The Exponential Map for the Conformal Group 0(2,4)

We present a general method to obtain a closed, finite formula for the exponential map from the Lie algebra to the Lie group, for the defining representation of the orthogonal groups. Our method is based on the Hamilton-Cayley theorem and some special properties of the generators of the orthogonal group, and is also independent of the metric. We present an explicit formula for the exponential of generators of the $SO_+(p,q)$ groups, with $p+q = 6$, in particular we are dealing with the conformal group $SO_+(2,4)$, which is homomorphic to the $SU(2,2)$ group. This result is needed in the generalization of U(1) gauge transformations to spin gauge transformations, where the exponential plays an essential role. We also present some new expressions for the coefficients of the secular equation of a matrix.Comment: 16pages,plain-TeX,(corrected TeX

The exponential map for the unitary group SU(2,2)

In this article we extend our previous results for the orthogonal group, $SO(2,4)$, to its homomorphic group $SU(2,2)$. Here we present a closed, finite formula for the exponential of a $4\times 4$ traceless matrix, which can be viewed as the generator (Lie algebra elements) of the $SL(4,C)$ group. We apply this result to the $SU(2,2)$ group, which Lie algebra can be represented by the Dirac matrices, and discuss how the exponential map for $SU(2,2)$ can be written by means of the Dirac matrices.Comment: 10 page

Relativistic Chasles' theorem and the conjugacy classes of the inhomogeneous Lorentz group

This work is devoted to the relativistic generalization of Chasles' theorem, namely to the proof that every proper orthochronous isometry of Minkowski spacetime, which sends some point to its chronological future, is generated through the frame displacement of an observer which moves with constant acceleration and constant angular velocity. The acceleration and angular velocity can be chosen either aligned or perpendicular, and in the latter case the angular velocity can be chosen equal or smaller than than the acceleration. We start reviewing the classical Euler's and Chasles' theorems both in the Lie algebra and group versions. We recall the relativistic generalization of Euler's theorem and observe that every (infinitesimal) transformation can be recovered from information of algebraic and geometric type, the former being identified with the conjugacy class and the latter with some additional geometric ingredients (the screw axis in the usual non-relativistic version). Then the proper orthochronous inhomogeneous Lorentz Lie group is studied in detail. We prove its exponentiality and identify a causal semigroup and the corresponding Lie cone. Through the identification of new Ad-invariants we classify the conjugacy classes, and show that those which admit a causal representative have special physical significance. These results imply a classification of the inequivalent Killing vector fields of Minkowski spacetime which we express through simple representatives. Finally, we arrive at the mentioned generalization of Chasles' theorem.Comment: Latex2e, 49 pages. v2: few typos correcte

Ultra--Planck Scattering in D=3 Gravity Theories

We obtain the high energy, small angle, 2-particle gravitational scattering amplitudes in topologically massive gravity (TMG) and its two non-dynamical constituents, Einstein and Chern--Simons gravity. We use 't Hooft's approach, formally equivalent to a leading order eikonal approximation: one of the particles is taken to scatter through the classical spacetime generated by the other, which is idealized to be lightlike. The required geometries are derived in all three models; in particular, we thereby provide the first explicit asymptotically flat solution generated by a localized source in TMG. In contrast to $D$=4, the metrics are not uniquely specified, at least by naive asymptotic requirements -- an indeterminacy mirrored in the scattering amplitudes. The eikonal approach does provide a unique choice, however. We also discuss the discontinuities that arise upon taking the limits, at the level of the solutions, from TMG to its constituents, and compare with the analogous topologically massive vector gauge field models.Comment: 20 pages, preprint BRX TH--337, DAMTP R93/5, ADP-93-204/M1

