Morphological properties of superclusters of galaxies

We studied superclusters of galaxies in a volume-limited sample extracted from the Sloan Digital Sky Survey Data Release 7 and from mock catalogues based on a semi-analytical model of galaxy evolution in the Millennium Simulation. A density field method was applied to a sample of galaxies brighter than M(r) = -21+5 log h(100) to identify superclusters, taking into account selection and boundary effects. In order to evaluate the influence of the threshold density, we have chosen two thresholds: the first maximizes the number of objects (D1) and the second constrains the maximum supercluster size to similar to 120 h(-1) Mpc (D2). We have performed a morphological analysis, using Minkowski Functionals, based on a parameter, which increases monotonically from filaments to pancakes. An anticorrelation was found between supercluster richness (and total luminosity or size) and the morphological parameter, indicating that filamentary structures tend to be richer, larger and more luminous than pancakes in both observed and mock catalogues. We have also used the mock samples to compare supercluster morphologies identified in position and velocity spaces, concluding that our morphological classification is not biased by the peculiar velocities. Monte Carlo simulations designed to investigate the reliability of our results with respect to random fluctuations show that these results are robust. Our analysis indicates that filaments and pancakes present different luminosity and size distributions.

Horo-tight spheres in hyperbolic space

We study horo-tight immersions of manifolds into hyperbolic spaces. The main result gives several characterizations of horo-tightness of spheres, answering a question proposed by Cecil and Ryan. For instance, we prove that a sphere is horo-tight if and only if it is tight in the hyperbolic sense. For codimension bigger than one, it follows that horo-tight spheres in hyperbolic space are metric spheres. We also prove that horo-tight hyperspheres are characterized by the property that both of its total absolute horospherical curvatures attend their minimum value. We also introduce the notion of weak horo-tightness: an immersion is weak horo-tight if only one of its total absolute curvature attends its minimum. We prove a characterization theorem for weak horo-tight hyperspheres.

Verifiable Visualization for Isosurface Extraction

Visual representations of isosurfaces are ubiquitous in the scientific and engineering literature. In this paper, we present techniques to assess the behavior of isosurface extraction codes. Where applicable, these techniques allow us to distinguish whether anomalies in isosurface features can be attributed to the underlying physical process or to artifacts from the extraction process. Such scientific scrutiny is at the heart of verifiable visualization - subjecting visualization algorithms to the same verification process that is used in other components of the scientific pipeline. More concretely, we derive formulas for the expected order of accuracy (or convergence rate) of several isosurface features, and compare them to experimentally observed results in the selected codes. This technique is practical: in two cases, it exposed actual problems in implementations. We provide the reader with the range of responses they can expect to encounter with isosurface techniques, both under ""normal operating conditions"" and also under adverse conditions. Armed with this information - the results of the verification process - practitioners can judiciously select the isosurface extraction technique appropriate for their problem of interest, and have confidence in its behavior.

Observing the Solubilization of Lipid Bilayers by Detergents with Optical Microscopy of GUVs

The solubilization of lipid bilayers by detergents was studied with optical microscopy of giant unilamellar vesicles (GUVs) composed of palmitoyl oleoyl phoshatidylcholine (POPC). A solution of the detergents Triton X-100 (TX-100) and sodium dodecyl sulfate (SDS) was injected with a micropipette close to single GUVs. The solubilization process was observed with phase contrast and fluorescence microscopy and found to be dependent on the detergent nature. In the presence of TX-100, GUVs initially showed an increase in their surface area, due to insertion of TX-100 with rapid equilibration between the two leaflets of the bilayer. Then, above a solubility threshold, several holes opened, rendering the bilayer a lace fabric appearance, and the bilayer gradually vanished. On the other hand, injection of SDS caused initially an increase in the membrane spontaneous curvature, which is mainly associated with incorporation of SDS in the outer layer only. This created a stress in the membrane, which caused either opening of transient macropores with substantial decrease in vesicle size or complete vesicle bursting. In another experimental setup, the extent of solubilization/destruction of a collection of GUVs was measured as a function of either TX-100 or SDS concentration.

Upper limit on the cosmic-ray photon flux above 10(19) eV using the surface detector of the Pierre Auger Observatory

A method is developed to search for air showers initiated by photons using data recorded by the surface detector of the Auger Observatory. The approach is based on observables sensitive to the longitudinal shower development, the signal risetime and the curvature of the shower front. Applying this method to the data, tipper limits on the flux of photons of 3.8 x 10(-3), 2.5 x 10(-3), and 2.2 x 10(-3) km(-2) sr(-1) yr(-1) above 10(19) eV, 2 x 10(19) eV, and 4 x 10(19) eV are derived, with corresponding limits on the fraction of photons being 2.0%, 5.1%, and 31% (all limits at 95% c.l.). These photon limits disfavor certain exotic models of sources of cosmic rays. The results also show that the approach adopted by the Auger Observatory to calibrate the shower energy is not strongly biased by a contamination from photons. (C) 2008 Elsevier B.V. All rights reserved.

