Bundle gerbes and moduli spaces

In this paper, we construct the index bundle gerbe of a family of self-adjoint Dirac-type operators, refining a construction of Segal. In a special case, we construct a geometric bundle gerbe called the caloron bundle gerbe, which comes with a natural connection and curving, and show that it is isomorphic to the analytically constructed index bundle gerbe. We apply these constructions to certain moduli spaces associated to compact Riemann surfaces, constructing on these moduli spaces, natural bundle gerbes with connection and curving, whose 3-curvature represent Dixmier-Douady classes that are generators of the third de Rham cohomology groups of these moduli spaces.Comment: 19 pages. Latex2e, typos corrected, a reference adde

On the deconfining limit in (2+1)-dimensional Yang-Mills theory

We consider (2+1)-dimensional Yang-Mills theory on $S^1 \times S^1 \times {\bf R}$ in the framework of a Hamiltonian approach developed by Karabali, Kim and Nair. The deconfining limit in the theory can be discussed in terms of one of the $S^1$ radii of the torus ($S^1 \times S^1$), while the other radius goes to infinity. We find that the limit agrees with the previously known result for a dynamical propagator mass of a gluon. We also make comparisons with numerical data.Comment: 21 pages; v2. lattice data references updated, comparative statements revised; v3. minor corrections; v4. section 6 extended, published versio

Chern-Simons theory and BCS superconductivity

We study the relationship between the holomorphic unitary connection of Chern-Simons theory with temporal Wilson lines and the Richardson's exact solution of the reduced BCS Hamiltonian. We derive the integrals of motion of the BCS model, their eigenvalues and eigenvectors as a limiting case of the Chern-Simons theory.Comment: 23 page

Twenty-five years of two-dimensional rational conformal field theory

In this article we try to give a condensed panoramic view of the development of two-dimensional rational conformal field theory in the last twenty-five years.Comment: A review for the 50th anniversary of the Journal of Mathematical Physics. Some references added, typos correcte

A role for core planar polarity proteins in cell contact-mediated orientation of planar cell division across the mammalian embryonic skin

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. © The Author(s) 2017. Supplementary information accompanies this paper at doi:10.1038/s41598-017-01971-2.The question of how cell division orientation is determined is fundamentally important for understanding tissue and organ shape in both healthy or disease conditions. Here we provide evidence for cell contact-dependent orientation of planar cell division in the mammalian embryonic skin. We propose a model where the core planar polarity proteins Celsr1 and Frizzled-6 (Fz6) communicate the long axis orientation of interphase basal cells to neighbouring basal mitoses so that they align their horizontal division plane along the same axis. The underlying mechanism requires a direct, cell surface, planar polarised cue, which we posit depends upon variant post-translational forms of Celsr1 protein coupled to Fz6. Our hypothesis has parallels with contact-mediated division orientation in early C. elegans embryos suggesting functional conservation between the adhesion-GPCRs Celsr1 and Latrophilin-1. We propose that linking planar cell division plane with interphase neighbour long axis geometry reinforces axial bias in skin spreading around the mouse embryo body.Peer reviewe

Van Gogh and Frizzled Act Redundantly in the Drosophila Sensory Organ Precursor Cell to Orient Its Asymmetric Division

Drosophila sensory organ precursor cells (SOPs) divide asymmetrically along the anterior-posterior (a-p) body axis to generate two different daughter cells. Planar Cell Polarity (PCP) regulates the a-p orientation of the SOP division. The localization of the PCP proteins Van Gogh (Vang) and Frizzled (Fz) define anterior and posterior apical membrane domains prior to SOP division. Here, we investigate the relative contributions of Vang, Fz and Dishevelled (Dsh), a membrane-associated protein acting downstream of Fz, in orienting SOP polarity. Genetic and live imaging analyses suggest that Dsh restricts the localization of a centrosome-attracting activity to the anterior cortex and that Vang is a target of Dsh in this process. Using a clone border assay, we provide evidence that the Vang and fz genes act redundantly in SOPs to orient its polarity axis in response to extrinsic local PCP cues. Additionally, we find that the activity of Vang is dispensable for the non-autonomous polarizing activity of fz. These observations indicate that both Vang and Fz act as cues for downstream effectors orienting the planar polarity axis of dividing SOPs

