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#### Faculty / Organisational entity

In this paper a group of participants of the 12th European Summer Institute which took place in Tenerifa, Spain in June 1995 present their views on the state of the art and the future trends in Locational Analysis. The issue discussed includes modelling aspects in discrete, network and continuous location, heuristic techniques, the state of technology and undesirable facility location. Some general questions are stated reagrding the applicability of location models, promising research directions and the way technology affects the development of solution techniques.

A new and systematic basic approach to force- and vision-based robot manipulation of deformable (non-rigid) linear objects is introduced. This approach reduces the computational needs by using a simple state-oriented model of the objects. These states describe the relation between the deformable and rigid obstacles, and are derived from the object image and its features. We give an enumeration of possible contact states and discuss the main characteristics of each state. We investigate the performance of robust transitions between the contact states and derive criteria and conditions for each of the states and for two sensor systems, i.e. a vision sensor and a force/torque sensor. This results in a new and task-independent approach in regarding the handling of deformable objects and in a sensor-based implementation of manipulation primitives for industrial robots. Thus, the usage of sensor processing is an appropriate solution for our problem. Finally, we apply the concept of contact states and state transitions to the description of a typical assembly task. Experimental results show the feasibility of our approach: A robot performs several contact state transitions which can be combined for solving a more complex task.

A geoscientifically relevant wavelet approach is established for the classical (inner) displacement problem corresponding to a regular surface (such as sphere, ellipsoid, actual earth's surface). Basic tools are the limit and jump relations of (linear) elastostatics. Scaling functions and wavelets are formulated within the framework of the vectorial Cauchy-Navier equation. Based on appropriate numerical integration rules a pyramid scheme is developed providing fast wavelet transform (FWT). Finally multiscale deformation analysis is investigated numerically for the case of a spherical boundary.

Building interoperation among separately developed software units requires checking their conceptual assumptions and constraints. However, eliciting such assumptions and constraints is time consuming and is a challenging task as it requires analyzing each of the interoperating software units. To address this issue we proposed a new conceptual interoperability analysis approach which aims at decreasing the analysis cost and the conceptual mismatches between the interoperating software units. In this report we present the design of a planned controlled experiment for evaluating the effectiveness, efficiency, and acceptance of our proposed conceptual interoperability analysis approach. The design includes the study objectives, research questions, statistical hypotheses, and experimental design. It also provides the materials that will be used in the execution phase of the planned experiment.

This paper deals with the handling of deformable linear objects (DLOs), such as hoses, wires, or leaf springs. It investigates usable features for the vision-based detection of a changing contact situation between a DLO and a rigid polyhedral obstacle and a classification of such contact state transitions. The result is a complete classification of contact state transitions and of the most significant features for each class. This knowledge enables reliable detection of changes in the DLO contact situation, facilitating implementation of sensor-based manipulation skills for all possible contact changes.

Dynamics of Excited Electrons in Copper and Ferromagnetic Transition Metals: Theory and Experiment
(2000)

Both theoretical and experimental results for the dynamics of photoexcited electrons at surfaces of Cu and the ferromagnetic transition metals Fe, Co, and Ni are presented. A model for the dynamics of excited electrons is developed, which is based on the Boltzmann equation and includes effects of photoexcitation, electron-electron scattering, secondary electrons (cascade and Auger electrons), and transport of excited carriers out of the detection region. From this we determine the time-resolved two-photon photoemission (TR-2PPE). Thus a direct comparison of calculated relaxation times with experimental results by means of TR-2PPE becomes possible. The comparison indicates that the magnitudes of the spin-averaged relaxation time t and of the ratio t_up/t_down of majority and minority relaxation times for the different ferromagnetic transition metals result not only from density-of-states effects, but also from different Coulomb matrix elements M. Taking M_Fe > M_Cu > M_Ni = M_Co we get reasonable agreement with experiments.

We present a constructive theory for locally supported approximate identities on the unit ball in \(\mathbb{R}^3\). The uniform convergence of the convolutions of the derived kernels with an arbitrary continuous function \(f\) to \(f\), i.e. the defining property of an approximate identity, is proved. Moreover, an explicit representation for a class of such kernels is given. The original publication is available at www.springerlink.com

In these notes we will discuss some aspects of a problem arising in carindustry. For the sake of clarity we will set the problem into an extremely simplified scheme. Suppose that we have a body which is emitting sound, and that the sound is measured at a finite number of points around the body. We wish to determine the intensity of the sound at an observation point which is moving.

A growing share of all software development project work is being done by geographically distributed teams. To satisfy shorter product design cycles, expert team members for a development project may need to be r ecruited globally. Yet to avoid extensive travelling or r eplacement costs, distributed project work is preferred. Current-generation software engineering tools and ass ociated systems, processes, and methods were for the most part developed to be used within a single enterprise. Major innovations have lately been introduced to enable groupware applications on the Internet to support global collaboration. However, their deployment for distributed software projects requires further research. In partic ular, groupware methods must seamlessly be integrated with project and product management systems to make them attractive for industry. In this position paper we outline the major challenges concerning distributed (virtual) software projects. Based on our experiences with software process modeling and enactment environments, we then propose approaches to solve those challenges.

Evaluation is an important issue for every scientific field and a necessity for an emerging soft-ware technology like case- based reasoning. This paper is a supplementation to the review of industrial case-based reasoning tools by K.-D. Althoff, E. Auriol, R. Barletta and M. Manago which describes the most detailed evaluation of commercial case-based reasoning tools currently available. The author focuses on some important aspects that correspond to the evaluation ofcase-based reasoning systems and gives links to ongoing research.

