The MobyDick Project: A Mobile Heterogeneous All-IP Architecture

Proceedings of Advanced Technologies, Applications and Market Strategies for 3G (ATAMS 2001). Cracow, Poland: 17-20 June, 2001.This paper presents the current stage of an IP-based architecture for heterogeneous environments, covering UMTS-like W-CDMA wireless access technology, wireless and wired LANs, that is being developed under the aegis of the IST Moby Dick project. This architecture treats all transmission capabilities as basic physical and data-link layers, and attempts to replace all higher-level tasks by IP-based strategies. The proposed architecture incorporates aspects of mobile-IPv6, fast handover, AAA-control, and Quality of Service. The architecture allows for an optimised control on the radio link layer resources. The Moby dick architecture is currently under refinement for implementation on field trials. The services planned for trials are data transfer and voice-over-IP.Publicad

Tropical surface singularities

In this paper, we study tropicalisations of singular surfaces in toric threefolds. We completely classify singular tropical surfaces of maximal-dimensional type, show that they can generically have only finitely many singular points, and describe all possible locations of singular points. More precisely, we show that singular points must be either vertices, or generalized midpoints and baricenters of certain faces of singular tropical surfaces, and, in some cases, there may be additional metric restrictions to faces of singular tropical surfaces.Comment: A gap in the classification was closed. 37 pages, 29 figure

Partner orbits and action differences on compact factors of the hyperbolic plane. Part I: Sieber-Richter pairs

Physicists have argued that periodic orbit bunching leads to universal spectral fluctuations for chaotic quantum systems. To establish a more detailed mathematical understanding of this fact, it is first necessary to look more closely at the classical side of the problem and determine orbit pairs consisting of orbits which have similar actions. In this paper we specialize to the geodesic flow on compact factors of the hyperbolic plane as a classical chaotic system. We prove the existence of a periodic partner orbit for a given periodic orbit which has a small-angle self-crossing in configuration space which is a `2-encounter'; such configurations are called `Sieber-Richter pairs' in the physics literature. Furthermore, we derive an estimate for the action difference of the partners. In the second part of this paper [13], an inductive argument is provided to deal with higher-order encounters.Comment: to appear on Nonlinearit

Almost Sure Frequency Independence of the Dimension of the Spectrum of Sturmian Hamiltonians

We consider the spectrum of discrete Schr\"odinger operators with Sturmian potentials and show that for sufficiently large coupling, its Hausdorff dimension and its upper box counting dimension are the same for Lebesgue almost every value of the frequency.Comment: 12 pages, to appear in Commun. Math. Phy

Rational approximation and arithmetic progressions

A reasonably complete theory of the approximation of an irrational by rational fractions whose numerators and denominators lie in prescribed arithmetic progressions is developed in this paper. Results are both, on the one hand, from a metrical and a non-metrical point of view and, on the other hand, from an asymptotic and also a uniform point of view. The principal novelty is a Khintchine type theorem for uniform approximation in this context. Some applications of this theory are also discussed

The subconvexity problem for \GL_{2}

Generalizing and unifying prior results, we solve the subconvexity problem for the $L$-functions of \GL_{1} and \GL_{2} automorphic representations over a fixed number field, uniformly in all aspects. A novel feature of the present method is the softness of our arguments; this is largely due to a consistent use of canonically normalized period relations, such as those supplied by the work of Waldspurger and Ichino--Ikeda.Comment: Almost final version to appear in Publ. Math IHES. References updated

Ultrametric Logarithm Laws, II

We prove positive characteristic versions of the logarithm laws of Sullivan and Kleinbock-Margulis and obtain related results in Metric Diophantine Approximation.Comment: submitted to Montasefte Fur Mathemati

The Hausdorff and dynamical dimensions of self-affine sponges : a dimension gap result

We construct a self-affine sponge in R 3 whose dynamical dimension, i.e. the supremum of the Hausdorff dimensions of its invariant measures, is strictly less than its Hausdorff dimension. This resolves a long-standing open problem in the dimension theory of dynamical systems, namely whether every expanding repeller has an ergodic invariant measure of full Hausdorff dimension. More generally we compute the Hausdorff and dynamical dimensions of a large class of self-affine sponges, a problem that previous techniques could only solve in two dimensions. The Hausdorff and dynamical dimensions depend continuously on the iterated function system defining the sponge, implying that sponges with a dimension gap represent a nonempty open subset of the parameter space