Lorentzian homogeneous spaces admitting a homogeneous structure of type T1+T3

We show that a Lorentzian homogeneous space admitting a homogeneous structure of type T1 + T3 is either a (locally) symmetric space or a singular homogeneous plane wave.Comment: 7 pages, Latex2e, a small note and a reference adde

Almost Hermitian Structures with Parallel Torsion

The characteristic connection of an almost hermitian structure is a hermitian connection with totally skew-symmetric torsion. The case of parallel torsion in dimension six is of particular interest. In this work, we give a full classification of the algebraic types of the torsion form, and, based on this, undertake a systematic investigation into the possible geometries. Numerous naturally reductive spaces are constructed and classified as well as examples on nilmanifolds given.Comment: 36 page

The Chern-Ricci flow on complex surfaces

The Chern-Ricci flow is an evolution equation of Hermitian metrics by their Chern-Ricci form, first introduced by Gill. Building on our previous work, we investigate this flow on complex surfaces. We establish new estimates in the case of finite time non-collapsing, anologous to some known results for the Kahler-Ricci flow. This provides evidence that the Chern-Ricci flow carries out blow-downs of exceptional curves on non-minimal surfaces. We also describe explicit solutions to the Chern-Ricci flow for various non-Kahler surfaces. On Hopf surfaces and Inoue surfaces these solutions, appropriately normalized, collapse to a circle in the sense of Gromov-Hausdorff. For non-Kahler properly elliptic surfaces, our explicit solutions collapse to a Riemann surface. Finally, we define a Mabuchi energy functional for complex surfaces with vanishing first Bott-Chern class and show that it decreases along the Chern-Ricci flow.Comment: 45 page

Naturally reductive pseudo-Riemannian spaces

A family of naturally reductive pseudo-Riemannian spaces is constructed out of the representations of Lie algebras with ad-invariant metrics. We exhibit peculiar examples, study their geometry and characterize the corresponding naturally reductive homogeneous structure.Comment: A shorter, clearer and more concise versio

Mathematical and Numerical Modeling of Healthy and Unhealthy Cerebral Arterial Tissues

Over the last two decades, we have witnessed an increasing application of mathematical models and numerical simulations for the study of the cardiovascular system. Indeed, both tools provide an important contribution to the analysis of the functioning of the different components of the cardiovascular system (i.e. heart, vessels and blood) and of their interactions either in physiological and pathological conditions. For this reason, reliable constitutive models for the cardiac, arterial and venous tissues as well as for the blood are an essential prerequisite for a number of different objectives that range from the improved diagnostic to the study of the onset and development of cardiovascular diseases (e.g atherosclerosis or aneurysms). This work focuses on the mathematical and numerical modeling of healthy and unhealthy cerebral arterial tissue. In particular, it presents a detailed analysis of different constitutive models for the arterial tissue by means of finite element numerical simulations of arterial wall mechanics and fluid-structure interaction problems occurring in hemodynamics. Hyperelastic isotropic and anisotropic constitutive laws are considered for the description of the passive mechanical behavior of the vessels. An anisotropic multi-mechanism model, specifically proposed for the cerebral arterial tissue, for which the activation of the collagen fibers occurs at finite strains is employed. Firstly, the constitutive laws are numerically validated by considering numerical simulations of static inflation tests on a cylindrical geometry representing a specimen of anterior cerebral artery. With this regard, the material parameters for the constitutive law are obtained from the data fitting of experimental measurements obtained on the same vessel. The constitutive models are critically discussed according to their capability of describing the physiogical highly nonlinear behavior of arteries and on other numerical aspects related to the computational simulation of arterial wall mechanics. Afterwards, simulations of the blood flow and vessel wall interactions are carried out on idealized blood vessels in order to analyze the influence of the modeling choice for the arterial wall on hemodynamic and mechanical quantities that are commonly considered as indicators of physiological or pathological conditions of arteries. We also consider the numerical simulations of unhealthy cerebral arterial tissues by taking into account the mechanical weakening of the vessel wall that occurs during early development stages of cerebral aneurysms by means of static inflation and FSI simulations. We employ both isotropic and anisotropic models study the effects of the mechanical degradation on hemodynamic and mechanical quantities of interest. The FSI simulations are carried out both on idealized geometries of blood vessels and on domains representing idealized and anatomically realistic cerebral aneurysms

