Spatiotemporal stochastic resonance in the Swift-Hohenberg equation

We show the appearance of spatiotemporal stochastic resonance in the Swift-Hohenberg equation. This phenomenon emerges when a control parameter varies periodically in time around the bifurcation point. By using general scaling arguments and by taking into account the common features occurring in a bifurcation, we outline possible manifestations of the phenomenon in other pattern-forming systems.

Coherent stochastic resonance

We consider Brownian motion on a line terminated by two trapping points. A bias term in the form of a telegraph signal is applied to this system. It is shown that the first two moments of survival time exhibit a minimum at the same resonant frequency.

Harmonic oscillators driven by colored noise: crossovers, resonances and spectra

We study second-order properties of linear oscillators driven by exponentially correlated noise. We focus our attention on dynamical exponents and crossovers and also on resonance phenomena that appear when the driving noise is dichotomous. We also obtain the power spectrum and show its different behaviors according to the color of the noise.

Stochastic resonance in nonpotential systems

We propose a method to analytically show the possibility for the appearance of a maximum in the signal-to-noise ratio in nonpotential systems. We apply our results to the FitzHugh-Nagumo model under a periodic external forcing, showing that the model exhibits stochastic resonance. The procedure that we follow is based on the reduction to a one-dimensional dynamics in the adiabatic limit and in the topology of the phase space of the systems under study. Its application to other nonpotential systems is also discussed.

Stochastic resonance in a system of magnetic particles

We show that a dispersion of monodomain ferromagnetic particles in a solid phase exhibits stochastic resonance when a driven linearly polarized magnetic field is applied. By using an adiabatic approach, we calculate the power spectrum, the distribution of residence times, and the mean first passage time. The behavior of these quantities is similar to the behavior of corresponding quantities in other systems where stochastic resonance has also been observed.

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.

Design, data management, and population baseline characteristics of the PERFORM magnetic resonance imaging project.

Quantitative information from magnetic resonance imaging (MRI) may substantiate clinical findings and provide additional insight into the mechanism of clinical interventions in therapeutic stroke trials. The PERFORM study is exploring the efficacy of terutroban versus aspirin for secondary prevention in patients with a history of ischemic stroke. We report on the design of an exploratory longitudinal MRI follow-up study that was performed in a subgroup of the PERFORM trial. An international multi-centre longitudinal follow-up MRI study was designed for different MR systems employing safety and efficacy readouts: new T2 lesions, new DWI lesions, whole brain volume change, hippocampal volume change, changes in tissue microstructure as depicted by mean diffusivity and fractional anisotropy, vessel patency on MR angiography, and the presence of and development of new microbleeds. A total of 1,056 patients (men and women ≥ 55 years) were included. The data analysis included 3D reformation, image registration of different contrasts, tissue segmentation, and automated lesion detection. This large international multi-centre study demonstrates how new MRI readouts can be used to provide key information on the evolution of cerebral tissue lesions and within the macrovasculature after atherothrombotic stroke in a large sample of patients.

Exact temporal evolution for some non-linear diffusion process

Exact solutions to FokkerPlanck equations with nonlinear drift are considered. Applications of these exact solutions for concrete models are studied. We arrive at the conclusion that for certain drifts we obtain divergent moments (and infinite relaxation time) if the diffusion process can be extended without any obstacle to the whole space. But if we introduce a potential barrier that limits the diffusion process, moments converge with a finite relaxation time.

Variational localized-site cluster expansions. X. Dimerization in linear Heisenberg chains

Ground-state instability to bond alternation in long linear chains is considered from the point of view of valence-bond (VB) theory. This instability is viewed as the consequence of a long-range order (LRO) which is expected if the ground state is reasonably described in terms of the Kekulé states (with nearest-neighbor singlet pairing). It is argued that the bond alternation and associated LRO predicted by this simple, VB picture is retained for certain linear Heisenberg models; many-body VB calculations on spin s=1 / 2 and s=1 chains are carried out in a test of this argument.

Three-dimensional black-blood cardiac magnetic resonance coronary vessel wall imaging detects positive arterial remodeling in patients with nonsignificant coronary artery disease.

BACKGROUND: Direct noninvasive visualization of the coronary vessel wall may enhance risk stratification by quantifying subclinical coronary atherosclerotic plaque burden. We sought to evaluate high-resolution black-blood 3D cardiovascular magnetic resonance (CMR) imaging for in vivo visualization of the proximal coronary artery vessel wall. METHODS AND RESULTS: Twelve adult subjects, including 6 clinically healthy subjects and 6 patients with nonsignificant coronary artery disease (10% to 50% x-ray angiographic diameter reduction) were studied with the use of a commercial 1.5 Tesla CMR scanner. Free-breathing 3D coronary vessel wall imaging was performed along the major axis of the right coronary artery with isotropic spatial resolution (1.0x1.0x1.0 mm(3)) with the use of a black-blood spiral image acquisition. The proximal vessel wall thickness and luminal diameter were objectively determined with an automated edge detection tool. The 3D CMR vessel wall scans allowed for visualization of the contiguous proximal right coronary artery in all subjects. Both mean vessel wall thickness (1.7+/-0.3 versus 1.0+/-0.2 mm) and wall area (25.4+/-6.9 versus 11.5+/-5.2 mm(2)) were significantly increased in the patients compared with the healthy subjects (both P<0.01). The lumen diameter (3.6+/-0.7 versus 3.4+/-0.5 mm, P=0.47) and lumen area (8.9+/-3.4 versus 7.9+/-3.5 mm(2), P=0.47) were similar in both groups. CONCLUSIONS: Free-breathing 3D black-blood coronary CMR with isotropic resolution identified an increased coronary vessel wall thickness with preservation of lumen size in patients with nonsignificant coronary artery disease, consistent with a "Glagov-type" outward arterial remodeling. This novel approach has the potential to quantify subclinical disease.

To select or to weigh: a comparative study of linear combination schemes for superparent-one-dependence estimators

We conduct a large-scale comparative study on linearly combining superparent-one-dependence estimators (SPODEs), a popular family of seminaive Bayesian classifiers. Altogether, 16 model selection and weighing schemes, 58 benchmark data sets, and various statistical tests are employed. This paper's main contributions are threefold. First, it formally presents each scheme's definition, rationale, and time complexity and hence can serve as a comprehensive reference for researchers interested in ensemble learning. Second, it offers bias-variance analysis for each scheme's classification error performance. Third, it identifies effective schemes that meet various needs in practice. This leads to accurate and fast classification algorithms which have an immediate and significant impact on real-world applications. Another important feature of our study is using a variety of statistical tests to evaluate multiple learning methods across multiple data sets.

Analysis of linear networks with inconsistent initial conditions

This paper presents a new method to analyze timeinvariant linear networks allowing the existence of inconsistent initial conditions. This method is based on the use of distributions and state equations. Any time-invariant linear network can be analyzed. The network can involve any kind of pure or controlled sources. Also, the transferences of energy that occur at t=O are determined, and the concept of connection energy is introduced. The algorithms are easily implemented in a computer program.

Linear least squares estimation of the first order moving average parameter

We propose an iterative procedure to minimize the sum of squares function which avoids the nonlinear nature of estimating the first order moving average parameter and provides a closed form of the estimator. The asymptotic properties of the method are discussed and the consistency of the linear least squares estimator is proved for the invertible case. We perform various Monte Carlo experiments in order to compare the sample properties of the linear least squares estimator with its nonlinear counterpart for the conditional and unconditional cases. Some examples are also discussed