Conceptual modelling: Towards detecting modelling errors in engineering applications

Rapid advancements of modern technologies put high demands on mathematical modelling of engineering systems. Typically, systems are no longer “simple” objects, but rather coupled systems involving multiphysics phenomena, the modelling of which involves coupling of models that describe different phenomena. After constructing a mathematical model, it is essential to analyse the correctness of the coupled models and to detect modelling errors compromising the final modelling result. Broadly, there are two classes of modelling errors: (a) errors related to abstract modelling, eg, conceptual errors concerning the coherence of a model as a whole and (b) errors related to concrete modelling or instance modelling, eg, questions of approximation quality and implementation. Instance modelling errors, on the one hand, are relatively well understood. Abstract modelling errors, on the other, are not appropriately addressed by modern modelling methodologies. The aim of this paper is to initiate a discussion on abstract approaches and their usability for mathematical modelling of engineering systems with the goal of making it possible to catch conceptual modelling errors early and automatically by computer assistant tools. To that end, we argue that it is necessary to identify and employ suitable mathematical abstractions to capture an accurate conceptual description of the process of modelling engineering systems

Applying Graph Coloring To Schedule Doctors' Work In A Hospital.

Scheduling shifts is a tiresome and time consuming task in any business, and particularly in hospitals where errors are costly, rules are plentiful and changes are rapid. The person performing this function (Rota Organizer) will have to keep track of all the employees concerned, distributing hours fairly and avoiding collisions. Rules regulating working hours and breaks have to be followed and the qualifications of individual employees need to be considered. Hours are spent every day on this task in every ward. The goal of this paper is to solve Doctors Scheduling Problem (DSP) and initialize a fair roster for two wards of Pediatric Department (PD) in Prince Sultan Military Medical City (PSMMC) in Saudi Arabia. So to find a solution of DSP, we used Graph Coloring which is one of the methods used mostly to solve this problem

Banach's fixed point theorem for partial metric spaces

In 1994, S.G. Matthews introduced the notion of a par- tial metric space and obtained, among other results, a Banach contraction mapping for these spaces. Later on, S.J. O’Neill gen- eralized Matthews’ notion of partial metric, in order to establish connections between these structures and the topological aspects of domain theory. Here, we obtain a Banach fixed point theorem for complete partial metric spaces in the sense of O’Neill. Thus, Matthews’ fixed point theorem follows as special case of our result

Approximation in quantale-enriched categories

Our work is a fundamental study of the notion of approximation in V-categories and in (U,V)-categories, for a quantale V and the ultrafilter monad U. We introduce auxiliary, approximating and Scott-continuous distributors, the way-below distributor, and continuity of V- and (U,V)-categories. We fully characterize continuous V-categories (resp. (U,V)-categories) among all cocomplete V-categories (resp. (U,V)-categories) in the same ways as continuous domains are characterized among all dcpos. By varying the choice of the quantale V and the notion of ideals, and by further allowing the ultrafilter monad to act on the quantale, we obtain a flexible theory of continuity that applies to partial orders and to metric and topological spaces. We demonstrate on examples that our theory unifies some major approaches to quantitative domain theory.Comment: 17 page

Dead code elimination based pointer analysis for multithreaded programs

This paper presents a new approach for optimizing multitheaded programs with pointer constructs. The approach has applications in the area of certified code (proof-carrying code) where a justification or a proof for the correctness of each optimization is required. The optimization meant here is that of dead code elimination. Towards optimizing multithreaded programs the paper presents a new operational semantics for parallel constructs like join-fork constructs, parallel loops, and conditionally spawned threads. The paper also presents a novel type system for flow-sensitive pointer analysis of multithreaded programs. This type system is extended to obtain a new type system for live-variables analysis of multithreaded programs. The live-variables type system is extended to build the third novel type system, proposed in this paper, which carries the optimization of dead code elimination. The justification mentioned above takes the form of type derivation in our approach.Comment: 19 page

A Comparison of Petri Net Semantics under the Collective Token Philosophy

In recent years, several semantics for place/transition Petri nets have been proposed that adopt the collective token philosophy. We investigate distinctions and similarities between three such models, namely configuration structures, concurrent transition systems, and (strictly) symmetric (strict) monoidal categories. We use the notion of adjunction to express each connection. We also present a purely logical description of the collective token interpretation of net behaviours in terms of theories and theory morphisms in partial membership equational logic

Towards "dynamic domains": totally continuous cocomplete Q-categories

It is common practice in both theoretical computer science and theoretical physics to describe the (static) logic of a system by means of a complete lattice. When formalizing the dynamics of such a system, the updates of that system organize themselves quite naturally in a quantale, or more generally, a quantaloid. In fact, we are lead to consider cocomplete quantaloid-enriched categories as fundamental mathematical structure for a dynamic logic common to both computer science and physics. Here we explain the theory of totally continuous cocomplete categories as generalization of the well-known theory of totally continuous suplattices. That is to say, we undertake some first steps towards a theory of "dynamic domains''.Comment: 29 pages; contains a more elaborate introduction, corrects some typos, and has a sexier title than the previously posted version, but the mathematics are essentially the sam