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.

Informing patients about limits to confidentiality: A qualitative study in prisons.

AIM: Confidentiality is important in healthcare practice, however, under certain circumstances, confidentiality is breached. In this paper, mental health professionals' (MHPs) practices related to informing imprisoned patients about confidentiality and its limits are presented. METHODS: Twenty-four MHPs working in Swiss prisons were interviewed. Data analysis involved qualitative thematic coding and was validated by discussing results with external experts and study participants. RESULTS: For expert evaluations and court-ordered therapies, participants informed patients that information revealed during these consultations is not bound by confidentiality rules. The practice of routinely informing patients about confidentiality and its limits became more complex in voluntary therapies, for which participants described four approaches and provided justifications in favour of or against their use. CONCLUSIONS: Further training and continued education are needed to improve physicians' ethical and legal knowledge about confidentiality disclosures. In order to promote ethical practices, it is important to understand and address existing motivations, attitudes and behaviours that impede appropriate patient information. Our study adds important new knowledge about the limits to confidentiality, particularly for providers working with vulnerable populations. Results from this study reflect typical ethical and practical dilemmas faced by and of interest to physicians working in forensic medicine and other related settings.

Impact of Sleep and Circadian Disruption on Energy Balance and Diabetes: A Summary of Workshop Discussions.

ABSTRACT: A workshop was held at the National Institute for Diabetes and Digestive and Kidney Diseases with a focus on the impact of sleep and circadian disruption on energy balance and diabetes. The workshop identified a number of key principles for research in this area and a number of specific opportunities. Studies in this area would be facilitated by active collaboration between investigators in sleep/circadian research and investigators in metabolism/diabetes. There is a need to translate the elegant findings from basic research into improving the metabolic health of the American public. There is also a need for investigators studying the impact of sleep/circadian disruption in humans to move beyond measurements of insulin and glucose and conduct more in-depth phenotyping. There is also a need for the assessments of sleep and circadian rhythms as well as assessments for sleep-disordered breathing to be incorporated into all ongoing cohort studies related to diabetes risk. Studies in humans need to complement the elegant short-term laboratory-based human studies of simulated short sleep and shift work etc. with studies in subjects in the general population with these disorders. It is conceivable that chronic adaptations occur, and if so, the mechanisms by which they occur needs to be identified and understood. Particular areas of opportunity that are ready for translation are studies to address whether CPAP treatment of patients with pre-diabetes and obstructive sleep apnea (OSA) prevents or delays the onset of diabetes and whether temporal restricted feeding has the same impact on obesity rates in humans as it does in mice.

Prevalence of sleep apnoea syndrome in the middle to old age general population.

On the basis of a large populationbased sample who underwent full polysomnography at home (HypnoLaus cohort), we recently reported that 49·7% of men and 23·4% of women aged 40 years or older had an apnoea-hypopnoea index of 15 events per h or more1 according to the American Academy of Sleep Medicine (AASM) 2013 scoring criteria. When excessive daytime sleepiness (ie, Epworth score >10 [maximum score 24]) was included in the definition with an apnoea-hypopnoea index of 5 events per h or more, the prevalence was 12·5% in men and 5·9% in women. This high prevalence of sleep disordered breathing reinforced the idea that the treatment decision should not only be based the apnoeahypopnoea index, but should also take into account associated symptoms and cardiovascular and metabolic comorbidities. After this Article was published, several readers contacted us to ask for the prevalence of sleep apnoea syndrome in our sample according to the International Classification of Sleep Disorders (ICSD-3) criteria. These criteria include either the presence of an apnoea-hypopnoea index of 5 events per h or more associated with obstructive sleep apnoearelated symptoms or cardiovascular and metabolic comorbidities, or an apnoea-hypopnoea index of 15 events per h or more (figure).

Sleep Characteristics in Early Stages of Chronic Kidney Disease in the HypnoLaus Cohort.

STUDY OBJECTIVES: To evaluate the association between early stages of chronic kidney disease (CKD) and sleep disordered breathing (SDB), restless legs syndrome (RLS), and subjective and objective sleep quality (SQ). METHODS: Cross-sectional analysis of a general population-based cohort (HypnoLaus). 1,760 adults (862 men, 898 women; age 59.3 (± 11.4) y) underwent complete polysomnography at home. RESULTS: 8.2% of participants had mild CKD (stage 1-2, estimated glomerular filtration rate [eGFR] ≥ 60 mL/min/1.73 m(2) with albuminuria) and 7.8% moderate CKD (stage 3, eGFR 30-60 mL/min/1.73 m(2)). 37.3% of our sample had moderate-to-severe SDB (apnea-hypopnea index [AHI] ≥ 15/h) and 15.3% had severe SDB (AHI ≥ 30/h). SDB prevalence was positively associated with CKD stages and negatively with eGFR. In multivariate analysis, age, male sex, and body mass index were independently associated with SDB (all P < 0.001), but kidney function was not. The prevalence of RLS was 17.5%, without difference between CKD stages. Periodic leg movements index (PLMI) was independently associated with CKD stages. Subjective and objective SQ decreased and the use of sleep medication was more frequent with declining kidney function. Older age, female sex, and the severity of SDB were the strongest predictors of poor SQ in multivariate regression analysis but CKD stage was also independently associated with reduced objective SQ. CONCLUSIONS: Patients with early stages of CKD have impaired SQ, use more hypnotic drugs, and have an increased prevalence of SDB and PLM. After controlling for confounders, objective SQ and PLMI were still independently associated with declining kidney function.