Krein's strings whose spectral functions are of polynomial growth

In case Krein's strings with spectral functions of polynomial growth a necessary and su fficient condition for the Krein's correspondence to be continuous is given.

Redox dysregulation in schizophrenia : implication for oligodendrocyte maturation and structural connectivity

Schizophrenia, which results from an interaction between gene and environmental factors, is a psychiatric disorder characterized by reality distortion. The clinical symptoms, which are generally diagnosed in late adolescence or early adulthood, partly derive from altered brain connectivity especially in prefrontal cortex. Disruption of neuronal networks implies oligodendrocyte and myelin abnormalities in schizophrenia pathophysiology. The mechanisms of these impairments are still unclear. Converging evidences indicate a role of redox dysregulation, generated by an imbalance between pro-oxidants and antioxidant defense mechanisms, in the development of schizophrenia pathophysiology. In particular, genetic and biochemical data indicate impaired synthesis of glutathione, the main cellular antioxidant and redox regulator. As oligodendrocyte maturation is dependent on redox state, we evaluated whether abnormal redox control could contribute to oligodendrocyte and myelin impairments in schizophrenia. We found that glutathione in prefrontal cortex of early psychosis patients and control subjects positively correlated with white matter integrity. We then further explored the interplay between glutathione and myelin using a translational approach. Our data showed that in mice with genetically impaired glutathione synthesis, oligodendrocyte late maturation as well as myelination was delayed in the anterior cingulate cortex. Specifically, oligodendrocyte number and myelin levels were lowered at peripubertal age, coincident in time with the peak of myelin- related gene expression during normal brain development. These data suggest that early adolescence is a vulnerable developmental period during which an adequate redox control is required for oligodendrocyte maturation and active myelination process. Consistently, oxidative stress mediated by psychosocial stress also delayed myelination in peripubertal mice. At cellular levels, impaired glutathione synthesis altered oligodendrocyte development at several levels. Using oligodendrocyte progenitor cells cultures, our data showed that glutathione deficiency was associated with (i) cell cycle arrest and a reduction in oligodendrocyte proliferation, and (ii) an impairment in oligodendrocyte maturation. Abnormal oligodendrocyte proliferation was mediated by upregulation of Fyn kinase activity. Consistently, under oxidative stress conditions, we observed abnormal regulation of Fyn kinase in fibroblasts of patients deficient in glutathione synthesis. Together, our data support that a redox dysregulation due to glutathione deficit could underlie myelination impairment in schizophrenia, possibly mediated by dysregulated Fyn pathway. Better characterization of Fyn mechanisms would pave the way towards new drug targets. -- La schizophrénie est une maladie psychiatrique qui se définit par une distorsion de la perception de la réalité. Les symptômes cliniques sont généralement diagnostiqués durant l'adolescence ou au début de l'âge adulte et proviennent de troubles de la connectivité, principalement au niveau du cortex préfrontal. Les dysfonctionnements des réseaux neuronaux impliquent des anomalies au niveau des oligodendrocytes et de la myéline dans la pathophysiologie de la schizophrénie. Les mécanismes responsables des ces altérations restent encore mal compris. Dans le développement de la schizophrénie, des évidences mettent en avant un rôle de la dérégulation rédox, traduit par un déséquilibre entre facteurs pro-oxydants et défenses antioxydantes. Des données génétiques et biochimiques indiquent notamment un défaut de la synthèse du glutathion, le principal antioxydant et rédox régulateur des cellules. Etant donné que la maturation des oligodendrocytes est dépendante de l'état rédox, nous avons regardé si une dérégulation rédox contribue aux anomalies de la myéline dans le cadre de la schizophrénie. Dans le cortex préfrontal des sujets contrôles et des patients en phase précoce de psychose, nous avons montré que le glutathion était positivement associé à l'intégrité de matière blanche. Afin d'explorer plus en détail la relation entre le glutathion et la myéline, nous avons mené une étude translationnelle. Nos résultats ont montré que des souris ayant un déficit de la synthèse du glutathion présentaient un retard dans les processus de maturation des oligodendrocytes et de la myélinisation dans le cortex cingulaire antérieure. Plus précisément, le nombre d'oligodendrocytes et le taux de myéline étaient uniquement diminués durant la période péripubertaire. Cette même période correspond au pic de l'expression des gènes en lien avec la myéline. Ces données soulignent le fait que l'adolescence est une période du développement particulièrement sensible durant laquelle un contrôle adéquat de l'état rédox est nécessaire aux processus de maturation des oligodendrocytes et de myélinisation. Ceci est en accord avec la diminution de myéline observée suite à un stress oxydatif généré par un stress psychosocial. Au niveau cellulaire, un déficit du glutathion affecte le développement des oligodendrocytes à différents stades. En effet, dans des cultures de progéniteurs d'oligodendrocytes, nos résultats montrent qu'une réduction du taux de glutathion était associée à (i) un arrêt du cycle cellulaire ainsi qu'une diminution de la prolifération des oligodendrocytes, et à (ii) des dysfonctionnements de la maturation des oligodendrocytes. Par ailleurs, au niveau moléculaire, les perturbations de la prolifération étaient générées par une augmentation de l'activité de la kinase Fyn. Ceci est en accord avec la dérégulation de Fyn observée dans les fibroblastes de patients ayant une déficience en synthèse du glutathion en condition de stress oxydatif. Les résultats de cette thèse soulignent qu'une dérégulation rédox induite par un déficit en glutathion peut contribuer aux anomalies des oligodendrocytes et de la myéline via le dysfonctionnement des voies de signalisation Fyn. Une recherche plus avancée de l'implication de Fyn dans la maladie pourrait ouvrir la voie à de nouvelles cibles thérapeutiques.

