Simultaneous dense and nondense orbits for commuting maps

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.We show that, for two commuting automorphisms of the torus and for two elements of the Cartan action on compact higher rank homogeneous spaces, many points have drastically different orbit structures for the two maps. Specifically, using measure rigidity, we show that the set of points that have dense orbit under one map and nondense orbit under the second has full Hausdorff dimension.V. B. acknowledges support received from the National Science Foundation via Grant DMS-1162073 M. E. acknowledges support by the SNF (200021-152819). J. T. acknowledges the research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement n. 291147

Simultaneous dense and nondense orbits for commuting maps

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.We show that, for two commuting automorphisms of the torus and for two elements of the Cartan action on compact higher rank homogeneous spaces, many points have drastically different orbit structures for the two maps. Specifically, using measure rigidity, we show that the set of points that have dense orbit under one map and nondense orbit under the second has full Hausdorff dimension.V. B. acknowledges support received from the National Science Foundation via Grant DMS-1162073 M. E. acknowledges support by the SNF (200021-152819). J. T. acknowledges the research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement n. 291147

Tropical polyhedra are equivalent to mean payoff games

We show that several decision problems originating from max-plus or tropical convexity are equivalent to zero-sum two player game problems. In particular, we set up an equivalence between the external representation of tropical convex sets and zero-sum stochastic games, in which tropical polyhedra correspond to deterministic games with finite action spaces. Then, we show that the winning initial positions can be determined from the associated tropical polyhedron. We obtain as a corollary a game theoretical proof of the fact that the tropical rank of a matrix, defined as the maximal size of a submatrix for which the optimal assignment problem has a unique solution, coincides with the maximal number of rows (or columns) of the matrix which are linearly independent in the tropical sense. Our proofs rely on techniques from non-linear Perron-Frobenius theory.Comment: 28 pages, 5 figures; v2: updated references, added background materials and illustrations; v3: minor improvements, references update

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

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

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

Spherical averages in the space of marked lattices

A marked lattice is a $d$-dimensional Euclidean lattice, where each lattice point is assigned a mark via a given random field on ${\mathbb Z}^d$. We prove that, if the field is strongly mixing with a faster-than-logarithmic rate, then for every given lattice and almost every marking, large spheres become equidistributed in the space of marked lattices. A key aspect of our study is that the space of marked lattices is not a homogeneous space, but rather a non-trivial fiber bundle over such a space. As an application, we prove that the free path length in a crystal with random defects has a limiting distribution in the Boltzmann-Grad limit

VirtuWind: Virtual and programmable industrial network prototype deployed in operational wind park.

With anticipated exponential growth of connected devices, future industrial networks require an open solutions architecture facilitated by standards and a strong ecosystem. Such solutions should also deal with range of quality of service requirements imposed by industrial networks. Preserving strict quality of service is particularly challenging when services pass across domains of multiple provides. VirtuWind aims to develop and demonstrate a Software Defined Networking and Network Function Virtualization ecosystem, based on an open, modular and secure framework to address stringent requirements of the industrial networks. A prototype of the framework for intra-domain and inter-domain scenarios will be showcased in real Wind Parks, as a representative use case of industrial networks. This paper details this vision and explains steps forward

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

A Survey of Differentiated Services Proposals for the Internet

Abstract TR/1998/020 Technical Report SSC/1998/020 Authors: Constant Gbaguidi, Hans J. Einsiedler, Paul Hurley, Werner Almesberger and Jean-Pierre Hubaux Date: Title: A Survey of Differentiated Services Proposals for the Internet Abstract Differentiated services are a suitable solution to Quality of Service (QoS) provisioning in the Internet while the number of users keeps growing. The solution is suitable, because it scales well with increasing number of network users and it does not alter the current Internet paradigm much. In this article, we review the state of the art in this ÒnewÓ area, and compare some of the main existing differentiated services architectures. We outline the common solutions across these architectures, thus paving the road to a unified architecture. Lastly, we mention the issues that have not been thoroughly addressed yet