Simultaneity as an Invariant Equivalence Relation

This paper deals with the concept of simultaneity in classical and relativistic physics as construed in terms of group-invariant equivalence relations. A full examination of Newton, Galilei and Poincar\'e invariant equivalence relations in $\R^4$ is presented, which provides alternative proofs, additions and occasionally corrections of results in the literature, including Malament's theorem and some of its variants. It is argued that the interpretation of simultaneity as an invariant equivalence relation, although interesting for its own sake, does not cut in the debate concerning the conventionality of simultaneity in special relativity.Comment: Some corrections, mostly of misprints. Keywords: special relativity, simultaneity, invariant equivalence relations, Malament's theore

Monitoring Wound Healing with Contactless Measurements and Augmented Reality

Objective: This work presents a device for non-invasive wound parameters assessment, designed to overcome the drawbacks of traditional methods, which are mostly rough, inaccurate, and painful for the patient. The device estimates the morphological parameters of the wound and provides augmented reality (AR) visual feedback on the wound healing status by projecting the wound border acquired during the last examination, thus improving doctor-patient communication. Methods: An accurate 3D model of the wound is created by stereophotogrammetry and refined through self-organizing maps. The 3D model is used to estimate physical parameters for wound healing assessment and integrates AR functionalities based on a miniaturized projector. The physical parameter estimation functionalities are evaluated in terms of precision, accuracy, inter-operator variability, and repeatability, whereas AR wound border projection is evaluated in terms of accuracy on the same phantom. Results: The accuracy and precision of the device are respectively 2% and 1.2% for linear parameters, and 1.7% and 1.3% for area and volume. The AR projection shows an error distance <1 mm. No statistical difference was found between the measurements of different operators. Conclusion: The device has proven to be an objective and non-operator-dependent tool for assessing the morphological parameters of the wound. Comparison with non-contact devices shows improved accuracy, offering reliable and rigorous measurements. Clinical Impact: Chronic wounds represent a significant health problem with high recurrence rates due to the ageing of the population and diseases such as diabetes and obesity. The device presented in this work provides an easy-to-use non-invasive tool to obtain useful information for treatment

Potentials for hyper-Kahler metrics with torsion

We prove that locally any hyper-K\"ahler metric with torsion admits an HKT potential.Comment: 9 page

B field and squeezed states in Vacuum String Field Theory

We show that squeezed state solutions for solitonic lumps in Vacuum String Field Theory still exist in the presence of a constant B field. We show in particular that, just as in the B=0 case, we can write down a compact explicit form for such solutions.Comment: 15 pages, Latex, typos corrected, final versio

Photodynamic therapy of cutaneous T-cell lymphoma cell lines mediated by 5-aminolevulinic acid and derivatives

The delta-amino acid 5-aminolevulinic acid (ALA), is the precursor of the endogenous photosensitiser Protoporphyrin IX (PpIX), and is currently approved for Photodynamic Therapy (PDT) of certain superficial cancers. However, ALA-PDT is not very effective in diseases in which T-cells play a significant role. Cutaneous T-cell lymphomas (CTCL) is a group of non-Hodgkin malignant diseases, which includes mycosis fungoides (MF) and Sézary syndrome (SS). In previous work, we have designed new ALA esters synthesised by three-component Passerini reactions, and some of them showed higher performance as compared to ALA. This work aimed to determine the efficacy as pro-photosensitisers of five new ALA esters of 2-hydroxy-N-arylacetamides (1f, 1 g, 1 h, 1i and 1 k) of higher lipophilicity than ALA in Myla cells of MF and HuT-78 cells of SS. We have also tested its effectiveness against ALA and the already marketed ALA methyl ester (Me-ALA) and ALA hexyl ester (He-ALA). Both cell Myla and SS cells were effectively and equally photoinactivated by ALA-PDT. Besides, the concentration of ALA required to induce half the maximal porphyrin synthesis was 209 μM for Myla and 169 μM for HuT-78 cells. As a criterion of efficacy, we calculated the concentration of the ALA derivatives necessary to induce half the plateau porphyrin values obtained from ALA. These values were achieved at concentrations 4 and 12 times lower compared to ALA, according to the derivative used. For He-ALA, concentrations were 24 to 25 times lower than required for ALA for inducing comparable porphyrin synthesis in both CTCL cells. The light doses for inducing 50% of cell death (LD50) for He-ALA, 1f, 1 g, 1 h and 1i were around 18 and 25 J/cm2 for Myla and HuT-78 cells respectively, after exposure to 0.05 mM concentrations of the compounds. On the other hand, the LD50s for the compound 1 k were 40 and 57 J/cm2 for Myla and HuT-78, respectively. In contrast, 0.05 mM of ALA and Me-ALA did not provoke photokilling since the concentration employed was far below the porphyrin saturation point for these compounds. Our results suggest the potential use of ALA derivatives for topical application in PDT treatment of MF and extracorporeal PDT for the depletion of activated T-cells in SS