Intracortical connectivity of layer VI pyramidal neurons in the somatosensory cortex of normal and barrelless mice.

In mice, barrels in layer IV of the somatosensory cortex correspond to the columnar representations of whisker follicles. In barrelless (BRL) mice, barrels are absent, but functionally, a columnar organization persists. Previously we characterized the aberrant geometry of thalamic projection of BRL mice using axonal reconstructions of individual neurons. Here we proceeded with the analysis of the intracortical projections from layer VI pyramidal neurons, to assess their contribution to the columnar organization. From series of tangential sections we reconstructed the axon collaterals of individual layer VI pyramidal neurons in the C2 barrel column that were labelled with biocytin [controls from normal (NOR) strain, 19 cells; BRL strain, nine cells]. Using six morphological parameters in a cluster analysis, we showed that layer VI neurons in NOR mice are distributed into four clusters distinguished by the radial and tangential extent of their intracortical projections. These clusters correlated with the cortical or subcortical projection of the main axon. In BRL mice, neurons were distributed within the same four clusters, but their projections to the granular and supragranular layers were significantly smaller and their tangential projection was less columnar than in NOR mice. However, in both strains the intracortical projections had a preference for the appropriate barrel column (C2), indicating that layer VI pyramidal cells could participate in the functional columnar organization of the barrel cortex. Correlative light and electron microscopy analyses provided morphometric data on the intracortical synaptic boutons and synapses of layer VI pyramidal neurons and revealed that projections to layer IV preferentially target excitatory dendritic spines and shafts.

Bernstein's problem on weighted polynomial approximation

We formulate a necessary and sufficient condition for polynomials to be dense in a space of continuous functions on the real line, with respect to Bernstein's weighted uniform norm. Equivalently, for a positive finite measure [lletra "mu" minúscula de l'alfabet grec] on the real line we give a criterion for density of polynomials in Lp[lletra "mu" minúscula de l'alfabet grec entre parèntesis].

Global and local connectivity changes in schizophrenia investigated by diffusion connectome

