Bounds for the Betti numbers of generalized Cohen-Macaulay ideals

Upper bounds for the Betti numbers of generalized Cohen-Macaulay ideals are given. In particular, for the case of non-degenerate, reduced and ir- reducible projective curves we get an upper bound which only depends on their degree.

Galois representations, embedding problems and modular forms

To an odd irreducible 2-dimensional complex linear representation of the absolute Galois group of the field Q of rational numbers, a modular form of weight 1 is associated (modulo Artin's conjecture on the L-series of the representation in the icosahedral case). In addition, linear liftings of 2-dimensional projective Galois representations are related to solutions of certain Galois embedding problems. In this paper we present some recent results on the existence of liftings of projective representations and on the explicit resolution of embedding problems associated to orthogonal Galois representations, and explain how these results can be used to construct modular forms.

Threefolds with nef anticanonical bundles

In this paper we study the global structure of projective threefolds X whose anticanonical bundle K is nef.

Semi-purity of tempered Deligne cohomology

In this paper we define the formal and tempered Deligne cohomology groups, that are obtained by applying the Deligne complex functor to the complexes of formal differential forms and tempered currents respectively. We then prove the existence of a duality between them, a vanishing theorem for the former and a semipurity property for the latter. The motivation of these results comes from the study of covariant arithmetic Chow groups. The semipurity property of tempered Deligne cohomology implies, in particular, that several definitions of covariant arithmetic Chow groups agree for projective arithmetic varieties.

A note on quadrics through an algebraic curve

In this note we describe the intersection of all quadric hypersur- faces containing a given linearly normal smooth projective curve of genus n and degree 2n + 1

EEG alpha activity reflects motor preparation rather than the mode of action selection

Alpha-band activity (8-13 Hz) is not only suppressed by sensory stimulation and movements, but also modulated by attention, working memory and mental tasks, and could be sensitive to higher motor control functions. The aim of the present study was to examine alpha oscillatory activity during the preparation of simple left or right finger movements, contrasting the external and internal mode of action selection. Three preparation conditions were examined using a precueing paradigm with S1 as the preparatory and S2 as the imperative cue: Full, laterality instructed by S1; Free, laterality freely selected and None, laterality instructed by S2. Time-frequency (TF) analysis was performed in the alpha frequency range during the S1-S2 interval, and alpha motor-related amplitude asymmetries (MRAA) were also calculated. The significant MRAA during the Full and Free conditions indicated effective external and internal motor response preparation. In the absence of specific motor preparation (None), a posterior alpha event-related desynchronization (ERD) dominated, reflecting the main engagement of attentional resources. In Full and Free motor preparation, posterior alpha ERD was accompanied by a midparietal alpha event-related synchronization (ERS), suggesting a concomitant inhibition of task-irrelevant visual activity. In both Full and Free motor preparation, analysis of alpha power according to MRAA amplitude revealed two types of functional activation patterns: (1) a motor alpha pattern, with predominantly midparietal alpha ERS and large MRAA corresponding to lateralized motor activation/visual inhibition and (2) an attentional alpha pattern, with dominating right posterior alpha ERD and small MRAA reflecting visuospatial attention. The present results suggest that alpha oscillatory patterns do not resolve the selection mode of action, but rather distinguish separate functional strategies of motor preparation.

De la dyschronie chez les enfants instables : hyptohèse d'une difficulté d'instauration d'un temps transitionnel.

