Parameter-free extraction of the functional network topology from intracranial EEG recordings: a time-resolved study of graph properties in focal onset seizures

Rationale: Focal onset epileptic seizures are due to abnormal interactions between distributed brain areas. By estimating the cross-correlation matrix of multi-site intra-cerebral EEG recordings (iEEG), one can quantify these interactions. To assess the topology of the underlying functional network, the binary connectivity matrix has to be derived from the cross-correlation matrix by use of a threshold. Classically, a unique threshold is used that constrains the topology [1]. Our method aims to set the threshold in a data-driven way by separating genuine from random cross-correlation. We compare our approach to the fixed threshold method and study the dynamics of the functional topology. Methods: We investigate the iEEG of patients suffering from focal onset seizures who underwent evaluation for the possibility of surgery. The equal-time cross-correlation matrices are evaluated using a sliding time window. We then compare 3 approaches assessing the corresponding binary networks. For each time window: * Our parameter-free method derives from the cross-correlation strength matrix (CCS)[2]. It aims at disentangling genuine from random correlations (due to finite length and varying frequency content of the signals). In practice, a threshold is evaluated for each pair of channels independently, in a data-driven way. * The fixed mean degree (FMD) uses a unique threshold on the whole connectivity matrix so as to ensure a user defined mean degree. * The varying mean degree (VMD) uses the mean degree of the CCS network to set a unique threshold for the entire connectivity matrix. * Finally, the connectivity (c), connectedness (given by k, the number of disconnected sub-networks), mean global and local efficiencies (Eg, El, resp.) are computed from FMD, CCS, VMD, and their corresponding random and lattice networks. Results: Compared to FMD and VMD, CCS networks present: *topologies that are different in terms of c, k, Eg and El. *from the pre-ictal to the ictal and then post-ictal period, topological features time courses that are more stable within a period, and more contrasted from one period to the next. For CCS, pre-ictal connectivity is low, increases to a high level during the seizure, then decreases at offset. k shows a ‘‘U-curve’’ underlining the synchronization of all electrodes during the seizure. Eg and El time courses fluctuate between the corresponding random and lattice networks values in a reproducible manner. Conclusions: The definition of a data-driven threshold provides new insights into the topology of the epileptic functional networks.

Direct linking of Greenland and Antarctic ice cores at the Toba eruption (74 ka BP)

The Toba eruption that occurred some 74 ka ago in Sumatra, Indonesia, is among the largest volcanic events on Earth over the last 2 million years. Tephra from this eruption has been spread over vast areas in Asia, where it constitutes a major time marker close to the Marine Isotope Stage 4/5 boundary. As yet, no tephra associated with Toba has been identified in Greenland or Antarctic ice cores. Based on new accurate dating of Toba tephra and on accurately dated European stalagmites, the Toba event is known to occur between the onsets of Greenland interstadials (GI) 19 and 20. Furthermore, the existing linking of Greenland and Antarctic ice cores by gas records and by the bipolar seesaw hypothesis suggests that the Antarctic counterpart is situated between Antarctic Isotope Maxima (AIM) 19 and 20. In this work we suggest a direct synchronization of Greenland (NGRIP) and Antarctic (EDML) ice cores at the Toba eruption based on matching of a pattern of bipolar volcanic spikes. Annual layer counting between volcanic spikes in both cores allows for a unique match. We first demonstrate this bipolar matching technique at the already synchronized Laschamp geomagnetic excursion (41 ka BP) before we apply it to the suggested Toba interval. The Toba synchronization pattern covers some 2000 yr in GI-20 and AIM-19/20 and includes nine acidity peaks that are recognized in both ice cores. The suggested bipolar Toba synchronization has decadal precision. It thus allows a determination of the exact phasing of inter-hemispheric climate in a time interval of poorly constrained ice core records, and it allows for a discussion of the climatic impact of the Toba eruption in a global perspective. The bipolar linking gives no support for a long-term global cooling caused by the Toba eruption as Antarctica experiences a major warming shortly after the event. Furthermore, our bipolar match provides a way to place palaeo-environmental records other than ice cores into a precise climatic context.

