QMusExt: A Minimal (Un)satisfiable Core Extractor for Quantified Boolean Formulas

In this paper, we present QMusExt, a tool for the extraction of minimal unsatisfiable sets (MUS) from quantified Boolean formulas (QBFs) in prenex conjunctive normal form (PCNF). Our tool generalizes an efficient algorithm for MUS extraction from propositional formulas that analyses and rewrites resolution proofs generated by SAT solvers. In addition to extracting unsatisfiable cores from false formulas in PCNF, we apply QMusExt also to obtain satisfiable cores from Q-resolution proofs of true formulas in prenex disjunctive normal form (PDNF)

Zylindrische Dekomposition unter anwendungsorientierten Paradigmen

Quantifier elimination (QE) is a powerful tool for problem solving. Once a problem is expressed as a formula, such a method converts it to a simpler, quantifier-free equivalent, thus solving the problem. Particularly many problems live in the domain of real numbers, which makes real QE very interesting. Among the so far implemented methods, QE by cylindrical algebraic decomposition (CAD) is the most important complete method. The aim of this thesis is to develop CAD-based algorithms, which can solve more problems in practice and/or provide more interesting information as output. An algorithm that satisfies these standards would concentrate on generic cases and postpone special and degenerated ones to be treated separately or to be abandoned completely. It would give a solution, which is locally correct for a region the user is interested in. It would give answers, which can provide much valuable information in particular for decision problems. It would combine these methods with more specialized ones, for subcases that allow for. It would exploit degrees of freedom in the algorithms by deciding to proceed in a way that promises to be efficient. It is the focus of this dissertation to treat these challenges. Algorithms described here are implemented in the computer logic system REDLOG and ship with the computer algebra system REDUCE

Utilizing Multi-Level Concepts for Multi-Phase Modeling

In model-based systems engineering projects, engineers from multiple domains collaborate by establishing a common system model. Multi-level modeling is a technique that can be used to model the development from abstract ideas to concrete implementations. However, current multi-level modeling approaches are not adequate for processes with multiple modeling phases that might have to be rearranged later. In this paper, we introduce multi-phase modeling that utilizes concepts of multi-level modeling by considering a description of the expected phase ordering per domain. Constraints aware of this context can express that certain elements are only valid in specific phases without having to determine a concrete phase ordering for a particular model. This enables using multi-phase modeling in flexible workflows, adapting to changing requirements and the definition of access rules in domain notation. We show feasibility of this multi-phase modeling by applying it to multiple real-life systems engineering projects of the aerospace domain

Intracule densities in the strong-interaction limit of density functional theory

The correlation energy in density functional theory can be expressed exactly in terms of the change in the probability of finding two electrons at a given distance $r_{12}$ (intracule density) when the electron-electron interaction is multiplied by a real parameter $\lambda$ varying between 0 (Kohn-Sham system) and 1 (physical system). In this process, usually called adiabatic connection, the one-electron density is (ideally) kept fixed by a suitable local one-body potential. While an accurate intracule density of the physical system can only be obtained from expensive wavefunction-based calculations, being able to construct good models starting from Kohn-Sham ingredients would highly improve the accuracy of density functional calculations. To this purpose, we investigate the intracule density in the $\lambda\to\infty$ limit of the adiabatic connection. This strong-interaction limit of density functional theory turns out to be, like the opposite non-interacting Kohn-Sham limit, mathematically simple and can be entirely constructed from the knowledge of the one-electron density. We develop here the theoretical framework and, using accurate correlated one-electron densities, we calculate the intracule densities in the strong interaction limit for few atoms. Comparison of our results with the corresponding Kohn-Sham and physical quantities provides useful hints for building approximate intracule densities along the adiabatic connection of density functional theory.Comment: 20 pages, 8 figures. Submitted to Phys. Chem. Chem. Phy

A Cadaveric Pilot Study

This study investigates the adhesion capacity of a polyglycolic acid- (PGA-) hyaluronan scaffold with a structural modification based on a planar polymer (PM) surface in a cadaver cartilage defect model. Two cadaver specimens were used to serially test multiple chondral matrices. In a cadaver hip model, cell free polymer-based cartilage implants with a planar bioinspired PM surface (PGA-PM-scaffolds) were implanted arthroscopically on 10 mm × 15 mm full- thickness femoral hip cartilage lesions. Unprocessed cartilage implants without a bioinspired PM surface were used as control group. The cartilage implants were fixed without and with the use of fibrin glue on femoral hip cartilage defects. After 50 movement cycles and removal of the distraction, a rearthroscopy was performed to assess the outline attachment and integrity of the scaffold. The fixation techniques without and with fibrin fixation showed marginal differences for outline attachment, area coverage, scaffold integrity, and endpoint fixation after 50 cycles. The PGA-PM-scaffolds with fibrin fixation achieved a higher score in terms of the attachment, integrity, and endpoint fixation than the PGA-scaffold on the cartilage defect. Relating to the outline attachment, area coverage, scaffold integrity, and endpoint fixation, the fixation with PGA-PM-scaffolds accomplished significantly better results compared to the PGA-scaffolds . PGA-PM-scaffolds demonstrate increased observed initial fixation strength in cadaver femoral head defects relative to PGA-scaffold, particularly when fibrin glue is used for fixation