Résumé - De la dyschronie chez les enfants instables, hypothèse d'une difficulté d'instauration d'un temps transitionnel. Du syndrome d'asynergie motrice et mentale de Wallon (1925) au déficit d'inhibition du comportement de Barkley (1997), l'agitation de l'enfant a souvent été liée à une difficulté à penser, organiser et partager les représentations inhérentes à la temporalité. La dyschronie, telle que formulée par Gibello (1976), constitue une théorie heuristique pour penser ce défaut de symbolisation du temps. Pour mieux comprendre ces phénomènes, plusieurs épreuves projectives (Rorschach, TAT, dessins) ont été proposées à un jeune garçon instable dyschronique. Les analyses mettent en évidence une discontinuité des capacités représentatives. Si une différence entre un protocole Rorschach qui s'est révélé restreint et un TAT abondant en constitue le premier signe, des indices spécifiques montrent une difficulté d'instauration d'une aire de jeu imaginaire stable ou plus précisément un manque de continuité dans les phénomènes transitionnels (Winnicott, 1975). Peut-on dès lors envisager un lien entre la difficulté de représentation des transformations (Gibello, 2004) et ce déficit d'instauration, non plus seulement d'un espace, mais aussi d'un temps où se représentent les transitions ?

BPSK to ASK signal conversion using injection-locked oscillators-part II: experiment

This paper demonstrates the feasibility of a new circuit for the conversion of binary phase-shift keying signals into amplitude-shift keying signals. In its simplest form, the converter circuit is composed by a power divider, a couple of second harmonic injection-locked oscillators, and a power combiner. The operation of the converter circuit relies on the frequency synchronization of both oscillators and the generation of an interference pattern by combining their outputs, which reproduces the original phase modulation. Two prototypes of the converter have been implemented. The first one is a hybrid version working in the 400-530-MHz frequency range. The second one has been implemented using multichip-module technology, and is intended to work in the 1.8-2.2-GHz frequency range.

Synchronizability of EEG-Based Functional Networks in Early Alzheimer's Disease.

Recently graph theory and complex networks have been widely used as a mean to model functionality of the brain. Among different neuroimaging techniques available for constructing the brain functional networks, electroencephalography (EEG) with its high temporal resolution is a useful instrument of the analysis of functional interdependencies between different brain regions. Alzheimer's disease (AD) is a neurodegenerative disease, which leads to substantial cognitive decline, and eventually, dementia in aged people. To achieve a deeper insight into the behavior of functional cerebral networks in AD, here we study their synchronizability in 17 newly diagnosed AD patients compared to 17 healthy control subjects at no-task, eyes-closed condition. The cross-correlation of artifact-free EEGs was used to construct brain functional networks. The extracted networks were then tested for their synchronization properties by calculating the eigenratio of the Laplacian matrix of the connection graph, i.e., the largest eigenvalue divided by the second smallest one. In AD patients, we found an increase in the eigenratio, i.e., a decrease in the synchronizability of brain networks across delta, alpha, beta, and gamma EEG frequencies within the wide range of network costs. The finding indicates the destruction of functional brain networks in early AD.

Event-related potentials and changes of brain rhythm oscillations during working memory activation in patients with first-episode psychosis.

Background: Earlier contributions have documented significant changes in sensory, attention-related endogenous event-related potential (ERP) components and θ band oscillatory responses during working memory activation in patients with schizophrenia. In patients with first-episode psychosis, such studies are still scarce and mostly focused on auditory sensory processing. The present study aimed to explore whether subtle deficits of cortical activation are present in these patients before the decline of working memory performance. Methods: We assessed exogenous and endogenous ERPs and frontal θ event-related synchronization (ERS) in patients with first-episode psychosis and healthy controls who successfully performed an adapted 2-back working memory task, including 2 visual n-backworking memory tasks as well as oddball detection and passive fixation tasks. Results: We included 15 patients with first-episode psychosis and 18 controls in this study. Compared with controls, patients with first-episode psychosis displayed increased latencies of early visual ERPs and phasic θ ERS culmination peak in all conditions. However, they also showed a rapid recruitment of working memory-related neural generators, even in pure attention tasks, as indicated by the decreased N200 latency and increased amplitude of sustained θ ERS in detection compared with controls. Limitations: Owing to the limited sample size, no distinction was made between patients with first-episode psychosis with positive and negative symptoms. Although we controlled for the global load of neuroleptics, medication effect cannot be totally ruled out. Conclusion: The present findings support the concept of a blunted electroencephalographic response in patients with first-episode psychosis who recruit the maximum neural generators in simple attention conditions without being able to modulate their brain activation with increased complexity of working memory tasks.

