We provide the operations of matrix addition, multiplication, transposition, and matrix comparisons as executable functions over ordered semirings. Moreover, it is proven that strongly normalizing (monotone) orders can be lifted to strongly normalizing (monotone) orders over matrices. We further show that the standard semirings over the naturals, integers, and rationals, as well as the arctic s...

We prove cocompleteness of the category of CASL signatures , of monotone signatures, of strongly regular signatures and of strongly locally ltered signatures. This shows that using these signature categories is compatible with a pushout or colimit based module system.

In this paper, we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive nonself-mapping and the set of solutions of the variational inequality for an inversestrongly-monotone mapping in a Hilbert space. Then we show that the sequence converges strongly to a common element of two sets. Using this result, we consider the problem of finding a commo...

The subject of this paper is Modal μ-Calculus, an extension of Modal Logic with operators for least and greatest fixpoints of monotone functions on sets. This logic, introduced by Kozen in [17], is a powerful formalism capable of expressing inductive as well as coinductive concepts and beyond (e.g. safety, liveness, fairness, termination, etc.) and is widely used in the area of verification of ...

Two classes of distributions that are widely used in the analysis of Bayesian auctions are the Monotone Hazard Rate (MHR) and Regular distributions. They can both be characterized in terms of the rate of change of the associated virtual value functions: for MHR distributions the condition is that for values v < v, φ(v) − φ(v) ≥ v − v, and for regular distributions, φ(v) − φ(v) ≥ 0. Cole and Rou...

Recently, there has been considerable interest in efficiently computing strongly correlated pairs in large databases. Most previous studies require the specification of a minimum correlation threshold to perform the computation. However, it may be difficult for users to provide an appropriate threshold in practice, since different data sets typically have different characteristics. To this end,...