A study on the expressive power of some fragments of the modal µ-Calculus

Résumé Le μ-calcul est une extension de la logique modale par des opérateurs de point fixe. Dans ce travail nous étudions la complexité de certains fragments de cette logique selon deux points de vue, différents mais étroitement liés: l'un syntaxique (ou combinatoire) et l'autre topologique. Du point de vue syn¬taxique, les propriétés définissables dans ce formalisme sont classifiées selon la complexité combinatoire des formules de cette logique, c'est-à-dire selon le nombre d'alternances des opérateurs de point fixe. Comparer deux ensembles de modèles revient ainsi à comparer la complexité syntaxique des formules as¬sociées. Du point de vue topologique, les propriétés définissables dans cette logique sont comparées à l'aide de réductions continues ou selon leurs positions dans la hiérarchie de Borel ou dans celle projective. Dans la première partie de ce travail nous adoptons le point de vue syntax¬ique afin d'étudier le comportement du μ-calcul sur des classes restreintes de modèles. En particulier nous montrons que: (1) sur la classe des modèles symétriques et transitifs le μ-calcul est aussi expressif que la logique modale; (2) sur la classe des modèles transitifs, toute propriété définissable par une formule du μ-calcul est définissable par une formule sans alternance de points fixes, (3) sur la classe des modèles réflexifs, il y a pour tout η une propriété qui ne peut être définie que par une formule du μ-calcul ayant au moins η alternances de points fixes, (4) sur la classe des modèles bien fondés et transitifs le μ-calcul est aussi expressif que la logique modale. Le fait que le μ-calcul soit aussi expressif que la logique modale sur la classe des modèles bien fondés et transitifs est bien connu. Ce résultat est en ef¬fet la conséquence d'un théorème de point fixe prouvé indépendamment par De Jongh et Sambin au milieu des années 70. La preuve que nous donnons de l'effondrement de l'expressivité du μ-calcul sur cette classe de modèles est néanmoins indépendante de ce résultat. Par la suite, nous étendons le langage du μ-calcul en permettant aux opérateurs de point fixe de lier des occurrences négatives de variables libres. En montrant alors que ce formalisme est aussi ex¬pressif que le fragment modal, nous sommes en mesure de fournir une nouvelle preuve du théorème d'unicité des point fixes de Bernardi, De Jongh et Sambin et une preuve constructive du théorème d'existence de De Jongh et Sambin. RÉSUMÉ Pour ce qui concerne les modèles transitifs, du point de vue topologique cette fois, nous prouvons que la logique modale correspond au fragment borélien du μ-calcul sur cette classe des systèmes de transition. Autrement dit, nous vérifions que toute propriété définissable des modèles transitifs qui, du point de vue topologique, est une propriété borélienne, est nécessairement une propriété modale, et inversement. Cette caractérisation du fragment modal découle du fait que nous sommes en mesure de montrer que, modulo EF-bisimulation, un ensemble d'arbres est définissable dans la logique temporelle Ε F si et seulement il est borélien. Puisqu'il est possible de montrer que ces deux propriétés coïncident avec une caractérisation effective de la définissabilité dans la logique Ε F dans le cas des arbres à branchement fini donnée par Bojanczyk et Idziaszek [24], nous obtenons comme corollaire leur décidabilité. Dans une deuxième partie, nous étudions la complexité topologique d'un sous-fragment du fragment sans alternance de points fixes du μ-calcul. Nous montrons qu'un ensemble d'arbres est définissable par une formule de ce frag¬ment ayant au moins η alternances si et seulement si cette propriété se trouve au moins au n-ième niveau de la hiérarchie de Borel. Autrement dit, nous vérifions que pour ce fragment du μ-calcul, les points de vue topologique et combina- toire coïncident. De plus, nous décrivons une procédure effective capable de calculer pour toute propriété définissable dans ce langage sa position dans la hiérarchie de Borel, et donc le nombre d'alternances de points fixes nécessaires à la définir. Nous nous intéressons ensuite à la classification des ensembles d'arbres par réduction continue, et donnons une description effective de l'ordre de Wadge de la classe des ensembles d'arbres définissables dans le formalisme considéré. En particulier, la hiérarchie que nous obtenons a une hauteur (ωω)ω. Nous complétons ces résultats en décrivant un algorithme permettant de calculer la position dans cette hiérarchie de toute propriété définissable.

Predictors of HIV-protection behaviour in HIV-positive men who have sex with casual male partners: a test of the explanatory power of an extended Information-Motivation-Behavioural Skills model.

