Geometry, stochastic calculus and quantum fields in a non-commutative space-time

The algebras of non-relativistic and of classical mechanics are unstable algebraic structures. Their deformation towards stable structures leads, respectively, to relativity and to quantum mechanics. Likewise, the combined relativistic quantum mechanics algebra is also unstable. Its stabilization requires the non-commutativity of the space-time coordinates and the existence of a fundamental length constant. The new relativistic quantum mechanics algebra has important consequences on the geometry of space-time, on quantum stochastic calculus and on the construction of quantum fields. Some of these effects are studied in this paper.Comment: 36 pages Latex, 1 eps figur

Lie Superalgebra Stability and Branes

The algebra of the generators of translations in superspace is unstable, in the sense that infinitesimal perturbations of its structure constants lead to non-isomorphic algebras. We show how superspace extensions remedy this situation (after arguing that remedy is indeed needed) and review the benefits reaped in the description of branes of all kinds in the presence of the extra dimensions.Comment: Talk given at the conference ``Brane New World and Non-commutative Geometry'', held in Torino, October 2000. To appear in the proceedings by World Scientific. 10 pages, 1 figur

Exact results of the limited penetrable horizontal visibility graph associated to random time series and its application

The limited penetrable horizontal visibility algorithm is a new time analysis tool and is a further development of the horizontal visibility algorithm. We present some exact results on the topological properties of the limited penetrable horizontal visibility graph associated with random series. We show that the random series maps on a limited penetrable horizontal visibility graph with exponential degree distribution $P(k)\sim exp[-\lambda (k-2\rho-2)], \lambda = ln[(2\rho+3)/(2\rho+2)],\rho=0,1,2,...,k=2\rho+2,2\rho+3,...$, independent of the probability distribution from which the series was generated. We deduce the exact expressions of the mean degree and the clustering coefficient and demonstrate the long distance visibility property. Numerical simulations confirm the accuracy of our theoretical results. We then examine several deterministic chaotic series (a logistic map, the H$\acute{e}$non map, the Lorentz system, and an energy price chaotic system) and a real crude oil price series to test our results. The empirical results show that the limited penetrable horizontal visibility algorithm is direct, has a low computational cost when discriminating chaos from uncorrelated randomness, and is able to measure the global evolution characteristics of the real time series.Comment: 23 pages, 12 figure

Stratification of the orbit space in gauge theories. The role of nongeneric strata

Gauge theory is a theory with constraints and, for that reason, the space of physical states is not a manifold but a stratified space (orbifold) with singularities. The classification of strata for smooth (and generalized) connections is reviewed as well as the formulation of the physical space as the zero set of a momentum map. Several important features of nongeneric strata are discussed and new results are presented suggesting an important role for these strata as concentrators of the measure in ground state functionals and as a source of multiple structures in low-lying excitations.Comment: 22 pages Latex, 1 figur

Field sexual attraction in the sorghum midge, Contarinia sorghicola (Coquillett, 1899) (Diptera, Cecidomyiidae).

No campo, fêmeas da mosca do sorgo, Contarinia sorghicola (Coquillett, 1899), atraem machos da especie para o acasalamento atraves da emissao de feromonio, o que foi comprovado atraves da utilizacao de armadilhas adesivas contendo femeas virgens ou extratos destas, a nivel de campo. O periodo de maior atratividade ocorreu entre 7:30 e 8:30 horas.Suplemento