Existence and multiplicity of solutions for a prescribed mean-curvature problem with critical growth

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Ocular dimensions, corneal thickness, and corneal curvature in quarter horses with hereditary equine regional dermal asthenia

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Maximal power output during incremental cycling test is dependent on the curvature constant of the power-time relationship

The aim of this study was to investigate whether the maximal power output (Pmax) during an incremental test was dependent on the curvature constant (W') of the power-time relationship. Thirty healthy male subjects (maximal oxygen uptake = 3.58 ± 0.40 L·min(-1)) performed a ramp incremental cycling test to determine the maximal oxygen uptake and Pmax, and 4 constant work rate tests to exhaustion to estimate 2 parameters from the modeling of the power-time relationship (i.e., critical power (CP) and W'). Afterwards, the participants were ranked according to their magnitude of W'. The median third was excluded to form a high W' group (HIGH, n = 10), and a low W' group (LOW, n = 10). Maximal oxygen uptake (3.84 ± 0.50 vs. 3.49 ± 0.37 L·min(-1)) and CP (213 ± 22 vs. 200 ± 29 W) were not significantly different between HIGH and LOW, respectively. However, Pmax was significantly greater for the HIGH (337 ± 23 W) than for the LOW (299 ± 40 W). Thus, in physically active individuals with similar aerobic parameters, W' influences the Pmax during incremental testing.

Repeated sprint ability tests and intensity-time curvature constant to predict short-distance running performances

Anaerobic efforts are commonly required through repeated sprint during efforts in many sports, making the anaerobic pathway a target of training. Nevertheless, to identify improvements on such energetic way it is necessary to assess anaerobic capacity or power, which is usually complex. For this purpose, authors have postulated the use of short running performances to anaerobic ability assessment. Thus, the aim of this study was to find a relationship between running performances on anaerobic power, anaerobic capacity or repeated sprint ability. Methods Thirteen military performed maximal running of 50 (P50), 100 (P100) and 300 (P300) m on track, beyond of running-based anaerobic sprint test (RAST; RSA and anaerobic power test), maximal anaerobic running test (MART; RSA and anaerobic capacity test) and the W′ from critical power model (anaerobic capacity test). Results By RAST variables, peak and average power (absolute and relative) and maximum velocity were significantly correlated with P50 (r = −0.68, p = 0.03 and −0.76, p = 0.01; −0.83, p < 0.01 and −0.83, p < 0.01; and −0.78, p < 0.01), respectively. The maximum intensity of MART was negatively and significantly correlated with P100 (r = −0.59) and W′ was not statistically correlated with any of the performances. Conclusion MART and W′ were not correlated with short running performances, having a weak performance predicting probably due to its longer duration in relation to assessed performances. Observing RAST outcomes, we postulated that such a protocol can be used during daily training as short running performance predictor.

Shape analysis using fractal dimension: A curvature based approach

The present work shows a novel fractal dimension method for shape analysis. The proposed technique extracts descriptors from a shape by applying a multi-scale approach to the calculus of the fractal dimension. The fractal dimension is estimated by applying the curvature scale-space technique to the original shape. By applying a multi-scale transform to the calculus, we obtain a set of descriptors which is capable of describing the shape under investigation with high precision. We validate the computed descriptors in a classification process. The results demonstrate that the novel technique provides highly reliable descriptors, confirming the efficiency of the proposed method. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4757226]

EFFECT OF HEAD GROUP AND CURVATURE ON BINDING OF THE ANTIMICROBIAL PEPTIDE TRITRPTICIN TO LIPID MEMBRANES

In this work we examine the interaction between the 13-residue cationic antimicrobial peptide (AMP) tritrpticin (VRRFPWWWPFLRR, TRP3) and model membranes of variable lipid composition. The effect on peptide conformational properties was investigated by means of CD (circular dichroism) and fluorescence spectroscopies. Based on the hypothesis that the antibiotic acts through a mechanism involving toroidal pore formation, and taking into account that models of toroidal pores imply the formation of positive curvature, we used large unilamellar vesicles (LUV) to mimic the initial step of peptide-lipid interaction, when the peptide binds to the bilayer membrane, and micelles to mimic the topology of the pore itself, since these aggregates display positive curvature. In order to more faithfully assess the role of curvature, micelles were prepared with lysophospholipids containing (qualitatively and quantitatively) head groups identical to those of bilayer phospholipids. CD and fluorescence spectra showed that, while TRP3 binds to bilayers only when they carry negatively charged phospholipids. binding to micelles occurs irrespective of surface charge, indicating that electrostatic interactions play a less predominant role in the latter case. Moreover, the conformations acquired by the peptide were independent of lipid composition in both bilayers and micelles. However, the conformations were different in bilayers and in micelles, suggesting that curvature has an influence on the secondary structure acquired by the peptide. Fluorescence data pointed to an interfacial location of TRP3 in both types of aggregates. Nevertheless, experiments with a water soluble fluorescence quencher suggested that the tryptophan residues are more accessible to the quencher in micelles than in bilayers. Thus, we propose that bilayers and micelles can be used as models for the two steps of toroidal pore formation. (C) 2011 Elsevier Ireland Ltd. All rights reserved.