Case-Based Reasoning for Decision Support and Diagnostic Problem Solving: The INRECA Approach
(1995)

INRECA offers tools and methods for developing, validating, and maintaining decision support systems. INRECA's basic technologies are inductive and case-based reasoning, namely KATE -INDUCTION (cf., e.g., Manago, 1989; Manago, 1990) and S3-CASE, a software product based on PATDEX (cf., e.g., Wess,1991; Richter & Wess, 1991; Althoff & Wess, 1991). Induction extracts decision knowledge from case databases. It brings to light patterns among cases and helps monitoring trends over time. Case-based rea -soning relates the engineer's current problem to past experiences.

MOLTKE is a research project dealing with a complex technical application. After describing the domain of CNCmachining centers and the applied KA methods, we summarize the concrete KA problems which we have to handle. Then we describe a KA mechanism which supports an engineer in developing a diagnosis system. In chapter 6 weintroduce learning techniques operating on diagnostic cases and domain knowledge for improving the diagnostic procedure of MOLTKE. In the last section of this chapter we outline some essential aspects of organizationalknowledge which is heavily applied by engineers for analysing such technical systems (Qualitative Engineering). Finally we give a short overview of the actual state of realization and our future plans.

In this paper we will present a design model (in the sense of KADS) for the domain of technical diagnosis. Based on this we will describe the fully implemented expert system shell MOLTKE 3.0, which integrates common knowledge acquisition methods with techniques developed in the fields of Model-Based Diagnosis and Machine Learning, especially Case-Based Reasoning.

Case-based knowledge acquisition, learning and problem solving for diagnostic real world tasks
(1999)

Within this paper we focus on both the solution of real, complex problems using expert system technology and the acquisition of the necessary knowledge from a case-based reasoning point of view. The development of systems which can be applied to real world problems has to meet certain requirements. E.g., all available information sources have to be identified and utilized. Normally, this involves different types of knowledge for which several knowledge representation schemes are needed, because no scheme is equally natural for all sources. Facing empirical knowledge it is important to complement the use of manually compiled, statistic and otherwise induced knowledge by the exploitation of the intuitive understandability of case-based mechanisms. Thus, an integration of case-based and alternative knowledge acquisition and problem solving mechanisms is necessary. For this, the basis is to define the "role" which case-based inference can "play" within a knowledge acquisition workbench. We will discuss a concrete casebased architecture, which has been applied to technical diagnosis problems, and its integration into a knowledge acquisition workbench which includes compiled knowledge and explicit deep models, additionally.

Retrieval of cases is one important step within the case-based reasoning paradigm. We propose an improvement of this stage in the process model for finding most similar cases with an average effort of O[log2n], n number of cases. The basic idea of the algorithm is to use the heterogeneity of the search space for a density-based structuring and to employ this precomputed structure, a k-d tree, for efficient case retrieval according to a given similarity measure sim. In addition to illustrating the basic idea, we present the expe- rimental results of a comparison of four different k-d tree generating strategies as well as introduce the notion of virtual bounds as a new one that significantly reduces the retrieval effort from a more pragmatic perspective. The presented approach is fully implemented within the (Patdex) system, a case-based reasoning system for diagnostic applications in engineering domains.

In this paper we construct spline functions based on a reproducing kernel Hilbert space to interpolate/approximate the velocity field of earthquake waves inside the Earth based on traveltime data for an inhomogeneous grid of sources (hypocenters) and receivers (seismic stations). Theoretical aspects including error estimates and convergence results as well as numerical results are demonstrated.

In this paper we study the space-time asymptotic behavior of the solutions and derivatives to th incompressible Navier-Stokes equations. Using moment estimates we obtain that strong solutions to the Navier-Stokes equations which decay in \(L^2\) at the rate of \(||u(t)||_2 \leq C(t+1)^{-\mu}\) will have the following pointwise space-time decay \[|D^{\alpha}u(x,t)| \leq C_{k,m} \frac{1}{(t+1)^{ \rho_o}(1+|x|^2)^{k/2}} \]
where \( \rho_o = (1-2k/n)( m/2 + \mu) + 3/4(1-2k/n)\), and \(|a |= m\). The dimension n is \(2 \leq n \leq 5\) and \(0\leq k\leq n\) and \(\mu \geq n/4\)

The paper presents some adaptive load balance techniques for the simulation of rarefied gas flows on parallel computers. It is shown that a static load balance is insufficient to obtain a scalable parallel efficiency. Hence, two adaptive techniques are investigated which are based on simple algorithms. Numerical results show that using heuristic techniques one can achieve a sufficiently high efficiency over a wide range of different hardware platforms.

The increasing parallelisation of development processes as well as the ongoing trends towards virtual product development and outsourcing of development activities strengthen the need for 3D co-operative design via communication networks. Regarding the field of CAx, none of the existing systems meets all the requirements of very complex process chain. This leads to a tremendous need for the integration of heterogeneous CAx systems. Therefore, MACAO, a platform-independent client for a distributed CAx component system, the so-called ANICA CAx object bus, is presented. The MACAO client is able to access objects and functions provided by different CAx servers distributed over a communication network. Thus, MACAO is a new solution for engineering design and visualisation in shared distributed virtual environments. This paper describes the underlying concepts, the actual prototype implementation, as well as possible application scenarios in the area of co-operative design and visualisation.

Interoperability between different CAx systems involved in the development process of cars is presently one of the most critical issues in the automotive industry. None of the existing CAx systems meets all requirements of the very complex process network of the lifecycle of a car. With this background, industrial engineers have to use various CAx systems to get an optimal support for their daily work. Today, the communication between different CAx systems is done via data files using special direct converters or neutral system independent standards like IGES, VDAFS, and recently STEP, the international standard for product data description. To reduce the dependency on individual CAx s ystem vendors, the German automotive industry developed an open CAx system architecture based on STEP as guiding principle for CAx system development. The central component of this architecture is a common, system-independent access interface to CAx functions and data of all involved CAx systems, which is under development in the project ANICA. Within this project, a CAx object bus has been developed based on a STEP data description using CORBA as an integration platform. This new approach allows a transparent access to data and functions of the integrated CAx systems without file-based data exchange. The product development process with various CAx systems concerns objects from different CAx systems. Thus, mechanisms are needed to handle the persistent storage of the CAx objects distributed over the CAx object bus to give the developing engineers a consistent view of the data model of their product. The following paper discusses several possibilities to guarantee consistent data management and storage of distributed CAx models. One of the most promising approaches is the enhancement of the CAx object bus by a STEP-based object-oriented data server to realise a central data management.

