Open String Field Theory around Universal Solutions

We study the physical spectrum of cubic open string field theory around universal solutions, which are constructed using the matter Virasoro operators and the ghost and anti-ghost fields. We find the cohomology of the new BRS charge around the solutions, which appear with a ghost number that differs from that of the original theory. Considering the gauge-unfixed string field theory, we conclude that open string excitations perturbatively disappear after the condensation of the string field to the solutions.Comment: 14 pages, LaTeX with ptptex.cls, typos correcte

Regularization of identity based solution in string field theory

We demonstrate that an Erler-Schnabl type solution in cubic string field theory can be naturally interpreted as a gauge invariant regularization of an identity based solution. We consider a solution which interpolates between an identity based solution and ordinary Erler-Schnabl one. Two gauge invariant quantities, the classical action and the closed string tadpole, are evaluated for finite value of the gauge parameter. It is explicitly checked that both of them are independent of the gauge parameter.Comment: 9 pages, minor typos corrected and references adde

Computationally efficient algorithms for the two-dimensional Kolmogorov-Smirnov test

Goodness-of-fit statistics measure the compatibility of random samples against some theoretical or reference probability distribution function. The classical one-dimensional Kolmogorov-Smirnov test is a non-parametric statistic for comparing two empirical distributions which defines the largest absolute difference between the two cumulative distribution functions as a measure of disagreement. Adapting this test to more than one dimension is a challenge because there are 2^d-1 independent ways of ordering a cumulative distribution function in d dimensions. We discuss Peacock's version of the Kolmogorov-Smirnov test for two-dimensional data sets which computes the differences between cumulative distribution functions in 4n^2 quadrants. We also examine Fasano and Franceschini's variation of Peacock's test, Cooke's algorithm for Peacock's test, and ROOT's version of the two-dimensional Kolmogorov-Smirnov test. We establish a lower-bound limit on the work for computing Peacock's test of Omega(n^2.lg(n)), introducing optimal algorithms for both this and Fasano and Franceschini's test, and show that Cooke's algorithm is not a faithful implementation of Peacock's test. We also discuss and evaluate parallel algorithms for Peacock's test