Physical Sciences and Mathematics Commons^™

Topology Tracking For The Visualization Of Time-Dependent Two-Dimensional Flows, Xavier Tricoche, Thomas Wischgoll, Gerik Scheuermann, Hans Hagen

Computer Science and Engineering Faculty Publications

The paper presents a topology-based visualization method for time-dependent two-dimensional vector fields. A time interpolation enables the accurate tracking of critical points and closed orbits as well as the detection and identification of structural changes. This completely characterizes the topology of the unsteady flow. Bifurcation theory provides the theoretical framework. The results are conveyed by surfaces that separate subvolumes of uniform flow behavior in a three-dimensional space–time domain.

Towards Nonmonotonic Reasoning On Hierarchical Knowledge, Pascal Hitzler

Computer Science and Engineering Faculty Publications

W.C. Rounds and G.Q. Zhang have recently proposed to study a form of disjunctive logic programming generalized to algebraic domains [RZ01]. This system allows reasoning with information which is hierarchically structured and forms a (suitable) domain. We extend this framework to include reasoning with negative information, i.e. the implicit or explicit absence of bits of information. These investigations will naturally lead to a form of default reasoning which is strongly related to programming with answer sets to stable models, which has recently created much interest amongst artificial intelligence researchers concerned with knowledge representation and reasoning.

Ilp Operators For Propositional Connectionist Networks, Miguel Angel Gutierrez-Naranjo, Pascal Hitzler

Computer Science and Engineering Faculty Publications

No abstract provided.

Closed Streamlines In Flow Visualization, Thomas Wischgoll

Computer Science and Engineering Faculty Publications

Vector Fields occur in many of the problems in science and engineering. In combustion processes for instance, vector fields describe the flow of the gas. This process can be enhanced using vector field visualization techniques. Also wind tunnel experiments can be analyzed. An example is the design of an air wing. The wing can be optimized to crate a smoother flow around it. Vector field visualization methods help the engineer to detect critical features of the flow. Consequently, feature detection methods gained great importance during the last years.

Topological methods are often used to visualize vector fields because they clearly …

The Fixed-Point Theorems Of Priess-Crampe And Ribenboim In Logic Programming, Pascal Hitzler, Anthony K. Seda

Computer Science and Engineering Faculty Publications

Sibylla Priess-Crampe and Paulo Ribenboim recently established a general fixed-point theorem for multivalued mappings defined on generalized ultrametric spaces, and introduced it to the area of logic programming semantics. We discuss, in this context, the applications which have been made so far of this theorem and of its corollaries. In particular, we will relate these results to Scott-Ershov domains, familiar in programming language semantics, and to the generalized metrics of Khamsi, Kreinovich, and Misane which have been applied, by these latter authors, to logic programming. Amongst other things, we will also show that a unified treatment of the fixed-point theory …

Characterizing Logic Programming Semantics With Level Mappings, Pascal Hitzler, Matthias Wendt

Computer Science and Engineering Faculty Publications

Declarative semantics in logic programming and nonmonotonic reasoning are often defined via fixed points of semantic operators. While many relationships between different semantics known from the literature have been studied, a uniform treatment is still missing. In this paper, we provide uniform operator-free characterizations for some of the most important semantics, more precisely, for the stable, the well-founded, and the Fitting semantics, for the weakly-perfect model semantics, and for the least model semantics for negation-free programs.