Today, the worlds and terminologies of mechanical engineering and software engineering coexist, but they do not always work together seamlessly. Both worlds have developed their own separate formal vocabulary for expressing their concepts as well as for capturing and communicating their respective domain knowledge. But, these two vocabularies are not unified, interwoven, or at least interconnected in a reasonable manner. Thus, the subject of this paper is a comparison of the vocabularies of the two fields, namely feature technology from the area of mechanical engineering and software design patterns from the software engineering domain. Therefore, a certain amount of definitions, history, examples, etc. is presented for features as well as for design patterns. After this, an analysis is carried out to identify analogies and differences. The main intention of this paper is to inform both worlds - mechanical and software engineering - about the other side's terminology and to start a discussion about potential mutual benefits and possibilities to bridge the gap between these two worlds, e.g. to improve the manageability of CAx product development processes.

PANDA is a run-time package based on a very small operating system kernel which supports distributed applications written in C++. It provides powerful abstractions such as very efficient user-level threads, a uniform global address space, object and thread mobility, garbage collection, and persistent objects. The paper discusses the design ration- ales underlying the PANDA system. The fundamental features of PANDA are surveyed, and their implementation in the current prototype environment is outlined.

Distributed systems are an alternative to shared-memorymultiprocessors for the execution of parallel applications.PANDA is a runtime system which provides architecturalsupport for efficient parallel and distributed program-ming. PANDA supplies means for fast user-level threads,and for a transparent and coordinated sharing of objectsacross a homogeneous network. The paper motivates themajor architectural choices that guided our design. Theproblem of sharing data in a distributed environment isdiscussed, and the performance of appropriate mecha-nisms provided by the PANDA prototype implementation isassessed.

In this paper we propose a phenomenological model for the formation of an interstitial gap between the tumor and the stroma. The gap
is mainly filled with acid produced by the progressing edge of the tumor front. Our setting extends existing models for acid-induced tumor invasion models to incorporate
several features of local invasion like formation of gaps, spikes, buds, islands, and cavities. These behaviors are obtained mainly due to the random dynamics at the intracellular
level, the go-or-grow-or-recede dynamics on the population scale, together with the nonlinear coupling between the microscopic (intracellular) and macroscopic (population)
levels. The wellposedness of the model is proved using the semigroup technique and 1D and 2D numerical simulations are performed to illustrate model predictions and draw
conclusions based on the observed behavior.

We propose and analyze a multiscale model for acid-mediated tumor invasion
accounting for stochastic effects on the subcellular level.
The setting involves a PDE of reaction-diffusion-taxis type describing the evolution of the tumor cell density,
the movement being directed towards pH gradients in the local microenvironment,
which is coupled to a PDE-SDE system characterizing the
dynamics of extracellular and intracellular proton concentrations, respectively.
The global well-posedness of the model is shown and
numerical simulations are performed in order to illustrate the solution behavior.

As the properties of components have gradually become clearer, attention has started to turn to the architectural issues which govern their interaction and composition. In this paper we identify some of the major architectural questions affecting component-based software develop-ment and describe the predominant architectural dimensions. Of these, the most interesting is the "architecture hierarchy" which we believe is needed to address the "interface vicissitude" problem that arises whenever interaction refinement is explicitly documented within a component-based system. We present a solution to this problem based on the concept of stratified architectures and object metamorphosis Finally, we describe how these concepts may assist in increasing the tailorability of component-based frameworks.

This paper presents a new kind of abstraction, which has been developed for the purpose of proofplanning. The basic idea of this paper is to abstract a given theorem and to find an abstractproof of it. Once an abstract proof has been found, this proof has to be refined to a real proofof the original theorem. We present a goal oriented abstraction for the purpose of equality proofplanning, which is parameterized by common parts of the left- and right-hand sides of the givenequality. Therefore, this abstraction technique provides an abstract equality problem which ismore adequate than those generated by the abstractions known so far. The presented abstractionalso supports the heuristic search process based on the difference reduction paradigm. We give aformal definition of the abstract space including the objects and their manipulation. Furthermore,we prove some properties in order to allow an efficient implementation of the presented abstraction.

Simultaneous quantifier elimination in sequent calculus is an improvement over the well-known skolemization. It allows a lazy handling of instantiations as well as of the order of certain reductions. We prove the soundness of a sequent calculus which incorporates a rule for simultaneous quantifier elimination. The proof is performed by semantical arguments and provides some insights into the dependencies between various formulas in a sequent.

In this paper we show that distributing the theorem proving task to several experts is a promising idea. We describe the team work method which allows the experts to compete for a while and then to cooperate. In the cooperation phase the best results derived in the competition phase are collected and the less important results are forgotten. We describe some useful experts and explain in detail how they work together. We establish fairness criteria and so prove the distributed system to be both, complete and correct. We have implementedour system and show by non-trivial examples that drastical time speed-ups are possible for a cooperating team of experts compared to the time needed by the best expert in the team.

This report contains a collection of abstracts for talks given at the "Deduktionstreffen" held at Kaiserslautern, October 6 to 8, 1993. The topics of the talks range from theoretical aspects of term rewriting systems and higher order resolution to descriptions of practical proof systems in various applications. They are grouped together according the following classification: Distribution and Combination of Theorem Provers, Termination, Completion, Functional Programs, Inductive Theorem Proving, Automatic Theorem Proving, Proof Presentation. The Deduktionstreffen is the annual meeting of the Fachgruppe Deduktionssysteme in the Gesellschaft für Informatik (GI), the German association for computer science.

