Pressure induced magnetic phase separation in La0.75_{0.75}Ca0.25_{0.25}MnO3_{3} manganite

The pressure dependence of the Curie temperature T$_{C}(P)$ in La$_{0.75}$Ca$_{0.25}$MnO$_{3}$ was determined by neutron diffraction up to 8 GPa, and compared with the metallization temperature T$_{IM}(P)$ \cite{irprl}. The behavior of the two temperatures appears similar over the whole pressure range suggesting a key role of magnetic double exchange also in the pressure regime where the superexchange interaction is dominant. Coexistence of antiferromagnetic and ferromagnetic peaks at high pressure and low temperature indicates a phase separated regime which is well reproduced with a dynamical mean-field calculation for a simplified model. A new P-T phase diagram has been proposed on the basis of the whole set of experimental data.Comment: 5 pages, 4 figure

Understanding the effect of cognitive/brain reserve and depression on regional atrophy in early Alzheimer’s disease

Introduction: Depression in patients with mild cognitive impairment (MCI) and dementia of the Alzheimer’s type (AD) is associated with worse prognosis. Indeed, depressed MCI patients have worse cognitive performance and greater loss of gray-matter volume in several brain areas. To date, knowledge of the factors that can mitigate this detrimental effect is still limited. The aim of the present study was to understand in what way cognitive reserve/brain reserve and depression interact and are linked to regional atrophy in early stage AD. Methods: Depression was evaluated with the Patient Health Questionnaire-9 in 90 patients with early AD, and a cutoff of ≥ 5 was used to separate depressed (n = 44) from non-depressed (n = 46) patients. Each group was further stratified into high/low cognitive reserve/brain reserve. Cognitive reserve was calculated using years of education as proxy, while normalized parenchymal volumes were used to estimate brain reserve. Voxel-based morphometry was carried out to extract and analyze gray-matter maps. 2 × 2 ANCOVAs were run to test the effect of the reserve-by-depression interaction on gray matter. Age and hippocampal ratio were used as covariates. Composite indices of major cognitive domains were also analyzed with comparable models. Results: No reserve-by-depression interaction was found in the analytical models of gray matter. Depression was associated with less gray matter volume in the cerebellum and parahippocampal gyrus. The brain reserve-by-depression interaction was a significant predictor of executive functioning. Among those with high brain reserve, depressed patients had poorer executive skills. No significant results were found in association with cognitive reserve. Conclusion: These findings suggest that brain reserve may modulate the association between neurodegeneration and depression in patients with MCI and dementia of the AD type, influencing in particular executive functioning

Sharp Global Bounds for the Hessian on Pseudo-Hermitian Manifolds

We find sharp bounds for the norm inequality on a Pseudo-hermitian manifold, where the L^2 norm of all second derivatives of the function involving horizontal derivatives is controlled by the L^2 norm of the sub-Laplacian. Perturbation allows us to get a-priori bounds for solutions to sub-elliptic PDE in non-divergence form with bounded measurable coefficients. The method of proof is through a Bochner technique. The Heisenberg group is seen to be en extremal manifold for our inequality in the class of manifolds whose Ricci curvature is non-negative.Comment: 13 page

Dispersion of the odd magnetic resonant mode in near-optimally doped Bi2Sr2CaCu2O8+d

We report a neutron scattering study of the spin excitation spectrum in the superconducting state of slightly overdoped Bi2Sr2CaCu2O8+d system (Tc=87 K). We focus on the dispersion of the resonance peak in the superconducting state that is due to a S=1 collective mode. The measured spin excitation spectrum bears a strong similarity to the spectrum of the YBa2Cu3O6+x system for a similar doping level i.e. x= 0.95-1), which consists of intersecting upward- and downward-dispersing branches. A close comparison of the threshold of the electron-hole spin flip continuum, deduced from angle resolved photo-emission measurements in the same system, indicates that the magnetic response in the superconducting state is confined, in both energy and momentum, below the gapped Stoner continuum. In contrast to YBa2Cu3O6+x, the spin excitation spectrum is broader than the experimental resolution. In the framework of an itinerant-electron model, we quantitatively relate this intrinsic energy width to the superconducting gap distribution observed in scanning tunnelling microscopy experiments. Our study further suggests a significant in-plane anisotropy of the magnetic response.Comment: 10 figure

On the Alexandrov Topology of sub-Lorentzian Manifolds

It is commonly known that in Riemannian and sub-Riemannian Geometry, the metric tensor on a manifold defines a distance function. In Lorentzian Geometry, instead of a distance function it provides causal relations and the Lorentzian time-separation function. Both lead to the definition of the Alexandrov topology, which is linked to the property of strong causality of a space-time. We studied three possible ways to define the Alexandrov topology on sub-Lorentzian manifolds, which usually give different topologies, but agree in the Lorentzian case. We investigated their relationships to each other and the manifold's original topology and their link to causality.Comment: 20 page

A Holder Continuous Nowhere Improvable Function with Derivative Singular Distribution

