Modular smoothed analysis of median-of-three Quicksort

Spielman’s smoothed complexity - a hybrid between worst and average case complexity measures - relies on perturbations of input instances to determine where average-case behavior turns to worst-case. This approach simplifies the smoothed analysis and achieves greater precession in the expression of the smoothed complexity, where a recurrence equation is obtained as opposed to bounds. Moreover, the approach addresses, in this context, the formation of input instances–an open problem in smoothed complexity. In [23], we proposed a method supporting modular smoothed analysis and illustrated the method by determining the modular smoothed complexity of Quicksort. Here, we use the modular approach to calculate the median of three variant and compare these results with those in [23]

Simple Current Actions of Cyclic Groups

Permutation actions of simple currents on the primaries of a Rational Conformal Field Theory are considered in the framework of admissible weighted permutation actions. The solution of admissibility conditions is presented for cyclic quadratic groups: an irreducible WPA corresponds to each subgroup of the quadratic group. As a consequence, the primaries of a RCFT with an order n integral or half-integral spin simple current may be arranged into multiplets of length k^2 (where k is a divisor of n) or 3k^2 if the spin of the simple current is half-integral and k is odd.Comment: Added reference, minor change

Verkenning van mogelijkheden voor mosselteelt op Noordzee

In dit rapport wordt nagegaan of er wereldwijd zodanig perspectiefrijke experimenten met invang dan wel kweek van mosselen in het open zee milieu (offshore) plaatsvinden, of dat er reeds volledig commercieel draaiende mosselculturen op open zee bestaan. Indien dit het geval is wordt bezien of hiervan gebruik kan worden gemaakt voor de innovatie van de Nederlandse mosselsector. Wij achten de studies het meest relevant voor het toepassen van installaties als de fysische omstandigheden (diepte, golfhoogte en stroomsnelheid) zoveel als mogelijk overeenkomen met die in de Noordzee

On Representations of Conformal Field Theories and the Construction of Orbifolds

We consider representations of meromorphic bosonic chiral conformal field theories, and demonstrate that such a representation is completely specified by a state within the theory. The necessary and sufficient conditions upon this state are derived, and, because of their form, we show that we may extend the representation to a representation of a suitable larger conformal field theory. In particular, we apply this procedure to the lattice (FKS) conformal field theories, and deduce that Dong's proof of the uniqueness of the twisted representation for the reflection-twisted projection of the Leech lattice conformal field theory generalises to an arbitrary even (self-dual) lattice. As a consequence, we see that the reflection-twisted lattice theories of Dolan et al are truly self-dual, extending the analogies with the theories of lattices and codes which were being pursued. Some comments are also made on the general concept of the definition of an orbifold of a conformal field theory in relation to this point of view.Comment: 11 pages, LaTeX. Updated references and added preprint n

Modular smoothed analysis

Spielman’s smoothed complexity - a hybrid between worst and average case complexity measures - relies on perturbations of input instances to determine where average-case behavior turns to worst-case. The paper proposes a method supporting modular smoothed analysis. The method, involving a novel permutation model, is developed for the discrete case, focusing on randomness preserving algorithms. This approach simplifies the smoothed analysis and achieves greater precession in the expression of the smoothed complexity, where a recurrence equation is obtained as opposed to bounds. Moreover, the approach addresses, in this context, the formation of input instances–an open problem in smoothed complexity. To illustrate the method, we determine the modular smoothed complexity of Quicksort

Poincare Polynomials and Level Rank Dualities in the N=2N=2 Coset Construction

We review the coset construction of conformal field theories; the emphasis is on the construction of the Hilbert spaces for these models, especially if fixed points occur. This is applied to the $N=2$ superconformal cosets constructed by Kazama and Suzuki. To calculate heterotic string spectra we reformulate the Gepner con- struction in terms of simple currents and introduce the so-called extended Poincar\'e polynomial. We finally comment on the various equivalences arising between models of this class, which can be expressed as level rank dualities. (Invited talk given at the III. International Conference on Mathematical Physics, String Theory and Quantum Gravity, Alushta, Ukraine, June 1993. To appear in Theor. Math. Phys.)Comment: 14 pages in LaTeX, HD-THEP-93-4