Disentangling the Cosmic Web I: Morphology of Isodensity Contours

We apply Minkowski functionals and various derived measures to decipher the morphological properties of large-scale structure seen in simulations of gravitational evolution. Minkowski functionals of isodensity contours serve as tools to test global properties of the density field. Furthermore, we identify coherent objects at various threshold levels and calculate their partial Minkowski functionals. We propose a set of two derived dimensionless quantities, planarity and filamentarity, which reduce the morphological information in a simple and intuitive way. Several simulations of the gravitational evolution of initial power-law spectra provide a framework for systematic tests of our method.Comment: 26 pages including 12 figures. Accepted for publication in Ap

Analytic Continuation for Asymptotically AdS 3D Gravity

We have previously proposed that asymptotically AdS 3D wormholes and black holes can be analytically continued to the Euclidean signature. The analytic continuation procedure was described for non-rotating spacetimes, for which a plane t=0 of time symmetry exists. The resulting Euclidean manifolds turned out to be handlebodies whose boundary is the Schottky double of the geometry of the t=0 plane. In the present paper we generalize this analytic continuation map to the case of rotating wormholes. The Euclidean manifolds we obtain are quotients of the hyperbolic space by a certain quasi-Fuchsian group. The group is the Fenchel-Nielsen deformation of the group of the non-rotating spacetime. The angular velocity of an asymptotic region is shown to be related to the Fenchel-Nielsen twist. This solves the problem of classification of rotating black holes and wormholes in 2+1 dimensions: the spacetimes are parametrized by the moduli of the boundary of the corresponding Euclidean spaces. We also comment on the thermodynamics of the wormhole spacetimes.Comment: 28 pages, 14 figure

The association between premorbid cognitive ability and social functioning and suicide among young men: A historical-prospective cohort study

Previous studies have found associations between low cognitive ability and later completed suicide. The aim of this study was to examine the association between cognitive ability and social functioning in adolescence, and later completed suicide in a large population-based longitudinal study. Data from the Israeli Draft Board Register for 634,655 Israeli male adolescents aged 16 and 17 was linked to a causes-of-death data registry, with a mean follow-up of 10.6 years for completed suicide. Our results show that in males without a psychiatric diagnosis, both low (adjusted HR=1.51, 95% CI: 1.19–1.92) and high (adjusted HR=1.36, 95% CI: 1.04–1.77) cognitive ability, and very poor (adjusted HR=2.30, 95% CI: 1.34–3.95) and poor (adjusted HR=1.64, 95% CI: 1.34–2.07) social functioning were associated with increased risk for later completed suicide; however positive predictive values were low (PPVs=0.09% and 0.10%, for low cognitive ability and very poor or poor social functioning, respectively). No association between cognitive ability or social functioning and risk for suicide was found in males with a psychiatric diagnosis. These data do not support the clinical utility of screening for such potential predictors

The compositional and evolutionary logic of metabolism

Metabolism displays striking and robust regularities in the forms of modularity and hierarchy, whose composition may be compactly described. This renders metabolic architecture comprehensible as a system, and suggests the order in which layers of that system emerged. Metabolism also serves as the foundation in other hierarchies, at least up to cellular integration including bioenergetics and molecular replication, and trophic ecology. The recapitulation of patterns first seen in metabolism, in these higher levels, suggests metabolism as a source of causation or constraint on many forms of organization in the biosphere. We identify as modules widely reused subsets of chemicals, reactions, or functions, each with a conserved internal structure. At the small molecule substrate level, module boundaries are generally associated with the most complex reaction mechanisms and the most conserved enzymes. Cofactors form a structurally and functionally distinctive control layer over the small-molecule substrate. Complex cofactors are often used at module boundaries of the substrate level, while simpler ones participate in widely used reactions. Cofactor functions thus act as "keys" that incorporate classes of organic reactions within biochemistry. The same modules that organize the compositional diversity of metabolism are argued to have governed long-term evolution. Early evolution of core metabolism, especially carbon-fixation, appears to have required few innovations among a small number of conserved modules, to produce adaptations to simple biogeochemical changes of environment. We demonstrate these features of metabolism at several levels of hierarchy, beginning with the small-molecule substrate and network architecture, continuing with cofactors and key conserved reactions, and culminating in the aggregation of multiple diverse physical and biochemical processes in cells.Comment: 56 pages, 28 figure

Partial differential equations for self-organization in cellular and developmental biology

Understanding the mechanisms governing and regulating the emergence of structure and heterogeneity within cellular systems, such as the developing embryo, represents a multiscale challenge typifying current integrative biology research, namely, explaining the macroscale behaviour of a system from microscale dynamics. This review will focus upon modelling how cell-based dynamics orchestrate the emergence of higher level structure. After surveying representative biological examples and the models used to describe them, we will assess how developments at the scale of molecular biology have impacted on current theoretical frameworks, and the new modelling opportunities that are emerging as a result. We shall restrict our survey of mathematical approaches to partial differential equations and the tools required for their analysis. We will discuss the gap between the modelling abstraction and biological reality, the challenges this presents and highlight some open problems in the field

MRI in multiple myeloma : a pictorial review of diagnostic and post-treatment findings