This prospective study applies an extended Information-Motivation-Behavioural Skills (IMB) model to establish predictors of HIV-protection behaviour among HIV-positive men who have sex with men (MSM) during sex with casual partners. Data have been collected from anonymous, self-administered questionnaires and analysed by using descriptive and backward elimination regression analyses. In a sample of 165 HIV-positive MSM, 82 participants between the ages of 23 and 78 (M=46.4, SD=9.0) had sex with casual partners during the three-month period under investigation. About 62% (n=51) have always used a condom when having sex with casual partners. From the original IMB model, only subjective norm predicted condom use. More important predictors that increased condom use were low consumption of psychotropics, high satisfaction with sexuality, numerous changes in sexual behaviour after diagnosis, low social support from friends, alcohol use before sex and habitualised condom use with casual partner(s). The explanatory power of the calculated regression model was 49% (p<0.001). The study reveals the importance of personal and social resources and of routines for condom use, and provides information for the research-based conceptualisation of prevention offers addressing especially people living with HIV ("positive prevention").

The discriminatory power of MALDI-TOF mass spectrometry to differentiate between isogenic teicoplanin-susceptible and teicoplanin-resistant strains of methicillin-resistant Staphylococcus aureus.

To explore the discriminatory power of matrix-assisted laser desorption ionization-time of flight mass spectrometry (MALDI-TOF MS) for detecting subtle differences in isogenic isolates, we tested isogenic strains of Staphylococcus aureus differing in their expression of resistance to methicillin or teicoplanin. More important changes in MALDI-TOF MS spectra were found with strains differing in methicillin than in teicoplanin resistance. In comparison, very minor or no changes were recorded in pulsed-field gel electrophoresis profiles or peptidoglycan muropeptide digest patterns of these strains, respectively. MALDI-TOF MS might be useful to detect subtle strain-specific differences in ionizable components released from bacterial surfaces and not from their peptidoglycan network.

Measurement of the mechanical power of walking by satellite positioning system (GPS).

PURPOSE: This descriptive article illustrates the application of Global Positioning System (GPS) professional receivers in the field of locomotion studies. The technological challenge was to assess the external mechanical work in outdoor walking. METHODS: Five subjects walked five times during 5 min on an athletic track at different imposed stride frequency (from 70-130 steps x min(-1)). A differential GPS system (carrier phase analysis) measured the variation of the position of the trunk at 5 Hz. A portable indirect calorimeter recorded breath-by-breath energy expenditure. RESULTS: For a walking speed of 1.05 +/- 0.11 m x s(-1), the vertical lift of the trunk (43 +/- 14 mm) induced a power of 46.0 +/- 20.4 W. The average speed variation per step (0.15 +/- 0.03 m x s(-1)) produced a kinetic power of 16.9 +/- 7.2 W. As compared with commonly admitted values, the energy exchange (recovery) between the two energy components was low (39.1 +/- 10.0%), which induced an overestimated mechanical power (38.9 +/- 18.3 W or 0.60 W x kg(-1) body mass) and a high net mechanical efficiency (26.9 +/- 5.8%). CONCLUSION: We assumed that the cause of the overestimation was an unwanted oscillation of the GPS antenna. It is concluded that GPS (in phase mode) is now able to record small body movements during human locomotion, and constitutes a promising tool for gait analysis of outdoor unrestrained walking. However, the design of the receiver and the antenna must be adapted to human experiments and a thorough validation study remains to be conducted.

Research involving biological material from forensic autopsies: legal and ethical issues.

Recommendations and laws do not always contain specific and clear provisions on the use of cadaveric material in research, and even more rarely do they address explicitly the ethical issues related to research on material obtained during forensic autopsy. In this article we analyse existing legal frameworks in Europe by comparing the legal provisions in 2 European Countries which are member states of the Council of Europe, the UK and Switzerland. They were chosen because they have distinct legal frameworks that make comparisons interesting. In addition, the detailed laws of the UK and a specific law project and national ethical recommendations in Switzerland permit us to define more clearly the legal range of options for researchers using cadaveric material obtained during forensic investigations. The Human Tissue Act 2004 in England, Wales and Northern Ireland, its Scottish equivalent with the same title (2006) and the national ethical guidelines in Switzerland all require consent from the deceased person, an appropriate relative or a person with power of attorney for healthcare decisions before cadaveric biological material can be obtained and used for research. However, if the purpose of the autopsy is purely forensic, no such authorization will be sought to carry out the autopsy and related analyses, which might include genetic testing. In order to be allowed to carry out future research projects, families need to be approached for informed consent, unless the deceased person had left written directives including permission to use his or her tissues for research.