Synchronization and desynchronization in epilepsy: controversies and hypotheses

Epilepsy has been historically seen as a functional brain disorder associated with excessive synchronization of large neuronal populations leading to a hypersynchronous state. Recent evidence showed that epileptiform phenomena, particularly seizures, result from complex interactions between neuronal networks characterized by heterogeneity of neuronal firing and dynamical evolution of synchronization. Desynchronization is often observed preceding seizures or during their early stages; in contrast, high levels of synchronization observed towards the end of seizures may facilitate termination. In this review we discuss cellular and network mechanisms responsible for such complex changes in synchronization. Recent work has identified cell-type-specific inhibitory and excitatory interactions, the dichotomy between neuronal firing and the non-local measurement of local field potentials distant to that firing, and the reflection of the neuronal dark matter problem in non-firing neurons active in seizures. These recent advances have challenged long-established views and are leading to a more rigorous and realistic understanding of the pathophysiology of epilepsy.

A set of canonical problems in sloshing. Part 0: Experimental setup and data processing

In a series of attempts to research and document relevant sloshing type phenomena, a series of experiments have been conducted. The aim of this paper is to describe the setup and data processing of such experiments. A sloshing tank is subjected to angular motion. As a result pressure registers are obtained at several locations, together with the motion data, torque and a collection of image and video information. The experimental rig and the data acquisition systems are described. Useful information for experimental sloshing research practitioners is provided. This information is related to the liquids used in the experiments, the dying techniques, tank building processes, synchronization of acquisition systems, etc. A new procedure for reconstructing experimental data, that takes into account experimental uncertainties, is presented. This procedure is based on a least squares spline approximation of the data. Based on a deterministic approach to the first sloshing wave impact event in a sloshing experiment, an uncertainty analysis procedure of the associated first pressure peak value is described.

Synchronization waves in geometric networks

We report synchronization of networked excitable nodes embedded in a metric space, where the connectivity properties are mostly determined by the distance between units. Such a high clustered structure, combined with the lack of long-range connections, prevents full synchronization and yields instead the emergence of synchronization waves. We show that this regime is optimal for information transmission through the system, as it enhances the options of reconstructing the topology from the dynamics. Measurements of topological and functional centralities reveal that the wave-synchronization state allows detection of the most structurally relevant nodes from a single observation of the dynamics, without any a priori information on the model equations ruling the evolution of the ensemble

Contribución al estudio del criptoanálisis y diseño de los criptosistemas caóticos