We study deterministic conditional rewrite systems, i.e. conditional rewrite systemswhere the extra variables are not totally free but 'input bounded'. If such a systemR is quasi-reductive then !R is decidable and terminating. We develop a critical paircriterion to prove confluence if R is quasi-reductive and strongly deterministic. In thiscase we prove that R is logical, i.e./!R==R holds. We apply our results to proveHorn clause programs to be uniquely terminating.This research was supported by the Deutsche Forschungsgemeinschaft, SFB 314, Project D4

We investigate one of the classical problems of the theory ofterm rewriting, namely termination. We present an ordering for compar-ing higher-order terms that can be utilized for testing termination anddecreasingness of higher-order conditional term rewriting systems. Theordering relies on a first-order interpretation of higher-order terms anda suitable extension of the RPO.

In this paper we are interested in an algebraic specification language that (1) allowsfor sufficient expessiveness, (2) admits a well-defined semantics, and (3) allows for formalproofs. To that end we study clausal specifications over built-in algebras. To keep thingssimple, we consider built-in algebras only that are given as the initial model of a Hornclause specification. On top of this Horn clause specification new operators are (partially)defined by positive/negative conditional equations. In the first part of the paper wedefine three types of semantics for such a hierarchical specification: model-theoretic,operational, and rewrite-based semantics. We show that all these semantics coincide,provided some restrictions are met. We associate a distinguished algebra A spec to ahierachical specification spec. This algebra is initial in the class of all models of spec.In the second part of the paper we study how to prove a theorem (a clause) valid in thedistinguished algebra A spec . We first present an abstract framework for inductive theoremprovers. Then we instantiate this framework for proving inductive validity. Finally wegive some examples to show how concrete proofs are carried out.This report was supported by the Deutsche Forschungsgemeinschaft, SFB 314 (D4-Projekt)

Finding a delivery plan for cancer radiation treatment using multileaf collimators operating in ''step-and-shoot mode'' can be formulated mathematically as a problem of decomposing an integer matrix into a weighted sum of binary matrices having the consecutive-ones property - and sometimes other properties related to the collimator technology. The efficiency of the delivery plan is measured by both the sum of weights in the decomposition, known as the total beam-on time, and the number of different binary matrices appearing in it, referred to as the cardinality, the latter being closely related to the set-up time of the treatment. In practice, the total beam-on time is usually restricted to its minimum possible value, (which is easy to find), and a decomposition that minimises cardinality (subject to this restriction) is sought.

In this paper we consider the problem of decomposing a given integer matrix A into
a positive integer linear combination of consecutive-ones matrices with a bound on the
number of columns per matrix. This problem is of relevance in the realization stage
of intensity modulated radiation therapy (IMRT) using linear accelerators and multileaf
collimators with limited width. Constrained and unconstrained versions of the problem
with the objectives of minimizing beam-on time and decomposition cardinality are considered.
We introduce a new approach which can be used to find the minimum beam-on
time for both constrained and unconstrained versions of the problem. The decomposition
cardinality problem is shown to be NP-hard and an approach is proposed to solve the
lexicographic decomposition problem of minimizing the decomposition cardinality subject
to optimal beam-on time.

As an alternative to the commonly used Monte Carlo Simulation methods for solving the Boltzmann equation we have developed a new code with certain important improvements. We present results of calculations on the reentry phase of a space shuttle. One aim was to test physical models of internal energies and of gas-surface interactions.

Chains of Recurrences (CRs) are a tool for expediting the evaluation of elementary expressions over regular grids. CR based evaluations of elementaryexpressions consist of 3 major stages: CR construction, simplification, and evaluation. This paper addresses CR simplifications. The goal of CRsimplifications is to manipulate a CR such that the resulting expression is more efficiently to evaluate. We develop CR simplification strategies which takethe computational context of CR evaluations into account. Realizing that it is infeasible to always optimally simplify a CR expression, we give heuristicstrategies which, in most cases, result in a optimal, or close-to-optimal expressions. The motivations behind our proposed strategies are discussed and theresults are illustrated by various examples.

MP Prototype Specification
(1997)

The problem of providing connectivity for a collection of applications is largely one of data integration: the communicating parties must agree on thesemantics and syntax of the data being exchanged. In earlier papers [#!mp:jsc1!#,#!sg:BSG1!#], it was proposed that dictionaries of definitions foroperators, functions, and symbolic constants can effectively address the problem of semantic data integration. In this paper we extend that earlier work todiscuss the important issues in data integration at the syntactic level and propose a set of solutions that are both general, supporting a wide range of dataobjects with typing information, and efficient, supporting fast transmission and parsing.

Monomial representations and operations for Gröbner bases computations are investigated from an implementation point of view. The technique ofvectorized monomial operations is introduced and it is shown how it expedites computations of Gröbner bases. Furthermore, a rank-based monomialrepresentation and comparison technique is examined and it is concluded that this technique does not yield an additional speedup over vectorizedcomparisons. Extensive benchmark tests with the Computer Algebra System SINGULAR are used to evaluate these concepts.

This paper discusses the benefits and drawbacks of caching and replication strategies in the WWW with respect to the Internet infrastructure. Bandwidth consumption, latency, and overall error rates are considered to be most important from a network point of view. The dependencies of these values with input parameters like degree of replication, document popularity, actual cache hit rates, and error rates are highlighted. In order to determine the influence of different caching and replication strategies on the behavior of a single proxy server with respect to these values, trace-based simulations are used. Since the overall effects of such strate- gies can hardly be decided with this approach alone, a mathematical model has been developed to deal with their influence on the network as a whole. Together, this two-tiered approach permits us to propose quantita- tive assessments on the influence different caching and replication proposals (are going to) have on the Inter- net infrastructure.