Zenith angle distributions at Super-Kamiokande and SNO and the solution of the solar neutrino problem

We have performed a detailed study of the zenith angle dependence of the regeneration factor and distributions of events at SNO and SK for different solutions of the solar neutrino problem. In particular, we discuss the oscillatory behavior and the synchronization effect in the distribution for the LMA solution, the parametric peak for the LOW solution, etc. A physical interpretation of the effects is given. We suggest a new binning of events which emphasizes the distinctive features of the zenith angle distributions for the different solutions. We also find the correlations between the integrated day-night asymmetry and the rates of events in different zenith angle bins. The study of these correlations strengthens the identification power of the analysis.

Self-sustained spatiotemporal oscillations induced by membrane-bulk coupling

We propose a novel mechanism leading to spatiotemporal oscillations in extended systems that does not rely on local bulk instabilities. Instead, oscillations arise from the interaction of two subsystems of different spatial dimensionality. Specifically, we show that coupling a passive diffusive bulk of dimension d with an excitable membrane of dimension d-1 produces a self-sustained oscillatory behavior. An analytical explanation of the phenomenon is provided for d=1. Moreover, in-phase and antiphase synchronization of oscillations are found numerically in one and two dimensions. This novel dynamic instability could be used by biological systems such as cells, where the dynamics on the cellular membrane is necessarily different from that of the cytoplasmic bulk.

Solvable dynamics in a system of interacting random tops

A new solvable model of synchronization dynamics is introduced. It consists of a system of long range interacting tops or magnetic moments with random precession frequencies. The model allows for an explicit study of orientational effects in synchronization phenomena as well as nonlinear processes in resonance phenomena in strongly coupled magnetic systems. A stability analysis of the incoherent solution is performed for different types of orientational disorder. A system with orientational disorder always synchronizes in the absence of noise.

Exactly solvable phase oscillator models with syncrhonization dynamics

Populations of phase oscillators interacting globally through a general coupling function f(x) have been considered. We analyze the conditions required to ensure the existence of a Lyapunov functional giving close expressions for it in terms of a generating function. We have also proposed a family of exactly solvable models with singular couplings showing that it is possible to map the synchronization phenomenon into other physical problems. In particular, the stationary solutions of the least singular coupling considered, f(x) = sgn(x), have been found analytically in terms of elliptic functions. This last case is one of the few nontrivial models for synchronization dynamics which can be analytically solved.

Interhemispheric visual integration in humans explored by multimodal brain imaging

