Partial Evaluation of the Euclidian Algorithm (Extended Version)

Some programs are easily amenable to partial evaluation becausetheir control flow clearly depends on one of their parameters. Specializingsuch programs with respect to this parameter eliminates theassociated interpretive overhead. Some other programs, however, donot exhibit this interpreter-like behavior. Each of them presents a challengefor partial evaluation. The Euclidian algorithm is one of them,and in this article, we make it amenable to partial evaluation.We observe that the number of iterations in the Euclidian algorithmis bounded by a number that can be computed given either of the twoarguments. We thus rephrase this algorithm using bounded recursion.The resulting program is better suited for automatic unfolding andthus for partial evaluation. Its specialization is efficient.Keywords: partial evaluation, scientific computation

The Complexity Of The NP-Class

This paper presents a novel and straight formulation, and gives a complete insight towards the understanding of the complexity of the problems of the so called NP-Class. In particular, this paper focuses in the Searching of the Optimal Geometrical Structures and the Travelling Salesman Problems. The main results are the polynomial reduction procedure and the solution to the Noted Conjecture of the NP-Class

Timbre space as synthesis space: towards a navigation based approach to timbre specification

Much research into timbre, its perception and classification over the last forty years has modelled timbre as an n-dimensional co-ordinate space or timbre space, whose axes are measurable acoustical quantities (variously, spectral density, simultaneity of partial onsets etc). Typically, these spaces have been constructed from data generated from similarity/dissimilarity listening tests, using multidimensional scaling (MDS) analysis techniques. Our current research is the computer assisted synthesis of new timbres using a timbre space search strategy, in which a previously constructed simple timbre space is used as a search space by an algorithm designed to synthesize desired new timbres steered by iterative user input. The success of such an algorithm clearly depends on establishing suitable mapping between its quantifiable features and its perceptual features. We therefore present here, firstly, some of the findings of a series of listening tests aimed at establishing the perceptual topography and granularity of a simple, predefined timbre space, and secondly, the results of preliminary tests of two search strategies designed to navigate this space. The behaviour of these strategies in a circumscribed space of this kind, together with the corresponding user experience is intended to provide a baseline to applications in a more complex space

A nonintrusive Reduced Basis Method applied to aeroacoustic simulations

The Reduced Basis Method can be exploited in an efficient way only if the so-called affine dependence assumption on the operator and right-hand side of the considered problem with respect to the parameters is satisfied. When it is not, the Empirical Interpolation Method is usually used to recover this assumption approximately. In both cases, the Reduced Basis Method requires to access and modify the assembly routines of the corresponding computational code, leading to an intrusive procedure. In this work, we derive variants of the EIM algorithm and explain how they can be used to turn the Reduced Basis Method into a nonintrusive procedure. We present examples of aeroacoustic problems solved by integral equations and show how our algorithms can benefit from the linear algebra tools available in the considered code.Comment: 28 pages, 7 figure