Analysis of exploratory eye movements in patients with schizophrenia during visual scanning of projective tests' figures

OBJECTIVE: Compare pattern of exploratory eye movements during visual scanning of the Rorschach and TAT test cards in people with schizophrenia and controls. METHOD: 10 participants with schizophrenia and 10 controls matched by age, schooling and intellectual level participated in the study. Severity of symptoms was evaluated with the Positive and Negative Syndrome Scale. Test cards were divided into three groups: TAT cards with scenes content, TAT cards with interaction content (TAT-faces), and Rorschach cards with abstract images. Eye movements were analyzed for: total number, duration and location of fixation; and length of saccadic movements. RESULTS: Different pattern of eye movement was found, with schizophrenia participants showing lower number of fixations but longer fixation duration in Rorschach cards and TAT-faces. The biggest difference was observed in Rorschach, followed by TAT-faces and TAT-scene cards. CONCLUSIONS: Results suggest alteration in visual exploration mechanisms possibly related to integration of abstract visual information.

Difference sets from projective planes

Magdeburg, Univ., Fak. für Mathematik, Diss., 2013

Breakdown and restoration of brain synchronization in blindness

Magdeburg, Univ., Fak. für Naturwiss., Diss., 2015

In search of mathematical primitives for deriving universal projective hash families

We provide some guidelines for deriving new projective hash families of cryptographic interest. Our main building blocks are so called group action systems; we explore what properties of this mathematical primitives may lead to the construction of cryptographically useful projective hash families. We point out different directions towards new constructions, deviating from known proposals arising from Cramer and Shoup's seminal work.

Mixed Hodge structures and vector bundles on the projective Plane I

We describe an equivalence of categories between the category of mixed Hodge structures and a category of vector bundles on the toric complex projective plane which verify some semistability condition. We then apply this correspondence to define an invariant which generalises the notion of R-split mixed Hodge structure and compute extensions in the category of mixed Hodge structures in terms of extensions of the corresponding vector bundles. We also give a relative version of this correspondence and apply it to define stratifications of the bases of the variations of mixed Hodge structure.

Diophantine approximation on projective varieties I: algebraic distance and metric Bézout theorem

"Vegeu el resum a l'inici del document del fitxer adjunt."

Projective modules over the Gerasimov-Sakhaev counterexample

We investigate the structure of the so-called Gerasimov- Sakhaev counterexample, which is a particular example of a universal localization, and classify (both finitely and infinitely generated) projective modules over it.

Wireless GPS-based phase-locked synchronization system for outdoor environment.

Synchronization of data coming from different sources is of high importance in biomechanics to ensure reliable analyses. This synchronization can either be performed through hardware to obtain perfect matching of data, or post-processed digitally. Hardware synchronization can be achieved using trigger cables connecting different devices in many situations; however, this is often impractical, and sometimes impossible in outdoors situations. The aim of this paper is to describe a wireless system for outdoor use, allowing synchronization of different types of - potentially embedded and moving - devices. In this system, each synchronization device is composed of: (i) a GPS receiver (used as time reference), (ii) a radio transmitter, and (iii) a microcontroller. These components are used to provide synchronized trigger signals at the desired frequency to the measurement device connected. The synchronization devices communicate wirelessly, are very lightweight, battery-operated and thus very easy to set up. They are adaptable to every measurement device equipped with either trigger input or recording channel. The accuracy of the system was validated using an oscilloscope. The mean synchronization error was found to be 0.39 μs and pulses are generated with an accuracy of <2 μs. The system provides synchronization accuracy about two orders of magnitude better than commonly used post-processing methods, and does not suffer from any drift in trigger generation.

Counting polygon dissections in the projective plane

"Vegeu el resum a l'inici del document del fitxer adjunt."