Sample size and statistical power in the hierarchical analysis of variance: applications in morphometry of the nervous system.

Analysis of variance is commonly used in morphometry in order to ascertain differences in parameters between several populations. Failure to detect significant differences between populations (type II error) may be due to suboptimal sampling and lead to erroneous conclusions; the concept of statistical power allows one to avoid such failures by means of an adequate sampling. Several examples are given in the morphometry of the nervous system, showing the use of the power of a hierarchical analysis of variance test for the choice of appropriate sample and subsample sizes. In the first case chosen, neuronal densities in the human visual cortex, we find the number of observations to be of little effect. For dendritic spine densities in the visual cortex of mice and humans, the effect is somewhat larger. A substantial effect is shown in our last example, dendritic segmental lengths in monkey lateral geniculate nucleus. It is in the nature of the hierarchical model that sample size is always more important than subsample size. The relative weight to be attributed to subsample size thus depends on the relative magnitude of the between observations variance compared to the between individuals variance.

A program for the computation of power and determination of sample size in hierarchical experimental designs.

We have devised a program that allows computation of the power of F-test, and hence determination of appropriate sample and subsample sizes, in the context of the one-way hierarchical analysis of variance with fixed effects. The power at a fixed alternative is an increasing function of the sample size and of the subsample size. The program makes it easy to obtain the power of F-test for a range of values of sample and subsample sizes, and therefore the appropriate sizes based on a desired power. The program can be used for the 'ordinary' case of the one-way analysis of variance, as well as for hierarchical analysis of variance with two stages of sampling. Examples are given of the practical use of the program.

Beyond Conditionality versus Cooperation: Power and Resistance in the Case of EU Mobility Partnerships and Swiss Migration Partnerships

Migration partnerships (MPs) have become a key instrument in global migration governance. In contrast to traditional unilateral approaches, MPs emphasize a more comprehensive and inclusive tackling of migration issues between countries of origin, transit, and destination. Due to this cooperation-oriented concept, most of the existing studies on MPs neglect power questions within partnerships in line with the official discourse, reflecting a broader trend in the international migration governance literature. Others take an instrumentalist view in analysing the power of partnerships or focus on soft power. Illustrated with the examples of the European Mobility Partnerships (EU MPs) and the Swiss Migration Partnerships (CH MPs), we conduct an analysis based on a concept of productive power drawing on post-structural and post-colonial insights. Our main argument is that in contrast to their seemingly consent-oriented and technical character, MPs are sites of intense (discursive) struggles, and (re-)produce meanings, subjects, and resistances. A productive power analysis allows us to move beyond the dichotomy in the literature between coercion and cooperation, as well as between power and resistance more broadly.

Species distribution models reveal apparent competitive and facilitative effects of a dominant species on the distribution of tundra plants

Abiotic factors are considered strong drivers of species distribution and assemblages. Yet these spatial patterns are also influenced by biotic interactions. Accounting for competitors or facilitators may improve both the fit and the predictive power of species distribution models (SDMs). We investigated the influence of a dominant species, Empetrum nigrum ssp. hermaphroditum, on the distribution of 34 subordinate species in the tundra of northern Norway. We related SDM parameters of those subordinate species to their functional traits and their co-occurrence patterns with E. hermaphroditum across three spatial scales. By combining both approaches, we sought to understand whether these species may be limited by competitive interactions and/or benefit from habitat conditions created by the dominant species. The model fit and predictive power increased for most species when the frequency of occurrence of E. hermaphroditum was included in the SDMs as a predictor. The largest increase was found for species that 1) co-occur most of the time with E. hermaphroditum, both at large (i.e. 750 m) and small spatial scale (i.e. 2 m) or co-occur with E. hermaphroditum at large scale but not at small scale and 2) have particularly low or high leaf dry matter content (LDMC). Species that do not co-occur with E. hermaphroditum at the smallest scale are generally palatable herbaceous species with low LDMC, thus showing a weak ability to tolerate resource depletion that is directly or indirectly induced by E. hermaphroditum. Species with high LDMC, showing a better aptitude to face resource depletion and grazing, are often found in the proximity of E. hermaphroditum. Our results are consistent with previous findings that both competition and facilitation structure plant distribution and assemblages in the Arctic tundra. The functional and co-occurrence approaches used were complementary and provided a deeper understanding of the observed patterns by refinement of the pool of potential direct and indirect ecological effects of E. hermaphroditum on the distribution of subordinate species. Our correlative study would benefit being complemented by experimental approaches.