## Institut für Informatik und Computational Science

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We discuss the relaxation of a class of nonlinear elliptic Cauchy problems with data on a piece S of the boundary surface by means of a variational approach known in the optimal control literature as "equation error method". By the Cauchy problem is meant any boundary value problem for an unknown function y in a domain X with the property that the data on S, if combined with the differential equations in X, allow one to determine all derivatives of y on S by means of functional equations. In the case of real analytic data of the Cauchy problem, the existence of a local solution near S is guaranteed by the Cauchy-Kovalevskaya theorem. We also admit overdetermined elliptic systems, in which case the set of those Cauchy data on S for which the Cauchy problem is solvable is very "thin". For this reason we discuss a variational setting of the Cauchy problem which always possesses a generalised solution.

Owing to the loose coupling between replicas, the replica-exchange (RE) class of algorithms should be able to benefit greatly from using as many resources as available. However, the ability to effectively use multiple distributed resources to reduce the time to completion remains a challenge at many levels. Additionally, an implementation of a pleasingly distributed algorithm such as replica-exchange, which is independent of infrastructural details, does not exist. This paper proposes an extensible and scalable framework based on Simple API for Grid Applications that provides a general-purpose, opportunistic mechanism to effectively use multiple resources in an infrastructure-independent way. By analysing the requirements of the RE algorithm and the challenges of implementing it on real production systems, we propose a new abstraction (BIGJOB), which forms the basis of the adaptive redistribution and effective scheduling of replicas.

This paper presents a concept for automated architecture synthesis for adaptive multiprocessors on chip, in particular for Field-Programmable Gate-Array (FPGA) devices. Given a parallel program, the intent is to simultaneously allocate processor resources and the corresponding communication network, and at the same time, to map the parallel application to get an optimum application-specific architecture. This approach builds up on a previously proposed design platform that automates system integration and FPGA synthesis for such architectures. As a result, the overall concept offers an automated design approach from application mapping to system and FPGA configuration. The automated synthesis is based on combinatorial optimization. Automation is possible because a solvable Integer Linear Programming (ILP) model that captures all necessary design trade-off parameters of such systems has been found. Experimental results to study the feasibility of the automated synthesis indicate that problems with sizes that can be encountered in the embedded domain can be readily solved. Results obtained underscore the need for an automated synthesis for design space exploration.

We investigate the descriptional complexity of the nondeterministic finite automaton (NFA) to the deterministic finite automaton (DFA) conversion problem, for automata accepting subregular languages such as combinational languages, definite languages and variants thereof, (strictly) locally testable languages, star-free languages, ordered languages, prefix-, suffix-, and infix-closed languages, and prefix-, Suffix-, and infix-free languages. Most of the bounds for the conversion problem are shown to be tight ill the exact number of states, that is, the number is sufficient and necessary in the worst case. Otherwise tight bounds in order of magnitude are shown.

We address classification problems for which the training instances are governed by an input distribution that is allowed to differ arbitrarily from the test distribution-problems also referred to as classification under covariate shift. We derive a solution that is purely discriminative: neither training nor test distribution are modeled explicitly. The problem of learning under covariate shift can be written as an integrated optimization problem. Instantiating the general optimization problem leads to a kernel logistic regression and an exponential model classifier for covariate shift. The optimization problem is convex under certain conditions; our findings also clarify the relationship to the known kernel mean matching procedure. We report on experiments on problems of spam filtering, text classification, and landmine detection.

The ellipticity of operators on a manifold with edge is defined as the bijectivity of the components of a principal symbolic hierarchy sigma = (sigma(psi), sigma(boolean AND)), where the second component takes values in operators on the infinite model cone of the local wedges. In the general understanding of edge problems there are two basic aspects: Quantisation of edge-degenerate operators in weighted Sobolev spaces, and verifying the ellipticity of the principal edge symbol sigma(boolean AND) which includes the (in general not explicity known) number of additional conditions of trace and potential type on the edge. We focus here on these questions and give explicit answers for a wide class of elliptic operators that are connected with the ellipticity of edge boundary value problems and reductions to the boundary. In particular, we study the edge quantisation and ellipticity for Dirichlet-Neumann operators with respect to interfaces of some codimension on a boundary. We show analogues of the Agranovich-Dynin formula for edge boundary value problems.

