Epicycles and Poincar\'{e} Resonances in General Relativity

The method of geodesic deviations provides analytic approximations to geodesics in arbitrary background space-times. As such the method is a useful tool in many practical situations. In this note we point out some subtleties in the application of the method related to secular motions, in first as well as in higher order. In particular we work out the general second-order contribution to bound orbits in Schwarzschild space-time and show that it provides very good analytical results all the way up to the innermost stable circular orbit.Comment: 24 pages, 4 figure

GRAIL, an omni-directional gravitational wave detector

A cryogenic spherical and omni-directional resonant-mass detector proposed by the GRAIL collaboration is described.Comment: 5 pages, 4 figs., contribution to proceedings GW Data Analysis Workshop, Paris, nov. 199

Dynamics of (SUSY) AdS Space Isometry Breaking

Actions governing the dynamics of the Nambu-Goldstone modes resulting from the spontaneous breaking of the SO(4,2) and $SU(2,2|1)$ isometries of five dimensional anti-de Sitter space ($AdS_{5}$) and SUSY $AdS_{5}\times S_1$ spaces respectively due to a restriction of the motion to embedded four dimensional $AdS_{4}$ space and four dimensional Minkowski space ($M_4$) probe branes are presented. The dilatonic Nambu-Goldstone mode governing the motion of the $M_4$ space probe brane into the covolume of the SUSY $AdS_5\times S_1$ space is found to be unstable. No such instablility appears in the other cases. Gauging these symmetries leads to an Einstein-Hilbert action containing, in addition to the gravitational vierbein, a massive Abelian vector field coupled to gravity.Comment: 6 pages, 0 figures, to appear in Proceedings of IRGAC 2006: 2nd International Conference on Quantum Theories and Renormalization Group in Gravity and Cosmology, Barcelon

Visualization of Frequent Itemsets with Nested Circular Layout and Bundling Algorithm

International audienceFrequent itemset mining is one of the major data mining issues. Once generated by algorithms, the itemsets can be automatically processed, for instance to extract association rules. They can also be explored with visual tools, in order to analyze the emerging patterns. Graphical itemsets representation is a convenient way to obtain an overview of the global interaction structure. However, when the complexity of the database increases, the network may become unreadable. In this paper, we propose to display itemsets on concentric circles, each one being organized to lower the intricacy of the graph through an optimization process. Thanks to a graph bundling algorithm, we finally obtain a compact representation of a large set of itemsets that is easier to exploit. Colors accumulation and interaction operators facilitate the exploration of the new bundle graph and to illustrate how much an itemset is supported by the data

Supersymmetry and discrete transformations of the Dirac operators in Taub-NUT geometry

It is shown that the N=4 superalgebra of the Dirac theory in Taub-NUT space has different unitary representations related among themselves through unitary U(2) transformations. In particular the SU(2) transformations are generated by the spin-like operators constructed with the help of the same covariantly constant Killing-Yano tensors which generate Dirac-type operators. A parity operator is defined and some explicit transformations which connect the Dirac-type operators among themselves are given. These transformations form a discrete group which is a realization of the quaternion discrete group. The fifth Dirac operator constructed using the non-covariant Killing-Yano tensor of the Taub-NUT space is quite special. This non-standard Dirac operator is connected with the hidden symmetry and is not equivalent to the Dirac-type operators of the standard N=4 supersymmetry.Comment: 14 pages, latex, no figure

Nonrelativistic Chern-Simons Vortices on the Torus

A classification of all periodic self-dual static vortex solutions of the Jackiw-Pi model is given. Physically acceptable solutions of the Liouville equation are related to a class of functions which we term Omega-quasi-elliptic. This class includes, in particular, the elliptic functions and also contains a function previously investigated by Olesen. Some examples of solutions are studied numerically and we point out a peculiar phenomenon of lost vortex charge in the limit where the period lengths tend to infinity, that is, in the planar limit.Comment: 25 pages, 2+3 figures; improved exposition, corrected typos, added one referenc

On minimal coupling of the ABC-superparticle to supergravity background

By rigorous application of the Hamiltonian methods we show that the ABC-formulation of the Siegel superparticle admits consistent minimal coupling to external supergravity. The consistency check proves to involve all the supergravity constraints.Comment: 8 pages RevTex file, to appear in Phys. Rev.

Radiation reaction and renormalization in classical electrodynamics of point particle in any dimension

The effective equations of motion for a point charged particle taking account of radiation reaction are considered in various space-time dimensions. The divergencies steaming from the pointness of the particle are studied and the effective renormalization procedure is proposed encompassing uniformly the cases of all even dimensions. It is shown that in any dimension the classical electrodynamics is a renormalizable theory if not multiplicatively beyond d=4. For the cases of three and six dimensions the covariant analogs of the Lorentz-Dirac equation are explicitly derived.Comment: minor changes in concluding section, misprints corrected, LaTeX2e, 15 page

Chiral gravity as a covariant formulation of massive gravity

We present a covariant nonlinear completion of the Fierz-Pauli (FP) mass term for the graviton. The starting observation is that the FP mass is immediately obtained by expanding the cosmological constant term, i.e. the determinant of the vielbein, around Minkowski space to second order in the vielbein perturbations. Since this is an unstable expansion in the standard case, we consider an extended theory of gravity which describes two vielbeins that give rise to chiral spin--connections (consequently, fermions of a definite chirality only couple to one of the gravitational sectors). As for Einstein gravity with a cosmological constant, a single fine-tuning is needed to recover a Minkowski background; the two sectors then differ only by a constant conformal factor. The spectrum of this theory consists of a massless and a massive graviton, with FP mass term. The theory possesses interesting limits in which only the massive graviton is coupled to matter at the linearized level.Comment: 1+16 pages LaTeX, typos corrected, and some references adde