Probing negative-dimensional integration: Two-loop covariant vertex and one-loop light-cone integrals

The negative-dimensional integration method (NDIM) seems to be a very promising technique for evaluating massless and/or massive Feynman diagrams. It is unique in the sense that the method gives solutions in different regions of external momenta simultaneously. Moreover, it is a technique whereby the difficulties associated with performing parametric integrals in the standard approach are transferred to a simpler solving of a system of linear algebraic equations, thanks to the polynomial character of the relevant integrands. We employ this method to evaluate a scalar integral for a massless two-loop three-point vertex with all the external legs off-shell, and consider several special cases for it, yielding results, even for distinct simpler diagrams. We also consider the possibility of NDIM in non-covariant gauges such as the light-cone gauge and do some illustrative calculations, showing that for one-degree violation of covariance (i.e. one external, gauge-breaking, light-like vector n μ) the ensuing results are concordant with the ones obtained via either the usual dimensional regularization technique, or the use of the principal value prescription for the gauge-dependent pole, while for two-degree violation of covariance - i.e. two external, light-like vectors n μ, the gauge-breaking one, and (its dual) n * μ - the ensuing results are concordant with the ones obtained via causal constraints or the use of the so-called generalized Mandelstam-Leibbrandt prescription. © 1999 Elsevier Science B.V.

Massive superstring vertex operator in D = 10 superspace

Using the pure spinor formalism for the superstring, the vertex operator for the first massive states of the open superstring is constructed in a manifestly super-Poincaré covariant manner. This vertex operator describes a massive spin-two multiplet in terms of ten-dimensional superfields. © SISSA/ISAS 2002.

A Markov random field model for combining optimum-path forest classifiers using decision graphs and game strategy approach

The research on multiple classifiers systems includes the creation of an ensemble of classifiers and the proper combination of the decisions. In order to combine the decisions given by classifiers, methods related to fixed rules and decision templates are often used. Therefore, the influence and relationship between classifier decisions are often not considered in the combination schemes. In this paper we propose a framework to combine classifiers using a decision graph under a random field model and a game strategy approach to obtain the final decision. The results of combining Optimum-Path Forest (OPF) classifiers using the proposed model are reported, obtaining good performance in experiments using simulated and real data sets. The results encourage the combination of OPF ensembles and the framework to design multiple classifier systems. © 2011 Springer-Verlag.

Probing the infraed behavior of the ghost-gluon vertex in quantum chromodynamics

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A construction of integrated vertex operator in the pure spinor sigma-model in AdS(5) x S-5

Vertex operators in string theory me in two varieties: integrated and unintegrated. Understanding both types is important for the calculation of the string theory amplitudes. The relation between them is a descent procedure typically involving the b-ghost. In the pure spinor formalism vertex operators can be identified as cohomology classes of an infinite-dimensional Lie superalgebra formed by covariant derivatives. We show that in this language the construction of the integrated vertex from an unintegrated vertex is very straightforward, and amounts to the evaluation of the cocycle on the generalized Lax currents.

Correspondence between the one-loop three-point vertex and the Y and Delta electric resistor networks

Different mathematical methods have been applied to obtain the analytic result for the massless triangle Feynman diagram yielding a sum of four linearly independent (LI) hypergeometric functions of two variables F-4. This result is not physically acceptable when it is embedded in higher loops, because all four hypergeometric functions in the triangle result have the same region of convergence and further integration means going outside those regions of convergence. We could go outside those regions by using the well-known analytic continuation formulas obeyed by the F-4, but there are at least two ways we can do this. Which is the correct one? Whichever continuation one uses, it reduces a number of F-4 from four to three. This reduction in the number of hypergeometric functions can be understood by taking into account the fundamental physical constraint imposed by the conservation of momenta flowing along the three legs of the diagram. With this, the number of overall LI functions that enter the most general solution must reduce accordingly. It remains to determine which set of three LI solutions needs to be taken. To determine the exact structure and content of the analytic solution for the three-point function that can be embedded in higher loops, we use the analogy that exists between Feynman diagrams and electric circuit networks, in which the electric current flowing in the network plays the role of the momentum flowing in the lines of a Feynman diagram. This analogy is employed to define exactly which three out of the four hypergeometric functions are relevant to the analytic solution for the Feynman diagram. The analogy is built based on the equivalence between electric resistance circuit networks of types Y and Delta in which flows a conserved current. The equivalence is established via the theorem of minimum energy dissipation within circuits having these structures.

Unsupervised manifold learning using Reciprocal kNN Graphs in image re-ranking and rank aggregation tasks

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Description and performance of track and primary-vertex reconstruction with the CMS tracker

A description is provided of the software algorithms developed for the CMS tracker both for reconstructing charged-particle trajectories in proton-proton interactions and for using the resulting tracks to estimate the positions of the LHC luminous region and individual primary-interaction vertices. Despite the very hostile environment at the LHC, the performance obtained with these algorithms is found to be excellent. For t (t) over bar events under typical 2011 pileup conditions, the average track-reconstruction efficiency for promptly-produced charged particles with transverse momenta of p(T) > 0.9GeV is 94% for pseudorapidities of vertical bar eta vertical bar < 0.9 and 85% for 0.9 < vertical bar eta vertical bar < 2.5. The inefficiency is caused mainly by hadrons that undergo nuclear interactions in the tracker material. For isolated muons, the corresponding efficiencies are essentially 100%. For isolated muons of p(T) = 100GeV emitted at vertical bar eta vertical bar < 1.4, the resolutions are approximately 2.8% in p(T), and respectively, 10 m m and 30 mu m in the transverse and longitudinal impact parameters. The position resolution achieved for reconstructed primary vertices that correspond to interesting pp collisions is 10-12 mu m in each of the three spatial dimensions. The tracking and vertexing software is fast and flexible, and easily adaptable to other functions, such as fast tracking for the trigger, or dedicated tracking for electrons that takes into account bremsstrahlung.

Caracterização topológica dos motivos das redes biológicas integradas da Escherichia coli e da Saccharomyces cerevisiae

The reducionism method has helped in the clari cation of functioning of many biological process. However, such process are extremely complex and have emergent properties that can not be explained or even predicted by reducionism methods. To overcome these limits, researchers have been used a set of methods known as systems biology, a new area of biology aiming to understand the interactions between the multiple components of biological processes. These interactions can be represented by a mathematical object called graph or network, where the interacting elements are represented by a vertex and the interactions by edges that connect a pair of vertexes. Into graphs it is possible to nd subgraphs, occurring in complex networks at numbers that are signi cantly higher than those in randomized networks, they are de ned as motifs. As motifs in biological networks may represent the structural units of biological processess, their detection is important. Therefore, the aim of this present work was detect, count and classify motifs present in biological integrated networks of bacteria Escherichia coli and yeast Saccharomyces cere- visiae. For this purpose, we implemented codes in MathematicaR and Python environments for detecting, counting and classifying motifs in these networks. The composition and types of motifs detected in these integrated networks indicate that such networks are organized in three main bridged modules composed by motifs in which edges are all the same type. The connecting bridges are composed by motifs in which the types of edges are diferent

Open-closed superstring amplitudes using vertex operators in AdS5xS5

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Open-closed superstring amplitudes using vertex operators in AdS(5) x S-5

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)