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.

Visual stimulus-dependent changes in interhemispheric EEG coherence in humans.

We analyzed the coherence of electroencephalographic (EEG) signals recorded symmetrically from the two hemispheres, while subjects (n = 9) were viewing visual stimuli. Considering the many common features of the callosal connectivity in mammals, we expected that, as in our animal studies, interhemispheric coherence (ICoh) would increase only with bilateral iso-oriented gratings located close to the vertical meridian of the visual field, or extending across it. Indeed, a single grating that extended across the vertical meridian significantly increased the EEG ICoh in normal adult subjects. These ICoh responses were obtained from occipital and parietal derivations and were restricted to the gamma frequency band. They were detectable with different EEG references and were robust across and within subjects. Other unilateral and bilateral stimuli, including identical gratings that were effective in anesthetized animals, did not affect ICoh in humans. This fact suggests the existence of regulatory influences, possibly of a top-down kind, on the pattern of callosal activation in conscious human subjects. In addition to establishing the validity of EEG coherence analysis for assaying cortico-cortical connectivity, this study extends to the human brain the finding that visual stimuli cause interhemispheric synchronization, particularly in frequencies of the gamma band. It also indicates that the synchronization is carried out by cortico-cortical connection and suggests similarities in the organization of visual callosal connections in animals and in man.

Quantifying network properties in multi-electrode recordings: spatiotemporal characterization and inter-trial variation of evoked gamma oscillations in mouse somatosensory cortex in vitro.

Linking the structural connectivity of brain circuits to their cooperative dynamics and emergent functions is a central aim of neuroscience research. Graph theory has recently been applied to study the structure-function relationship of networks, where dynamical similarity of different nodes has been turned into a "static" functional connection. However, the capability of the brain to adapt, learn and process external stimuli requires a constant dynamical functional rewiring between circuitries and cell assemblies. Hence, we must capture the changes of network functional connectivity over time. Multi-electrode array data present a unique challenge within this framework. We study the dynamics of gamma oscillations in acute slices of the somatosensory cortex from juvenile mice recorded by planar multi-electrode arrays. Bursts of gamma oscillatory activity lasting a few hundred milliseconds could be initiated only by brief trains of electrical stimulations applied at the deepest cortical layers and simultaneously delivered at multiple locations. Local field potentials were used to study the spatio-temporal properties and the instantaneous synchronization profile of the gamma oscillatory activity, combined with current source density (CSD) analysis. Pair-wise differences in the oscillation phase were used to determine the presence of instantaneous synchronization between the different sites of the circuitry during the oscillatory period. Despite variation in the duration of the oscillatory response over successive trials, they showed a constant average power, suggesting that the rate of expenditure of energy during the gamma bursts is consistent across repeated stimulations. Within each gamma burst, the functional connectivity map reflected the columnar organization of the neocortex. Over successive trials, an apparently random rearrangement of the functional connectivity was observed, with a more stable columnar than horizontal organization. This work reveals new features of evoked gamma oscillations in developing cortex.

Neonatal and adult ICU ventilators to provide ventilation in neonates, infants, and children: a bench model study.

BACKGROUND: Using a bench test model, we investigated the hypothesis that neonatal and/or adult ventilators equipped with neonatal/pediatric modes currently do not reliably administer pressure support (PS) in neonatal or pediatric patient groups in either the absence or presence of air leaks. METHODS: PS was evaluated in 4 neonatal and 6 adult ventilators using a bench model to evaluate triggering, pressurization, and cycling in both the absence and presence of leaks. Delivered tidal volumes were also assessed. Three patients were simulated: a preterm infant (resistance 100 cm H2O/L/s, compliance 2 mL/cm H2O, inspiratory time of the patient [TI] 400 ms, inspiratory effort 1 and 2 cm H2O), a full-term infant (resistance 50 cm H2O/L/s, compliance 5 mL/cm H2O, TI 500 ms, inspiratory effort 2 and 4 cm H2O), and a child (resistance 30 cm H2O/L/s, compliance 10 mL/cm H2O, TI 600 ms, inspiratory effort 5 and 10 cm H2O). Two PS levels were tested (10 and 15 cm H2O) with and without leaks and with and without the leak compensation algorithm activated. RESULTS: Without leaks, only 2 neonatal ventilators and one adult ventilator had trigger delays under a given predefined acceptable limit (1/8 TI). Pressurization showed high variability between ventilators. Most ventilators showed TI in excess high enough to seriously impair patient-ventilator synchronization (> 50% of the TI of the subject). In some ventilators, leaks led to autotriggering and impairment of ventilation performance, but the influence of leaks was generally lower in neonatal ventilators. When a noninvasive ventilation algorithm was available, this was partially corrected. In general, tidal volume was calculated too low by the ventilators in the presence of leaks; the noninvasive ventilation algorithm was able to correct this difference in only 2 adult ventilators. CONCLUSIONS: No ventilator performed equally well under all tested conditions for all explored parameters. However, neonatal ventilators tended to perform better in the presence of leaks. These findings emphasize the need to improve algorithms for assisted ventilation modes to better deal with situations of high airway resistance, low pulmonary compliance, and the presence of leaks.