Magnetic resonance imaging (MRI) is increasingly being used in the diagnostic work-up of patients with multiple myeloma. Since 2014, MRI findings are included in the new diagnostic criteria proposed by the International Myeloma Working Group. Patients with smouldering myeloma presenting with more than one unequivocal focal lesion in the bone marrow on MRI are considered having symptomatic myeloma requiring treatment, regardless of the presence of lytic bone lesions. However, bone marrow evaluation with MRI offers more than only morphological information regarding the detection of focal lesions in patients with MM. The overall performance of MRI is enhanced by applying dynamic contrast-enhanced MRI and diffusion weighted imaging sequences, providing additional functional information on bone marrow vascularization and cellularity. This pictorial review provides an overview of the most important imaging findings in patients with monoclonal gammopathy of undetermined significance, smouldering myeloma and multiple myeloma, by performing a 'total' MRI investigation with implications for the diagnosis, staging and response assessment. Main message aEuro cent Conventional MRI diagnoses multiple myeloma by assessing the infiltration pattern. aEuro cent Dynamic contrast-enhanced MRI diagnoses multiple myeloma by assessing vascularization and perfusion. aEuro cent Diffusion weighted imaging evaluates bone marrow composition and cellularity in multiple myeloma. aEuro cent Combined morphological and functional MRI provides optimal bone marrow assessment for staging. aEuro cent Combined morphological and functional MRI is of considerable value in treatment follow-up

On multiplicities in length spectra of arithmetic hyperbolic three-orbifolds

Asymptotic laws for mean multiplicities of lengths of closed geodesics in arithmetic hyperbolic three-orbifolds are derived. The sharpest results are obtained for non-compact orbifolds associated with the Bianchi groups SL(2,o) and some congruence subgroups. Similar results hold for cocompact arithmetic quaternion groups, if a conjecture on the number of gaps in their length spectra is true. The results related to the groups above give asymptotic lower bounds for the mean multiplicities in length spectra of arbitrary arithmetic hyperbolic three-orbifolds. The investigation of these multiplicities is motivated by their sensitive effect on the eigenvalue spectrum of the Laplace-Beltrami operator on a hyperbolic orbifold, which may be interpreted as the Hamiltonian of a three-dimensional quantum system being strongly chaotic in the classical limit.Comment: 29 pages, uuencoded ps. Revised version, to appear in NONLINEARIT

Common carotid intima media thickness and ankle-brachial pressure index correlate with local but not global atheroma burden:a cross sectional study using whole body magnetic resonance angiography

Common carotid intima media thickness (CIMT) and ankle brachial pressure index (ABPI) are used as surrogate marker of atherosclerosis, and have been shown to correlate with arterial stiffness, however their correlation with global atherosclerotic burden has not been previously assessed. We compare CIMT and ABPI with atheroma burden as measured by whole body magnetic resonance angiography (WB-MRA).50 patients with symptomatic peripheral arterial disease were recruited. CIMT was measured using ultrasound while rest and exercise ABPI were performed. WB-MRA was performed in a 1.5T MRI scanner using 4 volume acquisitions with a divided dose of intravenous gadolinium gadoterate meglumine (Dotarem, Guerbet, FR). The WB-MRA data was divided into 31 anatomical arterial segments with each scored according to degree of luminal narrowing: 0 = normal, 1 = <50%, 2 = 50-70%, 3 = 70-99%, 4 = vessel occlusion. The segment scores were summed and from this a standardized atheroma score was calculated.The atherosclerotic burden was high with a standardised atheroma score of 39.5±11. Common CIMT showed a positive correlation with the whole body atheroma score (β 0.32, p = 0.045), however this was due to its strong correlation with the neck and thoracic segments (β 0.42 p = 0.01) with no correlation with the rest of the body. ABPI correlated with the whole body atheroma score (β -0.39, p = 0.012), which was due to a strong correlation with the ilio-femoral vessels with no correlation with the thoracic or neck vessels. On multiple linear regression, no correlation between CIMT and global atheroma burden was present (β 0.13 p = 0.45), while the correlation between ABPI and atheroma burden persisted (β -0.45 p = 0.005).ABPI but not CIMT correlates with global atheroma burden as measured by whole body contrast enhanced magnetic resonance angiography in a population with symptomatic peripheral arterial disease. However this is primarily due to a strong correlation with ilio-femoral atheroma burden

Array algorithms for H^2 and H^∞ estimation

Currently, the preferred method for implementing H^2 estimation algorithms is what is called the array form, and includes two main families: square-root array algorithms, that are typically more stable than conventional ones, and fast array algorithms, which, when the system is time-invariant, typically offer an order of magnitude reduction in the computational effort. Using our recent observation that H^∞ filtering coincides with Kalman filtering in Krein space, in this chapter we develop array algorithms for H^∞ filtering. These can be regarded as natural generalizations of their H^2 counterparts, and involve propagating the indefinite square roots of the quantities of interest. The H^∞ square-root and fast array algorithms both have the interesting feature that one does not need to explicitly check for the positivity conditions required for the existence of H^∞ filters. These conditions are built into the algorithms themselves so that an H^∞ estimator of the desired level exists if, and only if, the algorithms can be executed. However, since H^∞ square-root algorithms predominantly use J-unitary transformations, rather than the unitary transformations required in the H^2 case, further investigation is needed to determine the numerical behavior of such algorithms