Invariance principle, multifractional Gaussian processes and long-range dependence

This paper is devoted to establish an invariance principle where the limit process is a multifractional Gaussian process with a multifractional function which takes its values in $(1/2,1)$. Some properties, such as regularity and local self-similarity of this process are studied. Moreover the limit process is compared to the multifractional Brownian motion.Comment: Published in at http://dx.doi.org/10.1214/07-AIHP127 the Annales de l'Institut Henri Poincar\'e - Probabilit\'es et Statistiques (http://www.imstat.org/aihp/) by the Institute of Mathematical Statistics (http://www.imstat.org

Vertebral fractures are associated with increased cortical porosity in iliac crest bone biopsy of men with idiopathic osteoporosis

In men, vertebral fractures are poorly associated with bone density, and both cortical and trabecular micro-architectural changes could contribute to bone fragility. Bone histomorphometry makes it possible to investigate both the thickness and porosity of cortical bone, which has been reported to have a major impact on the biomechanical properties of bone. We therefore conducted a cross sectional study using iliac crest biopsies to investigate the trabecular and cortical bone structure in men with or without vertebral fractures.We selected 93 bone biopsies from men with idiopathic osteoporosis (defined as a T-score <− 2.5), between 40 and 70 years of age. Patients were divided into two groups on the basis of the presence (n = 46) or absence (n = 47) of prevalent vertebral fracture (VFX). We measured micro-architectural indices in trabecular and cortical bone by histomorphometry at the iliac crest. Patients with VFX had lower trabecular bone volume (BV/TV: 12.4 ± 3.8 versus 14.7 ± 3.1 % (m ± SD)), p < 0.01), higher trabecular separation (Tb.Sp: 871 ± 279 versus 719 ± 151 μm, p < 0.01), and higher marrow star volume (V*m.space: 1.617 ± 1.257 versus 0.945 ± 0.466 mm3, p < 0.01). Cortical thickness (Ct.Th) was the same in patients with or without VFX, whereas cortical porosity (Ct.Po) was higher in patients with VFX (6.5 ± 2.6 versus 5.0 ± 2.0 %, p < 0.01), because their Haversian canals had higher mean areas (8291 ± 4135 versus 5438 ± 2809 μm2, p < 0.001). There was no correlation between any trabecular and cortical micro-architectural parameters. Using a logistic regression model, we evaluated the VFX as a function of the V⁎m.space and Ct.Po, adjusted for age. The odds-ratio of having a VFX was 3.89 (95% CI 1.19–12.7, p = 0.02) for the third tertile of V*m.space (adjusted on age and Ct.Po), and 4.07 (95% CI 1.25–13.3, p = 0.02) for the third tertile of Ct.Po (adjusted on age and V*m.space). Our data show that both trabecular and cortical bone microarchitecture contribute independently to vertebral fractures in men with idiopathic osteoporosis. In contrast to data reported in women, in men it is cortical porosity, and not cortical width, that is associated with vertebral fractures. This suggests that the cortical deficit is different in men and in women with fragility fractures

Stat-tracks and mediotypes: powerful tools for modern ichnology based on 3D models.

Vertebrate tracks are subject to a wide distribution of morphological types. A single trackmaker may be associated with a range of tracks reflecting individual pedal anatomy and behavioural kinematics mediated through substrate properties which may vary both in space and time. Accordingly, the same trackmaker can leave substantially different morphotypes something which must be considered in creating ichnotaxa. In modern practice this is often captured by the collection of a series of 3D track models. We introduce two concepts to help integrate these 3D models into ichnological analysis procedures. The mediotype is based on the idea of using statistically-generated three-dimensional track models (median or mean) of the type specimens to create a composite track to support formal recognition of a ichno type. A representative track (mean and/or median) is created from a set of individual reference tracks or from multiple examples from one or more trackways. In contrast, stat-tracks refer to other digitally generated tracks which may explore variance. For example, they are useful in: understanding the preservation variability of a given track sample; identifying characteristics or unusual track features; or simply as a quantitative comparison tool. Both concepts assist in making ichnotaxonomical interpretations and we argue that they should become part of the standard procedure when instituting new ichnotaxa. As three-dimensional models start to become a standard in publications on vertebrate ichnology, the mediotype and stat-track concepts have the potential to help guiding a revolution in the study of vertebrate ichnology and ichnotaxonomy

Dissociation of sensitivity to spatial frequency in word and face preferential areas of the fusiform gyrus

Different cortical regions within the ventral occipitotemporal junction have been reported to show preferential responses to particular objects. Thus, it is argued that there is evidence for a left-lateralized visual word form area and a right-lateralized fusiform face area, but the unique specialization of these areas remains controversial. Words are characterized by greater power in the high spatial frequency (SF) range, whereas faces comprise a broader range of high and low frequencies. We investigated how these high-order visual association areas respond to simple sine-wave gratings that varied in SF. Using functional magnetic resonance imaging, we demonstrated lateralization of activity that was concordant with the low-level visual property of words and faces; left occipitotemporal cortex is more strongly activated by high than by low SF gratings, whereas the right occipitotemporal cortex responded more to low than high spatial frequencies. Therefore, the SF of a visual stimulus may bias the lateralization of processing irrespective of its higher order properties

Plastic Response of a 2D Lennard-Jones amorphous solid: Detailed analysis of the local rearrangements at very slow strain-rate

We analyze in details the atomistic response of a model amorphous material submitted to plastic shear in the athermal, quasistatic limit. After a linear stress-strain behavior, the system undergoes a noisy plastic flow. We show that the plastic flow is spatially heterogeneous. Two kinds of plastic events occur in the system: quadrupolar localized rearrangements, and shear bands. The analysis of the individual motion of a particle shows also two regimes: a hyper-diffusive regime followed by a diffusive regime, even at zero temperature

Earth and Terrestrial Planet Formation

The growth and composition of Earth is a direct consequence of planet formation throughout the Solar System. We discuss the known history of the Solar System, the proposed stages of growth and how the early stages of planet formation may be dominated by pebble growth processes. Pebbles are small bodies whose strong interactions with the nebula gas lead to remarkable new accretion mechanisms for the formation of planetesimals and the growth of planetary embryos. Many of the popular models for the later stages of planet formation are presented. The classical models with the giant planets on fixed orbits are not consistent with the known history of the Solar System, fail to create a high Earth/Mars mass ratio, and, in many cases, are also internally inconsistent. The successful Grand Tack model creates a small Mars, a wet Earth, a realistic asteroid belt and the mass-orbit structure of the terrestrial planets. In the Grand Tack scenario, growth curves for Earth most closely match a Weibull model. The feeding zones, which determine the compositions of Earth and Venus follow a particular pattern determined by Jupiter, while the feeding zones of Mars and Theia, the last giant impactor on Earth, appear to randomly sample the terrestrial disk. The late accreted mass samples the disk nearly evenly.Comment: Accepted for publication in Early Earth an AGU Monograph edited by James Badro and Michael J. Walte