The Rank four Heterotic Modular Invariant Partition Functions

In this paper, we develop several general techniques to investigate modular invariants of conformal field theories whose algebras of the holomorphic and anti-holomorphic sectors are different. As an application, we find all such ``heterotic'' WZNW physical invariants of (horizontal) rank four: there are exactly seven of these, two of which seem to be new. Previously, only those of rank $\le 3$ have been completely classified. We also find all physical modular invariants for $su(2)_{k_1}\times su(2)_{k_2}$, for $22>k_1>k_2$, and $k_1=28$, $k_2<22$, completing the classification of ref.{} \SUSU.Comment: 25 pp., plain te

Detecting Similarity of Rational Plane Curves

A novel and deterministic algorithm is presented to detect whether two given rational plane curves are related by means of a similarity, which is a central question in Pattern Recognition. As a by-product it finds all such similarities, and the particular case of equal curves yields all symmetries. A complete theoretical description of the method is provided, and the method has been implemented and tested in the Sage system for curves of moderate degrees.Comment: 22 page

Exceptional knot homology

The goal of this article is twofold. First, we find a natural home for the double affine Hecke algebras (DAHA) in the physics of BPS states. Second, we introduce new invariants of torus knots and links called "hyperpolynomials" that address the "problem of negative coefficients" often encountered in DAHA-based approaches to homological invariants of torus knots and links. Furthermore, from the physics of BPS states and the spectra of singularities associated with Landau-Ginzburg potentials, we also describe a rich structure of differentials that act on homological knot invariants for exceptional groups and uniquely determine the latter for torus knots.Comment: 44 pages, 4 figure

Summary-based inference of quantitative bounds of live heap objects

This article presents a symbolic static analysis for computing parametric upper bounds of the number of simultaneously live objects of sequential Java-like programs. Inferring the peak amount of irreclaimable objects is the cornerstone for analyzing potential heap-memory consumption of stand-alone applications or libraries. The analysis builds method-level summaries quantifying the peak number of live objects and the number of escaping objects. Summaries are built by resorting to summaries of their callees. The usability, scalability and precision of the technique is validated by successfully predicting the object heap usage of a medium-size, real-life application which is significantly larger than other previously reported case-studies.Fil: Braberman, Victor Adrian. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Garbervetsky, Diego David. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Hym, Samuel. Universite Lille 3; FranciaFil: Yovine, Sergio Fabian. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin