A game theoretical approach to the algebraic counterpart of the Wagner hierarchy

La hiérarchie de Wagner constitue à ce jour la plus fine classification des langages ω-réguliers. Par ailleurs, l'approche algébrique de la théorie de langages formels montre que ces ensembles ω-réguliers correspondent précisément aux langages reconnaissables par des ω-semigroupes finis pointés. Ce travail s'inscrit dans ce contexte en fournissant une description complète de la contrepartie algébrique de la hiérarchie de Wagner, et ce par le biais de la théorie descriptive des jeux de Wadge. Plus précisément, nous montrons d'abord que le degré de Wagner d'un langage ω-régulier est effectivement un invariant syntaxique. Nous définissons ensuite une relation de réduction entre ω-semigroupes pointés par le biais d'un jeu infini de type Wadge. La collection de ces structures algébriques ordonnée par cette relation apparaît alors comme étant isomorphe à la hiérarchie de Wagner, soit un quasi bon ordre décidable de largeur 2 et de hauteur ω. Nous exposons par la suite une procédure de décidabilité de cette hiérarchie algébrique : on décrit une représentation graphique des ω-semigroupes finis pointés, puis un algorithme sur ces structures graphiques qui calcule le degré de Wagner de n'importe quel élément. Ainsi le degré de Wagner de tout langage ω-régulier peut être calculé de manière effective directement sur son image syntaxique. Nous montrons ensuite comment construire directement et inductivement une structure de n''importe quel degré. Nous terminons par une description détaillée des invariants algébriques qui caractérisent tous les degrés de cette hiérarchie. Abstract The Wagner hierarchy is known so far to be the most refined topological classification of ω-rational languages. Also, the algebraic study of formal languages shows that these ω-rational sets correspond precisely to the languages recognizable by finite pointed ω-semigroups. Within this framework, we provide a construction of the algebraic counterpart of the Wagner hierarchy. We adopt a hierarchical game approach, by translating the Wadge theory from the ω-rational language to the ω-semigroup context. More precisely, we first show that the Wagner degree is indeed a syntactic invariant. We then define a reduction relation on finite pointed ω-semigroups by means of a Wadge-like infinite two-player game. The collection of these algebraic structures ordered by this reduction is then proven to be isomorphic to the Wagner hierarchy, namely a well-founded and decidable partial ordering of width 2 and height $\omega^\omega$. We also describe a decidability procedure of this hierarchy: we introduce a graph representation of finite pointed ω-semigroups allowing to compute their precise Wagner degrees. The Wagner degree of every ω-rational language can therefore be computed directly on its syntactic image. We then show how to build a finite pointed ω-semigroup of any given Wagner degree. We finally describe the algebraic invariants characterizing every Wagner degree of this hierarchy.

Predictive Factors for Intraocular Pressure Reduction after Phacoemulsification in Swiss Patients.

Background: Phacoemulsification is known to induce postoperative intraocular pressure (IOP) reduction, the degree of which varies according to glaucoma subtype and race. The authors set out to investigate the effect of cataract surgery on IOP, in a Swiss Caucasian population, and identify ocular predictive factors. Patients and Methods: 234 consecutive cases of 188 patients undergoing phacoemulsification between January 2011 and December 2012 were retrospectively reviewed and data collected. Exclusion criteria included acute angle closure, malignant glaucoma and pre-existing or subsequent glaucoma surgery. Pre- and post-operative visual acuity, IOP, gonioscopic findings, glaucoma medications, and laser treatments were recorded for eligible eyes. All eyes received the same postoperative regimen. Using multivariate analysis the predictive power of preoperative IOP, iridocorneal angle width, axial length on IOP reduction following phacoemulsification at months 3, 6 and 12 postoperatively were assessed. Eyes with narrow angles were compared against those with open angles. Results: 172 eyes of 121 patients met the inclusion criteria; mean age was 70.3 years (SD ± 10.7 years), with 77 males. Preoperatively median IOP was 16 mmHg (range 9-32 mmHg), mean number of glaucoma medications was 1.2 (SD ± 1.1), median visual acuity was 0.28 LogMAR (range 0-2.3LogMar). At 3 months post-operatively mean IOP decreased to 14 mmHg (p < 0.01) and remained statistically significantly reduced until 12 months, mean number of glaucoma medications was reduced to 1.0 and mean Snellen visual acuity increased to 0.8. Multivariate analysis revealed that pre-operative IOP and iridocorneal angle width (at 3 months) were significant predictive indicators of IOP reduction. At 12 months, IOP reduction was similar between open and narrow angle groups and total IOP reduction was no longer statistically significant. No intraoperative complications were recorded. Conclusions: Intraocular pressure reduction following phacoemulsification was greatest during the very early post-operative period, particularly in narrow angle patients. By one year, angle size was no longer predictive of IOP lowering, however pre-operative IOP and number of anti-glaucoma medications remained correlated with total IOP reduction.

Image Resilience after Multiple Crises : The Case of Switzerland in the United States

In der heutigen Welt sind die Reputation und das Image eines Landes als wichtige Faktoren für den wirtschaftlichen und politischen Erfolg angesehen. Jedoch ist die Pflege der Marke eines Landes komplex und führt zu zwei Positionen, die sich potentiell widersprechen: Einerseits kann ein positives Erscheinungsbild eines Landes durch aktive Massnahmen gefördert werden. Andererseits ist es schwierig, das Bild eines Landes abzugrenzen und es ist mit Klischees behaftet. Dieser Beitrag analysiert die Auswirkungen von zwei grösseren Krisen auf das Image der Schweiz in den Vereinigten Staaten: die Krise um die nachrichtenlosen Vermögen aus der Zeit des 2. Weltkriegs im Jahr 2000 sowie die Krise um die UBS und das Bankgeheimnis im Jahr 2009. Die Studie zeigt, dass das Erscheinungsbild der Schweiz unberührt blieb, obwohl ein beachtlicher Teil der Bevölkerung und der Meinungsführer von beiden Krisen wusste. Dies stützt die Hypothese, dass das Image eines Landes eine hohe Beständigkeit aufweist. In today's world, country's reputation and image have become key issues, widely believed to be success factors both economically and politically. Nevertheless, managing a country's brand is complex and leads to two positions that are potentially contradictory: On the one hand, a country's image can be influenced either by promotional activities. On the other hand, a country's image is a construct that is very difficult to delimit and is highly stereotyped. This contribution study the impact of two major crises on the image of Switzerland in the United States: the unclaimed wartime deposits crisis in 2000 and the UBS and banking secrecy crisis in 2009. It shows that despite the fact that a substantial proportion of the public and of opinion leaders was aware of both crises, the image of Switzerland was unaffected, which tends to support the hypothesis of strong stability of a country's image.