Transient Receptor Potential Ion Channels Control Thermoregulatory Behaviour in Reptiles

Biological functions are governed by thermodynamics, and animals regulate their body temperature to optimise cellular performance and to avoid harmful extremes. The capacity to sense environmental and internal temperatures is a prerequisite for the evolution of thermoregulation. However, the mechanisms that enable ectothermic vertebrates to sense heat remain unknown. The recently discovered thermal characteristics of transient receptor potential ion channels (TRP) render these proteins suitable to act as temperature sensors. Here we test the hypothesis that TRPs are present in reptiles and function to control thermoregulatory behaviour. We show that the hot-sensing TRPV1 is expressed in a crocodile (Crocodylus porosus), an agamid (Amphibolurus muricatus) and a scincid (Pseudemoia entrecasteauxii) lizard, as well as in the quail and zebrafinch (Coturnix chinensis and Poephila guttata). The TRPV1 genes from all reptiles form a unique clade that is delineated from the mammalian and the ancestral Xenopus sequences by an insertion of two amino acids. TRPV1 and the cool-sensing TRPM8 are expressed in liver, muscle (transversospinalis complex), and heart tissues of the crocodile, and have the potential to act as internal thermometer and as external temperatures sensors. Inhibition of TRPV1 and TRPM8 in C. porosus abolishes the typically reptilian shuttling behaviour between cooling and heating environments, and leads to significantly altered body temperature patterns. Our results provide the proximate mechanism of thermal selection in terrestrial ectotherms, which heralds a fundamental change in interpretation, because TRPs provide the mechanism for a tissue-specific input into the animals' thermoregulatory response

Beyond aridification: multiple explanations for the elevated diversification of cacti in the New World Succulent Biome

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106989/1/nph12752.pd

Order and Stochastic Dynamics in Drosophila Planar Cell Polarity

Cells in the wing blade of Drosophila melanogaster exhibit an in-plane polarization causing distal orientation of hairs. Establishment of the Planar Cell Polarity (PCP) involves intercellular interactions as well as a global orienting signal. Many of the genetic and molecular components underlying this process have been experimentally identified and a recently advanced system-level model has suggested that the observed mutant phenotypes can be understood in terms of intercellular interactions involving asymmetric localization of membrane bound proteins. Among key open questions in understanding the emergence of ordered polarization is the effect of stochasticity and the role of the global orienting signal. These issues relate closely to our understanding of ferromagnetism in physical systems. Here we pursue this analogy to understand the emergence of PCP order. To this end we develop a semi-phenomenological representation of the underlying molecular processes and define a “phase diagram” of the model which provides a global view of the dependence of the phenotype on parameters. We show that the dynamics of PCP has two regimes: rapid growth in the amplitude of local polarization followed by a slower process of alignment which progresses from small to large scales. We discuss the response of the tissue to various types of orienting signals and show that global PCP order can be achieved with a weak orienting signal provided that it acts during the early phase of the process. Finally we define and discuss some of the experimental predictions of the model

LSST Science Book, Version 2.0

A survey that can cover the sky in optical bands over wide fields to faint magnitudes with a fast cadence will enable many of the exciting science opportunities of the next decade. The Large Synoptic Survey Telescope (LSST) will have an effective aperture of 6.7 meters and an imaging camera with field of view of 9.6 deg^2, and will be devoted to a ten-year imaging survey over 20,000 deg^2 south of +15 deg. Each pointing will be imaged 2000 times with fifteen second exposures in six broad bands from 0.35 to 1.1 microns, to a total point-source depth of r~27.5. The LSST Science Book describes the basic parameters of the LSST hardware, software, and observing plans. The book discusses educational and outreach opportunities, then goes on to describe a broad range of science that LSST will revolutionize: mapping the inner and outer Solar System, stellar populations in the Milky Way and nearby galaxies, the structure of the Milky Way disk and halo and other objects in the Local Volume, transient and variable objects both at low and high redshift, and the properties of normal and active galaxies at low and high redshift. It then turns to far-field cosmological topics, exploring properties of supernovae to z~1, strong and weak lensing, the large-scale distribution of galaxies and baryon oscillations, and how these different probes may be combined to constrain cosmological models and the physics of dark energy.Comment: 596 pages. Also available at full resolution at http://www.lsst.org/lsst/sciboo