Triangular curves and cyclotomic Zariski tuples

The purpose of this paper is to exhibit infinite families of conjugate projective curves in a number field whose complement have the same abelian fundamental group, but are non-homeomorphic. In particular, for any $d>3$ we find Zariski tuples parametrized by the $d$-roots of unity up to complex conjugation. As a consequence, for any divisor $m$ of $d$, $m\neq 1,2,3,4,6$, we find arithmetic Zariski $\frac{\phi(m)}{2}$-tuples with coefficients in the corresponding cyclotomic field. These curves have abelian fundamental group and they are distinguished using a linking invariant.Comment: 15 pages, 3 figures. To appear in Collectanea Mathematic

SL: a "quick and dirty" but working intermediate language for SVP systems

The CSA group at the University of Amsterdam has developed SVP, a framework to manage and program many-core and hardware multithreaded processors. In this article, we introduce the intermediate language SL, a common vehicle to program SVP platforms. SL is designed as an extension to the standard C language (ISO C99/C11). It includes primitive constructs to bulk create threads, bulk synchronize on termination of threads, and communicate using word-sized dataflow channels between threads. It is intended for use as target language for higher-level parallelizing compilers. SL is a research vehicle; as of this writing, it is the only interface language to program a main SVP platform, the new Microgrid chip architecture. This article provides an overview of the language, to complement a detailed specification available separately.Comment: 22 pages, 3 figures, 18 listings, 1 tabl

Geometric Configurations, Regular Subalgebras of E10 and M-Theory Cosmology

We re-examine previously found cosmological solutions to eleven-dimensional supergravity in the light of the E_{10}-approach to M-theory. We focus on the solutions with non zero electric field determined by geometric configurations (n_m, g_3), n\leq 10. We show that these solutions are associated with rank $g$ regular subalgebras of E_{10}, the Dynkin diagrams of which are the (line) incidence diagrams of the geometric configurations. Our analysis provides as a byproduct an interesting class of rank-10 Coxeter subgroups of the Weyl group of E_{10}.Comment: 48 pages, 27 figures, 5 tables, references added, typos correcte

Ising Model Observables and Non-Backtracking Walks

This paper presents an alternative proof of the connection between the partition function of the Ising model on a finite graph $G$ and the set of non-backtracking walks on $G$. The techniques used also give formulas for spin-spin correlation functions in terms of non-backtracking walks. The main tools used are Viennot's theory of heaps of pieces and turning numbers on surfaces.Comment: 33 pages, 11 figures. Typos and errors corrected, exposition improved, results unchange