ELECTROCORTICAL DYNAMICS OF MOTOR INHIBITORY CONTROL WITH AGING

Motor inhibitory control plays a central role in adaptive behaviors during the entire lifespan. Inhibitory motor control refers to the ability to stop all (global) or a part (selective) of a planned or ongoing motor action. Although the neural processing underlying the global inhibitory control has received much attention from cognitive neuroscientists, brain modulations that occur during selective inhibitory motor control remain unknown. The aim of the present thesis is to investigate the spatio-temporal brain processes of selective inhibitory motor control in young and old adults using high-density electroencephalography. In the first part, we focus on early (preparatory period) spatio-temporal brain processes involved in selective and global inhibitory control in young (study I) and old adults (study II) using a modified Go/No-go task. In study I, we distinguished global from selective inhibition in the early attentional stage of inhibitory control and provided neurophysiological evidence in favor of the combination model. In study II, we showed an under-recruitment of neural resources associated with preservation of performance in old adults during selective inhibition, suggesting efficient cerebral and behavioral adaptations to environmental changes. In the second part, we investigate beta oscillations in the late (post-execution period) spatio-temporal brain processes of selective inhibition during a motor Switching task (i.e., tapping movement from bimanual to unimanual) in young (study III) and old adults (study IV). In study III, we identified concomitant beta synchronization related (i) to sensory reafference processes, which enabled the stabilization of the movement that was perturbed after switching, and (ii) to active inhibition processes that prevented movement of the stopping hand. In study IV, we demonstrated a larger beta synchronization in frontal and parietal regions in old adults compared to young adults, suggesting age-related brain modulations in active inhibition processes. Apart from contributing to a basic understanding of the electrocortical dynamics underlying inhibitory motor control, the findings of the present studies contribute to knowledge regarding the further establishment of specific trainings with aging. -- Le contrôle de l'inhibition motrice joue un rôle central dans les adaptations comportementales quel que soit l'âge. L'inhibition motrice se réfère à la capacité à arrêter entièrement (globale) ou en partie (sélective) une action motrice planifiée ou en cours. Bien que les processus neuronaux sous-jacents de l'inhibition globale aient suscité un grand intérêt auprès des neurosciences cognitives, les modulations cérébrales dans le contrôle de l'inhibition motrice sélective sont encore peu connues. Le but de cette thèse est d'étudier les processus cérébraux spatio-temporels du contrôle de l'inhibition motrice sélective chez les adultes jeunes et âgés en utilisant l'électroencéphalogramme à haute densité. Dans la première partie, nous comparons les processus cérébraux spatio-temporels précoces (préparation motrice) de l'inhibition sélective et globale chez des adultes jeunes (étude I) et âgés (étude II) en utilisant une tâche Go/No-go modifiée. Dans l'étude I, nous avons distingué l'inhibition globale et sélective au niveau des processus attentionnels précoces du contrôle de l'inhibition et nous avons apporté des preuves neurophysiologiques de l'existence d'un modèle de combinaison. Dans l'étude II, nous avons montré une sous-activation neuronale associée à un maintien de la performance dans l'inhibition sélective chez les adultes âgés, suggérant des adaptations cérébrales et comportementales aux contraintes environnementales. Dans la seconde partie, nous examinons les processus cérébraux spatio-temporels tardifs (post-exécution motrice) de l'inhibition sélective pendant une tâche de Switching (tapping bimanuel vers un tapping unimanuel) chez des adultes jeunes (étude III) et âgés (étude IV). Dans l'étude III, nous avons distingué des synchronisations beta liées (i) au traitement des réafférences sensorielles permettant de stabiliser le mouvement perturbé après le switching, et (ii) aux processus d'inhibition active afin d'empêcher les mouvements de la main arrêtée. Dans l'étude IV, cette synchronisation beta était plus forte dans les régions frontales et pariétales chez les âgés par rapport aux jeunes adultes suggérant des modulations cérébrales de l'inhibition active avec l'âge. Outre la contribution fondamentale sur la compréhension des dynamiques électrocorticales dans le contrôle de l'inhibition motrice, les résultats de ces études contribuent à développer les connaissances pour la mise en place de programmes d'entraînements adaptés aux personnes âgées.

