The two components of the SO(3)-character space of the fundamental group of a closed surface of genus 2

We use geometric techniques to explicitly find the topological structure of the space of SO(3)-representations of the fundamental group of a closed surface of genus 2 quotient by the conjugation action by SO(3). There are two components of the space. We will describe the topology of both components and describe the corresponding SU(2)-character spaces by parametrizing them by spherical triangles. There is the sixteen to one branch-covering for each component, and the branch locus is a union of 2-spheres or 2-tori. Along the way, we also describe the topology of both spaces. We will later relate this result to future work into higher-genus cases and the SL(3,R)-representations

Generalizations of Tucker-Fan-Shashkin lemmas

Tucker and Ky Fan's lemma are combinatorial analogs of the Borsuk-Ulam theorem (BUT). In 1996, Yu. A. Shashkin proved a version of Fan's lemma, which is a combinatorial analog of the odd mapping theorem (OMT). We consider generalizations of these lemmas for BUT-manifolds, i.e. for manifolds that satisfy BUT. Proofs rely on a generalization of the OMT and on a lemma about the doubling of manifolds with boundaries that are BUT-manifolds.Comment: 10 pages, 2 figure

Retinotopic organization in children measured with fMRI

Many measures of visual function reach adult levels by about age 5, but some visual abilities continue to develop throughout adolescence. Little is known about the underlying functional anatomy of visual cortex in human infants or children. We used fMRI to measure the retinotopic organization of visual cortex in 15 children aged 7–12 years. Overall, we obtained adult-like patterns for most children tested. We found that significant head motion accounted for poor quality maps in a few tested children who were excluded from further analysis. When the maps from 10 children were compared with those obtained from 10 adults, the magnitude of retinotopic signals in visual areas V1, V2, V3, V3A, VP, and V4v was essentially the same between children and adults. Furthermore, one measure of intra-area organization, the cortical magnification function, did not significantly differ between adults and children for V1 or V2. However, quantitative analysis of visual area size revealed some significant differences beyond V1. Adults had larger extrastriate areas (V2, V3, VP, and V4v), when measured absolutely or as a proportion of the entire cortical sheet. We found that the extent and laterality of retinotopic signals beyond these classically defined areas, in parietal and lateral occipital cortex, showed some differences between adults and children. These data serve as a useful reference for studies of higher cognitive function in pediatric populations and for studies of children with vision disorders, such as amblyopia

Geometric K-Homology of Flat D-Branes

We use the Baum-Douglas construction of K-homology to explicitly describe various aspects of D-branes in Type II superstring theory in the absence of background supergravity form fields. We rigorously derive various stability criteria for states of D-branes and show how standard bound state constructions are naturally realized directly in terms of topological K-cycles. We formulate the mechanism of flux stabilization in terms of the K-homology of non-trivial fibre bundles. Along the way we derive a number of new mathematical results in topological K-homology of independent interest.Comment: 45 pages; v2: References added; v3: Some substantial revision and corrections, main results unchanged but presentation improved, references added; to be published in Communications in Mathematical Physic

Gut microbiota utilize immunoglobulin A for mucosal colonization

The immune system responds vigorously to microbial infection while permitting lifelong colonization by the microbiome. Mechanisms that facilitate the establishment and stability of the gut microbiota remain poorly described. We found that a regulatory system in the prominent human commensal Bacteroides fragilis modulates its surface architecture to invite binding of immunoglobulin A (IgA) in mice. Specific immune recognition facilitated bacterial adherence to cultured intestinal epithelial cells and intimate association with the gut mucosal surface in vivo. The IgA response was required for B. fragilis (and other commensal species) to occupy a defined mucosal niche that mediates stable colonization of the gut through exclusion of exogenous competitors. Therefore, in addition to its role in pathogen clearance, we propose that IgA responses can be co-opted by the microbiome to engender robust host-microbial symbiosis

Water channel pore size determines exclusion properties but not solute selectivity

Aquaporins (AQPs) are a ubiquitous family of transmembrane water channel proteins. A subgroup of AQP water channels also facilitates transmembrane diffusion of small, polar solutes. A constriction within the pore, the aromatic/arginine (ar/R) selectivity filter, is thought to control solute permeability: previous studies on single representative water channel proteins suggest narrow channels conduct water, whilst wider channels permit passage of solutes. To assess this model of selectivity, we used mutagenesis, permeability measurements and in silico comparisons of water-specific as well as glycerol-permeable human AQPs. Our studies show that single amino acid substitutions in the selectivity filters of AQP1, AQP4 and AQP3 differentially affect glycerol and urea permeability in an AQP-specific manner. Comparison between in silico-calculated channel cross-sectional areas and in vitro permeability measurements suggests that selectivity filter cross-sectional area predicts urea but not glycerol permeability. Our data show that substrate discrimination in water channels depends on a complex interplay between the solute, pore size, and polarity, and that using single water channel proteins as representative models has led to an underestimation of this complexity

The STACEE-32 Ground Based Gamma-ray Detector

We describe the design and performance of the Solar Tower Atmospheric Cherenkov Effect Experiment detector in its initial configuration (STACEE-32). STACEE is a new ground-based gamma ray detector using the atmospheric Cherenkov technique. In STACEE, the heliostats of a solar energy research array are used to collect and focus the Cherenkov photons produced in gamma-ray induced air showers. The large Cherenkov photon collection area of STACEE results in a gamma-ray energy threshold below that of previous detectors.Comment: 45 pages, 25 figures, Accepted for publication in Nuclear Instruments and Methods