The extraordinary increase of new information technologies, the development of Internet, the electronic commerce, the e-government, mobile telephony and future cloud computing and storage, have provided great benefits in all areas of society. Besides these, there are new challenges for the protection of information, such as the loss of confidentiality and integrity of electronic documents. Cryptography plays a key role by providing the necessary tools to ensure the safety of these new media. It is imperative to intensify the research in this area, to meet the growing demand for new secure cryptographic techniques. The theory of chaotic nonlinear dynamical systems and the theory of cryptography give rise to the chaotic cryptography, which is the field of study of this thesis. The link between cryptography and chaotic systems is still subject of intense study. The combination of apparently stochastic behavior, the properties of sensitivity to initial conditions and parameters, ergodicity, mixing, and the fact that periodic points are dense, suggests that chaotic orbits resemble random sequences. This fact, and the ability to synchronize multiple chaotic systems, initially described by Pecora and Carroll, has generated an avalanche of research papers that relate cryptography and chaos. The chaotic cryptography addresses two fundamental design paradigms. In the first paradigm, chaotic cryptosystems are designed using continuous time, mainly based on chaotic synchronization techniques; they are implemented with analog circuits or by computer simulation. In the second paradigm, chaotic cryptosystems are constructed using discrete time and generally do not depend on chaos synchronization techniques. The contributions in this thesis involve three aspects about chaotic cryptography. The first one is a theoretical analysis of the geometric properties of some of the most employed chaotic attractors for the design of chaotic cryptosystems. The second one is the cryptanalysis of continuos chaotic cryptosystems and finally concludes with three new designs of cryptographically secure chaotic pseudorandom generators. The main accomplishments contained in this thesis are: v Development of a method for determining the parameters of some double scroll chaotic systems, including Lorenz system and Chua’s circuit. First, some geometrical characteristics of chaotic system have been used to reduce the search space of parameters. Next, a scheme based on the synchronization of chaotic systems was built. The geometric properties have been employed as matching criterion, to determine the values of the parameters with the desired accuracy. The method is not affected by a moderate amount of noise in the waveform. The proposed method has been applied to find security flaws in the continuous chaotic encryption systems. Based on previous results, the chaotic ciphers proposed by Wang and Bu and those proposed by Xu and Li are cryptanalyzed. We propose some solutions to improve the cryptosystems, although very limited because these systems are not suitable for use in cryptography. Development of a method for determining the parameters of the Lorenz system, when it is used in the design of two-channel cryptosystem. The method uses the geometric properties of the Lorenz system. The search space of parameters has been reduced. Next, the parameters have been accurately determined from the ciphertext. The method has been applied to cryptanalysis of an encryption scheme proposed by Jiang. In 2005, Gunay et al. proposed a chaotic encryption system based on a cellular neural network implementation of Chua’s circuit. This scheme has been cryptanalyzed. Some gaps in security design have been identified. Based on the theoretical results of digital chaotic systems and cryptanalysis of several chaotic ciphers recently proposed, a family of pseudorandom generators has been designed using finite precision. The design is based on the coupling of several piecewise linear chaotic maps. Based on the above results a new family of chaotic pseudorandom generators named Trident has been designed. These generators have been specially designed to meet the needs of real-time encryption of mobile technology. According to the above results, this thesis proposes another family of pseudorandom generators called Trifork. These generators are based on a combination of perturbed Lagged Fibonacci generators. This family of generators is cryptographically secure and suitable for use in real-time encryption. Detailed analysis shows that the proposed pseudorandom generator can provide fast encryption speed and a high level of security, at the same time. El extraordinario auge de las nuevas tecnologías de la información, el desarrollo de Internet, el comercio electrónico, la administración electrónica, la telefonía móvil y la futura computación y almacenamiento en la nube, han proporcionado grandes beneficios en todos los ámbitos de la sociedad. Junto a éstos, se presentan nuevos retos para la protección de la información, como la suplantación de personalidad y la pérdida de la confidencialidad