Symmetry, singularities and integrability in complex dynamics III: approximate symmetries and invariants

The different natures of approximate symmetries and their corresponding first integrals/invariants are delineated in the contexts of both Lie symmetries of ordinary differential equations and Noether symmetries of the Action Integral. Particular note is taken of the effect of taking higher orders of the perturbation parameter. Approximate symmetries of approximate first integrals/invariants and the problems of calculating them using the Lie method are considered

Diffeomorphisms, Noether Charges and Canonical Formalism in 2D Dilaton Gravity

We carry out a parallel study of the covariant phase space and the conservation laws of local symmetries in two-dimensional dilaton gravity. Our analysis is based on the fact that the Lagrangian can be brought to a form that vanishes on-shell giving rise to a well-defined covariant potential for the symplectic current. We explicitly compute the symplectic structure and its potential and show that the requirement to be finite and independent of the Cauchy surface restricts the asymptotic symmetries.Comment: 14 pages, latex with psfig macro, one figur

The Quantum States and the Statistical Entropy of the Charged Black Hole

We quantize the Reissner-Nordstr\"om black hole using an adaptation of Kucha\v{r}'s canonical decomposition of the Kruskal extension of the Schwarzschild black hole. The Wheeler-DeWitt equation turns into a functional Schroedinger equation in Gaussian time by coupling the gravitational field to a reference fluid or dust. The physical phase space of the theory is spanned by the mass, $M$, the charge, $Q$, the physical radius, $R$, the dust proper time, $\tau$, and their canonical momenta. The exact solutions of the functional Schroedinger equation imply that the difference in the areas of the outer and inner horizons is quantized in integer units. This agrees in spirit, but not precisely, with Bekenstein's proposal on the discrete horizon area spectrum of black holes. We also compute the entropy in the microcanonical ensemble and show that the entropy of the Reissner-Nordstr\"om black hole is proportional to this quantized difference in horizon areas.Comment: 31 pages, 3 figures, PHYZZX macros. Comments on the wave-functional in the interior and one reference added. To appear in Phys. Rev.

Gauging kinematical and internal symmetry groups for extended systems: the Galilean one-time and two-times harmonic oscillators

The possible external couplings of an extended non-relativistic classical system are characterized by gauging its maximal dynamical symmetry group at the center-of-mass. The Galilean one-time and two-times harmonic oscillators are exploited as models. The following remarkable results are then obtained: 1) a peculiar form of interaction of the system as a whole with the external gauge fields; 2) a modification of the dynamical part of the symmetry transformations, which is needed to take into account the alteration of the dynamics itself, induced by the {\it gauge} fields. In particular, the Yang-Mills fields associated to the internal rotations have the effect of modifying the time derivative of the internal variables in a scheme of minimal coupling (introduction of an internal covariant derivative); 3) given their dynamical effect, the Yang-Mills fields associated to the internal rotations apparently define a sort of Galilean spin connection, while the Yang-Mills fields associated to the quadrupole momentum and to the internal energy have the effect of introducing a sort of dynamically induced internal metric in the relative space.Comment: 32 pages, LaTex using the IOP preprint macro package (ioplppt.sty available at: http://www.iop.org/). The file is available at: http://www.fis.unipr.it/papers/1995.html The file is a uuencoded tar gzip file with the IOP preprint style include

Quasigroups, Asymptotic Symmetries and Conservation Laws in General Relativity

A new quasigroup approach to conservation laws in general relativity is applied to study asymptotically flat at future null infinity spacetime. The infinite-parametric Newman-Unti group of asymptotic symmetries is reduced to the Poincar\'e quasigroup and the Noether charge associated with any element of the Poincar\'e quasialgebra is defined. The integral conserved quantities of energy-momentum and angular momentum are linear on generators of Poincar\'e quasigroup, free of the supertranslation ambiguity, posess the flux and identically equal to zero in Minkowski spacetime.Comment: RevTeX4, 5 page

