The Hamilton-Jacobi Formalism for Higher Order Field Theories

We extend the geometric Hamilton-Jacobi formalism for hamiltonian mechanics to higher order field theories with regular lagrangian density. We also investigate the dependence of the formalism on the lagrangian density in the class of those yelding the same Euler-Lagrange equations.Comment: 25 page

On the Strong Homotopy Lie-Rinehart Algebra of a Foliation

It is well known that a foliation F of a smooth manifold M gives rise to a rich cohomological theory, its characteristic (i.e., leafwise) cohomology. Characteristic cohomologies of F may be interpreted, to some extent, as functions on the space P of integral manifolds (of any dimension) of the characteristic distribution C of F. Similarly, characteristic cohomologies with local coefficients in the normal bundle TM/C of F may be interpreted as vector fields on P. In particular, they possess a (graded) Lie bracket and act on characteristic cohomology H. In this paper, I discuss how both the Lie bracket and the action on H come from a strong homotopy structure at the level of cochains. Finally, I show that such a strong homotopy structure is canonical up to isomorphisms.Comment: 41 pages, v2: almost completely rewritten, title changed; v3: presentation partly changed after numerous suggestions by Jim Stasheff, mathematical content unchanged; v4: minor revisions, references added. v5: (hopefully) final versio

Geometric Hamilton-Jacobi Field Theory

I briefly review my proposal about how to extend the geometric Hamilton-Jacobi theory to higher derivative field theories on fiber bundles.Comment: 9 Pages, contains material presented at the workshop FunInGeo, 08-12 June 2011, Ischia (NA) Italy, In honour of Giuseppe Marmos's 65th birthday. No proof

On Higher Derivatives as Constraints in Field Theory: a Geometric Perspective

We formalize geometrically the idea that the (de Donder) Hamiltonian formulation of a higher derivative Lagrangian field theory can be constructed understanding the latter as a first derivative theory subjected to constraints.Comment: 7 page

The cosmological constant and the relaxed universe

We study the role of the cosmological constant (CC) as a component of dark energy (DE). It is argued that the cosmological term is in general unavoidable and it should not be ignored even when dynamical DE sources are considered. From the theoretical point of view quantum zero-point energy and phase transitions suggest a CC of large magnitude in contrast to its tiny observed value. Simply relieving this disaccord with a counterterm requires extreme fine-tuning which is referred to as the old CC problem. To avoid it, we discuss some recent approaches for neutralising a large CC dynamically without adding a fine-tuned counterterm. This can be realised by an effective DE component which relaxes the cosmic expansion by counteracting the effect of the large CC. Alternatively, a CC filter is constructed by modifying gravity to make it insensitive to vacuum energy.Comment: 6 pages, no figures, based on a talk presented at PASCOS 201

Calibration of GRB Luminosity Relations with Cosmography

For the use of Gamma-Ray Bursts (GRBs) to probe cosmology in a cosmology-independent way, a new method has been proposed to obtain luminosity distances of GRBs by interpolating directly from the Hubble diagram of SNe Ia, and then calibrating GRB relations at high redshift. In this paper, following the basic assumption in the interpolation method that objects at the same redshift should have the same luminosity distance, we propose another approach to calibrate GRB luminosity relations with cosmographic fitting directly from SN Ia data. In cosmography, there is a well-known fitting formula which can reflect the Hubble relation between luminosity distance and redshift with cosmographic parameters which can be fitted from observation data. Using the Cosmographic fitting results from the Union set of SNe Ia, we calibrate five GRB relations using GRB sample at $z\leq1.4$ and deduce distance moduli of GRBs at $1.4< z \leq 6.6$ by generalizing above calibrated relations at high redshift. Finally, we constrain the dark energy parameterization models of the Chevallier-Polarski-Linder (CPL) model, the Jassal-Bagla-Padmanabhan (JBP) model and the Alam model with GRB data at high redshift, as well as with the Cosmic Microwave Background radiation (CMB) and the baryonic acoustic oscillation (BAO) observations, and we find the $\Lambda$CDM model is consistent with the current data in 1-$\sigma$ confidence region.Comment: 15 pages, 4 figures, 2 tables; accepted for publication in IJMP