Pulsating strings in Lunin-Maldacena backgrounds

We consider pulsating strings in Lunin-Maldacena backgrounds, specifically in deformed Minkowski spacetime and deformed AdS(5) x S(5). We find the relation between the energy and the oscillation number of the pulsating string when the deformation is small. Since the oscillation number is an adiabatic invariant it can be used to explore the regime of highly excited string states. We then quantize the string and look for such a sector. For the deformed Minkowski background we find a precise match with the classical results if the oscillation number is quantized as an even number. For the deformed AdS(5) x S(5) we find a contribution which depends on the deformation parameter.

Tight-binding model for carbon nanotubes from ab initio calculations

Here we present a parametrized tight-binding (TB) model to calculate the band structure of single-wall carbon nanotubes (SWNTs). On the basis of ab initio calculations we fit the band structure of nanotubes of different radii with results obtained with an orthogonal TB model to third neighbors, which includes the effects of orbital hybridization by means of a reduced set of parameters. The functional form for the dependence of these parameters on the radius of the tubes can be used to interpolate appropriate TB parameters for different SWNTs and to study the effects of curvature on their electronic properties. Additionally, we have shown that the model gives an appropriate description of the optical spectra of SWNTs, which can be useful for a proper assignation of SWNTs` specific chirality from optical absorption experiments.

Field on Poincare Group and Quantum Description of Orientable Objects

We propose an approach to the quantum-mechanical description of relativistic orientable objects. It generalizes Wigner`s ideas concerning the treatment of nonrelativistic orientable objects (in particular, a nonrelativistic rotator) with the help of two reference frames (space-fixed and body-fixed). A technical realization of this generalization (for instance, in 3+1 dimensions) amounts to introducing wave functions that depend on elements of the Poincar, group G. A complete set of transformations that test the symmetries of an orientable object and of the embedding space belongs to the group I =GxG. All such transformations can be studied by considering a generalized regular representation of G in the space of scalar functions on the group, f(x,z), that depend on the Minkowski space points xaG/Spin(3,1) as well as on the orientation variables given by the elements z of a matrix ZaSpin(3,1). In particular, the field f(x,z) is a generating function of the usual spin-tensor multi-component fields. In the theory under consideration, there are four different types of spinors, and an orientable object is characterized by ten quantum numbers. We study the corresponding relativistic wave equations and their symmetry properties.

Predictions from an anisotropic inflationary era

This paper investigates the predictions of an inflationary phase starting from a homogeneous and anisotropic universe of the Bianchi I type. After discussing the evolution of the background spacetime, focusing on the number of e-folds and the isotropization, we solve the perturbation equations and predict the power spectra of the curvature perturbations and gravity waves at the end of inflation. The main features of the early anisotropic phase is (1) a dependence of the spectra on the direction of the modes, (2) a coupling between curvature perturbations and gravity waves and (3) the fact that the two gravity wave polarizations do not share the same spectrum on large scales. All these effects are significant only on large scales and die out on small scales where isotropy is recovered. They depend on a characteristic scale that can, but a priori must not, be tuned to some observable scale. To fix the initial conditions, we propose a procedure that generalizes the one standardly used in inflation but that takes into account the fact that the WKB regime is violated at early times when the shear dominates. We stress that there exist modes that do not satisfy the WKB condition during the shear-dominated regime and for which the amplitude at the end of inflation depends on unknown initial conditions. On such scales, inflation loses its predictability. This study paves the way for the determination of the cosmological signature of a primordial shear, whatever the Bianchi I spacetime. It thus stresses the importance of the WKB regime to draw inflationary predictions and demonstrates that, when the number of e-folds is large enough, the predictions converge toward those of inflation in a Friedmann-Lemaitre spacetime but that they are less robust in the case of an inflationary era with a small number of e-folds.

A complex network-based approach for boundary shape analysis

This paper introduces a novel methodology to shape boundary characterization, where a shape is modeled into a small-world complex network. It uses degree and joint degree measurements in a dynamic evolution network to compose a set of shape descriptors. The proposed shape characterization method has all efficient power of shape characterization, it is robust, noise tolerant, scale invariant and rotation invariant. A leaf plant classification experiment is presented on three image databases in order to evaluate the method and compare it with other descriptors in the literature (Fourier descriptors, Curvature, Zernike moments and multiscale fractal dimension). (C) 2008 Elsevier Ltd. All rights reserved.

