Fuchsian groups of the second kind and representations carried by the limit set

We compute the cohomology of a Fuchsian group of the second kind with coefficients in the hyperfunction vectors of the principal series representations of $SL(2,R)$ supported on the limit set.Comment: 22 pages, LATE

The differential analytic index in Simons-Sullivan differential K-theory

We define the Simons-Sullivan differential analytic index by translating the Freed-Lott differential analytic index via explicit ring isomorphisms between Freed-Lott differential K-theory and Simons-Sullivan differential K-theory. We prove the differential Grothendieck-Riemann-Roch theorem in Simons-Sullivan differential K-theory using a theorem of Bismut.Comment: 14 pages. Comments are welcome. Final version. To appear in Annals of Global Analysis and Geometr

Discriminative prototype selection methods for graph embedding

Graphs possess a strong representational power for many types of patterns. However, a main limitation in their use for pattern analysis derives from their difficult mathematical treatment. One way of circumventing this problem is that of transforming the graphs into a vector space by means of graph embedding. Such an embedding can be conveniently obtained by using a set of prototype graphs and a dissimilarity measure. However, when we apply this approach to a set of class-labelled graphs, it is challenging to select prototypes capturing both the salient structure within each class and inter-class separation. In this paper, we introduce a novel framework for selecting a set of prototypes from a labelled graph set taking their discriminative power into account. Experimental results showed that such a discriminative prototype selection framework can achieve superior results in classification compared to other well-established prototype selection approaches. © 2012 Elsevier Ltd

Eaten alive: cannibalism is enhanced by parasites

Cannibalism is ubiquitous in nature and especially pervasive in consumers with stage-specific resource utilization in resource-limited environments. Cannibalism is thus influential in the structure and functioning of biological communities. Parasites are also pervasive in nature and, we hypothesize, might affect cannibalism since infection can alter host foraging behaviour. We investigated the effects of a common parasite, the microsporidian Pleistophora mulleri, on the cannibalism rate of its host, the freshwater amphipod Gammarus duebeni celticus. Parasitic infection increased the rate of cannibalism by adults towards uninfected juvenile conspecifics, as measured by adult functional responses, that is, the rate of resource uptake as a function of resource density. This may reflect the increased metabolic requirements of the host as driven by the parasite. Furthermore, when presented with a choice, uninfected adults preferred to cannibalize uninfected rather than infected juvenile conspecifics, probably reflecting selection pressure to avoid the risk of parasite acquisition. By contrast, infected adults were indiscriminate with respect to infection status of their victims, probably owing to metabolic costs of infection and the lack of risk as the cannibals were already infected. Thus parasitism, by enhancing cannibalism rates, may have previously unrecognized effects on stage structure and population dynamics for cannibalistic species and may also act as a selective pressure leading to changes in resource use

T-duality and Differential K-Theory

We give a precise formulation of T-duality for Ramond-Ramond fields. This gives a canonical isomorphism between the "geometrically invariant" subgroups of the twisted differential K-theory of certain principal torus bundles. Our result combines topological T-duality with the Buscher rules found in physics.Comment: 23 pages, typos corrected, submitted to Comm.Math.Phy

Gauge Theoretic Invariants of, Dehn Surgeries on Knots

New methods for computing a variety of gauge theoretic invariants for homology 3-spheres are developed. These invariants include the Chern-Simons invariants, the spectral flow of the odd signature operator, and the rho invariants of irreducible SU(2) representations. These quantities are calculated for flat SU(2) connections on homology 3-spheres obtained by 1/k Dehn surgery on (2,q) torus knots. The methods are then applied to compute the SU(3) gauge theoretic Casson invariant (introduced in [H U Boden and C M Herald, The SU(3) Casson invariant for integral homology 3--spheres, J. Diff. Geom. 50 (1998) 147-206]) for Dehn surgeries on (2,q) torus knots for q=3,5,7 and 9.Comment: Version 3: minor corrections from version 2. Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol5/paper6.abs.htm