On Kahan's Rules for Determining Branch Cuts

In computer algebra there are different ways of approaching the mathematical concept of functions, one of which is by defining them as solutions of differential equations. We compare different such approaches and discuss the occurring problems. The main focus is on the question of determining possible branch cuts. We explore the extent to which the treatment of branch cuts can be rendered (more) algorithmic, by adapting Kahan's rules to the differential equation setting.Comment: SYNASC 2011. 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing. (2011

Finding low-weight polynomial multiples using discrete logarithm

Finding low-weight multiples of a binary polynomial is a difficult problem arising in the context of stream ciphers cryptanalysis. The classical algorithm to solve this problem is based on a time memory trade-off. We will present an improvement to this approach using discrete logarithm rather than a direct representation of the involved polynomials. This gives an algorithm which improves the theoretical complexity, and is also very flexible in practice

A Metric Inequality for the Thompson and Hilbert Geometries

There are two natural metrics defined on an arbitrary convex cone: Thompson's part metric and Hilbert's projective metric. For both, we establish an inequality giving information about how far the metric is from being non-positively curved.Comment: 15 pages, 0 figures. To appear in J. Inequalities Pure Appl. Mat

Consistency without concurrency control in large, dynamic systems

ABSTRACT Replicas of a commutative replicated data type (CRDT) eventually converge without any complex concurrency control. We validate the design of a non-trivial CRDT, a replicated sequence, with performance measurements in the context of Wikipedia. Furthermore, we discuss how to eliminate a remaining scalability bottleneck: Whereas garbage collection previously required a system-wide consensus, here we propose a flexible two-tier architecture and a protocol for migrating between tiers. We also discuss how the CRDT concept can be generalised, and its limitations