The concept of quasi-integrability: a concrete example

We use the deformed sine-Gordon models recently presented by Bazeia et al [1] to take the first steps towards defining the concept of quasi-integrability. We consider one such definition and use it to calculate an infinite number of quasi-conserved quantities through a modification of the usual techniques of integrable field theories. Performing an expansion around the sine-Gordon theory we are able to evaluate the charges and the anomalies of their conservation laws in a perturbative power series in a small parameter which describes the ""closeness"" to the integrable sine-Gordon model. We show that in the case of the two-soliton scattering the charges, up to first order of perturbation, are conserved asymptotically, i.e. their values are the same in the distant past and future, when the solitons are well separated. We indicate that this property may hold or not to higher orders depending on the behavior of the two-soliton solution under a special parity transformation. For closely bound systems, such as breather-like field configurations, the situation however is more complex and perhaps the anomalies have a different structure implying that the concept of quasi-integrability does not apply in the same way as in the scattering of solitons. We back up our results with the data of many numerical simulations which also demonstrate the existence of long lived breather-like and wobble-like states in these models.

The Bullough-Dodd model coupled to matter fields

The Bullough-Dodd model is an important two-dimensional integrable field theory which finds applications in physics and geometry. We consider a conformally invariant extension of it, and study its integrability properties using a zero curvature condition based on the twisted Kac-Moody algebra A(2)((2)). The one- and two-soliton solutions as well as the breathers are constructed explicitly. We also consider integrable extensions of the Bullough-Dodd model by the introduction of spinor (matter) fields. The resulting theories are conformally invariant and present local internal symmetries. All the one-soliton solutions, for two examples of those models, are constructed using a hybrid of the dressing and Hirota methods. One model is of particular interest because it presents a confinement mechanism for a given conserved charge inside the solitons. (C) 2008 Elsevier B.V. All rights reserved.

Objective characterization of the course of the parasellar internal carotid artery using mathematical tools

Background Along the internal carotid artery (ICA), atherosclerotic plaques are often located in its cavernous sinus (parasellar) segments (pICA). Studies indicate that the incidence of pre-atherosclerotic lesions is linked with the complexity of the pICA; however, the pICA shape was never objectively characterized. Our study aims at providing objective mathematical characterizations of the pICA shape. Methods and results Three-dimensional (3D) computer models, reconstructed from contrast enhanced computed tomography (CT) data of 30 randomly selected patients (60 pICAs) were analyzed with modern visualization software and new mathematical algorithms. As objective measures for the pICA shape complexity, we provide calculations of curvature energy, torsion energy, and total complexity of 3D skeletons of the pICA lumen. We further measured the posterior knee of the so-called ""carotid siphon"" with a virtual goniometer and performed correlations between the objective mathematical calculations and the subjective angle measurements. Conclusions Firstly, our study provides mathematical characterizations of the pICA shape, which can serve as objective reference data for analyzing connections between pICA shape complexity and vascular diseases. Secondly, we provide an objective method for creating Such data. Thirdly, we evaluate the usefulness of subjective goniometric measurements of the angle of the posterior knee of the carotid siphon.

Fractal dimension applied to plant identification

This article discusses methods to identify plants by analysing leaf complexity based on estimating their fractal dimension. Leaves were analyzed according to the complexity of their internal and external shapes. A computational program was developed to process, analyze and extract the features of leaf images, thereby allowing for automatic plant identification. Results are presented from two experiments, the first to identify plant species from the Brazilian Atlantic forest and Brazilian Cerrado scrublands, using fifty leaf samples from ten different species, and the second to identify four different species from genus Passiflora, using twenty leaf samples for each class. A comparison is made of two methods to estimate fractal dimension (box-counting and multiscale Minkowski). The results are discussed to determine the best approach to analyze shape complexity based on the performance of the technique, when estimating fractal dimension and identifying plants. (C) 2008 Elsevier Inc. All rights reserved.

Three-dimensional description and mathematical characterization of the parasellar internal carotid artery in human infants

Inside the `cavernous sinus` or `parasellar region` the human internal carotid artery takes the shape of a siphon that is twisted and torqued in three dimensions and surrounded by a network of veins. The parasellar section of the internal carotid artery is of broad biological and medical interest, as its peculiar shape is associated with temperature regulation in the brain and correlated with the occurrence of vascular pathologies. The present study aims to provide anatomical descriptions and objective mathematical characterizations of the shape of the parasellar section of the internal carotid artery in human infants and its modifications during ontogeny. Three-dimensional (3D) computer models of the parasellar section of the internal carotid artery of infants were generated with a state-of-the-art 3D reconstruction method and analysed using both traditional morphometric methods and novel mathematical algorithms. We show that four constant, demarcated bends can be described along the infant parasellar section of the internal carotid artery, and we provide measurements of their angles. We further provide calculations of the curvature and torsion energy, and the total complexity of the 3D skeleton of the parasellar section of the internal carotid artery, and compare the complexity of this in infants and adults. Finally, we examine the relationship between shape parameters of the parasellar section of the internal carotid artery in infants, and the occurrence of intima cushions, and evaluate the reliability of subjective angle measurements for characterizing the complexity of the parasellar section of the internal carotid artery in infants. The results can serve as objective reference data for comparative studies and for medical imaging diagnostics. They also form the basis for a new hypothesis that explains the mechanisms responsible for the ontogenetic transformation in the shape of the parasellar section of the internal carotid artery.