Finite-Size Scaling Exponents in the Dicke Model

We consider the finite-size corrections in the Dicke model and determine the scaling exponents at the critical point for several quantities such as the ground state energy or the gap. Therefore, we use the Holstein-Primakoff representation of the angular momentum and introduce a nonlinear transformation to diagonalize the Hamiltonian in the normal phase. As already observed in several systems, these corrections turn out to be singular at the transition point and thus lead to nontrivial exponents. We show that for the atomic observables, these exponents are the same as in the Lipkin-Meshkov-Glick model, in agreement with numerical results. We also investigate the behavior of the order parameter related to the radiation mode and show that it is driven by the same scaling variable as the atomic one.Comment: 4 pages, published versio

Drought risk management in southern Africa. The potential of long lead climate forecasts for improved drought management

Although climate variability is the single most important factor affecting the livelihood of the people of southern Africa, there is no country in which drought risk is managed well. This mission set out to determine whether the social and economic benefits from making use of long lead climate forecast techniques for managing drought risk in southern Africa would justify investment directed towards bringing forward the techniques into operational usage. The four person mission consulted a wide range of decision makers, weather information users and technical specialists in Botswana, Malawi, South Africa and Zimbabwe during the month of July 1995. The views of those consulted were markedly positive and convergent. Reliable drought prediction is a very high priority for the people and economies of southern Africa. The mission found that: while climates are always changing, southern Africa does indeed appear to be becoming increasingly drought affected; for many governments, people and purposes in the region, reliable indication of the quality of the next wet season is probably the most useful single item of information that could be provided; ongoing climate research is much closer than is generally appreciated to being able to provide reliable and timely information of this kind; It is not logical to wait for forecast skill to be 100% reliable before beginning to incorporate forecasts into decision making meteorological institutions in the region are not capable of realising the full potential of their global links in their present state: they need both investment and development; while improved long lead forecasts offer the prospect of significant benefits, these will not be fully realised without a number of concurrent developments across the economy. The mission concludes that relatively modest investment towards both improving climate prediction and strengthening information dissemination and uptake pathways could revolutionise drought risk 'management-enhancing economic responsibility, food security and natural resource management throughout the region. Benefits from the better management of strategic grain reserves alone would justify the necessary investment. The mission recommends that ODA, the World Bank and other development organisations recognise the important potential of these techniques for mitigating many of the effects of recurrent drought, and seek the means to ensure their broad multi-disciplinary implementation for maximum impact and benefit

Introducing the locally stationary dual-tree complex wavelet model

This paper reconciles Kingsbury's dual-tree complex wavelets with Nason and Eckley's locally stationary model. We here establish that the dual-tree wavelets admit an invertible de-biasing matrix and that this matrix can be used to invert the covariance relation. We also show that the added directional selectivity of the proposed model adds utility to the standard two-dimensional local stationary model. Non-stationarity detection on random fields is used as a motivating example. Experiments confirm that the dual-tree model can distinguish anisotropic non-stationarities significantly better than the current model

Regularized Estimation of Piecewise Constant Gaussian Graphical Models:The Group-Fused Graphical Lasso

The time-evolving precision matrix of a piecewise-constant Gaussian graphical model encodes the dynamic conditional dependency structure of a multivariate time-series. Traditionally, graphical models are estimated under the assumption that data are drawn identically from a generating distribution. Introducing sparsity and sparse-difference inducing priors, we relax these assumptions and propose a novel regularized M-estimator to jointly estimate both the graph and changepoint structure. The resulting estimator possesses the ability to therefore favor sparse dependency structures and/or smoothly evolving graph structures, as required. Moreover, our approach extends current methods to allow estimation of changepoints that are grouped across multiple dependencies in a system. An efficient algorithm for estimating structure is proposed. We study the empirical recovery properties in a synthetic setting. The qualitative effect of grouped changepoint estimation is then demonstrated by applying the method on a genetic time-course dataset. Supplementary material for this article is available online

