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

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

Deterministic model to evaluate the impact of lactational treatment of subclinical mastitis due to coagulase-negative staphylococci

Coagulase-negative staphylococci (CNS) are the most frequently isolated bacteria from milk samples in several studies worldwide. Despite their relative frequency, specific measures aiming at their control are not well established. One possible measure to include in a control programme is lactational antimicrobial treatment. The decision to perform such treatment, as well as other actions on farm, should be based on the likelihood of financial return. A deterministic model was used to evaluate whether performing an antimicrobial treatment during the lactation for quarters infected with CNS was financially justifiable. Input variables for the impact of CNS on udder health were based on a previous study by the same authors and on available literature on the subject. Prices included in the model were based on 2009/2010 conditions in Portugal. The average result per antimicrobial treated quarter was a net loss of (sic)38.74. Performing a sensitivity analysis to evaluate how systematic variation of the input variables of the model would lead to outcome changes showed that variation in input variables nearly always led to a negative outcome, with the greatest variation in losses observed for variation in the length of treatment and milk withdrawal period (-(sic)46.26 to -(sic)28.49). The situations in which a net benefit was to be expected included the bulk tank somatic cell count decreasing to a level corresponding to a premium payment or to penalties being avoided, and the prevention of transmission of CNS in the milking parlour when the possibility of transmission was at its highest level. For most situations, lactational treatment of CNS subclinical mastitis was not financially justifiable

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