On time

This note describes the restoration of time in one-dimensional parameterization-invariant (hence timeless) models, namely the classically-equivalent Jacobi action and gravity coupled to matter. It also serves as a timely introduction by examples to the classical and quantum BV-BFV formalism as well as to the AKSZ method.Comment: 36 pages. Improved exposition. To appear in Lett. Math. Phy

The reduced phase space of Palatini-Cartan-Holst theory

General relativity in four dimensions can be reformulated as a gauge theory, referred to as Palatini-Cartan-Holst theory. This paper describes its reduced phase space using a geometric method due to Kijowski and Tulczyjew and its relation to that of the Einstein-Hilbert approach.Comment: Revised version comprising new results, a correction of Th 4.22 and the arguments leading to it. Manuscript accepted for publication in AHP. 31 page

BV-BFV approach to General Relativity: Palatini-Cartan-Holst action

We show that the Palatini--Cartan--Holst formulation of General Relativity in tetrad variables must be complemented with additional requirements on the fields when boundaries are taken into account for the associated BV theory to induce a compatible BFV theory on the boundary.Comment: 22 pages. Corrected typos in some formulae. Minor aesthetic fixe

Volumetric analysis of carotid plaque components and cerebral microbleeds: a correlative study

PURPOSE: The purpose of this work was to explore the association between carotid plaque volume (total and the subcomponents) and cerebral microbleeds (CMBs). MATERIALS AND METHODS: Seventy-two consecutive (male 53; median age 64) patients were retrospectively analyzed. Carotid arteries were studied by using a 16-detector-row computed tomography scanner whereas brain was explored with a 1.5 Tesla system. CMBs were studied using a T2*-weighted gradient-recalled echo sequence. CMBs were classified as from absent (grade 1) to severe (grade 4). Component types of the carotid plaque were defined according to the following Hounsfield unit (HU) ranges: lipid less than 60 HU; fibrous tissue from 60 to 130 HU; calcification greater than 130 HU, and plaque volumes of each component were calculated. Each carotid artery was analyzed by 2 observers. RESULTS: The prevalence of CMBs was 35.3%. A statistically significant difference was observed between symptomatic (40%) and asymptomatic (11%) patients (P value = .001; OR = 6.07). Linear regression analysis demonstrated an association between the number of CMBs and the symptoms (P = .0018). Receiver operating characteristics curve analysis found an association between the carotid plaque subcomponents and CMBs (Az = .608, .621, and .615 for calcified, lipid, and mixed components, respectively), and Mann-Whitney test confirmed this association in particular for the lipid components (P value = .0267). CONCLUSIONS: Results of this study confirm the association between CMBs and symptoms and that there is an increased number of CMBs in symptomatic patients. Moreover, we found that an increased volume of the fatty component is associated with the presence and number of CMBs

BV-equivalence between triadic gravity and BF theory in three dimensions

The triadic description of General Relativity in three dimensions is known to be a BF theory. Diffeomorphisms, as symmetries, are easily re- covered on shell from the symmetries of BF theory. This note describes an explicit off-shell BV symplectomorphism between the BV versions of the two theories, each endowed with their natural symmetries

BV-BFV approach to General Relativity, Einstein-Hilbert action

The present paper shows that general relativity in the Arnowitt-Deser-Misner formalism admits a BV-BFV formulation. More precisely, for any $d + 1 \not= 2$ (pseudo-) Riemannian manifold M with space-like or time-like boundary components, the BV data on the bulk induces compatible BFV data on the boundary. As a byproduct, the usual canonical formulation of general relativity is recovered in a straightforward way.Comment: 16 page

Critical Points for Elliptic Equations with Prescribed Boundary Conditions

This paper concerns the existence of critical points for solutions to second order elliptic equations of the form $\nabla\cdot \sigma(x)\nabla u=0$ posed on a bounded domain $X$ with prescribed boundary conditions. In spatial dimension $n=2$, it is known that the number of critical points (where $\nabla u=0$) is related to the number of oscillations of the boundary condition independently of the (positive) coefficient $\sigma$. We show that the situation is different in dimension $n\geq3$. More precisely, we obtain that for any fixed (Dirichlet or Neumann) boundary condition for $u$ on $\partial X$, there exists an open set of smooth coefficients $\sigma(x)$ such that $\nabla u$ vanishes at least at one point in $X$. By using estimates related to the Laplacian with mixed boundary conditions, the result is first obtained for a piecewise constant conductivity with infinite contrast, a problem of independent interest. A second step shows that the topology of the vector field $\nabla u$ on a subdomain is not modified for appropriate bounded, sufficiently high-contrast, smooth coefficients $\sigma(x)$. These results find applications in the class of hybrid inverse problems, where optimal stability estimates for parameter reconstruction are obtained in the absence of critical points. Our results show that for any (finite number of) prescribed boundary conditions, there are coefficients $\sigma(x)$ for which the stability of the reconstructions will inevitably degrade.Comment: 26 pages, 4 figure

Correlated bosons in a one-dimensional optical lattice: Effects of the trapping potential and of quasiperiodic disorder

We investigate the effect of the trapping potential on the quantum phases of strongly correlated ultracold bosons in one-dimensional periodic and quasiperiodic optical lattices. By means of a decoupling meanfield approach, we characterize the ground state of the system and its behavior under variation of the harmonic trapping, as a function of the total number of atoms. For a small atom number the system shows an incompressible Mott-insulating phase, as the size of the cloud remains unaffected when the trapping potential is varied. When the quasiperiodic potential is added the system develops a metastable-disordered phase which is neither compressible nor Mott insulating. This state is characteristic of quasidisorder in the presence of a strong trapping potential.Comment: Accepted for publication in PR