Mathematical Analysis of Regression Model Epidemiology

Statistical modeling techniques, specifically regression line analysis have become important analytical tools and are contributing immensely to the field of epidemiology. However, many users do not understand their effective use and applications. Underlying epidemiological concepts and not the statistics should govern or justify the proper use and application of any modeling exercise. Main utility of the regression line analysis lies in its ability to provide a general but practical conceptual framework for casual problems, explaining and evaluating the role of biases, confounders and effect modifiers. Successful modeling of complex data is a part science, part statistics and part experience, but the major part is logic or common sense. Findings of this research article focuses on the contributions of regression analysis towards the pedagogical study of epidemiological models by enhancing the research process and serving as an effective tool for communicating findings to public health managers and policymakers and fostering interdisciplinary collaboration

Aortic valve stenosis-multimodality assessment with PET/CT and PET/MRI

Aortic valve disease is the most common form of heart valve disease in developed countries and a growing healthcare burden with an ageing population. Transthoracic and transoesophageal echocardiography remains central to the diagnosis and surveillance of patients with aortic stenosis, providing gold standard assessments of valve haemodynamics and myocardial performance. However, other multimodality imaging techniques are being explored for the assessment of aortic stenosis, including combined PET/CT and PET/MR. Both approaches provide unique information with respect to disease activity in the valve alongside more conventional anatomic assessments of the valve and myocardium in this condition. This review investigates the emerging use of PET/CT and PET/MR to assess patients with aortic stenosis, examining how the complementary data provided by each modality may be used for research applications and potentially in future clinical practice

Building up or out? Disparate sequence architectures along an active rift margin—Corinth rift, Greece

Early Pleistocene synrift deltas developed along the southern Corinth rift margin were deposited in a single, dominantly lacustrine depocenter and were subject to the same climate-related base-level and sediment supply cyclicity. Two synrift deltas, just 50 km apart, show markedly different sequence geometry and evolution related to their location along the evolving border fault. In the west, strongly aggradational fan deltas (>600 m thick; 2–4 km radius) deposited in the immediate hanging wall of the active border fault comprise stacked 30–100-m-thick stratal units bounded by flooding surfaces. Each unit evolves from aggradational to progradational with no evidence for abrupt subaerial exposure or fluvial incision. In contrast, in the central rift, the border fault propagated upward into an already deep lacustrine environment, locating rift-margin deltas 15 km into the footwall. The deltas here have a radius of >9 km and comprise northward downstepping and offlapping units, 50–200 m thick, that unconformably overlie older synrift sediments and are themselves incised. The key factors driving the marked variation in sequence stratigraphic architecture are: (1) differential uplift and subsidence related to position with respect to the border fault system, and (2) inherited topography that influenced shoreline position and offshore bathymetry. Our work illustrates that stratal units and their bounding surfaces may have only local (<10 km) extent, highlighting the uncertainty involved in assigning chronostratigraphic significance to systems tracts and in calculating base-level changes from stratigraphy where marked spatial variations in uplift and subsidence occur

Vertex-Coloring with Star-Defects

Defective coloring is a variant of traditional vertex-coloring, according to which adjacent vertices are allowed to have the same color, as long as the monochromatic components induced by the corresponding edges have a certain structure. Due to its important applications, as for example in the bipartisation of graphs, this type of coloring has been extensively studied, mainly with respect to the size, degree, and acyclicity of the monochromatic components. In this paper we focus on defective colorings in which the monochromatic components are acyclic and have small diameter, namely, they form stars. For outerplanar graphs, we give a linear-time algorithm to decide if such a defective coloring exists with two colors and, in the positive case, to construct one. Also, we prove that an outerpath (i.e., an outerplanar graph whose weak-dual is a path) always admits such a two-coloring. Finally, we present NP-completeness results for non-planar and planar graphs of bounded degree for the cases of two and three colors

Current-density functional theory of time-dependent linear response in quantal fluids: recent progress

Vignale and Kohn have recently formulated a local density approximation to the time-dependent linear response of an inhomogeneous electron system in terms of a vector potential for exchange and correlation. The vector potential depends on the induced current density through spectral kernels to be evaluated on the homogeneous electron-gas. After a brief review of their theory, the case of inhomogeneous Bose superfluids is considered, with main focus on dynamic Kohn-Sham equations for the condensate in the linear response regime and on quantal generalized hydrodynamic equations in the weak inhomogeneity limit. We also present the results of calculations of the exchange-correlation spectra in both electron and superfluid boson systems.Comment: 12 pages, 2 figures, Postscript fil

Direct observation of growth and collapse of a Bose-Einstein condensate with attractive interactions

The dynamical behavior of Bose-Einstein condensation (BEC) in a gas with attractive interactions is striking. Quantum theory predicts that BEC of a spatially homogeneous gas with attractive interactions is precluded by a conventional phase transition into either a liquid or solid. When confined to a trap, however, such a condensate can form provided that its occupation number does not exceed a limiting value. The stability limit is determined by a balance between self-attraction and a repulsion arising from position-momentum uncertainty under conditions of spatial confinement. Near the stability limit, self-attraction can overwhelm the repulsion, causing the condensate to collapse. Growth of the condensate, therefore, is punctuated by intermittent collapses, which are triggered either by macroscopic quantum tunneling or thermal fluctuation. Previous observation of growth and collapse has been hampered by the stochastic nature of these mechanisms. Here we reduce the stochasticity by controlling the initial number of condensate atoms using a two-photon transition to a diatomic molecular state. This enables us to obtain the first direct observation of the growth of a condensate with attractive interactions and its subsequent collapse.Comment: 10 PDF pages, 5 figures (2 color), 19 references, to appear in Nature Dec. 7 200

Realization of a single Josephson junction for Bose-Einstein condensates

We report on the realization of a double-well potential for Rubidium-87 Bose-Einstein condensates. The experimental setup allows the investigation of two different dynamical phenomena known for this system - Josephson oscillations and self-trapping. We give a detailed discussion of the experimental setup and the methods used for calibrating the relevant parameters. We compare our experimental findings with the predictions of an extended two-mode model and find quantitative agreement