A New Method for ECG Tracking of Persistent Atrial Fibrillation Termination during Stepwise Ablation

Stepwise radiofrequency catheter ablation (step-CA) has become the treatment of choice for the restoration of sinus rhythm (SR) in patients with long-standing persistent atrial fibrillation (pers-AF). Its success rate appears limited as the amount of ablation to achieve long term SR is unknown. Multiple organization indexes (OIs) have been previously developed to track the organization of AF during step-CA, however, with limited success. We report an adaptive method for tracking AF termination (AF-term) based on OIs characterizing the relationship between harmonic components of atrial activity from the surface ECG of AF activity. By computing their relative evolution during the last two steps preceding AF-term, we found that the performance of our OIs was superior to classical indices to track the efficiency of step-CA "en route" to AF-term. Our preliminary results suggest that the gradual synchronization between the fundamental and its first harmonic of AF activity appears as a promising parameter for predicting AF-term during step-CA.

Contribution à une étude normative de l'épreuve de Rorschach auprès d'un groupe d'enfants de 8 à 14 ans non-consultants

Cette étude normative de l'épreuve de Rorschach porte sur une population suisse de 102 enfants et adolescents non-consultants de 8 à 14 ans, répartis par tranches d'âge, sexe et niveau intellectuel. Elle présente un aperçu des différentes méthodes utilisées dans l'interprétation du Rorschach et des normes francophones existantes. Une réflexion est aussi proposée autour de la question de l'utilité de l'analyse des facteurs quantitatifs au Rorschach. Suite à une présentation détaillée de la méthodologie de recherche, les résultats sont exposés et comparés aux normes antérieures. Ils ne révèlent pas de différences importantes avec ces dernières, à l'exception de la hausse du F%, de la baisse du F+% et du nombre de Banalités. Les comparaisons Age, Sexe et QI révèlent quelques différences entre les groupes.

Endoscopic low-coherence topography measurement for upper airways and hollow samples.

To evaluate the severity of airway pathologies, quantitative dimensioning of airways is of utmost importance. Endoscopic vision gives a projective image and thus no true scaling information can be directly deduced from it. In this article, an approach based on an interferometric setup, a low-coherence laser source and a standard rigid endoscope is presented, and applied to hollow samples measurements. More generally, the use of the low-coherence interferometric setup detailed here could be extended to any other endoscopy-related field of interest, e.g., gastroscopy, arthroscopy and other medical or industrial applications where tri-dimensional topology is required. The setup design with a multiple fibers illumination system is presented. Demonstration of the method ability to operate on biological samples is assessed through measurements on ex vivo pig bronchi.