Background: New ways of representing diffusion data emerged recently and achieved to create structural connectivitymaps in healthy brains (Hagmann P et al. (2008)). These maps have the capacity to study alterations over the entire brain at the connection and network level. This is of high interest in complex disconnection diseases like schizophrenia. In this Pathology where multiple lines of evidence suggest the association of the pathology with abnormalities in neural circuitry and impaired structural connectivity, the diffusion imaging has been widely applied. Despite the large findings, most of the research using the diffusion just uses some scalar map derived from diffusion to show that some markers of white matter integrity are diminished in several areas of the brain (Kyriakopoulos M et al (2008)). Thanks to the structural connectionmatrix constructed by the whole brain tractography, we report in this work the network connectivity alterations in the schizophrenic patients. Methods: We investigated 13 schizophrenic patients as assessed by the DIGS (Diagnostic Interview for genetic studies, DSM IV criteria) and 13 healthy controls. We have got from each volunteer a DT-MRI as well as Qball imaging dataset and a high resolution anatomic T1 performed during the same session; with a 3 T clinical MRI scanner. The controls were matched on age, gender, handedness, and parental social economic-status. For all the subjects, a low resolution connection matrix is obtained by dividing the cortex into 66 gyral based ROIs. A higher resolution matrix is constructed using 250 ROIs as described in Hagmann P et al. (2008). These ROIs are respectively used jointly with the diffusion tractography to construct the high and low resolution densities connection matrices for each subject. In a first step the matrices of the groups are compared in term of connectivity, and not in term of density to check if the pathological group shows a loss of global connectivity. In this context the density connection matrices were binarized. As some local connectivity changes were also suspected, especially in frontal and temporal areas, we have also looked for the areas where the connectivity showed significant changes. Results: The statistical analysis revealed a significant loss of global connectivity in the schizophrenic's brains at level 5%. Furthermore, by constructing specific statistics which represent local connectivity within the anatomical regions (66 ROIs) using the data obtained by the finest resolution (250 ROIs) to improve the robustness, we found the regions that cause this significant loss of connectivity. The significance is observed after multiple testing corrections by the False Discovery Rate. Discussion: The detected regions are almost the same as those reported in the literature as the involved regions in schizophrenia. Most of the connectivity decreases are noted in both hemispheres in the fronto-frontal and temporo-temporal regions as well as some temporal ROIs with their adjacent ROIs in parietal and occipital lobes.

Altered structural connectivity in patients with medial temporal lobe epilepsy: A Diffusion Spectrum Imaging and Graph Analysis study

In this study we investigated the effect of medial temporal lobe epilepsy (MTLE) on the global characteristics of brain connectivity estimated by topological measures. We used DSI (Diffusion Spectrum Imaging) to construct a connectivity matrix where the nodes represents the anatomical ROIs and the edges are the connections between any pair of ROIs weighted by the mean GFA/FA values. A significant difference was found between the patient group vs control group in characteristic path length, clustering coefficient and small-worldness. This suggests that the MTLE network is less efficient compared to the network of the control group.

Connectivity differences in brain networks.

The scenario considered here is one where brain connectivity is represented as a network and an experimenter wishes to assess the evidence for an experimental effect at each of the typically thousands of connections comprising the network. To do this, a univariate model is independently fitted to each connection. It would be unwise to declare significance based on an uncorrected threshold of α=0.05, since the expected number of false positives for a network comprising N=90 nodes and N(N-1)/2=4005 connections would be 200. Control of Type I errors over all connections is therefore necessary. The network-based statistic (NBS) and spatial pairwise clustering (SPC) are two distinct methods that have been used to control family-wise errors when assessing the evidence for an experimental effect with mass univariate testing. The basic principle of the NBS and SPC is the same as supra-threshold voxel clustering. Unlike voxel clustering, where the definition of a voxel cluster is unambiguous, 'clusters' formed among supra-threshold connections can be defined in different ways. The NBS defines clusters using the graph theoretical concept of connected components. SPC on the other hand uses a more stringent pairwise clustering concept. The purpose of this article is to compare the pros and cons of the NBS and SPC, provide some guidelines on their practical use and demonstrate their utility using a case study involving neuroimaging data.

Principal components of functional connectivity: A new approach to study dynamic brain connectivity during rest.

Functional connectivity (FC) as measured by correlation between fMRI BOLD time courses of distinct brain regions has revealed meaningful organization of spontaneous fluctuations in the resting brain. However, an increasing amount of evidence points to non-stationarity of FC; i.e., FC dynamically changes over time reflecting additional and rich information about brain organization, but representing new challenges for analysis and interpretation. Here, we propose a data-driven approach based on principal component analysis (PCA) to reveal hidden patterns of coherent FC dynamics across multiple subjects. We demonstrate the feasibility and relevance of this new approach by examining the differences in dynamic FC between 13 healthy control subjects and 15 minimally disabled relapse-remitting multiple sclerosis patients. We estimated whole-brain dynamic FC of regionally-averaged BOLD activity using sliding time windows. We then used PCA to identify FC patterns, termed "eigenconnectivities", that reflect meaningful patterns in FC fluctuations. We then assessed the contributions of these patterns to the dynamic FC at any given time point and identified a network of connections centered on the default-mode network with altered contribution in patients. Our results complement traditional stationary analyses, and reveal novel insights into brain connectivity dynamics and their modulation in a neurodegenerative disease.

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.