e integridad de los documentos electrónicos. La criptografía juega un papel fundamental aportando las herramientas necesarias para garantizar la seguridad de estos nuevos medios, pero es imperativo intensificar la investigación en este ámbito para dar respuesta a la demanda creciente de nuevas técnicas criptográficas seguras. La teoría de los sistemas dinámicos no lineales junto a la criptografía dan lugar a la ((criptografía caótica)), que es el campo de estudio de esta tesis. El vínculo entre la criptografía y los sistemas caóticos continúa siendo objeto de un intenso estudio. La combinación del comportamiento aparentemente estocástico, las propiedades de sensibilidad a las condiciones iniciales y a los parámetros, la ergodicidad, la mezcla, y que los puntos periódicos sean densos asemejan las órbitas caóticas a secuencias aleatorias, lo que supone su potencial utilización en el enmascaramiento de mensajes. Este hecho, junto a la posibilidad de sincronizar varios sistemas caóticos descrita inicialmente en los trabajos de Pecora y Carroll, ha generado una avalancha de trabajos de investigación donde se plantean muchas ideas sobre la forma de realizar sistemas de comunicaciones seguros, relacionando así la criptografía y el caos. La criptografía caótica aborda dos paradigmas de diseño fundamentales. En el primero, los criptosistemas caóticos se diseñan utilizando circuitos analógicos, principalmente basados en las técnicas de sincronización caótica; en el segundo, los criptosistemas caóticos se construyen en circuitos discretos u ordenadores, y generalmente no dependen de las técnicas de sincronización del caos. Nuestra contribución en esta tesis implica tres aspectos sobre el cifrado caótico. En primer lugar, se realiza un análisis teórico de las propiedades geométricas de algunos de los sistemas caóticos más empleados en el diseño de criptosistemas caóticos vii continuos; en segundo lugar, se realiza el criptoanálisis de cifrados caóticos continuos basados en el análisis anterior; y, finalmente, se realizan tres nuevas propuestas de diseño de generadores de secuencias pseudoaleatorias criptográficamente seguros y rápidos. La primera parte de esta memoria realiza un análisis crítico acerca de la seguridad de los criptosistemas caóticos, llegando a la conclusión de que la gran mayoría de los algoritmos de cifrado caóticos continuos —ya sean realizados físicamente o programados numéricamente— tienen serios inconvenientes para proteger la confidencialidad de la información ya que son inseguros e ineficientes. Asimismo una gran parte de los criptosistemas caóticos discretos propuestos se consideran inseguros y otros no han sido atacados por lo que se considera necesario más trabajo de criptoanálisis. Esta parte concluye señalando las principales debilidades encontradas en los criptosistemas analizados y algunas recomendaciones para su mejora. En la segunda parte se diseña un método de criptoanálisis que permite la identificaci ón de los parámetros, que en general forman parte de la clave, de algoritmos de cifrado basados en sistemas caóticos de Lorenz y similares, que utilizan los esquemas de sincronización excitador-respuesta. Este método se basa en algunas características geométricas del atractor de Lorenz. El método diseñado se ha empleado para criptoanalizar eficientemente tres algoritmos de cifrado. Finalmente se realiza el criptoanálisis de otros dos esquemas de cifrado propuestos recientemente. La tercera parte de la tesis abarca el diseño de generadores de secuencias pseudoaleatorias criptográficamente seguras, basadas en aplicaciones caóticas, realizando las pruebas estadísticas, que corroboran las propiedades de aleatoriedad. Estos generadores pueden ser utilizados en el desarrollo de sistemas de cifrado en flujo y para cubrir las necesidades del cifrado en tiempo real. Una cuestión importante en el diseño de sistemas de cifrado discreto caótico es la degradación dinámica debida a la precisión finita; sin embargo, la mayoría de los diseñadores de sistemas de cifrado discreto caótico no ha considerado seriamente este aspecto. En esta tesis se hace hincapié en la importancia de esta cuestión y se contribuye a su esclarecimiento con algunas consideraciones iniciales. Ya que las cuestiones teóricas sobre la dinámica de la degradación de los sistemas caóticos digitales no ha sido totalmente resuelta, en este trabajo utilizamos algunas soluciones prácticas para evitar esta dificultad teórica. Entre las técnicas posibles, se proponen y evalúan varias soluciones, como operaciones de rotación de bits y desplazamiento de bits, que combinadas con la variación dinámica de parámetros y con la perturbación cruzada, proporcionan un excelente remedio al problema de la degradación dinámica. Además de los problemas de seguridad sobre la degradación dinámica, muchos criptosistemas se rompen debido a su diseño descuidado, no a causa de los defectos esenciales de los sistemas caóticos digitales. Este hecho se ha tomado en cuenta en esta tesis y se ha logrado el diseño de generadores pseudoaleatorios caóticos criptogr áficamente seguros.

