A Shape Theorem for Riemannian First-Passage Percolation

Riemannian first-passage percolation (FPP) is a continuum model, with a distance function arising from a random Riemannian metric in $\R^d$. Our main result is a shape theorem for this model, which says that large balls under this metric converge to a deterministic shape under rescaling. As a consequence, we show that smooth random Riemannian metrics are geodesically complete with probability one

Classical Spin Models with Broken Continuous Symmetry: Random Field Induced Order and Persistence of Spontaneous Magnetization

We consider a classical spin model, of two-dimensional spins, with continuous symmetry, and investigate the effect of a symmetry breaking unidirectional quenched disorder on the magnetization of the system. We work in the mean field regime. We show, by numerical simulations and by perturbative calculations in the low as well as in the high temperature limits, that although the continuous symmetry of the magnetization is lost, the system still magnetizes, albeit with a lower value as compared to the case without disorder. The critical temperature at which the system starts magnetizing, also decreases with the introduction of disorder. However, with the introduction of an additional constant magnetic field, the component of magnetization in the direction that is transverse to the disorder field increases with the introduction of the quenched disorder. We discuss the same effects also for three-dimensional spins.Comment: 12 pages, 12 figures, RevTeX

The EarthCARE mission – science and system overview

The Earth Cloud, Aerosol and Radiation Explorer (EarthCARE) is a satellite mission implemented by the European Space Agency (ESA), in cooperation with the Japan Aerospace Exploration Agency (JAXA), to measure global profiles of aerosols, clouds and precipitation properties together with radiative fluxes and derived heating rates. The simultaneous measurements of the vertical structure and horizontal distribution of cloud and aerosol fields, together with outgoing radiation, will be used in particular to evaluate their representation in weather forecasting and climate models and to improve our understanding of cloud and aerosol radiative impact and feedback mechanisms. To achieve the objective, the goal is that a retrieved scene with footprint size of 10 km × 10 km is measured with sufficiently high resolution that the atmospheric vertical profile of short-wave (solar) and long-wave (thermal) flux can be reconstructed with an accuracy of 10 W m−2 at the top of the atmosphere. To optimise the performance of the two active instruments, the platform will fly at a relatively low altitude of 393 km, with an equatorial revisit time of 25 d. The scientific payload consists of four instruments: an atmospheric lidar, a cloud-profiling radar with Doppler capability, a multi-spectral imager and a broadband radiometer. Co-located measurements from these instruments are processed in the ground segment, which produces and distributes a wide range of science data products. As well as the Level 1 (L1) product of each instrument, a large number of multiple-instrument L2 products have been developed, in both Europe and Japan, benefiting from the data synergy. An end-to-end simulator and several test scenes have been developed that simulate EarthCARE observations and provide a development and test environment for L1 and L2 processors. Within this paper the EarthCARE observational requirements are addressed. An overview is given of the space segment with a detailed description of the four science instruments, demonstrating how the observational requirements will be met. Furthermore, the elements of the space segment and ground segment that are relevant for science data users are described and the data products are introduced.</p

Does Amazon forest leaf phenology mediate transpiration seasonality and hence, ecoclimate teleconnections?

Abstract OOS 11-5

Nonlinear time-series approaches in characterizing mood stability and mood instability in bipolar disorder

Bipolar disorder is a psychiatric condition characterized by episodes of elevated mood interspersed with episodes of depression. While treatment developments and understanding the disruptive nature of this illness have focused on these episodes, it is also evident that some patients may have chronic week-to-week mood instability. This is also a major morbidity. The longitudinal pattern of this mood instability is poorly understood as it has, until recently, been difficult to quantify. We propose that understanding this mood variability is critical for the development of cognitive neuroscience-based treatments. In this study, we develop a time-series approach to capture mood variability in two groups of patients with bipolar disorder who appear on the basis of clinical judgement to show relatively stable or unstable illness courses. Using weekly mood scores based on a self-rated scale (quick inventory of depressive symptomatology—self-rated; QIDS-SR) from 23 patients over a 220-week period, we show that the observed mood variability is nonlinear and that the stable and unstable patient groups are described by different nonlinear time-series processes. We emphasize the necessity in combining both appropriate measures of the underlying deterministic processes (the QIDS-SR score) and noise (uncharacterized temporal variation) in understanding dynamical patterns of mood variability associated with bipolar disorder

Geodesics and the competition interface for the corner growth model

We study the directed last-passage percolation model on the planar square lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, out- side of the class of exactly solvable models. Stationary cocycles are constructed for this percolation model from queueing fixed points. These cocycles serve as bound- ary conditions for stationary last-passage percolation, solve variational formulas that characterize limit shapes, and yield existence of Busemann functions in directions where the shape has some regularity. In a sequel to this paper the cocycles are used to prove results about semi-infinite geodesics and the competition interface

Impact of FTO genotypes on BMI and weight in polycystic ovary syndrome : a systematic review and meta-analysis

Aims/hypothesis FTO gene single nucleotide polymorphisms (SNPs) have been shown to be associated with obesity-related traits and type 2 diabetes. Several small studies have suggested a greater than expected effect of the FTO rs9939609 SNP on weight in polycystic ovary syndrome (PCOS). We therefore aimed to examine the impact of FTO genotype on BMI and weight in PCOS. Methods A systematic search of medical databases (PubMed, EMBASE and Cochrane CENTRAL) was conducted up to the end of April 2011. Seven studies describing eight distinct PCOS cohorts were retrieved; seven were genotyped for SNP rs9939609 and one for SNP rs1421085. The per allele effect on BMI and body weight increase was calculated and subjected to meta-analysis. Results A total of 2,548 women with PCOS were included in the study; 762 were TT homozygotes, 1,253 had an AT/CT genotype, and 533 were AA/CC homozygotes. Each additional copy of the effect allele (A/C) increased the BMI by a mean of 0.19 z score units (95% CI 0.13, 0.24; p = 2.26 × 10−11) and body weight by a mean of 0.20 z score units (95% CI 0.14, 0.26; p = 1.02 × 10−10). This translated into an approximately 3.3 kg/m2 increase in BMI and an approximately 9.6 kg gain in body weight between TT and AA/CC homozygotes. The association between FTO genotypes and BMI was stronger in the cohorts with PCOS than in the general female populations from large genome-wide association studies. Deviation from an additive genetic model was observed in heavier populations. Conclusions/interpretation The effect of FTO SNPs on obesity-related traits in PCOS seems to be more than two times greater than the effect found in large population-based studies. This suggests an interaction between FTO and the metabolic context or polygenic background of PCOS

Self-organization in the olfactory system: one shot odor recognition in insects

We show in a model of spiking neurons that synaptic plasticity in the mushroom bodies in combination with the general fan-in, fan-out properties of the early processing layers of the olfactory system might be sufficient to account for its efficient recognition of odors. For a large variety of initial conditions the model system consistently finds a working solution without any fine-tuning, and is, therefore, inherently robust. We demonstrate that gain control through the known feedforward inhibition of lateral horn interneurons increases the capacity of the system but is not essential for its general function. We also predict an upper limit for the number of odor classes Drosophila can discriminate based on the number and connectivity of its olfactory neurons