The down operator and expansions of near rectangular k-Schur functions

We prove that the Lam-Shimozono "down operator" on the affine Weyl group induces a derivation of the affine Fomin-Stanley subalgebra of the affine nilCoxeter algebra. We use this to verify a conjecture of Berg, Bergeron, Pon and Zabrocki describing the expansion of k-Schur functions of "near rectangles" in the affine nilCoxeter algebra. Consequently, we obtain a combinatorial interpretation of the corresponding k-Littlewood--Richardson coefficients

Advanced Design Concepts for Open Distributed Systems Development

Experience with the engineering of large scale open distributed systems has shown that their design should be specified at several well-defined levels of abstraction, in which each level aims at satisfying specific user, architectural, and implementation needs. Therefore, designers should dispose of a comprehensive design methodology, which allows them to conceive a specification at a certain abstraction level and transform this specification into a conforming specification at a lower abstraction level. The collection of these transformations should abridge the total design trajectory from initial user requirements to final implementation. The authors present and discuss some advanced design concepts that provide a basis for such a design methodolog

What makes industries believe in formal methods

The introduction of formal methods in the design and development departments of an industrial company has far reaching and long lasting consequences. In fact it changes the whole environment of methods, tools and skills that determine the design culture of that company. A decision to replace current design practice by formal methods, therefore, appears a vital one and is not lightly taken. The past has shown that efforts to introduce formal methods in industry has faced a lot of controversy and opposition at various hierarchical levels in companies, resulting in a marginal spread of such methods. This paper revisits the requirements for formal description techniques and identifies some critical success and inhibiting factors associated with the introduction of formal methods in the industrial practice. One of the inhibiting factors is the often encountered lack of appropriateness of the formal model to express and manipulate the design concerns that determine the world of the engineer. This factor motivated our research in the area of architectural and implementation design concepts. The last two sections of this paper report on some results of this research

Scalable Bayesian nonparametric measures for exploring pairwise dependence via Dirichlet Process Mixtures

In this article we propose novel Bayesian nonparametric methods using Dirichlet Process Mixture (DPM) models for detecting pairwise dependence between random variables while accounting for uncertainty in the form of the underlying distributions. A key criteria is that the procedures should scale to large data sets. In this regard we find that the formal calculation of the Bayes factor for a dependent-vs.-independent DPM joint probability measure is not feasible computationally. To address this we present Bayesian diagnostic measures for characterising evidence against a "null model" of pairwise independence. In simulation studies, as well as for a real data analysis, we show that our approach provides a useful tool for the exploratory nonparametric Bayesian analysis of large multivariate data sets

Advances in architectural concepts to support distributed systems design

This paper presents and discusses some architectural concepts for distributed systems design. These concepts are derived from an analysis of limitations of some currently available standard design languages. We conclude that language design should be based upon the careful consideration of architectural concepts. This paper aims at supporting designers by presenting a methodological design framework in which they can reason about the design and implementation of distributed systems. The paper is also meant for language developers and formalists by presenting a collection of architectural concepts which deserve consideration for formal support