization and grain growth upon isothermal annealing of these samples at 135 °C. The SAXS studies show the presence of large inhomogeneities even in the rapidly quenched as-prepared Mg62Cu25Y10Li3 alloy that is attributed to phase separation in the undercooled liquid during the cooling process. After isothermal annealing at 135 °C for longer than 30 min the samples exhibit a strong SAXS intensity that monotonically increases with increasing annealing time. During heat treatment, crystallization and growth of a nanocrystalline bcc-Mg7Li3 phase occurs in the Y-poor and MgLi-rich domains. The initially rough boundaries of the nanocrystals become sharper with increasing annealing time. Anomalous small-angle x-ray-scattering investigations near the Cu K edge indicate that while Cu is distributed homogeneously in the as-prepared sample, a Cu composition gradient develops between the matrix and the bcc-Mg7Li3 nanocrystals in the annealed sample

Teaching church and group reproduction : an adult-education approach for small groups

https://place.asburyseminary.edu/ecommonsatsdissertations/2425/thumbnail.jp

Strengths and Weaknesses of Parallel Tempering

Parallel tempering, also known as replica exchange Monte Carlo, is studied in the context of two simple free energy landscapes. The first is a double well potential defined by two macrostates separated by a barrier. The second is a `golf course' potential defined by microstates having two possible energies with exponentially more high energy states than low energy states. The equilibration time for replica exchange is analyzed for both systems. For the double well system, parallel tempering with a number of replicas that scales as the square root of the barrier height yields exponential speedup of the equilibration time. On the other hand, replica exchange yields only marginal speed-up for the golf course system. For the double well system, the free energy difference between the two wells has a large effect on the equilibration time. Nearly degenerate wells equilibrate much more slowly than strongly asymmetric wells. It is proposed that this difference in equilibration time may lead to a bias in measuring overlaps in spin glasses. These examples illustrate the strengths and weaknesses of replica exchange and may serve as a guide for understanding and improving the method in various applications.Comment: 18 pages, 4 figures. v2: typos fixed and wording changes to improve clarit

Proteomics of Cytochrome c Oxidase-Negative versus -Positive Muscle Fiber Sections in Mitochondrial Myopathy

The mosaic distribution of cytochrome c oxidase(+) (COX+) and COX - muscle fibers in mitochondrial disorders allows the sampling of fibers with compensated and decompensated mitochondrial function from the same individual. We apply laser capture microdissection to excise individual COX+ and COX- fibers from the biopsies of mitochondrial myopathy patients. Using mass spectrometry-based proteomics, we quantify >4,000 proteins per patient. While COX+ fibers show a higher expression of respiratory chain components, COX- fibers display protean adaptive responses, including upregulation of mitochondrial ribosomes, translation proteins, and chaperones. Upregulated proteins include C1QBP, required for mitoribosome formation and protein synthesis, and STOML2, which organizes cardiolipin-enriched microdomains and the assembly of respiratory supercomplexes. Factoring in fast/slow fiber type, COX (-) slow fibers show a compensatory upregulation of beta-oxidation, the AAA(+) protease AFG3L1, and the OPA1-dependent cristae remodeling program. These findings reveal compensatory mechanisms in muscle fibers struggling with energy shortage and metabolic stress