Infrared spectroscopy of small-molecule endofullerenes

Hydrogen is one of the few molecules which has been incarcerated in the molecular cage of C$_{60}$ and forms endohedral supramolecular complex H$_2$@C$_{60}$. In this confinement hydrogen acquires new properties. Its translational motion becomes quantized and is correlated with its rotations. We applied infrared spectroscopy to study the dynamics of hydrogen isotopologs H$_2$, D$_2$ and HD incarcerated in C$_{60}$. The translational and rotational modes appear as side bands to the hydrogen vibrational mode in the mid infrared part of the absorption spectrum. Because of the large mass difference of hydrogen and C$_{60}$ and the high symmetry of C$_{60}$ the problem is identical to a problem of a vibrating rotor moving in a three-dimensional spherical potential. The translational motion within the C$_{60}$ cavity breaks the inversion symmetry and induces optical activity of H$_2$. We derive potential, rotational, vibrational and dipole moment parameters from the analysis of the infrared absorption spectra. Our results were used to derive the parameters of a pairwise additive five-dimensional potential energy surface for H$_2$@C$_{60}$. The same parameters were used to predict H$_2$ energies inside C$_{70}$[Xu et al., J. Chem. Phys., {\bf 130}, 224306 (2009)]. We compare the predicted energies and the low temperature infrared absorption spectra of H$_2$@C$_{70}$.Comment: Updated author lis

The EPRL intertwiners and corrected partition function

Do the SU(2) intertwiners parametrize the space of the EPRL solutions to the simplicity constraint? What is a complete form of the partition function written in terms of this parametrization? We prove that the EPRL map is injective for n-valent vertex in case when it is a map from SO(3) into SO(3)xSO(3) representations. We find, however, that the EPRL map is not isometric. In the consequence, in order to be written in a SU(2) amplitude form, the formula for the partition function has to be rederived. We do it and obtain a new, complete formula for the partition function. The result goes beyond the SU(2) spin-foam models framework.Comment: RevTex4, 15 pages, 5 figures; theorem of injectivity of EPRL map correcte

Chan-Paton factors and Higgsing from Vacuum String Field Theory

We give a description of open strings stretched between N parallel D-branes in VSFT. We show how higgsing is generated as the branes are displaced: the shift in the mass formula for on-shell states stretched between different branes is due to a twist anomaly, a contribution localized at the midpoint.Comment: 20 pages, JHEP clas

Benzene at 1GHz. Magnetic field-induced fine structure

The deuterium NMR spectrum of benzene-d6 in a high field spectrometer (1 GHz protons) exhibits a magnetic field-induced deuterium quadrupolar splitting ??. The magnitude of ?? observed for the central resonance is smaller than that observed for the 13C satellite doublets ???. This difference, ?(??) = ??? ? ??, is due to unresolved fine structure contributions to the respective resonances. We determine the origins of and simulate this difference, and report pulse sequences that exploit the connectivity of the peaks in the 13C and 2H spectra to determine the relative signs of the indirect coupling, JCD, and ??. The positive sign found for ?? is consonant with the magnetic field biasing of an isolated benzene molecule—the magnetic energy of the aromatic ring is lowest for configurations where the C6 axis is normal to the field. In the neat liquid the magnitude of ?? is decreased by the pair correlations in this prototypical molecular liquid