In this paper we determine the class of four-dimensional Lorentzian manifolds that can be completely characterized by the scalar polynomial curvature invariants constructed from the Riemann tensor and its covariant derivatives. We introduce the notion of an I-non-degenerate spacetime metric, which implies that the spacetime metric is locally determined by its curvature invariants. By determinin...

Many graph problems were first shown to be fixed-parameter tractable using the results of Robertson and Seymour on graph minors. We show that the combination of finite, computable, obstruction sets and efficient order tests is not just one way of obtaining strongly uniform FPT algorithms, but that all of FPT may be captured in this way. Our new characterization of FPT has a strong connection to...

The complexity classes characterized by semirandom sources were investigated. U.V. Vazirani and V.V Vazirani [VV85] showed that 8 -RP = RP, and U.V. Vazirani [Vaz86] showed that 8 -BPP = BPP, where, for the random class C, the class 8 -C is a set of all languages which satisfy the condition for C by using any -random source. First, we show

The Coloring problem is to test whether a given graph can be colored with at most k colors for some given k, such that no two adjacent vertices receive the same color. The complexity of this problem on graphs that do not contain some graph H as an induced subgraph is known for each fixed graph H. A natural variant is to forbid a graph H only as a subgraph. We call such graphs strongly H-free an...

Methods for biological function recognition in silico appeared to be useful also for identifying characteristics of structure-to-function relations. The introduction of a three-dimensional Gauss function was assumed to represent the hydrophobic core in a protein molecule. The discrepancy between idealized "fuzzy oil-drop" and the observed one in real proteins appeared to be localized in the lig...