Random Tensors and Planted Cliques

The r-parity tensor of a graph is a generalization of the adjacency matrix, where the tensor's entries denote the parity of the number of edges in subgraphs induced by r distinct vertices. For r=2, it is the adjacency matrix with 1's for edges and -1's for nonedges. It is well-known that the 2-norm of the adjacency matrix of a random graph is O(\sqrt{n}). Here we show that the 2-norm of the r-parity tensor is at most f(r)\sqrt{n}\log^{O(r)}n, answering a question of Frieze and Kannan who proved this for r=3. As a consequence, we get a tight connection between the planted clique problem and the problem of finding a vector that approximates the 2-norm of the r-parity tensor of a random graph. Our proof method is based on an inductive application of concentration of measure

On the structure and evolution of a polar crown prominence/filament system

Polar crown prominences are made of chromospheric plasma partially circling the Suns poles between 60 and 70 degree latitude. We aim to diagnose the 3D dynamics of a polar crown prominence using high cadence EUV images from the Solar Dynamics Observatory (SDO)/AIA at 304 and 171A and the Ahead spacecraft of the Solar Terrestrial Relations Observatory (STEREO-A)/EUVI at 195A. Using time series across specific structures we compare flows across the disk in 195A with the prominence dynamics seen on the limb. The densest prominence material forms vertical columns which are separated by many tens of Mm and connected by dynamic bridges of plasma that are clearly visible in 304/171A two-color images. We also observe intermittent but repetitious flows with velocity 15 km/s in the prominence that appear to be associated with EUV bright points on the solar disk. The boundary between the prominence and the overlying cavity appears as a sharp edge. We discuss the structure of the coronal cavity seen both above and around the prominence. SDO/HMI and GONG magnetograms are used to infer the underlying magnetic topology. The evolution and structure of the prominence with respect to the magnetic field seems to agree with the filament linkage model.Comment: 24 pages, 14 figures, Accepted for publication in Solar Physics Journal, Movies can be found at http://www2.mps.mpg.de/data/outgoing/panesar

Absence of Scaling in the Integer Quantum Hall Effect

We have studied the conductivity peak in the transition region between the two lowest integer Quantum Hall states using transmission measurements of edge magnetoplasmons. The width of the transition region is found to increase linearly with frequency but remains finite when extrapolated to zero frequency and temperature. Contrary to prevalent theoretical pictures, our data does not show the scaling characteristics of critical phenomena.These results suggest that a different mechanism governs the transition in our experiment.Comment: Minor changes and new references include

Physics of Solar Prominences: I - Spectral Diagnostics and Non-LTE Modelling

This review paper outlines background information and covers recent advances made via the analysis of spectra and images of prominence plasma and the increased sophistication of non-LTE (ie when there is a departure from Local Thermodynamic Equilibrium) radiative transfer models. We first describe the spectral inversion techniques that have been used to infer the plasma parameters important for the general properties of the prominence plasma in both its cool core and the hotter prominence-corona transition region. We also review studies devoted to the observation of bulk motions of the prominence plasma and to the determination of prominence mass. However, a simple inversion of spectroscopic data usually fails when the lines become optically thick at certain wavelengths. Therefore, complex non-LTE models become necessary. We thus present the basics of non-LTE radiative transfer theory and the associated multi-level radiative transfer problems. The main results of one- and two-dimensional models of the prominences and their fine-structures are presented. We then discuss the energy balance in various prominence models. Finally, we outline the outstanding observational and theoretical questions, and the directions for future progress in our understanding of solar prominences.Comment: 96 pages, 37 figures, Space Science Reviews. Some figures may have a better resolution in the published version. New version reflects minor changes brought after proof editin