Two mapping populations of a cross between the Arabidopsis thaliana accessions Col-0 and C24 were cultivated and analyzed with respect to the levels of 181 metabolites to elucidate the biological phenomenon of heterosis at the metabolic level. The relative mid-parent heterosis in the F-1 hybrids was <20% for most metabolic traits. The first mapping population consisting of 369 recombinant inbred lines (RILs) and their test cross progeny with both parents allowed us to determine the position and effect of 147 quantitative trait loci (QTL) for metabolite absolute mid-parent heterosis (aMPH). Furthermore, we identified 153 and 83 QTL for augmented additive (Z(1)) and dominance effects (Z(2)), respectively. We identified putative candidate genes for these QTL using the ARACYC database (http://www.arabidopsis.org/ biocyc), and calculated the average degree of dominance, which was within the dominance and over-dominance range for most metabolites. Analyzing a second population of 41 introgression lines (ILs) and their test crosses with the recurrent parent, we identified 634 significant differences in metabolite levels. Nine per cent of these effects were classified as over-dominant, according to the mode of inheritance. A comparison of both approaches suggested epistasis as a major contributor to metabolite heterosis in Arabidopsis. A linear combination of metabolite levels was shown to significantly correlate with biomass heterosis (r = 0.62).

Introductory Bioinformatics
(2009)

Answer set programming (ASP) does not allow for incrementally constructing answer sets or locally validating constructions like proofs by only looking at a part of the given program. In this article, we elaborate upon an alternative approach to ASP that allows for incremental constructions. Our approach draws its basic intuitions from the area of default logics. We investigate the feasibility of the concept of semi-monotonicity known from default logics as a basis of incrementality. On the one hand, every logic program has at least one answer set in our alternative setting, which moreover can be constructed incrementally based on generating rules. On the other hand, the approach may produce answer sets lacking characteristic properties of standard answer sets, such as being a model of the given program. We show how integrity constraints can be used to re-establish such properties, even up to correspondence with standard answer sets. Furthermore, we develop an SLD-like proof procedure for our incremental approach to ASP, which allows for query-oriented computations. Also, we provide a characterization of our definition of answer sets via a modification of Clarks completion. Based on this notion of program completion, we present an algorithm for computing the answer sets of a logic program in our approach.

We introduce and investigate input-revolving finite automata, which are (nondeterministic) finite state automata with the additional ability to shift the remaining part of the input. Three different modes of shifting are considered, namely revolving to the left, revolving to the right, and circular-interchanging. We investigate the computational capacities of these three types of automata and their deterministic variants, comparing any of the six classes of automata with each other and with further classes of well-known automata. In particular, it is shown that nondeterminism is better than determinism, that is, for all three modes of shifting there is a language accepted by the nondeterministic model but not accepted by any deterministic automaton of the same type. Concerning the closure properties most of the deterministic language families studied are not closed under standard operations. For example, we show that the family of languages accepted by deterministic right-revolving finite automata is an anti-AFL which is not closed under reversal and intersection.

We study the complexity of two-person constraint satisfaction games. An instance of such a game is given by a collection of constraints on overlapping sets of variables, and the two players alternately make moves assigning values from a finite domain to the variables, in a specified order. The first player tries to satisfy all constraints, while the other tries to break at least one constraint: the goal is to decide whether the first player has a winning strategy. We show that such games can be conveniently represented by a logical form of quantified constraint satisfaction, where an instance is given by a first-order sentence in which quantifiers alternate and the quantifier-free part is a conjunction of (positive) atomic formulas; the goal is to decide whether the sentence is true. While the problem of deciding such a game is PSPACE-complete in general, by restricting the set of allowed constraint predicates, one can obtain infinite classes of constraint satisfaction games of lower complexity. We use the quantified constraint satisfaction framework to study how the complexity of deciding such a game depends on the parameter set of allowed predicates. With every predicate. one can associate certain predicate-preserving operations, called polymorphisms. We show that the complexity of our games is determined by the surjective polymorphisms of the constraint predicates. We illustrate how this result can be used by identifying the complexity of a wide variety of constraint satisfaction games.

Using the timing flexibility of modern automatic test equipment (ATE) test response data can be compacted without the need for additional X-masking logic. In this article the test response is compacted by several multiple input shift registers without feedback (NF-MISR). The shift registers are running on a k-times higher clock frequency than the test clock. For each test clock cycle only one out of the k outputs of each shift register is evaluated by the ATE. The impact of consecutive X values within the scan chains is reduced by a periodic permutation of the NF-MISR inputs. As a result, no additional external control signals or test set dependent control logic is required. The benefits of the proposed method are shown by the example of an implementation on a Verigy ATE. Experiments on three industrial circuits demonstrate the effectiveness of the proposed approach in comparison to a commercial DFT solution.