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

Microsatellites reveal genetic differentiation among populations in an insect species with high genetic variability in dispersal, the codling moth, Cydia pomonella (L.) (Lepidoptera: Tortricidae)

Little is known about genetic differentiation and gene flow in populations of insect species that have a high genetic variability in dispersal but lack morphologically visible morphs that disperse. These characteristics apply to the codling moth, Cydia pomonella L. (Lepidoptera: Tortricidae), a major pest of fruits and nuts. Larvae were collected from three orchards each of pome fruits, stone fruits and nut trees in a major fruit growing area of Switzerland (Valais) and from six further (mainly apple) orchards throughout this country. Nine microsatellite loci were used to investigate genetic differentiation and the amount of gene flow among the sampled populations. All the loci were shown to be polymorphic in all populations. The number of alleles ranged from five to 15 over nine loci for the 15 populations. Significant genetic differentiation was noted among the populations from apple, apricot and walnut in the Valais region. Furthermore, among the eight populations sampled from apple in different geographic regions throughout Switzerland, AMOVA and pairwise FST analysis revealed significant population genetic differentiation even between populations collected from orchards 10 km apart. These results indicate that a distinct prevailing characteristic, in the present case the sedentary behaviour of the moth, can shape population architectur

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

Linking the evolution of terrestrial interiors and an early outgassed atmosphere to astrophysical observations

A terrestrial planet is molten during formation and may remain so if subject to intense insolation or tidal forces. Observations continue to favour the detection and characterisation of hot planets, potentially with large outgassed atmospheres. We aim to determine the radius of hot Earth-like planets with large outgassed atmospheres and explore differences between molten and solid silicate planets and their influence on the mass-radius relationship and transmission and emission spectra. An interior-atmosphere model, combined with static structure calculations, tracks the evolving radius of a rocky mantle that is outgassing CO$_2$ and H$_2$O. Synthetic emission and transmission spectra are generated for CO$_2$ and H$_2$O dominated atmospheres. Atmospheres dominated by CO$_2$ suppress the outgassing of H$_2$O to a greater extent than previously realised, as previous studies have applied an erroneous relationship between volatile mass and partial pressure. We therefore predict more H$_2$O can be retained by the interior during the later stages of magma ocean crystallisation. Furthermore, formation of a lid at the surface can tie outgassing of H$_2$O to the efficiency of heat transport through the lid, rather than the atmosphere's radiative timescale. Contraction of the mantle as it solidifies gives $\sim5\%$ radius decrease, which can partly be offset by addition of a relatively light species to the atmosphere. We conclude that a molten silicate mantle can increase the radius of a terrestrial planet by around $5\%$ compared to its solid counterpart, or equivalently account for a $13\%$ decrease in bulk density. An outgassing atmosphere can perturb the total radius according to its speciation. Atmospheres of terrestrial planets around M-stars that are dominated by CO$_2$ or H$_2$O can be distinguished by observing facilities with extended wavelength coverage (e.g., JWST).Comment: 19 pages, published in A&A, abstract shortene

Some comments on spacelike minimal surfaces with null polygonal boundaries in AdSmAdS_m

We discuss some geometrical issues related to spacelike minimal surfaces in $AdS_m$ with null polygonal boundaries at conformal infinity. In particular for $AdS_4$, two holomorphic input functions for the Pohlmeyer reduced system are identified. This system contains two coupled differential equations for two functions $\alpha (z,\bar z)$ and $\beta (z,\bar z)$, related to curvature and torsion of the surface. Furthermore, we conjecture that, for a polynomial choice of the two holomorphic functions, the relative positions of their zeros encode the conformal invariant data of the boundary null $2n$-gon.Comment: 13 pages, a note and references added, version to appear in JHE