Interaction of high density lipoprotein particles with membranes containing cholesterol

In this study, free cholesterol (FC) efflux mediated by human HDL was investigated using fluorescence methodologies. The accessibility of FC to HDL may depend on whether it is located in regions rich in unsaturated phospholipids or in domains containing high levels of FC and sphingomyelin, known as "lipid rafts." Laurdan generalized polarization and two-photon microscopy were used to quantify FC removal from different pools in the bilayer of giant unilamellar vesicles (GUVs). GUVs made of POPC and FC were observed after incubation with reconstituted particles containing apolipoprotein A-I and POPC [78Å diameter reconstituted high density lipoprotein (rHDL)]. Fluorescence correlation spectroscopy data show an increase in rHDL size during the incubation period. GUVs made of two "raft-like" mixtures [DOPC/DPPC/FC (1:1:1) and POPC/SPM/FC (6:1:1)] were used to model liquid-ordered/liquid-disordered phase coexistence. Through these experiments, we conclude that rHDL preferentially removes cholesterol from the more fluid phases. These data, and their extrapolation to in vivo systems, show the significant role that phase separation plays in the regulation of cholesterol homeostasis.Instituto de Investigaciones Bioquímicas de La Plat

Laurdan generalized polarization fluctuations measures membrane packing micro-heterogeneity in vivo

Cellular membranes are heterogeneous in composition, and the prevailing theory holds that the structures responsible for this heterogeneity in vivo are small structures (10-200 nm), sterol- and sphingolipid-enriched, of different sizes, highly dynamic denominated rafts. Rafts are postulated to be platforms, which by sequestering different membrane components can compartmentalize cellular processes and regulate signaling pathways. Despite an enormous effort in this area, the existence of these domains is still under debate due to the characteristics of the structures itself: small in size and highly mobile, which from the technical point of view implies using techniques with high spatial and temporal resolution. In this report we measured rapid fluctuations of the normalized ratio of the emission intensity at two wavelengths of Laurdan, a membrane fluorescent dye sensitive to local membrane packing. We observed generalized polarization fluctuations in the plasma membrane of intact rabbit erythrocytes and Chinese hamster ovary cells that can be explained by the existence of tightly packed micro-domains moving in a more fluid background phase. These structures, which display different lipid packing, have different sizes; they are found in the same cell and in the entire cell population. The small size and characteristic high lipid packing indicate that these micro-domains have properties that have been proposed for lipid rafts.Instituto de Investigaciones Bioquímicas de La Plat

Complete curvature homogeneous pseudo-Riemannian manifolds

We exhibit 3 families of complete curvature homogeneous pseudo-Riemannian manifolds which are modeled on irreducible symmetric spaces and which are not locally homogeneous. All of the manifolds have nilpotent Jacobi operators; some of the manifolds are, in addition, Jordan Osserman and Jordan Ivanov-Petrova.Comment: Update paper to fix misprints in original versio

Lipid packing determines protein-membrane interactions: Challenges for apolipoprotein A-I and high density lipoproteins

Protein and protein-lipid interactions, with and within specific areas in the cell membrane, are critical in order to modulate the cell signaling events required to maintain cell functions and viability. Biological bilayers are complex, dynamic platforms, and thus in vivo observations usually need to be preceded by studies on model systems that simplify and discriminate the different factors involved in lipid-protein interactions. Fluorescence microscopy studies using giant unilamellar vesicles (GUVs) as membrane model systems provide a unique methodology to quantify protein binding, interaction, and lipid solubilization in artificial bilayers. The large size of lipid domains obtainable on GUVs, together with fluorescence microscopy techniques, provides the possibility to localize and quantify molecular interactions. Fluorescence Correlation Spectroscopy (FCS) can be performed using the GUV model to extract information on mobility and concentration. Two-photon Laurdan Generalized Polarization (GP) reports on local changes in membrane water content (related to membrane fluidity) due to protein binding or lipid removal from a given lipid domain. In this review, we summarize the experimental microscopy methods used to study the interaction of human apolipoprotein A-I (apoA-I) in lipid-free and lipid-bound conformations with bilayers and natural membranes. Results described here help us to understand cholesterol homeostasis and offer a methodological design suited to different biological systems.Instituto de Investigaciones Bioquímicas de La PlataFacultad de Ciencias Médica