Tracking of Stepwise Ablation of Persistent Atrial Fibrillation using Synchronization of nearby Electrogams

Intracardiac organization indices such as atrial fibril- lation (AF) cycle length (AFCL) have been used to track the efficiency of stepwise catheter ablation (step-CA) of long-standing persistent AF (pers-AF), however, with lim- ited success. The timing between nearby bipolar intracar- diac electrograms (EGMs) reflects the spatial dynamics of wavelets during AF. The extent of synchronization between EGMs is an indirect measure of AF spatial organization. The synchronization between nearby EGMs during step- CA of pers-AF was evaluated using new indices based on the cross-correlation. The first one (spar(W)) quantifies the sparseness of the cross-correlation of local activation times. The second one (OI(W)) reflects the local concen- tration around the largest peak of the cross-correlation. By computing their relative evolution during step-CA until AF termination (AF-term), we found that OI(W) appeared su- perior to AFCL and spar(W) to track the effect of step-CA "en route" to AF-term.

Binding under Conflict Conditions: State-Space Analysis of Multivariate EEG Synchronization.

Real-world objects are often endowed with features that violate Gestalt principles. In our experiment, we examined the neural correlates of binding under conflict conditions in terms of the binding-by-synchronization hypothesis. We presented an ambiguous stimulus ("diamond illusion") to 12 observers. The display consisted of four oblique gratings drifting within circular apertures. Its interpretation fluctuates between bound ("diamond") and unbound (component gratings) percepts. To model a situation in which Gestalt-driven analysis contradicts the perceptually explicit bound interpretation, we modified the original diamond (OD) stimulus by speeding up one grating. Using OD and modified diamond (MD) stimuli, we managed to dissociate the neural correlates of Gestalt-related (OD vs. MD) and perception-related (bound vs. unbound) factors. Their interaction was expected to reveal the neural networks synchronized specifically in the conflict situation. The synchronization topography of EEG was analyzed with the multivariate S-estimator technique. We found that good Gestalt (OD vs. MD) was associated with a higher posterior synchronization in the beta-gamma band. The effect of perception manifested itself as reciprocal modulations over the posterior and anterior regions (theta/beta-gamma bands). Specifically, higher posterior and lower anterior synchronization supported the bound percept, and the opposite was true for the unbound percept. The interaction showed that binding under challenging perceptual conditions is sustained by enhanced parietal synchronization. We argue that this distributed pattern of synchronization relates to the processes of multistage integration ranging from early grouping operations in the visual areas to maintaining representations in the frontal networks of sensory memory.

Rigid flat webs on the projective plane

This paper studies global webs on the projective plane with vanishing curvature. The study is based on an interplay of local and global arguments. The main local ingredient is a criterium for the regularity of the curvature at the neighborhood of a generic point of the discriminant. The main global ingredient, the Legendre transform, is an avatar of classical projective duality in the realm of differential equations. We show that the Legendre transform of what we call reduced convex foliations are webs with zero curvature, and we exhibit a countable infinity family of convex foliations which give rise to a family of webs with zero curvature not admitting non-trivial deformations with zero curvature.

Imaging EEG synchronization in schizophrenia patients with S-estimator

Recently a new measure of the cooperative behavior of simultaneous time series was introduced (Carmeli et al. NeuroImage 2005). This measure called S-estimator is defined from the embedding dimension in a state space. S-estimator quantifies the amount of synchronization within a data set by comparing the actual dimensionality of the set with the expected full dimensionality of the asynchronous set. It has the advantage of being a multivariate measure over traditionally used in systems neuroscience bivariate measures of synchronization. Multivariate measures of synchronization are of particular interest for applications in the field of modern multichannel EEG research, since they easily allow mapping of local and/or regional synchronization and are compatible with other imaging techniques. We applied Sestimator to the analysis of EEG synchronization in schizophrenia patients vs. matched controls. The whole-head mapping with S-estimator revealed a specific pattern of local synchronization in schizophrenia patients. The differences in the landscape of synchronization included decreased local synchronization in the territories over occipital and midline areas and increased synchronization over temporal areas. In frontal areas, the S-estimator revealed a tendency for an asymmetry: decreased S-values over the left hemisphere were adjacent to increased values over the right hemisphere. Separate calculations showed reproducibility of this pattern across the main EEG frequency bands. The maintenance of the same synchronization landscape across EEG frequencies probably implies the structural changes in the cortical circuitry of schizophrenia patients. These changes are regionally specific and suggest that schizophrenia is a misconnectivity rather than hypo- or hyper-connectivity disorder.

Synchronization of EEG: bivariate and multivariate measures.