Comprehensive feature selection for classifying the treatment outcome of high-intensity ultrasound therapy in uterine fibroids

The study aim was to utilise multiple feature selection methods in order to select the most important parameters from clinical patient data for high-intensity focused ultrasound (HIFU) treatment outcome classification in uterine fibroids. The study was retrospective using patient data from 66 HIFU treatments with 89 uterine fibroids. A total of 39 features were extracted from the patient data and 14 different filter-based feature selection methods were used to select the most informative features. The selected features were then used in a support vector classification (SVC) model to evaluate the performance of these parameters in predicting HIFU therapy outcome. The therapy outcome was defined as non-perfused volume (NPV) ratio in three classes: 80%. The ten most highly ranked features in order were: fibroid diameter, subcutaneous fat thickness, fibroid volume, fibroid distance, Funaki type I, fundus location, gravidity, Funaki type III, submucosal fibroid type and urinary symptoms. The maximum F1-micro classification score was 0.63 using the top ten features from Mutual Information Maximisation (MIM) and Joint Mutual Information (JMI) feature selection methods. Classification performance of HIFU therapy outcome prediction in uterine fibroids is highly dependent on the chosen feature set which should be determined prior using different classifiers

The Raychaudhuri equations: a brief review

We present a brief review on the Raychaudhuri equations. Beginning with a summary of the essential features of the original article by Raychaudhuri and subsequent work of numerous authors, we move on to a discussion of the equations in the context of alternate non--Riemannian spacetimes as well as other theories of gravity, with a special mention on the equations in spacetimes with torsion (Einstein--Cartan--Sciama--Kibble theory). Finally, we give an overview of some recent applications of these equations in General Relativity, Quantum Field Theory, String Theory and the theory of relativisitic membranes. We conclude with a summary and provide our own perspectives on directions of future research.Comment: 35 pages, two figures, to appear in the special issue of Pramana dedicated to the memory of A. K. Raychaudhur

Holography in asymptotically flat space-times and the BMS group

In a previous paper (hep-th/0306142) we have started to explore the holographic principle in the case of asymptotically flat space-times and analyzed in particular different aspects of the Bondi-Metzner-Sachs (BMS) group, namely the asymptotic symmetry group of any asymptotically flat space-time. We continue this investigation in this paper. Having in mind a S-matrix approach with future and past null infinity playing the role of holographic screens on which the BMS group acts, we connect the IR sectors of the gravitational field with the representation theory of the BMS group. We analyze the (complicated) mapping between bulk and boundary symmetries pointing out differences with respect to the AdS/CFT set up. Finally we construct a BMS phase space and a free hamiltonian for fields transforming w.r.t BMS representations. The last step is supposed to be an explorative investigation of the boundary data living on the degenerate null manifold at infinity.Comment: 31 pages, several changes in section 3 and 7 and references update

Energy and decay width of the pi-K atom

The energy and decay width of the pi-K atom are evaluated in the framework of the quasipotential-constraint theory approach. The main electromagnetic and isospin symmetry breaking corrections to the lowest-order formulas for the energy shift from the Coulomb binding energy and for the decay width are calculated. They are estimated to be of the order of a few per cent. We display formulas to extract the strong interaction S-wave pi-K scattering lengths from future experimental data concerning the pi-K atom.Comment: 37 pages, 5 figures, uses Axodra

Relativistic quantum clocks

The conflict between quantum theory and the theory of relativity is exemplified in their treatment of time. We examine the ways in which their conceptions differ, and describe a semiclassical clock model combining elements of both theories. The results obtained with this clock model in flat spacetime are reviewed, and the problem of generalizing the model to curved spacetime is discussed, before briefly describing an experimental setup which could be used to test of the model. Taking an operationalist view, where time is that which is measured by a clock, we discuss the conclusions that can be drawn from these results, and what clues they contain for a full quantum relativistic theory of time.Comment: 12 pages, 4 figures. Invited contribution for the proceedings for "Workshop on Time in Physics" Zurich 201