Fluorescence and Morphology of Self-Assembled Nucleobases and Their Diphenylalanine Hybrid Aggregates

Studies carried out in recent decades have revealed that the ability to self-assemble is a widespread property among biomolecules. Small nucleic acid moieties or very short peptides are able to generate intricate assemblies endowed with remarkable structural and spectroscopic properties. Herein, the structural/spectroscopic characterization of aggregates formed by nucleobases and peptide nucleic acid (PNA)-peptide conjugates are reported. At high concentration, all studied nucleobases form aggregates characterized by previously unreported fluorescence properties. The conjugation of these bases, as PNA derivatives, to the dipeptide Phe-Phe leads to the formation of novel hybrid assemblies, which are characterized by an amyloid-like association of the monomers. Although these compounds share the same basic cross-\u3b2 motif, the nature and number of PNA units have an important impact on both the level of structural order and the intrinsic fluorescence of the self-assembled nanostructure

Botulinum toxin type a reconstituted with lidocaine: A report of 1000 consecutive cases

(1) Background: There is an increasing demand for a reversal of the aging process and, nowadays, more patients are seeking minimally invasive methods instead of surgery to meet this goal. The purpose of this paper is to evaluate the predictability of the off-label aesthetic use of botulinum toxin type A (BoNTA) reconstituted with lidocaine. (2) Methods: One thousand treatments, between January 2010 and January 2020, with BoNTA reconstituted with lidocaine for the rejuvenation of the upper third of the face, were performed and retrospectively evaluated. (3) Results: A few seconds after the BoNTA injections, the effect of muscle paralysis was seen in all cases; this allowed providing an optimal symmetric result with no need for a touch-up procedure at the control after three weeks. A burning sensation during the injections was claimed by almost all patients. Major complications were not registered. No touch-up procedures were required. (4) Conclusions: The results of this study show how the reconstitution of BoNTA with lidocaine may avoid imperfect results after the injections; the immediate feedback on the extent of paralysis to be expected from the chemodenervation action of BoNTA allows the physician to have immediate control of the final result

Antenatal intervention for congenital fetal lower urinary tract obstruction (LUTO): a systematic review and meta-analysis.

To evaluate the effectiveness of antenatal intervention for the treatment of congenital lower urinary tract obstruction (LUTO) in improving perinatal survival and postnatal renal function. METHODS: Electronic databases were searched from their inception until May 2018. Selection criteria included randomized controlled trials and controlled nonrandomized observational studies including fetuses with ultrasound evidence of LUTO evaluating antenatal intervention for improving perinatal outcomes. Any type of intervention was analyzed. The primary outcome was perinatal survival. The secondary outcome was postnatal survival with normal renal function. The summary measures were reported as summary odds ratio (OR) with 95% of confidence interval (CI). RESULTS: Ten articles with a total of 355 fetuses were included in the meta-analysis. Inclusion criteria of the selected studies were singleton pregnancy with severe LUTO confirmed on detailed fetal ultrasound examination. Nine studies, analyzed the efficacy of vesico-amniotic shunt performed in the second trimester. The overall estimate survival was higher in the vesico-amniotic shunt group compared to the conservative group (OR 2.54, 95% CI 1.14-5.67). 64/112 fetuses (57.1%) survived in the vesico-amniotic shunt group compared to 52/134 (38.8%) in the control group. Five studies reported on postnatal renal function between 6 months and 2 years. Postnatal renal function was higher in the vesico-amniotic shunt group compared to the conservative group (OR 2.09, 95% CI 0.74-5.9). Fetal cystoscopy was performed in only two included studies. Overall, 45 fetuses underwent fetal cystoscopy. The perinatal survival was higher in the cystoscopy group compared to the conservative management group (OR 2.63, 95% CI 1.07-6.47). Normal renal function was noted in 13/34 fetuses in the cystoscopy group versus 12/61 in the conservative management group at 6 months follow-up (OR 1.75, 95% CI 1.05-2.92) Conclusions: Antenatal bladder drainage appears to improve perinatal survival in cases of LUTO. Further randomized trials with long-term follow-up are required to determine the role of antenatal treatment in clinical setting