Covariant Lagrangian Formulation of Chern-Simons and BF Theories

We investigate the covariant formulation of Chern-Simons theories in a general odd dimension which can be obtained by introducing a vacuum connection field as a reference. Field equations, Noether currents and superpotentials are computed so that results are easily compared with the well-known results in dimension 3. Finally we use this covariant formulation of Chern-Simons theories to investigate their relation with topological BF theories.Comment: 23 pages, refs. adde

A geometric model for magnetizable bodies with internal variables

In a geometrical framework for thermo-elasticity of continua with internal variables we consider a model of magnetizable media previously discussed and investigated by Maugin. We assume as state variables the magnetization together with its space gradient, subjected to evolution equations depending on both internal and external magnetic fields. We calculate the entropy function and necessary conditions for its existenc

New Cases of Universality Theorem for Gravitational Theories

The "Universality Theorem" for gravity shows that f(R) theories (in their metric-affine formulation) in vacuum are dynamically equivalent to vacuum Einstein equations with suitable cosmological constants. This holds true for a generic (i.e. except sporadic degenerate cases) analytic function f(R) and standard gravity without cosmological constant is reproduced if f is the identity function (i.e. f(R)=R). The theorem is here extended introducing in dimension 4 a 1-parameter family of invariants R' inspired by the Barbero-Immirzi formulation of GR (which in the Euclidean sector includes also selfdual formulation). It will be proven that f(R') theories so defined are dynamically equivalent to the corresponding metric-affine f(R) theory. In particular for the function f(R)=R the standard equivalence between GR and Holst Lagrangian is obtained.Comment: 10 pages, few typos correcte

Fluorescein for resection of high-grade gliomas: A safety study control in a single center and review of the literature

Background: The importance of a complete resection of high-grade gliomas (HGGs) has been highlighted in scientific literature, in order to limit tumor recurrence and above all to improve disease-free survival rates. Several fluorescent biomarkers have been tested to improve intraoperative identification of residual tumor; 5-aminolevulinic acid (5-ALA) and fluorescein sodium (FS) are now starting to play a central role in glioma surgery. We performed a retrospective analysis on 47 patients operated for HGGs. Here we report our preliminary data. Methods: Data of 47 consecutive patients with HGG have been collected in our study (25 males, 22 females; mean age: 60.3 years, range: 27-86 years). Fluorescein (5 mg/kg of body weight) was injected intravenously right after the induction of general anesthesia. A YELLOW 560 filter was used on an OPMI Pentero 900 microscope (Carl Zeiss Meditec, Oberkochen, Germany) to complete a microsurgical tumor removal. Glioma resection and quality of life were evaluated preoperative and postoperatively. Results: Gross total resection (GTR) was achieved in 53.2% (n = 25) of patients. A subtotal resection (STR) (>95%) was achieved in 29.8% (n = 14), while a partial resection (PR) (<95%) was obtained in 17% (n = 8) of patients. Overall, in 83% (n = 39) of patients who underwent fluorescence-guided surgery the resection rate achieved was >95%. No adverse effects correlated to fluorescein have been recorded. Conclusion: Fluorescein seems to be safe and effective in the resection of HGGs, allowing a high rate of gross total removal of contrast enhanced areas

Universality of Einstein Equations for the Ricci Squared Lagrangians

It has been recently shown that, in the first order (Palatini) formalism, there is universality of Einstein equations and Komar energy-momentum complex, in the sense that for a generic nonlinear Lagrangian depending only on the scalar curvature of a metric and a torsionless connection one always gets Einstein equations and Komar's expression for the energy-momentum complex. In this paper a similar analysis (also in the framework of the first order formalism) is performed for all nonlinear Lagrangians depending on the (symmetrized) Ricci square invariant. The main result is that the universality of Einstein equations and Komar energy-momentum complex also extends to this case (modulo a conformal transformation of the metric).Comment: 21 pages, Late

Degenerations of ideal hyperbolic triangulations

Let M be a cusped 3-manifold, and let T be an ideal triangulation of M. The deformation variety D(T), a subset of which parameterises (incomplete) hyperbolic structures obtained on M using T, is defined and compactified by adding certain projective classes of transversely measured singular codimension-one foliations of M. This leads to a combinatorial and geometric variant of well-known constructions by Culler, Morgan and Shalen concerning the character variety of a 3-manifold.Comment: 31 pages, 11 figures; minor changes; to appear in Mathematische Zeitschrif

Symmetries of Helmholtz forms and globally variational dynamical forms

Invariance properties of classes in the variational sequence suggested to Krupka et al. the idea that there should exist a close correspondence between the notions of variationality of a differential form and invariance of its exterior derivative. It was shown by them that the invariance of a closed Helmholtz form of a dynamical form is equivalent with local variationality of the Lie derivative of the dynamical form, so that the latter is locally the Euler--Lagrange form of a Lagrangian. We show that the corresponding local system of Euler--Lagrange forms is variationally equivalent to a global Euler--Lagrange form.Comment: Presented at QTS7 - Quantum Theory and Symmetries VII, Prague 7-13/08/201

Substantia Nigra Volumetry with 3-T MRI in De Novo and Advanced Parkinson Disease

Background: Magnetization transfer–prepared T1-weighted MRI can depict a hyperintense subregion of the substantia nigra involved in the degeneration process of Parkinson disease. / Purpose: To evaluate quantitative measurement of substantia nigra volume by using MRI to support clinical diagnosis and staging of Parkinson disease. / Materials and Methods: In this prospective study, a high-spatial-resolution magnetization transfer–prepared T1-weighted volumetric sequence was performed with a 3-T MRI machine between January 2014 and October 2015 for participants with de novo Parkinson disease, advanced Parkinson disease, and healthy control participants. A reproducible semiautomatic quantification analysis method that entailed mesencephalic intensity as an internal reference was used for hyperintense substantia nigra volumetry normalized to intracranial volume. A general linear model with age and sex as covariates was used to compare the three groups. / Results: Eighty participants were evaluated: 20 healthy control participants (mean age ± standard deviation, 56 years ± 11; 11 women), 29 participants with de novo Parkinson disease (64 years ± 10; 19 men), and 31 participants with advanced Parkinson disease (60 years ± 9; 16 women). Volumetric measurement of hyperintense substantia nigra from magnetization transfer–prepared T1-weighted MRI helped differentiate healthy control participants from participants with advanced Parkinson disease (mean difference for ipsilateral side, 64 mm3 ± 14, P < .001; mean difference for contralateral side, 109 mm3 ± 14, P < .001) and helped distinguish healthy control participants from participants with de novo Parkinson disease (mean difference for ipsilateral side, 45 mm3 ± 15, P < .01; mean difference for contralateral side, 66 mm3 ± 15, P < .001) and participants with de novo Parkinson disease from those with advanced Parkinson disease (mean difference for ipsilateral side, 20 mm3 ± 13, P = .40; mean difference for contralateral side, 43 mm3 ± 13, P = .004). / Conclusion: Magnetization transfer–prepared T1-weighted MRI volumetry of the substantia nigra helped differentiate the stages of Parkinson disease