The critical points of the continuous series are characterized by two complex numbers l_1,l_2 (Re(l_1,l_2)< 0), and a natural number n (n>=3) which enters the string susceptibility constant through gamma = -2/(n-1). The critical potentials are analytic functions with a convergence radius depending on l_1 or l_2. We use the orthogonal polynomial method and solve the Schwinger-Dyson equations with a technique borrowed from conformal field theory.

We present a complete derivation of the semiclassical limit of the coherent state propagator in one dimension, starting from path integrals in phase space. We show that the arbitrariness in the path integral representation, which follows from the overcompleteness of the coherent states, results in many different semiclassical limits. We explicitly derive two possible semiclassical formulae for the propagator, we suggest a third one, and we discuss their relationships. We also derive an initial value representation for the semiclassical propagator, based on an initial gaussian wavepacket. It turns out to be related to, but different from, Heller's thawed gaussian approximation. It is very different from the Herman - Kluk formula, which is not a correct semiclassical limit. We point out errors in two derivations of the latter. Finally we show how the semiclassical coherent state propagators lead to WKB-type quantization rules and to approximations for the Husimi distributions of stationary states.

In this article a diffusion equation is obtained as a limit of a reversible kinetic equation with an ad hoc scaling. The diffusion is produced by the collisions of the particles with the boundary. These particles are assumed to be reflected according to a reversible law having convenient mixing properties. Optimal convergence results are obtained in a very simple manner. This is made possible because the model, based on Arnold" s cat map can be handled with Fourier series instead of the symbolic dynamics associated to a Markow partition.

We will give explicit differentiation and integration rules for homogeneous harmonic polynomial polynomials and spherical harmonics in IR^3 with respect to the following differential operators: partial_1, partial_2, partial_3, x_3 partial_2 - x_2 partial_3, x_3 partial_1 - x_1 partial_3, x_2 partial_1 - x_1 partial_2 and x_1 partial_1 + x_2 partial_2 + x_3 partial_3. A numerical application to the problem of determining the geopotential field will be shown.

In the field of gravity determination a special kind of boundary value problem respectively ill-posed satellite problem occurs; the data and hence side condition of our PDE are oblique second order derivatives of the gravitational potential. In mathematical terms this means that our gravitational potential \(v\) fulfills \(\Delta v = 0\) in the exterior space of the Earth and \(\mathscr D v = f\) on the discrete data location which is on the Earth's surface for terrestrial measurements and on a satellite track in the exterior for spaceborne measurement campaigns. \(\mathscr D\) is a first order derivative for methods like geometric astronomic levelling and satellite-to-satellite tracking (e.g. CHAMP); it is a second order derivative for other methods like terrestrial gradiometry and satellite gravity gradiometry (e.g. GOCE). Classically one can handle first order side conditions which are not tangential to the surface and second derivatives pointing in the radial direction employing integral and pseudo differential equation methods. We will present a different approach: We classify all first and purely second order operators \(\mathscr D\) which fulfill \(\Delta \mathscr D v = 0\) if \(\Delta v = 0\). This allows us to solve the problem with oblique side conditions as if we had ordinary i.e. non-derived side conditions. The only additional work which has to be done is an inversion of \(\mathscr D\), i.e. integration.

The Earth's surface is an almost perfect sphere. Deviations from its spherical shape are less than 0,4% of its radius and essentially arise from its rotation. All equipotential surfaces are nearly spherical, too. In consequence, multiscale modelling of geoscientifically relevant data on the sphere involving rotational symmetry of the trial functions used for the approximation plays an important role. In this paper we deal with isotropic kernel functions showing local support and (one-dimensional) polynomial structure (briefly called isotropic finite elements) for reconstructing square--integrable functions on the sphere. Essential tool is the concept of multiresolution analysis by virtue of the spherical up function. The main result is a tree algorithm in terms of (low--order) isotropic finite elements.

Using a stereographical projection to the plane we construct an O(N log(N)) algorithm to approximate scattered data in N points by orthogonal, compactly supported wavelets on the surface of a 2-sphere or a local subset of it. In fact, the sphere is not treated all at once, but is split into subdomains whose results are combined afterwards. After choosing the center of the area of interest the scattered data points are mapped from the sphere to the tangential plane through that point. By combining a k-nearest neighbor search algorithm and the two dimensional fast wavelet transform a fast approximation of the data is computed and mapped back to the sphere. The algorithm is tested with nearly 1 million data points and yields an approximation with 0.35% relative errors in roughly 2 minutes on a standard computer using our MATLAB implementation. The method is very flexible and allows the application of the full range of two dimensional wavelets.

The mathematical formulation of many physical problems results in the task of inverting a compact operator. The only known sensible solution technique is regularization which poses a severe problem in itself. Classically one dealt with deterministic noise models and required both the knowledge of smoothness of the solution function and the overall error behavior. We will show that we can guarantee an asymptotically optimal regularization for a physically motivated noise model under no assumptions for the smoothness and rather weak assumptions on the noise behavior which can mostly obtained out of two input data sets. An application to the determination of the gravitational field out of satellite data will be shown.

The first observation of spatiotemporal self-focusing of spin waves is reported. The experimental results are obtained for dipolar spin waves in yttrium-iron-garnet films by means of a newly developed space- and time-resolved Brillouin light scattering technique. They demonstrate self-focusing of a moving wave pulse in two spatial dimensions, and formation of localized two-dimensional wave packets, the collapse of which is stopped by dissipation. The experimental results are in good qualitative agreement with numerical simulations.

We report results of the switching properties of Stoner-like magnetic particles subject to short magnetic field pulses, obtained by numerical investigations. We discuss the switching properties as a function of the external field pulse strength and direction, the pulse length and the pulse shape. For field pulses long compared to the ferromagnetic resonance precession time the switching behavior is governed by the magnetic damping term, whereas in the limit of short field pulses the switching properties are dominated by the details of the precession of the magnetic moment. In the latter case, by choosing the right field pulse parameters, the magnetic damping term is of minor importance and ultrafast switching can be achieved. Switching can be obtained in an enlarged angular range of the direction of the applied field compared to the case of long pulses.