Edge state transmission, duality relation and its implication to measurements

The duality in the Chalker-Coddington network model is examined. We are able to write down a duality relation for the edge state transmission coefficient, but only for a specific symmetric Hall geometry. Looking for broader implication of the duality, we calculate the transmission coefficient $T$ in terms of the conductivity $\sigma_{xx}$ and $\sigma_{xy}$ in the diffusive limit. The edge state scattering problem is reduced to solving the diffusion equation with two boundary conditions $(\partial_y-(\sigma_{xy})/(\sigma_{xx})\partial_x)\phi=0$ and $[\partial_x+(\sigma_{xy}-\sigma_{xy}^{lead})/(\sigma_{xx}) \partial_y]\phi=0$. We find that the resistances in the geometry considered are not necessarily measures of the resistivity and $\rho_{xx}=L/W R/T h/e^2$ ($R=1-T$) holds only when $\rho_{xy}$ is quantized. We conclude that duality alone is not sufficient to explain the experimental findings of Shahar et al and that Landauer-Buttiker argument does not render the additional condition, contrary to previous expectation.Comment: 16 pages, 3 figures, to appear in Phys. Rev.

Solar city indicator: a methodology to predict city level PV installed capacity by combining physical capacity and socio-economic factors

Shifting to renewable sources of electricity is imperative in achieving global reductions in carbon emissions and ensuring future energy security. One technology, solar photovoltaics (PV), has begun to generate a noticeable contribution to the electricity mix in numerous countries. However, the upper limits of this contribution have not been explored in a way that combines both building-by-building solar resource appraisals with the city-scale socio-economic contexts that dictate PV uptake. This paper presents such a method, whereby a ‘Solar City Indicator’ is calculated and used to rank cities by their capacity to generate electricity from roof-mounted PV. Seven major UK cities were chosen for analysis based on available data; Dundee, Derby, Edinburgh, Glasgow, Leicester, Nottingham and Sheffield. The physical capacity of each city was established using a GIS-based methodology, exploiting digital surface models and LiDAR data, with distinct methodologies for large and small properties. Socio-economic factors (income, education, environmental consciousness, building stock and ownership) were chosen based on existing literature and correlation with current levels of PV installations. These factors were enumerated using data that was readily available across each city. Results show that Derby has the greatest potential of all the cities analysed, as it offers both good physical and socio-economic potential. In terms of physical capacity it was seen that over a 15 year payback period there are two plateaus, showing a marked difference in viability between small and large PV arrays. It was found that both the physical and socio-economic potential of a city are strongly influenced by the nature of the local building stock. This study also identifies areas where policy needs to be focused in order to encourage uptake and highlights factors limiting maximum PV uptake. While this methodology has been demonstrated using UK cities, it is equally applicable to any country where city data is available

Mesoscopic conductance and its fluctuations at non-zero Hall angle

We consider the bilocal conductivity tensor, the two-probe conductance and its fluctuations for a disordered phase-coherent two-dimensional system of non-interacting electrons in the presence of a magnetic field, including correctly the edge effects. Analytical results are obtained by perturbation theory in the limit $\sigma_{xx} \gg 1$. For mesoscopic systems the conduction process is dominated by diffusion but we show that, due to the lack of time-reversal symmetry, the boundary condition for diffusion is altered at the reflecting edges. Instead of the usual condition, that the derivative along the direction normal to the wall of the diffusing variable vanishes, the derivative at the Hall angle to the normal vanishes. We demonstrate the origin of this boundary condition from different starting points, using (i) a simplified Chalker-Coddington network model, (ii) the standard diagrammatic perturbation expansion, and (iii) the nonlinear sigma-model with the topological term, thus establishing connections between the different approaches. Further boundary effects are found in quantum interference phenomena. We evaluate the mean bilocal conductivity tensor $\sigma_{\mu\nu}(r,r')$, and the mean and variance of the conductance, to leading order in $1/\sigma_{xx}$ and to order $(\sigma_{xy}/\sigma_{xx})^2$, and find that the variance of the conductance increases with the Hall ratio. Thus the conductance fluctuations are no longer simply described by the unitary universality class of the $\sigma_{xy}=0$ case, but instead there is a one-parameter family of probability distributions. In the quasi-one-dimensional limit, the usual universal result for the conductance fluctuations of the unitary ensemble is recovered, in contrast to results of previous authors. Also, a long discussion of current conservation.Comment: Latex, uses RevTex, 58 pages, 5 figures available on request at [email protected]. Submitted to Phys. Rev.

