The total space of the tangent bundle of a Kähler manifold admits a canonical Kähler structure. Parallel translation identifies the space T of oriented affine lines in R with the tangent bundle of S. Thus, the round metric on S induces a Kähler structure on T which turns out to have a metric of neutral signature. It is shown that the isometry group of this metric is isomorphic to the isometry g...

We show that the resonances of a smooth super-exponentially decaying self-adjoint perturbation of the Laplacian in R n ; n 3 odd, determine the Minakshisundaram coeecients d j ; j 2; of the expansion of the regularized heat (wave) trace, provided that there are no negative eigenvalues and zero is not a resonance. We use this to prove the existence of innnitely many resonances for the perturbati...

We develop some basic Lipschitz homotopy technique and apply it to manifolds with finite asymptotic dimension. In particular we show that the Higson compactification of a uniformly contractible manifold is mod p acyclic in the finite dimensional case. Then we give an alternative proof of the Higher Signature Novikov Conjecture for the groups with finite asymptotic dimension. Finally we define a...

Oblivious online routing (OOR) algorithms are suitable when applications only have local information available to make routing decisions. This paper presents two new OOR algorithms for Delaunay triangulations: the Ellipse Routing algorithm and the Arc Routing algorithm. Both of their names come from the shapes of their searching areas for the next-hop neighbor. This paper also evaluates and com...

We construct Dirac operators and spectral triples for certain, not necessarily selfsimilar, fractal sets built on curves. Connes’ distance formula of noncommutative geometry provides a natural metric on the fractal. To motivate the construction, we address Kigami’s measurable Riemannian geometry, which is a metric realization of the Sierpinski gasket as a self-affine space with continuously dif...

This paper is concerned with an empirical look at the magnitude of subspaces of Euclidean space. Magnitude was introduced under the name ‘cardinality’ by Leinster in [4] as a partially defined invariant of finite metric spaces; his motivation came from enriched category theory, but the invariant had already been considered in the biological diversity literature [6]. In [5] we started to extend ...

We study triangulated surface models with nontrivial surface metrices for membranes. The surface model is defined by a mapping r from a two-dimensional parameter space M to the three-dimensional Euclidean space R3. The metric variable gab, which is always fixed to the Euclidean metric δab, can be extended to a more general non-Euclidean metric on M in the continuous model. The problem we focus ...

Geographically Weighted Regression (GWR) is a local modelling technique to estimate regression models with spatially varying relationships. Generally, the Euclidean distance is the default metric for calibrating a GWR model in previous research and applications; however, it may not always be the most reasonable choice due to a partition by some natural or man-made features. Thus, we attempt to ...

In their critique of my book, Conner and Page fail to keep in mind that their own theory, the Big Bang, does not have a centre of mass. Thus they overlook an obvious contrast between the Big Bang and my cosmology, the existence of a centre of mass in my theory. The centre is crucial because it causes significant differences in gravitational potential energy between various places. During creati...

In this paper we study the property of generic global rigidity for frameworks of graphs embedded in d-dimensional complex space and in a d-dimensional pseudo-Euclidean space (R with a metric of indefinite signature). We show that a graph is generically globally rigid in Euclidean space iff it is generically globally rigid in a complex or pseudo-Euclidean space. We also establish that global rig...