Minimal kernels of Dirac operators along maps

Let $M$ be a closed spin manifold and let $N$ be a closed manifold. For maps $f\colon M\to N$ and Riemannian metrics $g$ on $M$ and $h$ on $N$, we consider the Dirac operator $D^f_{g,h}$ of the twisted Dirac bundle $\Sigma M\otimes_{\mathbb{R}} f^*TN$. To this Dirac operator one can associate an index in $KO^{-dim(M)}(pt)$. If $M$ is $2$-dimensional, one gets a lower bound for the dimension of the kernel of $D^f_{g,h}$ out of this index. We investigate the question whether this lower bound is obtained for generic tupels $(f,g,h)$

Evolutionary rates and gene dispensability associate with replication timing in the Archaeon Sulfolobus islandicus

In bacterial chromosomes, the position of a gene relative to the single origin of replication generally reflects its replication timing, how often it is expressed, and consequently, its rate of evolution. However, because some archaeal genomes contain multiple origins of replication, bias in gene dosage caused by delayed replication should be minimized and hence the substitution rate of genes should associate less with chromosome position. To test this hypothesis, six archaeal genomes from the genus Sulfolobus containing three origins of replication were selected, conserved orthologs were identified, and the evolutionary rates (dN and dS) of these orthologs were quantified. Ortholog families were grouped by their consensus position and designated by their proximity to one of the three origins (O1, O2, O3). Conserved orthologs were concentrated near the origins and most variation in genome content occurred distant from the origins. Linear regressions of both synonymous and nonsynonymous substitution rates on distance from replication origins were significantly positive, the rates being greatest in the region furthest from any of the origins and slowest among genes near the origins. Genes near O1 also evolved faster than those near O2 and O3, which suggest that this origin may fire later in the cell cycle. Increased evolutionary rates and gene dispensability are strongly associated with reduced gene expression caused in part by reduced gene dosage during the cell cycle. Therefore, in this genus of Archaea as well as in many Bacteria, evolutionary rates and variation in genome content associate with replication timing

Why genes evolve faster on secondary chromosomes in bacteria

In bacterial genomes composed of more than one chromosome, one replicon is typically larger, harbors more essential genes than the others, and is considered primary. The greater variability of secondary chromosomes among related taxa has led to the theory that they serve as an accessory genome for specific niches or conditions. By this rationale, purifying selection should be weaker on genes on secondary chromosomes because of their reduced necessity or usage. To test this hypothesis we selected bacterial genomes composed of multiple chromosomes from two genera, Burkholderia and Vibrio, and quantified the evolutionary rates (dN and dS) of all orthologs within each genus. Both evolutionary rate parameters were faster among orthologs found on secondary chromosomes than those on the primary chromosome. Further, in every bacterial genome with multiple chromosomes that we studied, genes on secondary chromosomes exhibited significantly weaker codon usage bias than those on primary chromosomes. Faster evolution and reduced codon bias could in turn result from global effects of chromosome position, as genes on secondary chromosomes experience reduced dosage and expression due to their delayed replication, or selection on specific gene attributes. These alternatives were evaluated using orthologs common to genomes with multiple chromosomes and genomes with single chromosomes. Analysis of these ortholog sets suggested that inherently fast-evolving genes tend to be sorted to secondary chromosomes when they arise; however, prolonged evolution on a secondary chromosome further accelerated substitution rates. In summary, secondary chromosomes in bacteria are evolutionary test beds where genes are weakly preserved and evolve more rapidly, likely because they are used less frequently

Charged-Current Disappearance Measurements in the NuMI Off-Axis Beam

This article studies the potential of combining charged-current disappearance measurements of \nu_{\mu} to \nu_{\tau} from MINOS and an off-axis beam. I find that the error on \Delta m^2 from a 100 kt-yr off-axis measurement is a few percent of itself. Further, I find little improvement to an off-axis measurement by combining it with MINOS.Comment: Presented at NuFact'02. Four pages, three figure

Topology of the three-qubit space of entanglement types

The three-qubit space of entanglement types is the orbit space of the local unitary action on the space of three-qubit pure states, and hence describes the types of entanglement that a system of three qubits can achieve. We show that this orbit space is homeomorphic to a certain subspace of R^6, which we describe completely. We give a topologically based classification of three-qubit entanglement types, and we argue that the nontrivial topology of the three-qubit space of entanglement types forbids the existence of standard states with the convenient properties of two-qubit standard states.Comment: 9 pages, 3 figures, v2 adds a referenc

Potential Benefits on Impairment of Endothelial Function after a High-Fat Meal of 4 Weeks of Flavonoid Supplementation

Studies with foods high in flavonoids have demonstrated improvement in endothelial function. We investigated whether 4 weeks of flavonoid supplementation would prevent an adverse impact on endothelial function of a high-fat meal. Endothelial function was measured by reactive hyperemia peripheral arterial tonometry (RH-PAT). The RH-PAT index was measured both before and 3 h after a high-fat meal, in 23 healthy volunteers. Subjects were randomized in a double-blind, cross-over design to 4 weeks of daily supplementation with OPC-3, or a matching placebo. RH-PAT index before and after the high-fat meal was measured at the beginning and end of each 4-week treatment phase. The high-fat meal caused a decline in endothelial function at baseline in the placebo (-10.71%, P = .006) and flavonoid [-9.97% (P = .077)] groups, and there was no difference in decline between arms (P = .906). The high-fat meal produced a decline after 4 weeks of placebo [-12.37% (P = .005)], but no decline after 4 weeks of flavonoid supplement [-3.16% (P = .663)], and the difference between the two responses was highly significant (P < .0001). Within-group comparisons revealed no difference in endothelial function decline in the placebo arm between baseline and 4 weeks [-10.71% versus -12.37% (P = .758)]. In the flavonoid supplement arm, the difference in endothelial function decline between baseline and 4 weeks was -9.97% versus -3.16%, but did not reach statistical significance (P = .451). These results suggest that the flavonoid supplement used in this study mitigates the impairment of endothelial function caused by a high-fat meal. Whether certain subpopulations derive greater or lesser benefit remains unclear