For the next generation of high data rate magnetic recording above 1 Gbit/s, a better understanding of the switching processes for both recording heads and media will be required. In order to maximize the switch-ing speed for such devices, the magnetization precession after the magnetic field pulse termination needs to be suppressed to a maximum degree. It is demonstrated experimentally for ferrite films that the appropriate adjustment of the field pulse parameters and/or the static applied field may lead to a full suppression of the magnetization precession immediately upon termination of the field pulse. The suppression is explained by taking into account the actual direction of the magnetization with respect to the static field direction at the pulse termination.

Wavelet transform originated in 1980's for the analysis of seismic signals has seen an explosion of applications in geophysics. However, almost all of the material is based on wavelets over Euclidean spaces. This paper deals with the generalization of the theory and algorithmic aspects of wavelets to a spherical earth's model and geophysically relevant vector fields such as the gravitational, magnetic, elastic field of the earth.A scale discrete wavelet approach is considered on the sphere thereby avoiding any type of tensor-valued 'basis (kernel) function'. The generators of the vector wavelets used for the fast evaluation are assumed to have compact supports. Thus the scale and detail spaces are finite-dimensional. As an important consequence, detail information of the vector field under consideration can be obtained only by a finite number of wavelet coefficients for each scale. Using integration formulas that are exact up to a prescribed polynomial degree, wavelet decomposition and reconstruction are investigated for bandlimited vector fields. A pyramid scheme for the recursive computation of the wavelet coefficients from level to level is described in detail. Finally, data compression is discussed for the EGM96 model of the earth's gravitational field.

A multiscale method is introduced using spherical (vector) wavelets for the computation of the earth's magnetic field within source regions of ionospheric and magnetospheric currents. The considerations are essentially based on two geomathematical keystones, namely (i) the Mie representation of solenoidal vector fields in terms of toroidal and poloidal parts and (ii) the Helmholtz decomposition of spherical (tangential) vector fields. Vector wavelets are shown to provide adequate tools for multiscale geomagnetic modelling in form of a multiresolution analysis, thereby completely circumventing the numerical obstacles caused by vector spherical harmonics. The applicability and efficiency of the multiresolution technique is tested with real satellite data.

We show how to prove ground confluence of term rewrite relations that areinduced by reductive systems of clausal rewrite rules. According to a well-knowncritical pair criterion it suffices for such systems to prove ground joinability ofa suitable set of 'critical clauses'. We outline how the latter can be done in asystematic fashion, using mathematical induction as a key concept of reasoning.

We describe a technique to make application programs fault tolerant. This techADnique is based on the concept of checkpointing from an active program to one ormore passive backup copies which serve as an abstraction of stable memory. Ifthe primary copy fails, one of the backup copies takes over and resumes processADing service requests. After each failure a new backup copy is created in order torestore the replication degree of the service. All mechanisms necessary to achieveand maintain fault tolerance can be added automatically to the code of a nonADfaulttolerant server, thus making fault tolerance completely transparent for the applicaADtion programmer.

We present a new software architecture in which all concepts necessary to achieve fault tolerance can be added to an appli- cation automatically without any source code changes. As a case study, we consider the problem of providing a reliable service despite node failures by executing a group of replicat- ed servers. Replica creation and management as well as fail- ure detection and recovery are performed automatically by a separate fault tolerance layer (ft-layer) which is inserted be- tween the server application and the operating system kernel. The layer is invisible for the application since it provides the same functional interface as the operating system kernel, thus making the fault tolerance property of the service completely transparent for the application. A major advantage of our ar- chitecture is that the layer encapsulates both fault tolerance mechanisms and policies. This allows for maximum flexibility in the choice of appropriate methods for fault tolerance with- out any changes in the application code.

This paper presents a completely systematic design procedure for asynchronous controllers.The initial step is the construction of a signal transition graph (STG, an interpreted Petri net) ofthe dialog between data path and controller: a formal representation without reference to timeor internal states. To implement concurrently operating control structures, and also to reducedesign effort and circuit cost, this STG can be decomposed into overlapping subnets. A univer-sal initial solution is then obtained by algorithmically constructing a primitive flow table fromeach component net. This step links the procedure to classical asynchronous design, in particu-lar to its proven optimization methods, without restricting the set of solutions. In contrast toother approaches, there is no need to extend the original STG intuitively.

Robust Reliability of Diagnostic Multi-Hypothesis Algorithms: Application to Rotating Machinery
(1998)

Damage diagnosis based on a bank of Kalman filters, each one conditioned on a specific hypothesized system condition, is a well recognized and powerful diagnostic tool. This multi-hypothesis approach can be applied to a wide range of damage conditions. In this paper, we will focus on the diagnosis of cracks in rotating machinery. The question we address is: how to optimize the multi-hypothesis algorithm with respect to the uncertainty of the spatial form and location of cracks and their resulting dynamic effects. First, we formulate a measure of the reliability of the diagnostic algorithm, and then we discuss modifications of the diagnostic algorithm for the maximization of the reliability. The reliability of a diagnostic algorithm is measured by the amount of uncertainty consistent with no-failure of the diagnosis. Uncertainty is quantitatively represented with convex models.

Coordinating distributed processes, especially engineering and software design processes, has been a research topic for some time now. Several approaches have been published that aim at coordinating large projects in general, and large software development processes in specific. However, most of these approaches focus on the technical part of the design process and omit management activities like planning and scheduling the project, or monitoring it during execution. In this paper, we focus on coordinating the management activities that accompany the technical software design process. We state the requirements for a Software Engineering Environm ent (SEE) accommodating management, and we describe a possible architecture for such an SEE.

