Fusion Frame Homotopy and Tightening Fusion Frames by Gradient Descent

Finite frames, or spanning sets for finite-dimensional Hilbert spaces, are a ubiquitous tool in signal processing. There has been much recent work on understanding the global structure of collections of finite frames with prescribed properties, such as spaces of unit norm tight frames. We extend some of these results to the more general setting of fusion frames -- a fusion frame is a collection of subspaces of a finite-dimensional Hilbert space with the property that any vector can be recovered from its list of projections. The notion of tightness extends to fusion frames, and we consider the following basic question: is the collection of tight fusion frames with prescribed subspace dimensions path connected? We answer (a generalization of) this question in the affirmative, extending the analogous result for unit norm tight frames proved by Cahill, Mixon and Strawn. We also extend a result of Benedetto and Fickus, who defined a natural functional on the space of unit norm frames (the frame potential), showed that its global minimizers are tight, and showed that it has no spurious local minimizers, meaning that gradient descent can be used to construct unit-norm tight frames. We prove the analogous result for the fusion frame potential of Casazza and Fickus, implying that, when tight fusion frames exist for a given choice of dimensions, they can be constructed via gradient descent. Our proofs use techniques from symplectic geometry and Mumford's geometric invariant theory

Distinguishing between those dying suddenly or not suddenly from coronary heart disease: long-term prospective results from the Northwick Park Heart Study.

AIM: To establish whether ECG findings are associated with subsequent risk of sudden death from coronary heart disease (CHD). METHODS AND RESULTS: Potential risk factors for CHD were measured at entry to the first Northwick Park Heart Study of 2167 men. ECG findings were coded as high or low risk for CHD according to definitions in the Minnesota code. Sudden or non-sudden deaths were defined as occurring in less than or more than 24 hours, respectively. The only factor independently associated with sudden death among the 262 men dying of CHD was high-risk ECG. Of 184 sudden CHD deaths, 34 men (18.5%) had had high-risk ECGs at entry to the study compared with 5 (6.4%) of 78 men who experienced non-sudden deaths (adjusted OR 3.94 (95% CI 1.33 to 11.67)) (p=0.006). Findings were also compared among all 2167 men, where high-risk ECGs were again associated with sudden death. T-wave changes were the main abnormalities associated with a high risk of sudden death. CONCLUSIONS: In a group of men who had not previously experienced major episodes of CHD but who subsequently died from it, there was strong evidence that high-risk ECG changes, mainly T-wave abnormalities, differentiated between those who later died sudden deaths and those who survived for >24 hours

An Electronic World Grass Flora

The development of an electronic world grass flora database is described in which data for 1090 morphological characters gathered for 11,000 species in 700 genera organized according to accepted names. This descriptive information is linked to a synonym database of 60,000 names. Authors, literature references, and the status of each name are also recorded in the database along with geographical distribution and type information. The list of accepted species is linked to a global herbarium of 350,000 specimens at Kew arranged in a phylogenetic sequence at the generic and species levels and according to broad phytogeographic divisions. From the database, descriptions can be generated for species, genera, and tribes. Character similarities or differences can be identified and character sets generated as an aid to key writing. Taxonomic and geographic subsets can be generated and specimens can be identified using an interactive key

Rees Jeffreys Road Fund study: Major roads for the future - Identifying network users and their characteristics

The Rees Jeffreys Road Fund (RJRF) has commissioned an ambitious two-year study of major roads in England with a horizon of 2040. There are seven topics of interest, and the first topic of interest has two tasks, one of which (Task 1B) is to identify network users and their characteristics.The RJRF Study Team needs a comprehensive picture of the nature of usage of major roads in England – who and where the users are, and what sort of journeys they are making.Bringing together data from National Road Traffic Estimates and the National Travel Survey, this reportprovides:• Explanations of the patterns of use of different types of user.• Identification of the factors that may be used to define the nature and extent of roads that could beclassified as forming part of a newly defined Major Road Network (MRN).• Analysis of usage of the SRN in England by region, road type, vehicle type, journey purpose and length

Recent respiratory infection and risk of venous thromboembolism: case–control study through a general practice database

Background The association between respiratory infection and risk of heart attacks and strokes is well established. However, less evidence exists for an association between respiratory infection and venous thromboembolism (VTE). In this article, we describe the associations between respiratory infection and VTE

Realistic assumptions about spatial locations and clustering of premises matter for models of foot-and-mouth disease spread in the United States

Spatially explicit livestock disease models require demographic data for individual farms or premises. In the U.S., demographic data are only available aggregated at county or coarser scales, so disease models must rely on assumptions about how individual premises are distributed within counties. Here, we addressed the importance of realistic assumptions for this purpose. We compared modeling of foot and mouth disease (FMD) outbreaks using simple randomization of locations to premises configurations predicted by the Farm Location and Agricultural Production Simulator (FLAPS), which infers location based on features such as topography, land-cover, climate, and roads. We focused on three premises-level Susceptible-Exposed-Infectious-Removed models available from the literature, all using the same kernel approach but with different parameterizations and functional forms. By computing the basic reproductive number of the infection (R0) for both FLAPS and randomized configurations, we investigated how spatial locations and clustering of premises affects outbreak predictions. Further, we performed stochastic simulations to evaluate if identified differences were consistent for later stages of an outbreak. Using Ripley's K to quantify clustering, we found that FLAPS configurations were substantially more clustered at the scales relevant for the implemented models, leading to a higher frequency of nearby premises compared to randomized configurations. As a result, R0 was typically higher in FLAPS configurations, and the simulation study corroborated the pattern for later stages of outbreaks. Further, both R0 and simulations exhibited substantial spatial heterogeneity in terms of differences between configurations. Thus, using realistic assumptions when de-aggregating locations based on available data can have a pronounced effect on epidemiological predictions, affecting if, where, and to what extent FMD may invade the population. We conclude that methods such as FLAPS should be preferred over randomization approaches

Do R Coronae Borealis Stars Form from Double White Dwarf Mergers?

A leading formation scenario for R Coronae Borealis (RCB) stars invokes the merger of degenerate He and CO white dwarfs (WD) in a binary. The observed ratio of 16O/18O for RCB stars is in the range of 0.3-20 much smaller than the solar value of ~500. In this paper, we investigate whether such a low ratio can be obtained in simulations of the merger of a CO and a He white dwarf. We present the results of five 3-dimensional hydrodynamic simulations of the merger of a double white dwarf system where the total mass is 0.9 Mdot and the initial mass ratio (q) varies between 0.5 and 0.99. We identify in simulations with $q\lesssim0.7$ a feature around the merged stars where the temperatures and densities are suitable for forming 18O. However, more 16O is being dredged-up from the C- and O-rich accretor during the merger than the amount of 18O that is produced. Therefore, on a dynamical time scale over which our hydrodynamics simulation runs, a 16O/18O ratio of ~2000 in the "best" case is found. If the conditions found in the hydrodynamic simulations persist for 10^6 seconds the oxygen ratio drops to 16 in one case studied, while in a hundred years it drops to ~4 in another case studied, consistent with the observed values in RCB stars. Therefore, the merger of two white dwarfs remains a strong candidate for the formation of these enigmatic stars.Comment: 42 pages, 19 figures. Accepted for publication in the Astrophysical Journa