Synchronization behavior of electroencephalographic (EEG) signals is important for decoding information processing in the human brain. Modern multichannel EEG allows a transition from traditional measurements of synchronization in pairs of EEG signals to whole-brain synchronization maps. The latter can be based on bivariate measures (BM) via averaging over pair-wise values or, alternatively, on multivariate measures (MM), which directly ascribe a single value to the synchronization in a group. In order to compare BM versus MM, we applied nine different estimators to simulated multivariate time series with known parameters and to real EEGs.We found widespread correlations between BM and MM, which were almost frequency-independent for all the measures except coherence. The analysis of the behavior of synchronization measures in simulated settings with variable coupling strength, connection probability, and parameter mismatch showed that some of them, including S-estimator, S-Renyi, omega, and coherence, aremore sensitive to linear interdependences,while others, like mutual information and phase locking value, are more responsive to nonlinear effects. Onemust consider these properties together with the fact thatMM are computationally less expensive and, therefore, more efficient for the large-scale data sets than BM while choosing a synchronization measure for EEG analysis.

Abnormal EEG Synchronization Correlates with Demyelination in Alzheimer's Disease

Introduction : The pathological processes caused by Alzheimer's disease (AD) supposedly disrupt communication between and within the distributed cortical networks due to the dysfunction/loss of synapses and myelination breakdown. Indeed, recently (Knyazeva et al. 2008), we have revealed the whole-head topography of EEG synchronization specific to AD. Here we analyze whether and how these abnormalities of synchronization are related to the demyelination of cortico-cortical fibers. Methods : Fifteen newly diagnosed AD patients (CDR 0.5-1) and 15 controls matched for age, participated in the study. Their multichannel (128) EEGs were recorded during 3-5 min at rest. They were submitted to the multivariate phase synchronization (MPS) analysis for mapping regional synchronization. To obtain individual whole-head maps, the MPS was computed for each sensor considering its 2nd nearest topographical neighbors. Separate calculations were performed for the delta, theta, alpha-1/−2, and beta-1/−2 EEG bands. The same subjects were scanned on a 3 Tesla Philips scanner. The protocol included a high-resolution T1-weighted sequence and a Magnetization Transfer Imaging (MTI) acquisition. For each subject, we defined a 3mm thick layer of white matter exactly below the cortical gray matter. The magnetization transfer ratio (MTR) - an estimator of myelination - was calculated for this layer in 39 Brodmann-defined ROIs per hemisphere. To assess the between-group differences, we used a permutation version of Hotelling's T2 test or two-sample T-test (Pcorrected <0.05). For correlation analysis, Spearman Rank Correlation was calculated. Results : In AD patients, we have found an abnormal landscape of synchronization characterized by a decrease in MPS over the fronto-temporal region of the left hemisphere and an increase over the temporo-parieto-occipital regions bilaterally. Also, we have shown a widespread decrease in regional MTR in the AD patients for all the areas excluding motor, premotor, and primary sensory ones. Assuming that AD-related changes in synchronization are associated with demyelination, we hypothesized a correlation between the regional MTR values and MPS values in the hypo- and hyper-synchronized clusters. We found that MPS in the left fronto-temporal hypo-synchronized cluster directly correlates with myelination in BA42-46 of the left hemisphere: the lower the myelination in individual patients, the lower the EEG synchronization. By contrast, in the posterior hyper-synchronized cluster, MPS inversely correlated with myelination, i.e., the lower the myelination, the higher the synchronization. This posterior hyper-synchronization, more characteristic for early-onset AD, probably, results from the initial effect of the disease on cortical inhibition, reducing cortical capacity for decoupling irrelevant connections. Remarkably, it showed different topography of correlations in early- vs. late-onset patients. In the early-onset patients, hyper-synchronization was mainly related to demyelination in posterior BAs, the effect being significant in all the EEG frequency bands. In the late-onset patients, widely distributed correlations were significant for the EEG delta band, suggesting an interaction between the cerebral manifestations of AD and the age of its onset, i.e., topographically selective impairment of cortical inhibition in early-onset AD vs. its wide-spread weakening in old age. Conclusions : Overall, our results document that the degradation of white matter is a significant factor of AD pathogenesis leading to functional dysconnection, the latter being reflected in EEG synchronization abnormalities.