Dynamic Programming for Graphs on Surfaces

We provide a framework for the design and analysis of dynamic programming algorithms for surface-embedded graphs on n vertices and branchwidth at most k. Our technique applies to general families of problems where standard dynamic programming runs in 2^{O(k log k)} n steps. Our approach combines tools from topological graph theory and analytic combinatorics. In particular, we introduce a new type of branch decomposition called "surface cut decomposition", generalizing sphere cut decompositions of planar graphs introduced by Seymour and Thomas, which has nice combinatorial properties. Namely, the number of partial solutions that can be arranged on a surface cut decomposition can be upper-bounded by the number of non-crossing partitions on surfaces with boundary. It follows that partial solutions can be represented by a single-exponential (in the branchwidth k) number of configurations. This proves that, when applied on surface cut decompositions, dynamic programming runs in 2^{O(k)} n steps. That way, we considerably extend the class of problems that can be solved in running times with a single-exponential dependence on branchwidth and unify/improve most previous results in this direction.Comment: 28 pages, 3 figure

Dynamic programming for graphs on surfaces

We provide a framework for the design and analysis of dynamic programming algorithms for surface-embedded graphs on n vertices and branchwidth at most k. Our technique applies to general families of problems where standard dynamic programming runs in 2O(k·log k). Our approach combines tools from topological graph theory and analytic combinatorics.Postprint (updated version

Coordinate representation of particle dynamics in AdS and in generic static spacetimes

We discuss the quantum dynamics of a particle in static curved spacetimes in a coordinate representation. The scheme is based on the analysis of the squared energy operator E^2, which is quadratic in momenta and contains a scalar curvature term. Our main emphasis is on AdS spaces, where this term is fixed by the isometry group. As a byproduct the isometry generators are constructed and the energy spectrum is reproduced. In the massless case the conformal symmetry is realized as well. We show the equivalence between this quantization and the covariant quantization, based on the Klein-Gordon type equation in AdS. We further demonstrate that the two quantization methods in an arbitrary (N+1)-dimensional static spacetime are equivalent to each other if the scalar curvature terms both in the operator E^2 and in the Klein-Gordon type equation have the same coefficient equal to (N-1)/(4N).Comment: 14 pages, no figures, typos correcte

Efficiency of vibrational sounding in parasitoid host location depends on substrate density

Parasitoids of concealed hosts have to drill through a substrate with their ovipositor for successful parasitization. Hymenopteran species in this drill-and-sting guild locate immobile pupal hosts by vibrational sounding, i.e., echolocation on solid substrate. Although this host location strategy is assumed to be common among the Orussidae and Ichneumonidae there is no information yet whether it is adapted to characteristics of the host microhabitat. This study examined the effect of substrate density on responsiveness and host location efficiency in two pupal parasitoids, Pimpla turionellae and Xanthopimpla stemmator (Hymenoptera: Ichneumonidae), with different host-niche specialization and corresponding ovipositor morphology. Location and frequency of ovipositor insertions were scored on cylindrical plant stem models of various densities. Substrate density had a significant negative effect on responsiveness, number of ovipositor insertions, and host location precision in both species. The more niche-specific species X. stemmator showed a higher host location precision and insertion activity. We could show that vibrational sounding is obviously adapted to the host microhabitat of the parasitoid species using this host location strategy. We suggest the attenuation of pulses during vibrational sounding as the energetically costly limiting factor for this adaptatio

Sources of semiochemicals mediating host finding in Callosobruchus chinensis (Coleoptera: Bruchidae)

Bruchid pests such as Callosobruchus chinensis (Linnaeus) endanger stored legume seeds throughout the tropical belt. The chemical composition of the headspace volatiles from healthy and fourth instar larvae-infested cowpea seeds were identified, characterized, and compared using gas chromatography-mass spectrometry. Y-tube olfactometer bioassays were performed to evaluate the effect of these chemicals on the orientation of conspecific adult females. Analysis of volatiles released from healthy and infested seeds revealed qualitative differences for three out of the 17 compounds identified. Dimethyl disulphide, isobutenyl methyl ketone and methyl trisulphide were found only in the blend emitted from infested but not from healthy seeds. Quantitative differences were apparent for tridecane which was released in larger amounts from infested seeds. While volatiles collected from healthy seeds were attractive to female bruchids, volatiles collected from infested seeds were repellent. To test the hypothesis that the qualitative differences in the chemical composition found may be due to insect-derived components, the volatiles from frass and fourth instar larvae combined were analysed. These volatiles contained both of the sulphides emitted from infested seed but not from healthy seeds. Although a limited induction of volatiles from cowpea seeds cannot be excluded, it is postulated that behavioural differences of the female weevils are largely due to insect-derived semiochemicals. The potential use of such semiochemicals as part of an integrated pest management strategy is discusse