This paper describes the architecture and concept of operation of a Framework for Adaptive Process Modeling and Execution (FAME). The research addresses the absence of robust methods for supporting the software process management life cycle. FAME employs a novel, model-based approach in providing automated support for different activities in the software development life cycle including project definition, process design, process analysis, process enactment, process execution status monitoring, and execution status-triggered process redesign. FAME applications extend beyond the software development domain to areas such as agile manufacturing, project management, logistics planning, and business process reengineering.

In this paper we present an extensional higher-order resolution calculus that iscomplete relative to Henkin model semantics. The treatment of the extensionality princi-ples - necessary for the completeness result - by specialized (goal-directed) inference rulesis of practical applicability, as an implentation of the calculus in the Leo-System shows.Furthermore, we prove the long-standing conjecture, that it is sufficient to restrict the orderof primitive substitutions to the order of input formulae.

In this paper we provide a semantical meta-theory that will support the development of higher-order calculi for automated theorem proving like the corresponding methodology has in first-order logic. To reach this goal, we establish classes of models that adequately characterize the existing theorem-proving calculi, that is, so that they are sound and complete to these calculi, and a standard methodology of abstract consistency methods (by providing the necessary model existence theorems) needed to analyze completeness of machine-oriented calculi.

Abstract: Random matrix theory (RMT) is a powerful statistical tool to model spectral fluctuations. In addition, RMT provides efficient means to separate different scales in spectra. Recently RMT has found application in quantum chromodynamics (QCD). In mesoscopic physics, the Thouless energy sets the universal scale for which RMT applies. We try to identify the equivalent of a Thouless energy in complete spectra of the QCD Dirac operator with staggered fermions and SU_(2) lattice gauge fields. Comparing lattice data with RMT predictions we find deviations which allow us to give an estimate for this scale.

Beyond the Thouless energy
(1999)

Abstract: The distribution and the correlations of the small eigenvalues of the Dirac operator are described by random matrix theory (RMT) up to the Thouless energy E_= 1 / sqrt (V), where V is the physical volume. For somewhat larger energies, the same quantities can be described by chiral perturbation theory (chPT). For most quantities there is an intermediate energy regime, roughly 1/V < E < 1/sqrt (V), where the results of RMT and chPT agree with each other. We test these predictions by constructing the connected and disconnected scalar susceptibilities from Dirac spectra obtained in quenched SU(2) and SU(3) simulations with staggered fermions for a variety of lattice sizes and coupling constants. In deriving the predictions of chPT, it is important totake into account only those symmetries which are exactly realized on the lattice.

Abstract: Recently, the chiral logarithms predicted by quenched chiral perturbation theory have been extracted from lattice calculations of hadron masses. We argue that the deviations of lattice results from random matrix theory starting around the so-called Thouless energy can be understood in terms of chiral perturbation theory as well. Comparison of lattice data with chiral perturbation theory formulae allows us to compute the pion decay constant. We present results from a calculation for quenched SU(2) with Kogut-Susskind fermions at ß = 2.0 and 2.2.

Abstract: Recently, the contributions of chiral logarithms predicted by quenched chiral perturbation theory have been extracted from lattice calculations of hadron masses. We argue that a detailed comparison of random matrix theory and lattice calculations allows for a precise determination of such corrections. We estimate the relative size of the m log(m), m, and m^2 corrections to the chiral condensate for quenched SU(2).

We have computed ensembles of complete spectra of the staggered Dirac operator using four-dimensional SU(2) gauge fields, both in the quenched approximation and with dynamical fermions. To identify universal features in the Dirac spectrum, we compare the lattice data with predictions from chiral random matrix theory for the distribution of the low-lying eigenvalues. Good agreement is found up to some limiting energy, the so-called Thouless energy, above which random matrix theory no longer applies. We determine the dependence of the Thouless energy on the simulation parameters using the scalar susceptibility and the number variance.

We present results from a study of the coherence properties of a system involving three discrete states coupled to each other by two-photon processes via a common continuum. This tripod linkage is an extension of the standard laser-induced continuum structure (LICS) which involves two discrete states and two lasers. We show that in the tripod scheme, there exist two population trapping conditions; in some cases these conditions are easier to satisfy than the single trapping condition in two-state LICS. Depending on the pulse timing, various effects can be observed. We derive some basic properties of the tripod scheme, such as the solution for coincident pulses, the behaviour of the system in the adiabatic limit for delayed pulses, the conditions for no ionization and for maximal ionization, and the optimal conditions for population transfer between the discrete states via the continuum. In the case when one of the discrete states is strongly coupled to the continuum, the population dynamics reduces to a standard two-state LICS problem (involving the other two states) with modified parameters; this provides the opportunity to customize the parameters of a given two-state LICS system.

Abstract: We propose a simple method for measuring the populations and the relative phase in a coherent superposition of two atomic states. The method is based on coupling the two states to a third common (excited) state by means of two laser pulses, and measuring the total fluorescence from the third state for several choices of the excitation pulses.

This paper presents a brief overview of the INRECA-II methodology for building and maintaining CBR applications. It is based on the experience factory and the software process modeling approach from software engineering. CBR development and maintenance experience is documented using software process models and stored in a three-layered experience packet.

For defining attribute types to be used in the case representation, taxonomies occur quite often. The symbolic values at any node of the taxonomy tree are used as attribute values in a case or a query. A taxonomy type represents a relationship between the symbols through their position within the taxonomy-tree which expresses knowledge about the similarity between the symbols. This paper analyzes several situations in which taxonomies are used in different ways and proposes a systematic way of specifying local similarity measures for taxonomy types. The proposed similarity measures have a clear semantics and are easy to compute at runtime.

Collecting Experience on the Systematic Development of CBR Applications using the INRECA Methodology
(1999)

This paper presents an overview of the INRECA methodology for building and maintaining CBR applications. This methodology supports the collection and reuse of experience on the systematic development of CBR applications. It is based on the experience factory and the software process modeling approach from software engineering. CBR development experience is documented using software process models and stored in different levels of generality in a three-layered experience base. Up to now, experience from 9 industrial projects enacted by all INRECA II partners has been collected.