We present a class of functions $\mathcal{K}$ in $C^0(\R)$ which is variant of the Knopp class of nowhere differentiable functions. We derive estimates which establish \mathcal{K} \sub C^{0,\al}(\R) for 0<\al<1 but no $K \in \mathcal{K}$ is pointwise anywhere improvable to C^{0,\be} for any \be>\al. In particular, all $K$'s are nowhere differentiable with derivatives singular distributions. $\mathcal{K}$ furnishes explicit realizations of the functional analytic result of Berezhnoi. Recently, the author and simulteously others laid the foundations of Vector-Valued Calculus of Variations in $L^\infty$ (Katzourakis), of $L^\infty$-Extremal Quasiconformal maps (Capogna and Raich, Katzourakis) and of Optimal Lipschitz Extensions of maps (Sheffield and Smart). The "Euler-Lagrange PDE" of Calculus of Variations in $L^\infty$ is the nonlinear nondivergence form Aronsson PDE with as special case the $\infty$-Laplacian. Using $\mathcal{K}$, we construct singular solutions for these PDEs. In the scalar case, we partially answered the open $C^1$ regularity problem of Viscosity Solutions to Aronsson's PDE (Katzourakis). In the vector case, the solutions can not be rigorously interpreted by existing PDE theories and justify our new theory of Contact solutions for fully nonlinear systems (Katzourakis). Validity of arguments of our new theory and failure of classical approaches both rely on the properties of $\mathcal{K}$.Comment: 5 figures, accepted to SeMA Journal (2012), to appea

Basic properties of nonsmooth Hormander's vector fields and Poincare's inequality

We consider a family of vector fields defined in some bounded domain of R^p, and we assume that they satisfy Hormander's rank condition of some step r, and that their coefficients have r-1 continuous derivatives. We extend to this nonsmooth context some results which are well-known for smooth Hormander's vector fields, namely: some basic properties of the distance induced by the vector fields, the doubling condition, Chow's connectivity theorem, and, under the stronger assumption that the coefficients belong to C^{r-1,1}, Poincare's inequality. By known results, these facts also imply a Sobolev embedding. All these tools allow to draw some consequences about second order differential operators modeled on these nonsmooth Hormander's vector fields.Comment: 60 pages, LaTeX; Section 6 added and Section 7 (6 in the previous version) changed. Some references adde

Relationship between cerebrospinal fluid neurodegeneration biomarkers and temporal brain atrophy in cognitively healthy older adults

It is unclear whether cerebrospinal fluid (CSF) biomarkers of neurodegeneration predict brain atrophy in cognitively healthy older adults, whether these associations can be explained by phosphorylated tau181 (p-tau) and the 42 amino acid form of amyloid-ꞵ (Aꞵ42) biomarkers, and which neural substrates may drive these associations. We addressed these questions in two samples of cognitively healthy older adults who underwent longitudinal structural MRI up to 7 years and had baseline CSF levels of heart-type fatty-acid binding protein [FABP3], total-tau, neurogranin, and neurofilament light [NFL] (n=189, scans=721). The results showed that NFL, total-tau, and FABP3 predicted entorhinal thinning and hippocampal atrophy. Brain atrophy was not moderated by Aꞵ42 and the associations between NFL and FABP3 with brain atrophy were independent of p-tau. The spatial pattern of cortical atrophy associated with the biomarkers overlapped with neurogenetic profiles associated with expression in the axonal (total-tau, NFL) and dendritic (neurogranin) components. CSF biomarkers of neurodegeneration are useful for predicting specific features of brain atrophy in older adults, independently of amyloid and tau pathology biomarkers

Heavy Carriers and Non-Drude Optical Conductivity in MnSi

Optical properties of the weakly helimagnetic metal MnSi have been determined in the photon energy range from 2 meV to 4.5 eV using the combination of grazing incidence reflectance at 80 degrees (2 meV to 0.8 eV) and ellipsometry (0.8 to 4.5 eV). As the sample is cooled below 100 K the effective mass becomes strongly frequency dependent at low frequencies, while the scattering rate developes a linear frequency dependence. The complex optical conductivity can be described by the phenomenological relation \sigma(\omega,T) \propto (\Gamma(T)+i\omega)^{-1/2} used for cuprates and ruthenates.Comment: 5 pages, ReVTeX 4, 5 figures in eps forma

Metamagnetism and critical fluctuations in high quality single crystals of the bilayer ruthenate Sr3Ru2O7

We report the results of low temperature transport, specific heat and magnetisation measurements on high quality single crystals of the bilayer perovskite Sr3Ru2O7, which is a close relative of the unconventional superconductor Sr2RuO4. Metamagnetism is observed, and transport and thermodynamic evidence for associated critical fluctuations is presented. These relatively unusual fluctuations might be pictured as variations in the Fermi surface topography itself. No equivalent behaviour has been observed in the metallic state of Sr2RuO4.Comment: 4 pages, 4 figures, Revtex 3.