Can neurally adjusted ventilatory assist (NAVA) improve patient-ventilator interaction? A preliminary study

INTRODUCTION. NAVA is a new spontaneous-assisted ventilatory mode based on thedetection of diaphragmatic electrical activity (Eadi) and its feedback to adjust ventilatorsettings. NAVA uses the Eadi, an expression of the respiratory center's activity, to initiatepressurization, set the level of pressure support and cycle the ventilator into exhalation.Therefore, NAVA should theoretically allow near-perfect synchronization between the patientand the ventilator. However there are few data documenting these effects in intensive carepatients.OBJECTIVES. To determine whether NAVA can improve patient-ventilator synchronycompared to standard pressure support (PS) in intubated intensive care patients.METHODS. Comparative study of patient-ventilator interaction during PS with cliniciandetermined ventilator settings and NAVA with NAVA gain (proportionality factor betweenEadi and the amount of delivered inspiratory pressure) set as to obtain the same peak airwaypressure as the total pressure obtained in PS. A 20 min continuous recording with eachventilatory mode was performed allowing determination of trigger delay (Td), patient neuralinspiratory time (Tin), duration of pressurization by the ventilator (Tiv), excess durationof pressurization (Ti excess = Tiv - Tin/Tin 9 100) and number of asynchrony events byminute: non-triggering breaths, auto-triggering, double triggering, premature and delayedcycling.Results are given in mean ± SD. p is considered significant if\0.05.RESULTS. Preliminary results (mean ± SD): five patients (age 75 ± 12 years, 1 M/4F,BMI 25.7 ± 4.1 kg m-2), two pts with COPD, 1 with restrictive disease, initial settings: PS14.6 ± 1.7 cm H2O, PEEP 6.4 ± 1.5 cm H2O, NAVA gain 2.8 ± 1.3PS NAVA % reduction NAVAversus PSTd (ms) 210.4 ± 63.0 51.8 ± 12.1* 74.5 ± 5.0Ti excess (%) 12.9 ± 19.6 2.2 ± 0.6 70.8 ± 37.8n asynchrony/minute 7.6 ± 6.4 4.1 ± 3.7* 47.5 ± 17.0Respiratory rate (min-1) 16.8 ± 2.6 20.4 ± 4.7 NA* p\0.05CONCLUSION. Compared to standard PS, NAVA improves patient ventilator interaction byreducing Td and the overall incidence of asynchrony events. There is also a strong trend inreducing delayed cycling. This ongoing trial should provide evidence that NAVA can indeedimprove patient-ventilator synchrony in intubated patients undergoing PS.REFERENCE(S). 1. Sinderby C, Navalesi P et al (1995) Neural control of mechanicalventilation in respiratory failure. Nat Med 5(12):1433-1436.2. Colombo D, Cammarota G et al (2008) Physiologic response to varying levels of pressuresupport and neurally adjusted ventilator assist in patients with acute respiratory failure.Intensive Care Med 34(11):2010-2018.

Constructing brain functional networks from EEG: partial and unpartial correlations.

We consider electroencephalograms (EEGs) of healthy individuals and compare the properties of the brain functional networks found through two methods: unpartialized and partialized cross-correlations. The networks obtained by partial correlations are fundamentally different from those constructed through unpartial correlations in terms of graph metrics. In particular, they have completely different connection efficiency, clustering coefficient, assortativity, degree variability, and synchronization properties. Unpartial correlations are simple to compute and they can be easily applied to large-scale systems, yet they cannot prevent the prediction of non-direct edges. In contrast, partial correlations, which are often expensive to compute, reduce predicting such edges. We suggest combining these alternative methods in order to have complementary information on brain functional networks.

Redox dysregulation in the pathophysiology of schizophrenia and bipolar disorder: insights from animal models.

Abstract Significance: Schizophrenia (SZ) and bipolar disorder (BD) are classified as two distinct diseases. However, accumulating evidence shows that both disorders share genetic, pathological, and epidemiological characteristics. Based on genetic and functional findings, redox dysregulation due to an imbalance between pro-oxidants and antioxidant defense mechanisms has been proposed as a risk factor contributing to their pathophysiology. Recent Advances: Altered antioxidant systems and signs of increased oxidative stress are observed in peripheral tissues and brains of SZ and BD patients, including abnormal prefrontal levels of glutathione (GSH), the major cellular redox regulator and antioxidant. Here we review experimental data from rodent models demonstrating that permanent as well as transient GSH deficit results in behavioral, morphological, electrophysiological, and neurochemical alterations analogous to pathologies observed in patients. Mice with GSH deficit display increased stress reactivity, altered social behavior, impaired prepulse inhibition, and exaggerated locomotor responses to psychostimulant injection. These behavioral changes are accompanied by N-methyl-D-aspartate receptor hypofunction, elevated glutamate levels, impairment of parvalbumin GABA interneurons, abnormal neuronal synchronization, altered dopamine neurotransmission, and deficient myelination. Critical Issues: Treatment with the GSH precursor and antioxidant N-acetylcysteine normalizes some of those deficits in mice, but also improves SZ and BD symptoms when given as adjunct to antipsychotic medication. Future Directions: These data demonstrate the usefulness of GSH-deficient rodent models to identify the mechanisms by which a redox imbalance could contribute to the development of SZ and BD pathophysiologies, and to develop novel therapeutic approaches based on antioxidant and redox regulator compounds. Antioxid. Redox Signal. 18, 1428-1443.