Data-driven simulation and characterisation of gold nanoparticle melting

The simulation and analysis of the thermal stability of nanoparticles, a stepping stone towards their application in technological devices, require fast and accurate force fields, in conjunction with effective characterisation methods. In this work, we develop efficient, transferable, and interpretable machine learning force fields for gold nanoparticles based on data gathered from Density Functional Theory calculations. We use them to investigate the thermodynamic stability of gold nanoparticles of different sizes (1 to 6 nm), containing up to 6266 atoms, concerning a solid-liquid phase change through molecular dynamics simulations. We predict nanoparticle melting temperatures in good agreement with available experimental data. Furthermore, we characterize the solid-liquid phase change mechanism employing an unsupervised learning scheme to categorize local atomic environments. We thus provide a data-driven definition of liquid atomic arrangements in the inner and surface regions of a nanoparticle and employ it to show that melting initiates at the outer layers

Lightlike infinity in GCA models of Spacetime

This paper discusses a 7 dimensional conformal geometric algebra model for spacetime based on the notion that spacelike and timelike infinities are distinct. I show how naturally of the dimensions represents the lightlike infinity and appears redundant in computations, yet usefull in interpretationComment: 12 page

Uso de extrato aquoso e óleo de eucaliptos no controle de fungos fitopatogênicos in vitro.

Resumo

Efficacy of non-immersive virtual reality-based telerehabilitation on postural stability in Parkinson's disease: a multicenter randomized controlled trial

BACKGROUND: The implementation of regular prolonged, and effective rehabilitation in people with Parkinson's disease is essential for ensuring a good quality of life. However, the continuity of rehabilitation care may find barriers related to economic, geographic, and social issues. In these scenarios, telerehabilitation could be a possible solution to guarantee the continuity of care. AIM: To investigate the efficacy of non-immersive virtual reality-based telerehabilitation on postural stability in people with Parkinson's disease, compared to at-home self-administered structured conventional motor activities. DESIGN: Multicenter randomized controlled trial. SETTING: Five rehabilitation hospitals of the Italian Neuroscience and Rehabilitation Network. POPULATION: Individuals diagnosed with Parkinson's disease. METHODS: Ninety-seven participants were randomized into two groups: 49 in the telerehabilitation group (non-immersive virtual reality-based telerehabilitation) and 48 in the control group (at-home self-administered structured conventional motor activities). Both treatments lasted 30 sessions (3-5 days/week for, 6-10 weeks). Static and dynamic balance, gait, and functional motor outcomes were registered before and after the treatments. RESULTS: All participants improved the outcomes at the end of the treatments. The primary outcome (mini-Balance Evaluation Systems Test) registered a greater significant improvement in the telerehabilitation group than in the control group. The gait and endurance significantly improved in the telerehabilitation group only, with significant within-group and between-group differences. CONCLUSIONS: Our results showed that non-immersive virtual reality-based telerehabilitation is feasible, improves static and dynamic balance, and is a reasonably valuable alternative for reducing postural instability in people with Parkinson's disease. CLINICAL REHABILITATION IMPACT: Non-immersive virtual reality-based telerehabilitation is an effective and well-tolerated modality of rehabilitation which may help to improve access and scale up rehabilitation services as suggested by the World Health Organization's Rehabilitation 2030 agenda

DNA Electrophoretic Migration Patterns Change after Exposure of Jurkat Cells to a Single Intense Nanosecond Electric Pulse

Intense nanosecond pulsed electric fields (nsPEFs) interact with cellular membranes and intracellular structures. Investigating how cells respond to nanosecond pulses is essential for a) development of biomedical applications of nsPEFs, including cancer therapy, and b) better understanding of the mechanisms underlying such bioelectrical effects. In this work, we explored relatively mild exposure conditions to provide insight into weak, reversible effects, laying a foundation for a better understanding of the interaction mechanisms and kinetics underlying nsPEF bio-effects. In particular, we report changes in the nucleus of Jurkat cells (human lymphoblastoid T cells) exposed to single pulses of 60 ns duration and 1.0, 1.5 and 2.5 MV/m amplitudes, which do not affect cell growth and viability. A dose-dependent reduction in alkaline comet-assayed DNA migration is observed immediately after nsPEF exposure, accompanied by permeabilization of the plasma membrane (YO-PRO-1 uptake). Comet assay profiles return to normal within 60 minutes after pulse delivery at the highest pulse amplitude tested, indicating that our exposure protocol affects the nucleus, modifying DNA electrophoretic migration patterns