The Decidability Frontier for Probabilistic Automata on Infinite Words

We consider probabilistic automata on infinite words with acceptance defined by safety, reachability, B\"uchi, coB\"uchi, and limit-average conditions. We consider quantitative and qualitative decision problems. We present extensions and adaptations of proofs for probabilistic finite automata and present a complete characterization of the decidability and undecidability frontier of the quantitative and qualitative decision problems for probabilistic automata on infinite words

The valuation criterion for normal basis generators

If $L/K$ is a finite Galois extension of local fields, we say that the valuation criterion $VC(L/K)$ holds if there is an integer $d$ such that every element $x \in L$ with valuation $d$ generates a normal basis for $L/K$. Answering a question of Byott and Elder, we first prove that $VC(L/K)$ holds if and only if the tamely ramified part of the extension $L/K$ is trivial and every non-zero $K[G]$-submodule of $L$ contains a unit. Moreover, the integer $d$ can take one value modulo $[L:K]$ only, namely $-d_{L/K}-1$, where $d_{L/K}$ is the valuation of the different of $L/K$. When $K$ has positive characteristic, we thus recover a recent result of Elder and Thomas, proving that $VC(L/K)$ is valid for all extensions $L/K$ in this context. When \char{\;K}=0, we identify all abelian extensions $L/K$ for which $VC(L/K)$ is true, using algebraic arguments. These extensions are determined by the behaviour of their cyclic Kummer subextensions

Annex 6 : What future for Social Europe ?.

‘Social Europe’ has various meanings. It may refer to the current intervention of European authorities in the fields of social protection and employment legislation, as a complement or sometimes as a substitute to national institutions interventions. The role of European authorities is clearly stated in European Treaties that assert that MS remain responsible for their social protection. At the same time, the logic of European construction, the rising interdependence of economies, the interconnection of economic and monetary issues lead European authorities to tend to increase their role in social issues and to pilot ‘the modernisation’ of national social protection systems. But social Europe may also refer to a political project, aiming at increasing the power of European authorities in social areas: there would be a social Europe like there is today an economic or monetary Europe. This social Europe would lead to unify gradually European social systems. This would imply a transfer of sovereignty which would be questionable since the role of social partners would be reduced and there would be no guarantee on the content of this social Europe, possibly moving towards a liberal or social-democrat system. Social Europe may imply a step back in social democracy in Europe. At the same time the explicit recognition that Social Europe exists and that it should be managed in an open and democratic way, could be a progress as compared to a situation of constrained convergence. Last, Social Europe may refer to a political project aiming at deepening the European Social Model, by unifying social protection, redistribution and employment legislation towards the top. This could take place through the gradual introduction of social norms in each country at high and progressively similar levels. But there is no consensus in Europe on the content of this social Europe.

Performance of CSMA in Multi-Channel Wireless Networks

We analyze the performance of CSMA in multi-channel wireless networks, accounting for the random nature of traffic. Specifically, we assess the ability of CSMA to fully utilize the radio resources and in turn to stabilize the network in a dynamic setting with flow arrivals and departures. We prove that CSMA is optimal in ad-hoc mode but not in infrastructure mode, when all data flows originate from or are destined to some access points, due to the inherent bias of CSMA against downlink traffic. We propose a slight modification of CSMA, that we refer to as flow-aware CSMA, which corrects this bias and makes the algorithm optimal in all cases. The analysis is based on some time-scale separation assumption which is proved valid in the limit of large flow sizes

Local Rules for Computable Planar Tilings

Aperiodic tilings are non-periodic tilings characterized by local constraints. They play a key role in the proof of the undecidability of the domino problem (1964) and naturally model quasicrystals (discovered in 1982). A central question is to characterize, among a class of non-periodic tilings, the aperiodic ones. In this paper, we answer this question for the well-studied class of non-periodic tilings obtained by digitizing irrational vector spaces. Namely, we prove that such tilings are aperiodic if and only if the digitized vector spaces are computable.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249

Research and calibration of Acoustic Sensors in ice within the SPATS (South Pole Acoustic Test Setup) project

We present development work aiming towards a large scale ice-based hybrid detector including acoustic sensors for the detection of neutrinos in the GZK range. A facility for characterization and calibration of acoustic sensors in clear (bubble-free) ice has been developed and the first measurements done at this facility are presented. Further, a resonant sensor intended primarily for characterization of the ambient noise in the ice at the South Pole has been developed and some data from its performance are given.Comment: 4 pages, 8 figures, ARENA 2010 conference proceeding