A dynamic nonstationary spatio-temporal model for short term prediction of precipitation

Precipitation is a complex physical process that varies in space and time. Predictions and interpolations at unobserved times and/or locations help to solve important problems in many areas. In this paper, we present a hierarchical Bayesian model for spatio-temporal data and apply it to obtain short term predictions of rainfall. The model incorporates physical knowledge about the underlying processes that determine rainfall, such as advection, diffusion and convection. It is based on a temporal autoregressive convolution with spatially colored and temporally white innovations. By linking the advection parameter of the convolution kernel to an external wind vector, the model is temporally nonstationary. Further, it allows for nonseparable and anisotropic covariance structures. With the help of the Voronoi tessellation, we construct a natural parametrization, that is, space as well as time resolution consistent, for data lying on irregular grid points. In the application, the statistical model combines forecasts of three other meteorological variables obtained from a numerical weather prediction model with past precipitation observations. The model is then used to predict three-hourly precipitation over 24 hours. It performs better than a separable, stationary and isotropic version, and it performs comparably to a deterministic numerical weather prediction model for precipitation and has the advantage that it quantifies prediction uncertainty.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS564 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Convectively driven shear and decreased heat flux

We report on direct numerical simulations of two-dimensional, horizontally periodic Rayleigh-B\'enard convection, focusing on its ability to drive large-scale horizontal flow that is vertically sheared. For the Prandtl numbers ($Pr$) between 1 and 10 simulated here, this large-scale shear can be induced by raising the Rayleigh number ($Ra$) sufficiently, and we explore the resulting convection for $Ra$ up to $10^{10}$. When present in our simulations, the sheared mean flow accounts for a large fraction of the total kinetic energy, and this fraction tends towards unity as $Ra\to\infty$. The shear helps disperse convective structures, and it reduces vertical heat flux; in parameter regimes where one state with large-scale shear and one without are both stable, the Nusselt number of the state with shear is smaller and grows more slowly with $Ra$. When the large-scale shear is present with $Pr\lesssim2$, the convection undergoes strong global oscillations on long timescales, and heat transport occurs in bursts. Nusselt numbers, time-averaged over these bursts, vary non-monotonically with $Ra$ for $Pr=1$. When the shear is present with $Pr\gtrsim3$, the flow does not burst, and convective heat transport is sustained at all times. Nusselt numbers then grow roughly as powers of $Ra$, but the growth rates are slower than any previously reported for Rayleigh-B\'enard convection without large-scale shear. We find the Nusselt numbers grow proportionally to $Ra^{0.077}$ when $Pr=3$ and to $Ra^{0.19}$ when $Pr=10$. Analogies with tokamak plasmas are described.Comment: 25 pages, 12 figures, 5 video

Bloch oscillations of cold atoms in optical lattices

This work is devoted to Bloch oscillations (BO) of cold neutral atoms in optical lattices. After a general introduction to the phenomenon of BO and its realization in optical lattices, we study different extentions of this problem, which account for recent developments in this field. These are two-dimensional BO, decoherence of BO, and BO in correlated systems. Although these problems are discussed in relation to the system of cold atoms in optical lattices, many of the results are of general validity and can be well applied to other systems showing the phenomenon of BO.Comment: submitted to the review section of IJMPB, few misprints are correcte

The Higgs Mechanism in Heterotic Orbifolds

We study spontaneous gauge symmetry breaking in the framework of orbifold compactifcations of heterotic string theory. In particular we investigate the electroweak symmetry breakdown via the Higgs mechanism. Such a breakdown can be achieved by continuous Wilson lines. Exploiting the geometrical properties of this scheme we develop a new technique which simplifies the analysis used in previous discussions.Comment: 38 pages, 10 figure

Rocketing rents the magnitude and attenuation of agglomeration economies in the commercial property market

Rocketing rents in urban areas are likely explained by agglomeration economies. This paper measures the impact of these external economies on commercial property values using unique micro�]data on commercial rents and employment. A measure of agglomeration is employed that is continuous over space, avoiding the modifiable areal unit problem. To distinguish agglomeration economies from unobserved endowments and shocks, I use temporal variation in densities and instrumental variables. The spatial extent of agglomeration economies is determined by estimating a spatial bandwidth within the model. The results show that agglomeration economies have a considerable impact on rents: a standard deviation increase in employment density leads to an increase in rents of about 10 percent. The geographical extent of these benefits is about 15 kilometres. The bias of ignoring time�]invariant unobserved endowments and unobserved shocks seems to be limited

Secondary homotopy groups

Secondary homotopy groups supplement the structure of classical homotopy groups. They yield a track functor on the track category of pointed spaces compatible with fiber sequences, suspensions and loop spaces. They also yield algebraic models of homotopy types with homotopy groups concentrated in two consecutive dimensions.Comment: We added further commets and references to make the paper more easily readabl

Percolation and number of phases in the 2D Ising model

We reconsider the percolation approach of Russo, Aizenman and Higuchi for showing that there exist only two phases in the Ising model on the square lattice. We give a fairly short alternative proof which is only based on FKG monotonicity and avoids the use of GKS-type inequalities originally needed for some background results. Our proof extends to the Ising model on other planar lattices such as the triangular and honeycomb lattice. We can also treat the Ising antiferromagnet in an external field and the hard-core lattice gas model on $Z^2$.Comment: 22 pages. Further details on extensions. To appear in J.Math.Phys., special issue on `Probabilistic Methods in Statistical Physics', March 200

The Alzheimer variant of Lewy body disease: A pathologically confirmed case-control study

The objective of the study was to identify clinical features that distinguish patients with dementia with Lewy bodies (DLB), who were classified as Alzheimer's disease ( AD) patients, from patients with AD. We examined a group of 27 patients from our memory clinic, originally diagnosed with AD, of whom 6 were postmortem found to have DLB. For the present study, we compared cognitive, noncognitive and neurological symptoms between the two groups. We found that there were no differences on ratings of dementia and scales for activities of daily living. Patients with DLB performed better on the MMSE and the memory subtest of the CAMCOG, but there was no difference in any other cognitive domain. Furthermore, genetic risk factors, including family history of dementia or allele frequency of the apolipoprotein epsilon 4, did not discriminate between the two groups, and there were no differences on CCT scans. Taken together, our findings suggest that Lewy body pathology may be present in patients who do not show the typical clinical features which distinguish DLB from AD. Copyright (C) 2005 S. Karger AG, Basel

Transverse instability of dunes

The simplest type of dune is the transverse one, which propagates with invariant profile orthogonally to a fixed wind direction. Here we show numerically and with a linear stability analysis that transverse dunes are unstable with respect to along-axis perturbations in their profile and decay on the bedrock into barchan dunes. Any forcing modulation amplifies exponentially with growth rate determined by the dune turnover time. We estimate the distance covered by a transverse dune before fully decaying into barchans and identify the patterns produced by different types of perturbation.Comment: 4 pages, 3 figures; To appear in Physical Review Letter