Redox dysregulation, neurodevelopment, and schizophrenia.

In schizophrenia, a developmental redox dysregulation constitutes one 'hub' on which converge genetic impairments of glutathione synthesis and environmental vulnerability factors generating oxidative stress. Their timing at critical periods of neurodevelopment could play a decisive role in inducing impairment of neural connectivity and synchronization as observed in schizophrenia. In experimental models, such redox dysregulation induces anomalies strikingly similar to those observed in patients. This is mediated by hypoactive NMDA receptors, impairment of fast-spiking parvalbumin GABA interneurons and deficit in myelination. A treatment restoring the redox balance without side effects yields improvements of negative symptoms in chronic patients. Novel interventions based on these mechanisms if applied in early phases of the disease hold great therapeutic promise.

Asymmetry of Functional Connectivity in Schizophrenia at Different Spatial Scales

Introduction: The interhemispheric asymmetries that originate from connectivity-related structuring of the cerebral cortex are compromised in schizophrenia (SZ). Recently, we have revealed the whole-head topography of EEG synchronization in SZ (Jalili et al. 2007; Knyazeva et al. 2008). Here we extended the analysis to assess the abnormality in the asymmetry of synchronization, which is further motivated by the evidence that the interhemispheric asymmetries suspected to be abnormal in SZ originate from the connectivity-related structuring of the cortex. Methods: Thirteen right-handed SZ patients and thirteen matched controls, participated in this study and the multichannel (128) EEGs were recorded for 3-5 minutes at rest. Then, Laplacian EEG (LEEG) were calculated using a 2-D spline. The LEEGs were analysis through calculating the power spectral density using Welch's average periodogram method. Furthermore, using a state-space based multivariate synchronization measure, S-estimator, we analyzed the correlate of the functional cortico-cortical connectivity in SZ patients compared to the controls. The values of S-estimator were obtained at three different special scales: first-order neighbors for each sensor location, second-order neighbors, and the whole hemisphere. The synchronization measures based on LEEG of alpha and beta bands were applied and tuned to various spatial scales including local, intraregional, and long-distance levels. To assess the between-group differences, we used a permutation version of Hotelling's T2 test. For correlation analysis, Spearman Rank Correlation was calculated. Results: Compared to the controls, who had rightward asymmetry at a local level (LEEG power), rightward anterior and leftward posterior asymmetries at an intraregional level (first- and second-order S-estimator), and rightward global asymmetry (hemispheric S-estimator), SZ patients showed generally attenuated asymmetry, the effect being strongest for intraregional synchronization. This deviation in asymmetry across the anterior-to-posterior axis is consistent with the cerebral form of the so-called Yakovlevian or anticlockwise cerebral torque. Moreover, the negative occipital and positive frontal asymmetry values suggest higher regional synchronization among the left occipital and the right frontal locations relative to their symmetrical counterparts. Correlation analysis linked the posterior intraregional and hemispheric abnormalities to the negative SZ symptoms, whereas the asymmetry of LEEG power appeared to be weakly coupled to clinical ratings. The posterior intraregional abnormalities of asymmetry were shown to increase with the duration of the disease. The tentative links between these findings and gross anatomical asymmetries, including the cerebral torque and gyrification pattern in normal subjects and SZ patients, are discussed. Conclusions: Overall, our findings reveal the abnormalities in the synchronization asymmetry in SZ patients and heavy involvement of the right hemisphere in these abnormalities. These results indicate that anomalous asymmetry of cortico-cortical connections in schizophrenia is amenable to electrophysiological analysis.