Asymptotics and Dimensional Dependence of the Number of Critical Points of Random Holomorphic Sections

We prove two conjectures from [M. R. Douglas, B. Shiffman and S. Zelditch, Critical points and supersymmetric vacua, II: Asymptotics and extremal metrics. J. Differential Geom. 72 (2006), no. 3, 381-427] concerning the expected number of critical points of random holomorphic sections of a positive line bundle. We show that, on average, the critical points of minimal Morse index are the most plentiful for holomorphic sections of {\mathcal O}(N) \to \CP^m and, in an asymptotic sense, for those of line bundles over general K\"ahler manifolds. We calculate the expected number of these critical points for the respective cases and use these to obtain growth rates and asymptotic bounds for the total expected number of critical points in these cases. This line of research was motivated by landscape problems in string theory and spin glasses.Comment: 14 pages, corrected typo

The future for global water assessment

The global water cycle is a fundamental component of our climate and Earth system. Many, if not the majority, of the impacts of climate change are water related. We have an imperfect description and understanding of components of the water cycle. This arises from an incomplete observation of some of the stores and fluxes in the water cycle (in particular: precipitation, evaporation, soil moisture and groundwater), problems with the simulation of precipitation by global climate models and the wide diversity of global hydrological models currently in use. This paper discusses these sources of errors and, in particular, explores the errors and advantages of bias correcting climate model outputs for hydrological models using a single large catchment as an example (the Rhine). One conclusion from this analysis is that bias correction is necessary and has an impact on the mean flows and their seasonal cycle. However choice of hydrological model has an equal, if not larger effect on the quality of the simulation. The paper highlights the importance of improving hydrological models, which run at a continental and global scale, and the importance of quantifying uncertainties in impact studies

Real-time PCR based on SYBR-Green I fluorescence: An alternative to the TaqMan assay for a relative quantification of gene rearrangements, gene amplifications and micro gene deletions

BACKGROUND: Real-time PCR is increasingly being adopted for RNA quantification and genetic analysis. At present the most popular real-time PCR assay is based on the hybridisation of a dual-labelled probe to the PCR product, and the development of a signal by loss of fluorescence quenching as PCR degrades the probe. Though this so-called 'TaqMan' approach has proved easy to optimise in practice, the dual-labelled probes are relatively expensive. RESULTS: We have designed a new assay based on SYBR-Green I binding that is quick, reliable, easily optimised and compares well with the published assay. Here we demonstrate its general applicability by measuring copy number in three different genetic contexts; the quantification of a gene rearrangement (T-cell receptor excision circles (TREC) in peripheral blood mononuclear cells); the detection and quantification of GLI, MYC-C and MYC-N gene amplification in cell lines and cancer biopsies; and detection of deletions in the OPA1 gene in dominant optic atrophy. CONCLUSION: Our assay has important clinical applications, providing accurate diagnostic results in less time, from less biopsy material and at less cost than assays currently employed such as FISH or Southern blotting

Giant Alcohol: A Worthy Opponent for the Children of the Band of Hope

From its foundation in 1847, the temperance organisation the Band of Hope addressed its young members as consumers, victims, and agents. In the first two roles they encountered the effects of drink of necessity, but in the third role they were encouraged to seek it out, attempting to influence individuals and wider society against 'Giant Alcohol'. With an estimated membership of half the school-age population by the early twentieth century, well over three million, the Band of Hope also acted more directly to influence policy, and encouraged young people to consider issues of policy and politics. With its wide range of activities and material to educate, entertain and empower millions of children, and its radical view of the place of the child, the Band of Hope not only mobilised its child members to lobby for legal change, including prohibition, but took an active part in pointing out the cost of alcohol to society, particularly during the 14-18 war. The organisation began to decline post 1918, and this paper focuses on the address made to children by the Band of Hope in the late nineteenth and early twentieth centuries, at a time when its innovative view of children as able to understand and influence policy decisions reflected developments in the construction of childhood. This article draws on the archive of the British National Temperance League, over 50,000 items located in the Livesey Collection, University of Central Lancashire

N3N^3 entropy of M5 branes from dielectric effect

We observe that the $N^3$ entropy behavior of near-extermal M5 branes can be reproduced from SYM side with the role of Myers' terms. We start by generalizing the Klebanov-Tseytlin (KT) supergravity solution that displays the $N^3$ entropy behavior. The new feature of the general solution is visibility of the "internal" degrees of the M5 branes, i.e., the M0 branes and the M2 branes. With the rationale provided by the supergravity analysis, we consider a D0 brane quantum mechanical setup with Myers' terms. Using localization technique, we show that the leading $N^3$ behavior of the free energy comes from the "classical contribution" with the rest sub-leading.Comment: latex, 21 pages, missing figure adde

Constrained Dynamics of an Anomalous (g/neq2)(g/neq 2) Relativistic Spinning Particle in Electromagnetic Background

In this paper we have considered the dynamics of an anomalous ($g\neq 2$) charged relativistic spinning particle in the presence of an external electromagnetic field. The constraint analysis is done and the complete set of Dirac brackets are provided that generate the canonical Lorentz algebra and dynamics through Hamiltonian equations of motion. The spin-induced effective curvature of spacetime and its possible connection with Analogue Gravity models are commented upon.Comment: 10 pages Latex, minor corrections and changes in ref., slightly enlarged version, to appear in EPJ

The Three-Dimensional Noncommutative Nonlinear Sigma Model in Superspace

We study the superspace formulation of the noncommutative nonlinear supersymmetric O(N) invariant sigma-model in 2+1 dimensions. We prove that the model is renormalizable to all orders of 1/N and explicitly verify that the model is asymptotically free.Comment: 16 pages, 5 figures, Revte

Inhomogeneous chiral symmetry breaking in noncommutative four fermion interactions

The generalization of the Gross-Neveu model for noncommutative 3+1 space-time has been analyzed. We find indications that the chiral symmetry breaking occurs for an inhomogeneous background as in the LOFF phase in condensed matter.Comment: 17 pages, 2 figures, published version, minor correction

The outer halos of elliptical galaxies

Recent progress is summarized on the determination of the density distributions of stars and dark matter, stellar kinematics, and stellar population properties, in the extended, low surface brightness halo regions of elliptical galaxies. With integral field absorption spectroscopy and with planetary nebulae as tracers, velocity dispersion and rotation profiles have been followed to ~4 and ~5-8 effective radii, respectively, and in M87 to the outer edge at ~150 kpc. The results are generally consistent with the known dichotomy of elliptical galaxy types, but some galaxies show more complex rotation profiles in their halos and there is a higher incidence of misalignments, indicating triaxiality. Dynamical models have shown a range of slopes for the total mass profiles, and that the inner dark matter densities in ellipticals are higher than in spiral galaxies, indicating earlier assembly redshifts. Analysis of the hot X-ray emitting gas in X-ray bright ellipticals and comparison with dynamical mass determinations indicates that non-thermal components to the pressure may be important in the inner ~10 kpc, and that the properties of these systems are closely related to their group environments. First results on the outer halo stellar population properties do not yet give a clear picture. In the halo of one bright galaxy, lower [alpha/Fe] abundances indicate longer star formation histories pointing towards late accretion of the halo. This is consistent with independent evidence for on-going accretion, and suggests a connection to the observed size evolution of elliptical galaxies with redshift.Comment: 8 pages. Invited review to appear in the proceedings of "Galaxies and their Masks" eds. Block, D.L., Freeman, K.C. & Puerari, I., 2010, Springer (New York