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Order-semi-primal lattices
(1994)

A nonequilibrium situation governed by kinetic equations with strongly contrasted Knudsen numbers in different subdomains is discussed. We consider a domain decomposition problem for Boltzmann- and Euler equations, establish the correct coupling conditions and prove the validity of the obtained coupled solution . Moreover numerical examples comparing different types of coupling conditions are presented.

Let (\(a_i)_{i\in \bf{N}}\) be a sequence of identically and independently distributed random vectors drawn from the \(d\)-dimensional unit ball \(B^d\)and let \(X_n\):= convhull \((a_1,\dots,a_n\)) be the random polytope generated by \((a_1,\dots\,a_n)\). Furthermore, let \(\Delta (X_n)\) : = (Vol \(B^d\) \ \(X_n\)) be the deviation of the polytope's volume from the volume of the ball. For uniformly distributed \(a_i\) and \(d\ge2\), we prove that tbe limiting distribution of \(\frac{\Delta (X_n)} {E(\Delta (X_n))}\) for \(n\to\infty\) satisfies a 0-1-law. Especially, we provide precise information about the asymptotic behaviour of the variance of \(\Delta (X_n\)). We deliver analogous results for spherically symmetric distributions in \(B^d\) with regularly varying tail.

We introduce the concept of streamballs for fluid flow visualization. Streamballs are based upon implicit surface generation techniques adopted from the well-known metaballs. Their property to split or merge automatically in areas of significant divergence or convergence makes them an ideal tool for the visualization of arbitrary complex flow fields. Using convolution surfaces generated by continuous skeletons for streamball construction offers the possibility to visualize even tensor fields.

The problem to interpolate Hermite-type data (i.e. two points with attached tangent vectors) with elastic curves of prescribed tension is known to have multiple solutions. A method is presented that finds all solutions of length not exceeding one period of its curvature function. The algorithm is based on algebraic relations between discrete curvature information which allow to transform the problem into a univariate one. The method operates with curves that by construction partially interpolate the given data. Hereby the objective function of the problem is drastically simplified. A bound on the maximum curvature value is established that provides an interval containing all solutions.

Best-Fit Pattern Matching
(1994)

This report shows that dispatching of methods in object oriented languages is in principle the same as best fit pattern matching. A general conceptual description of best fit pattern matching is presented. Many object oriented features are modelled by means of the general concept. This shows that simple methods, multi methods, overloading of functions, pattern matching,
dynamic and union types, and extendable records can be combined in a single comprehensive concept.

We study the complexity of local solution of Fredholm integral equations. This means that we want to compute not the full solution, but rather a functional (weighted mean, value in a point) of it. For certain Sobolev classes of multivariate periodic functions we prove matching upper and lower bounds and construct an algorithm of the optimal order, based on Fourier coefficients and a hyperbolic cross approximation.

In this paper the complexity of the local solution of Fredholm integral equations
is studied. For certain Sobolev classes of multivariate periodic functions with dominating mixed derivative we prove matching lower and upper bounds. The lower bound is shown using relations to s-numbers. The upper bound is proved in a constructive way providing an implementable algorithm of optimal order based on Fourier coefficients and a hyperbolic cross approximation.

The Basic Reference Model of ODP introduces a number of basic concepts in order to provide a common basis for the development of a coherent set of standards. To achieve this objective, a clear understanding of the basic concepts is one prerequisite. This paper makes an effort at clarifying some of the basic concepts independently of standardized or non-standardized formal description techniques. Among the basic concepts considered here are: agent, action, interaction, interaction point, architecture, behaviour, system, composition, refinement, and abstraction. In a case study, it is then shown how these basic concepts can be represented in a formal specification written in temporal logic.