Bipolar spintronics: From spin injection to spin-controlled logic

An impressive success of spintronic applications has been typically realized in metal-based structures which utilize magnetoresistive effects for substantial improvements in the performance of computer hard drives and magnetic random access memories. Correspondingly, the theoretical understanding of spin-polarized transport is usually limited to a metallic regime in a linear response, which, while providing a good description for data storage and magnetic memory devices, is not sufficient for signal processing and digital logic. In contrast, much less is known about possible applications of semiconductor-based spintronics and spin-polarized transport in related structures which could utilize strong intrinsic nonlinearities in current-voltage characteristics to implement spin-based logic. Here we discuss the challenges for realizing a particular class of structures in semiconductor spintronics: our proposal for bipolar spintronic devices in which carriers of both polarities (electrons and holes) contribute to spin-charge coupling. We formulate the theoretical framework for bipolar spin-polarized transport, and describe several novel effects in two- and three-terminal structures which arise from the interplay between nonequilibrium spin and equilibrium magnetization.Comment: 16 pages, 7 figure

Use of Anti-Inflammatory Drugs and Lower Esophageal Sphincter-Relaxing Drugs and Risk of Esophageal and Gastric Cancers

Background & Aims: The incidence of esophageal and gastric cardia adenocarcinoma has increased in Western countries in recent decades for largely unknown reasons. We investigated whether use of LES-relaxing drugs was related to an increased risk of esophageal and gastric cardia adenocarcinoma, and whether use of NSAIDs was related to a reduced risk of esophageal and gastric cancers. Methods: We examined these associations by using administrative databases in a case-control study in 2 integrated health care delivery systems. Cases were incident esophageal adenocarcinomas (n = 163) and squamous cell carcinomas (n = 114) and gastric cardia (n = 176) and non-cardia adenocarcinomas (n = 320), diagnosed between 1980-2002 in one health system and between 1993-2002 in the other. Matched controls (n = 3996) were selected. Complete prescription information was available for the study period. Results: Prescription of corticosteroids was associated with a decreased risk of esophageal adenocarcinoma (odds ratio [OR], 0.6; 95% confidence interval [CI], 0.4-0.9), esophageal squamous cell carcinoma (OR, 0.4; 95% CI, 0.2-0.6), and gastric non-cardia carcinoma (OR, 0.4, 95% CI, 0.3-0.6). Ever use of pharmacy-purchased aspirin was associated with 30%-60% decreased risks of the studied cancers. As a group, LES-relaxing drugs showed little evidence of association with increased risk of any esophageal or gastric cancer. Conclusions: Corticosteroid and aspirin use were associated with significantly decreased risks of esophageal and gastric cancer. LES-relaxing drugs as a group did not affect these risks, although we had limited power to assess individual drugs. The possibility that corticosteroids and aspirin might reduce esophageal cancer risk warrants further consideration

Physics of Solar Prominences: II - Magnetic Structure and Dynamics

Observations and models of solar prominences are reviewed. We focus on non-eruptive prominences, and describe recent progress in four areas of prominence research: (1) magnetic structure deduced from observations and models, (2) the dynamics of prominence plasmas (formation and flows), (3) Magneto-hydrodynamic (MHD) waves in prominences and (4) the formation and large-scale patterns of the filament channels in which prominences are located. Finally, several outstanding issues in prominence research are discussed, along with observations and models required to resolve them.Comment: 75 pages, 31 pictures, review pape