Depósito elevado, en Belfast

An outstanding feature of the buildings which constitute the modern Ulster Hospital, at Dundonald, Belfast, is the elevated tank which supplies the hospital with water. The shape of this tank is pleasant and it provides a charming and smooth outline against the sky: it is reminiscent of a large sized drinking cup. The structure, made of reinforced concrete, is of straighforward design. The central support is used as the chimney stack for the boiler room. The water tank has an overall height of 32.5 m and will hold 450 cubic metres of water. The tank itself is 15.5 m high and has a maximum diameter of 10 m. The walls vary in thickness between 0.32 and 0.15 m. The hoop reinforcement is provided by 19 mm bars, whilst the radial reinforcement consists of 9 mm wires. The central column, or stack, has a wall thickness of 0.15 m, and is of circular cross section. Vertical 35 mm rods provide the metal reinforcement. Externally, this central column has eight ribs, 20 cm wide and 30 cm deep. The whole structure rests on an octogonal slab, with a maximum horizontal dimension of 9 m and is 2 m thick. The maximum tensile strength allowed for the concrete, when working in the most unsatisfactory conditions, is 12 kg/cm2.Entre las distintas construcciones que constituyen el moderno hospital Ulster de Dundonald, en Belfast (Irlanda del Norte), destaca, particularmente, el depósito elevado para el suministro y reserva de agua. Desde el punto de vista arquitectónico, su forma es de plástica agradable y de línea suave y graciosa, puesto que reproduce la silueta de una copa, de gran tamaño, muy utilizada. Su estructura, de hormigón armado, es sencilla y ha permitido aprovechar el núcleo central o soporte, hueco, para chimenea de la sala, de calderas. La altura total del depósito es de 33,50 m y su capacidad de 450 m3. El depósito propiamente dicho tiene 15,5 m de altura y 10 m de diámetro máximo. El espesor de las paredes varía de 0,33 a 0,15 m. Las anillas de tracción de las armaduras están formadas con barras de 19 mm de diámetro, mientras que las armaduras radiales son barras de 9 mm de diámetro. El núcleo central o chimenea lleva una pared de 0,15 m de espesor, y es de sección circular. Las armaduras verticales están constituidas por barras de 35 mm de diámetro. Exteriormente, este núcleo o soporte presenta ocho nervios que se proyectan al exterior y tienen una sección de 0,30 de anchura por 0,30 m de profundidad. Toda la estructura se apoya sobre una losa octogonal de 9 m entre vértices opuestos y de 3 m de espesor. La tensión máxima prevista para el hormigón, trabajando a tracción y en las condiciones más desfavorables, es de 12 kg/cm2

Phytoplankton communities and acclimation in a cyclonic eddy in the southwest Indian Ocean

A study of phytoplankton in a cyclonic eddy was undertaken in the Mozambique Basin between Madagascar and southern Africa during austral winter. CHEMTAX analysis of pigment data indicated that the community comprised mainly haptophytes and diatoms, with Prochlorococcus, prasinophytes and pelagophytes also being prominent to the east and west of the eddy. There was little difference in community structure, chlorophyll-specific absorption [a*ph(440)] and pigment:TChla ratios between the surface and the sub-surface chlorophyll maximum (SCM), reflecting acclimation to fluctuating light conditions in a well mixed upper layer. Values for a*ph(440) were low for diatom dominance, high where prokaryote proportion was high, and intermediate for flagellate dominated communities. Chlorophyll c and fucoxanthin:TChla ratios were elevated over most of the eddy, while 19′-hexanoyloxyfucoxanthin ratios increased in the eastern and western sectors. In a community comprising mainly flagellates and Prochlorococcus to the west of the eddy, there was high a*ph(440) at the surface and elevated ratios for divinyl chlorophyll a, chlorophyll b and 19′-hexanoyloxyfucoxanthin at the SCM. An increase in diadinoxanthin:TChla ratios and a decline in the quantum efficiency of photochemistry in PSII under high light conditions, indicated some photoprotection and photoinhibition at the surface even in a well mixed environment. Diadinoxanthin was the main photoprotective carotenoid within the eddy, while zeaxanthin was the dominant photoprotective pigment outside the eddy. The results of this study will be useful inputs into appropriate remote sensing models for estimating primary production and the size class distribution of phytoplankton in eddies in the southwest Indian Ocean

Regularised estimation of 2D-locally stationary wavelet processes

Locally Stationary Wavelet processes provide a flexible way of describing the time/space evolution of autocovariance structure over an ordered field such as an image/time-series. Classically, estimation of such models assume continuous smoothness of the underlying spectra and are estimated via local kernel smoothers. We propose a new model which permits spectral jumps, and suggest a regularised estimator and algorithm which can recover such structure from images. We demonstrate the effectiveness of our method in a synthetic experiment where it shows desirable estimation properties. We conclude with an application to real images which illustrate the qualitative difference between the proposed and previous methods