Free Form Volumes
(1994)

Visualization of large data sets, especially on small machines, requires advanced techniques in image processing and image generation. Our hybrid raytracer is capable of rendering volumetric and geometric data simultaneously, without loss of accuracy due to data conversion. Compound data sets, consisting of several types of data, are called "hybrid data sets". There is only one rendering pipeline to obtain loss-less and efficient visualization of hybrid data. Algorithms apply to both types of data. Optical material properties are stored in the same data base for both volumetric and geometric objects, and anti-aliasing methods appeal to both data types. Stereoscopic display routines have been added to obtain true three-dimensional visualization on various media, and animation features allow generation of recordable 3-D sequences.

The main problem in computer graphics is to solve the global illumination problem,
which is given by a Fredholm integral equation of the second kind, called the radiance equation (REQ). In order to achieve realistic images, a very complex kernel
of the integral equation, modelling all physical effects of light, must be considered. Due to this complexity Monte Carlo methods seem to be an appropriate approach to solve the REQ approximately. We show that replacing Monte Carlo by quasi-Monte Carlo in some steps of the algorithm results in a faster convergence.

Optimization of Projection Methods for Solving ill-posed Problems. In this paper we propose a modification of the projection scheme for solving ill-posed problems. We show that this modification allows to obtain the best possible order of accuracy of Tikhonov Regularization using an amount of information which is far less than for the standard projection technique.

The rapid development of any field of knowledge brings with it unavoidable fragmentation and proliferation of new disciplines. The development of computer science is no exception. Software engineering (SE) and human-computer interaction (HCI) are both relatively new disciplines of computer science. Furthermore, as both names suggest, they each have strong connections with other subjects. SE is concerned with methods and tools for general software development based on engineering principles. This discipline has its roots not only in computer science but also in a number of traditional engineering disciplines. HCI is concerned with methods and tools for the development of human-computer interfaces, assessing the usability of computer systems and with broader issues about how people interact with computers. It is based on theories about how humans process information and interact with computers, other objects and other people in the organizational and social contexts in
which computers are used. HCI draws on knowledge and skills from psychology, anthropology and sociology in addition to computer science. Both disciplines need ways of measuring how well their products and development processes fulfil their intended requirements. Traditionally SE has been concerned with 'how software is constructed' and HCI with 'how people use software'. Given the
different histories of the disciplines and their different objectives, it is not surprising that they take different approaches to measurement. Thus, each has its own distinct 'measurement culture.' In this paper we analyse the differences and the commonalties of the two cultures by examining the measurement approaches used by each. We then argue the need for a common measurement taxonomy and framework, which is derived from our analyses of the two disciplines. Next we demonstrate the usefulness of the taxonomy and framework via specific example studies drawn from our own work and that of others and show that, in fact, the two disciplines have many important similarities as well as differences and that there is some evidence to suggest that they are growing closer. Finally, we discuss the role of the taxonomy as a framework to support: reuse, planning future studies, guiding practice and facilitating communication between the two disciplines.

Hardware / Software Codesign
(1994)

Monte Carlo integration is often used for antialiasing in rendering processes.
Due to low sampling rates only expected error estimates can be stated, and the variance can be high. In this article quasi-Monte Carlo methods are presented, achieving a guaranteed upper error bound and a convergence rate essentially as fast as usual Monte Carlo.

The radiance equation, which describes the global illumination problem in computer graphics, is a high dimensional integral equation. Estimates of the solution are usually computed on the basis of Monte Carlo methods. In this paper we propose and investigate quasi-Monte Carlo methods, which means that we replace (pseudo-) random samples by low discrepancy sequences, yielding deterministic algorithms. We carry out a comparative numerical study between Monte Carlo and quasi-Monte Carlo methods. Our results show that quasi-Monte Carlo converges considerably faster.

This report presents a generalization of tensor-product B-spline surfaces. The new scheme permits knots whose endpoints lie in the interior of the domain rectangle of a surface. This allows local refinement of the knot structure for approximation purposes as well as modeling surfaces with local tangent or curvature discontinuities. The surfaces are represented in terms of B-spline basis functions, ensuring affine invariance, local control, the convex hull property, and evaluation by de Boor's algorithm. A dimension formula for a class of generalized tensor-product spline spaces is developed.