This paper presents a new approach to a local time-space grid refinement for a staggered-grid finitedifference simulation of waves. The approach is based on approximation of a wave equation at the interface where two grids are coupled. As no interpolation or projection techniques are used, the finite-difference scheme preserves second order of convergence. We have proved that this approach is l...

We define texture mapping as an optimization problem for which the goal is to preserve the maximum amount of information in the mapped texture. We derive a solution that is optimal in the least-squares sense and that corresponds to the pseudo-inverse of the texturemapping transformation. In practice, a first-order approximation of the least-squares solution is used as an initial estimate for th...

We propose here a mathematical framework for incremental software construction and controlled software evolution. The framework allows incremental changes of a software system to be described on a high architecture level, but still with mathematical precision so that we can reason about the correctness of the changes. The framework introduces refinement diagrams as a visual way of presenting th...

Stepwise program refinement techniques can be used to simplify program verification. Programs are better understood since their main properties are clearly stated, and verification of rather complex algorithms is reduced to proving simple statements connecting successive program specifications. Additionally, it is easy to analyze similar algorithms and to compare their properties within a singl...

We establish a random variable substitution lemma and use it to investigate the role of refinement layer in multiple description coding, which clarifies the relationship among several existing achievable multiple description rate-distortion regions. Specifically, it is shown that the El Gamal-Cover (EGC) region is equivalent to the EGC* region (an antecedent version of the EGC region) while the...

Feature engineering (FE) deliberately stages the incorporation of elements of functionality into a system according to perceived user and market needs. Conventional refinement based techniques for FE suffer from the need to have successive features build smoothly on their predecessors, since contradicting what has already been established is anathema for any refinement technique. Real FE howeve...

An object based formal method for the development of real-time systems, called ATOM, is presented. The method is an integration of the real-time formal technique TAM (Temporal Agent Model) with an industry-strength structured methodology known as HRT-HOOD. ATOM is a systematic formal approach based on the refinement calculus. Within ATOM, a formal specification (or abstract description statemen...

Model-driven design of software for safety-critical applications often relies on mathematically grounded techniques such as the B method. Such techniques consist in the successive applications of refinements to derive a concrete implementation from an abstract specification. Refinement theory defines verification conditions to guarantee that such operations preserve the intended behaviour of th...

The ever growing pace at which medical knowledge is produced requires clinical practice guidelines (CPGs) to be regularly updated. Since clinical decision support systems (CDSSs) are effective means to implement guidelines in routine care, they have to be revised as their knowledge sources evolve. From one version to another, some parts are kept unchanged whereas others are more or less modifie...

Stepwise program refinement techniques can be used to simplify program verification. Programs are better understood since their main properties are clearly stated, and verification of rather complex algorithms is reduced to proving simple statements connecting successive program specifications. Additionally, it is easy to analyze similar algorithms and to compare their properties within a singl...