Complex problem solving can be substantially improved by the reuse of experience from previously solved problems. This requires that case libraries of successful problem solutions are transformed into problem solving knowledge with high utility, i.e. knowledge which causes high savings in search time, high application probability and low matching costs in a respective performance component. Planning can be improved by explanation-based learning (EBL) of abstract plans from detailed, successfully solved planning problems. Abstract plans, expressed in well-established terms of the domain, serve as useful problem decompositions which can drastically reduce the planning complexity. Abstractions which are valid for a class of planning cases rather than for a single case, ensure a successful application in a larger spectrum of new situations. The hierarchical organization of the learned shared abstractions causes low matching costs. The presented S-PABS procedure is an EBL-procedure in which abstraction, learning from multiple examples and hierarchical clustering are combined to automatically construct a hierarchy of shared abstract plans by analyzing concrete planning cases. A specific planning procedure has been designed to solve new planning problems guided by the knowledge learned by S-PABS. By allowing a feedback from this planning procedure to the learning component, the integrated system shows an increase in performance through past problem solving.

Although skeletal plan refinement is used in several planning systems, a procedure for the automatic acquisition of such high-level plans has not yet been developed. The proposed explanation- based knowledge acquisition procedure constructs a skeletal plan automatically from a sophisticated concrete planning case. The classification of that case into a well-described class of problems serves as an instrument for adjusting the applicability of the acquired skeletal plans to that class. The four phases of the proposed procedure are constituted as follows: In the first phase, the execution of the source plan is simulated, and explanations for the effects of the occurred operators are constructed. In the second phase, the generalization of these explanations is performed with respect to a criterion of operationality which specifies the vocabulary for defining abstract operators for the skeletal plan. The third phase, a dependency analysis of the resulting operator effects, unveils the interactions of the concrete plan which are substantial for the specified class. In the forth phase, the concept descriptions for the abstract operators of the skeletal plan are formed by collecting and normalizing the important constraints for each operation that were indicated by the dependencies. With this procedure sophisticated planning solutions from human experts can be generalized into skeletal plans and consequently be reused by a planning system in novel situations.

Abstraction is one of the most promising approaches to improve the performance of problem solvers. Abstraction by dropping sentences of a domain description - as used in most hierarchical planners - is known to be very representation dependent. To overcome these drawbacks, we propose a more general view of abstraction involving the change of representation language. We have developed a new abstraction methodology and a related sound and complete learning algorithm that allows the complete change of representation language of planning cases from concrete to abstract.

Recently, the use of abstraction in case-based reasoning (CBR) is getting more and more popular. The basic idea is to supply a CBR system with cases at many different levels of abstraction. When a new problem must be solved, one (or several) 'appropriate' concrete or abstract case are retrieved from the case base and the solution that the case contains is reused to derive a solution for the current problem, e.g. by filling in the details that a retrieved case at some higher level of abstraction does not contain. A major problem that occurs when using this approach is, that for a given new problem, usually several cases, e.g., from different levels of abstraction could be reused to solve the new problem. Choosing a wrong abstract case can slow down the problem solving process or even prevents the problem from being solved.

Hierachical planning can be improved by explanation-based learning (EBL) of abstract plans from detailed, successfully solved planning problems. Abstract plans, expressed in well-established terms of the domain, serve as useful problem decompositions which can drastically reduce the planning complexity. The learned plan abstraction must be valid for a class of planning cases rather than for a single case, to ensure their successful application in a larger spectrum of new situations. A hierarchical organization of the newly learned knowledge must be archieved to overcome the utility problem in EBL. This paper presents a new formal model of shared plan abstraction and the closely related explanation-based procedure S-PABS. Unlike other apporaches to plan abstraction, our model allows a total different terminology to be introduced at the abstract level. Finally, an unsupervised incremental procedure for constructing a hierachy of shared abstract plans is proposed, as a kind of concept formation over explanations.

As the previous chapters of this book have shown, case-based reasoning is a technology that has been successfully applied to a large range of different tasks. Through all the different CBR projects, both basic research projects as well as industrial development projects, lots of knowledge and experience about how to build a CBR application has been collected. Today, there is already an increasing number of successful companies developing industrial CBR applications. In former days, these companies could develop their early pioneering CBR applications in an ad-hoc manner. The highly-skilled CBR expert of the company was able to manage these projects and to provide the developers with the required expertise.

Planning means constructing a course of actions to achieve a specified set of goals when starting from an initial situation. For example, determining a sequence of actions (a plan) for transporting goods from an initial location to some destination is a typical planning problem in the transportation domain. Many planning problems are of practical interest.

Case-based problem solving can be significantly improved by applying domain knowledge (in opposition to problem solving knowledge), which can be acquired with reasonable effort, to derive explanations of the correctness of a case. Such explanations, constructed on several levels of abstraction, can be employed as the basis for similarity assessment as well as for adaptation by solution refinement. The general approach for explanation-based similarity can be applied to different real world problem solving tasks such as diagnosis and planning in technical areas. This paper presents the general idea as well as the two specific, completely implemented realizations for a diagnosis and a planning task.

Object-oriented case representations require approaches for similarity assessment that allow to compare two differently structured objects, in particular, objects belonging to different object classes. Currently, such similarity measures are developed more or less in an ad-hoc fashion. It is mostly unclear, how the structure of an object-oriented case model, e.g., the class hierarchy, influences similarity assessment. Intuitively, it is obvious that the class hierarchy contains knowledge about the similarity of the objects. However, how this knowledge relates to the knowledge that could be represented in similarity measures is not obvious at all. This paper analyzes several situations in which class hierarchies are used in different ways for case modeling and proposes a systematic way of specifying similarity measures for comparing arbitrary objects from the hierarchy. The proposed similarity measures have a clear semantics and are computationally inexpensive to compute at run-time.