Résumé: Les récents progrès techniques de l'imagerie cérébrale non invasives ont permis d'améliorer la compréhension des différents systèmes fonctionnels cérébraux. Les approches multimodales sont devenues indispensables en recherche, afin d'étudier dans sa globalité les différentes caractéristiques de l'activité neuronale qui sont à la base du fonctionnement cérébral. Dans cette étude combinée d'imagerie par résonance magnétique fonctionnelle (IRMf) et d'électroencéphalographie (EEG), nous avons exploité le potentiel de chacune d'elles, soit respectivement la résolution spatiale et temporelle élevée. Les processus cognitifs, de perception et de mouvement nécessitent le recrutement d'ensembles neuronaux. Dans la première partie de cette thèse nous étudions, grâce à la combinaison des techniques IRMf et EEG, la réponse des aires visuelles lors d'une stimulation qui demande le regroupement d'éléments cohérents appartenant aux deux hémi-champs visuels pour en faire une seule image. Nous utilisons une mesure de synchronisation (EEG de cohérence) comme quantification de l'intégration spatiale inter-hémisphérique et la réponse BOLD (Blood Oxygenation Level Dependent) pour évaluer l'activité cérébrale qui en résulte. L'augmentation de la cohérence de l'EEG dans la bande beta-gamma mesurée au niveau des électrodes occipitales et sa corrélation linéaire avec la réponse BOLD dans les aires de VP/V4, reflète et visualise un ensemble neuronal synchronisé qui est vraisemblablement impliqué dans le regroupement spatial visuel. Ces résultats nous ont permis d'étendre la recherche à l'étude de l'impact que le contenu en fréquence des stimuli a sur la synchronisation. Avec la même approche, nous avons donc identifié les réseaux qui montrent une sensibilité différente à l'intégration des caractéristiques globales ou détaillées des images. En particulier, les données montrent que l'implication des réseaux visuels ventral et dorsal est modulée par le contenu en fréquence des stimuli. Dans la deuxième partie nous avons a testé l'hypothèse que l'augmentation de l'activité cérébrale pendant le processus de regroupement inter-hémisphérique dépend de l'activité des axones calleux qui relient les aires visuelles. Comme le Corps Calleux présente une maturation progressive pendant les deux premières décennies, nous avons analysé le développement de la fonction d'intégration spatiale chez des enfants âgés de 7 à 13 ans et le rôle de la myelinisation des fibres calleuses dans la maturation de l'activité visuelle. Nous avons combiné l'IRMf et la technique de MTI (Magnetization Transfer Imaging) afin de suivre les signes de maturation cérébrale respectivement sous l'aspect fonctionnel et morphologique (myelinisation). Chez lés enfants, les activations associées au processus d'intégration entre les hémi-champs visuels sont, comme chez l'adulte, localisées dans le réseau ventral mais se limitent à une zone plus restreinte. La forte corrélation que le signal BOLD montre avec la myelinisation des fibres du splenium est le signe de la dépendance entre la maturation des fonctions visuelles de haut niveau et celle des connections cortico-corticales. Abstract: Recent advances in non-invasive brain imaging allow the visualization of the different aspects of complex brain dynamics. The approaches based on a combination of imaging techniques facilitate the investigation and the link of multiple aspects of information processing. They are getting a leading tool for understanding the neural basis of various brain functions. Perception, motion, and cognition involve the formation of cooperative neuronal assemblies distributed over the cerebral cortex. In this research, we explore the characteristics of interhemispheric assemblies in the visual brain by taking advantage of the complementary characteristics provided by EEG (electroencephalography) and fMRI (Functional Magnetic Resonance Imaging) techniques. These are the high temporal resolution for EEG and high spatial resolution for fMRI. In the first part of this thesis we investigate the response of the visual areas to the interhemispheric perceptual grouping task. We use EEG coherence as a measure of synchronization and BOLD (Blood Oxygenar tion Level Dependent) response as a measure of the related brain activation. The increase of the interhemispheric EEG coherence restricted to the occipital electrodes and to the EEG beta band and its linear relation to the BOLD responses in VP/V4 area points to a trans-hemispheric synchronous neuronal assembly involved in early perceptual grouping. This result encouraged us to explore the formation of synchronous trans-hemispheric networks induced by the stimuli of various spatial frequencies with this multimodal approach. We have found the involvement of ventral and medio-dorsal visual networks modulated by the spatial frequency content of the stimulus. Thus, based on the combination of EEG coherence and fMRI BOLD data, we have identified visual networks with different sensitivity to integrating low vs. high spatial frequencies. In the second part of this work we test the hypothesis that the increase of brain activity during perceptual grouping depends on the activity of callosal axons interconnecting the visual areas that are involved. To this end, in children of 7-13 years, we investigated functional (functional activation with fMRI) and morphological (myelination of the corpus callosum with Magnetization Transfer Imaging (MTI)) aspects of spatial integration. In children, the activation associated with the spatial integration across visual fields was localized in visual ventral stream and limited to a part of the area activated in adults. The strong correlation between individual BOLD responses in .this area and the myelination of the splenial system of fibers points to myelination as a significant factor in the development of the spatial integration ability.