Carbon flux, nutrient retention efficiency and the curvature of respiration depth-profiles in the ocean water column

Trabajo realizado por: Packard, T. T., Osma, N., Fernández Urruzola, I., Gómez, M

Mean curvature flow in SE (2) and applications to visual perception

Our goal in this thesis is to provide a result of existence of the degenerate non-linear, non-divergence PDE which describes the mean curvature flow in the Lie group SE(2) equipped with a sub-Riemannian metric. The research is motivated by problems of visual completion and models of the visual cortex.

Curvature induced nanoscale rafts in lipid membranes

We present a coarse grained model for computer simulations of lipid mixtures, which we use to study generic mechanisms for the formation of nanoscale membrane structures (lipid rafts). We observe that even a two component system can separate into rafts of finite size, and we study these rafts and other membrane structures in detail. We look at the characteristics of our model that enable these phenomena and how they may relate to lipid-cholesterol or lipid-lipid mixtures. We propose an explanation for our findings using elastic theory to describe a possible mechanism of raft stabilization via curvature differences between coexisting lipid phases and we investigate whether this theory can be used to explain the results of our computer simulations.

ADVENTURES IN FRIEDMANN COSMOLOGIES---INTERACTION OF POSITIVE ENERGY DENSITIES WITH NEGATIVE ENERGY DENSITIES AND CURVATURE OF THE UNIVERSE

In this report we will investigate the effect of negative energy density in a classic Friedmann cosmology. Although never measured and possibly unphysical, the evolution of a Universe containing a significant cosmological abundance of any of a number of hypothetical stable negative energy components is explored. These negative energy (Ω < 0) forms include negative phantom energy (w<-1), negative cosmological constant (w=-1), negative domain walls (w=-2/3), negative cosmic strings (w= -1/3), negative mass (w=0), negative radiation (w=1/3), and negative ultra-light (w > 1/3). Assuming that such universe components generate pressures as perfect fluids, the attractive or repulsive nature of each negative energy component is reviewed. The Friedmann equations can only be balanced when negative energies are coupled to a greater magnitude of positive energy or positive curvature, and minimal cases of both of these are reviewed. The future and fate of such universes in terms of curvature, temperature, acceleration, and energy density are reviewed including endings categorized as a Big Crunch, Big Void, or Big Rip and further qualified as "Warped", "Curved", or "Flat", "Hot" versus "Cold", "Accelerating" versus" Decelerating" versus "Coasting". A universe that ends by contracting to zero energy density is termed a Big Poof. Which contracting universes ``bounce" in expansion and which expanding universes ``turnover" into contraction are also reviewed. The name by which the ending of the Universe is mentioned is our own nomenclature.

Intact flagellar motor of Borrelia burgdorferi revealed by cryo-electron tomography: evidence for stator ring curvature and rotor/C-ring assembly flexion.

The bacterial flagellar motor is a remarkable nanomachine that provides motility through flagellar rotation. Prior structural studies have revealed the stunning complexity of the purified rotor and C-ring assemblies from flagellar motors. In this study, we used high-throughput cryo-electron tomography and image analysis of intact Borrelia burgdorferi to produce a three-dimensional (3-D) model of the in situ flagellar motor without imposing rotational symmetry. Structural details of B. burgdorferi, including a layer of outer surface proteins, were clearly visible in the resulting 3-D reconstructions. By averaging the 3-D images of approximately 1,280 flagellar motors, a approximately 3.5-nm-resolution model of the stator and rotor structures was obtained. flgI transposon mutants lacked a torus-shaped structure attached to the flagellar rod, establishing the structural location of the spirochetal P ring. Treatment of intact organisms with the nonionic detergent NP-40 resulted in dissolution of the outermost portion of the motor structure and the C ring, providing insight into the in situ arrangement of the stator and rotor structures. Structural elements associated with the stator followed the curvature of the cytoplasmic membrane. The rotor and the C ring also exhibited angular flexion, resulting in a slight narrowing of both structures in the direction perpendicular to the cell axis. These results indicate an inherent flexibility in the rotor-stator interaction. The FliG switching and energizing component likely provides much of the flexibility needed to maintain the interaction between the curved stator and the relatively symmetrical rotor/C-ring assembly during flagellar rotation.

Dimensions of projections of sets on Riemannian surfaces of constant curvature

We apply the theory of Peres and Schlag to obtain generic lower bounds for Hausdorff dimension of images of sets by orthogonal projections on simply connected two-dimensional Riemannian manifolds of constant curvature. As a conclusion we obtain appropriate versions of Marstrand's theorem, Kaufman's theorem, and Falconer's theorem in the above geometrical settings.