Early dysfunction of functional connectivity in healthy elderly with subjective memory complaints

It is still an open question whether subjective memory complaints (SMC) can actually be considered to be clinically relevant predictors for the development of an objective memory impairment and even dementia. There is growing evidence that suggests that SMC are associated with an increased risk of dementia and with the presence of biological correlates of early Alzheimer's disease. In this paper, in order to shed some light on this issue, we try to discern whether subjects with SMC showed a different profile of functional connectivity compared with subjects with mild cognitive impairment (MCI) and healthy elderly subjects. In the present study, we compare the degree of synchronization of brain signals recorded with magnetoencephalography between three groups of subjects (56 in total): 19 with MCI, 12 with SMC and 25 healthy controls during a memory task. Synchronization likelihood, an index based on the theory of nonlinear dynamical systems, was used to measure functional connectivity. Briefly, results show that subjects with SMC have a very similar pattern of connectivity to control group, but on average, they present a lower synchronization value. These results could indicate that SMC are representing an initial stage with a hypo-synchronization (in comparison with the control group) where the brain system is still not compensating for the failing memory networks, but behaving as controls when compared with the MCI subjects.

Grouped sparsity algorithm for multichannel intracardiac ECG synchronization

In this paper, a new method is presented to ensure automatic synchronization of intracardiac ECG data, yielding a three-stage algorithm. We first compute a robust estimate of the derivative of the data to remove low-frequency perturbations. Then we provide a grouped-sparse representation of the data, by means of the Group LASSO, to ensure that all the electrical spikes are simultaneously detected. Finally, a post-processing step, based on a variance analysis, is performed to discard false alarms. Preliminary results on real data for sinus rhythm and atrial fibrillation show the potential of this approach.

Intracortical and corticothalamic coherency of fast spontaneous oscillations.

We report that fast (mainly 30- to 40-Hz) coherent electric field oscillations appear spontaneously during brain activation, as expressed by electroencephalogram (EEG) rhythms, and they outlast the stimulation of mesopontine cholinergic nuclei in acutely prepared cats. The fast oscillations also appear during the sleep-like EEG patterns of ketamine/xylazine anesthesia, but they are selectively suppressed during the prolonged phase of the slow (<1-Hz) sleep oscillation that is associated with hyperpolarization of cortical neurons. The fast (30- to 40-Hz) rhythms are synchronized intracortically within vertical columns, among closely located cortical foci, and through reciprocal corticothalamic networks. The fast oscillations do not reverse throughout the depth of the cortex. This aspect stands in contrast with the conventional depth profile of evoked potentials and slow sleep oscillations that display opposite polarity at the surface and midlayers. Current-source-density analyses reveal that the fast oscillations are associated with alternating microsinks and microsources across the cortex, while the evoked potentials and the slow oscillation display a massive current sink in midlayers, confined by two sources in superficial and deep layers. The synchronization of fast rhythms and their high amplitudes indicate that the term "EEG desynchronization," used to designate brain-aroused states, is incorrect and should be replaced with the original term, "EEG activation" [Moruzzi, G. & Magoun, H.W. (1949) Electroencephalogr. Clin. Neurophysiol. 1, 455-473].

Temporal fluctuations in coherence of brain waves.

As a measure of dynamical structure, short-term fluctuations of coherence between 0.3 and 100 Hz in the electroencephalogram (EEG) of humans were studied from recordings made by chronic subdural macroelectrodes 5-10 mm apart, on temporal, frontal, and parietal lobes, and from intracranial probes deep in the temporal lobe, including the hippocampus, during sleep, alert, and seizure states. The time series of coherence between adjacent sites calculated every second or less often varies widely in stability over time; sometimes it is stable for half a minute or more. Within 2-min samples, coherence commonly fluctuates by a factor up to 2-3, in all bands, within the time scale of seconds to tens of seconds. The power spectrum of the time series of these fluctuations is broad, extending to 0.02 Hz or slower, and is weighted toward the slower frequencies; little power is faster than 0.5 Hz. Some records show conspicuous swings with a preferred duration of 5-15s, either irregularly or quasirhythmically with a broad peak around 0.1 Hz. Periodicity is not statistically significant in most records. In our sampling, we have not found a consistent difference between lobes of the brain, subdural and depth electrodes, or sleeping and waking states. Seizures generally raise the mean coherence in all frequencies and may reduce the fluctuations by a ceiling effect. The coherence time series of different bands is positively correlated (0.45 overall); significant nonindependence extends for at least two octaves. Coherence fluctuations are quite local; the time series of adjacent electrodes is correlated with that of the nearest neighbor pairs (10 mm) to a coefficient averaging approximately 0.4, falling to approximately 0.2 for neighbors-but-one (20 mm) and to < 0.1 for neighbors-but-two (30 mm). The evidence indicates fine structure in time and space, a dynamic and local determination of this measure of cooperativity. Widely separated frequencies tending to fluctuate together exclude independent oscillators as the general or usual basis of the EEG, although a few rhythms are well known under special conditions. Broad-band events may be the more usual generators. Loci only a few millimeters apart can fluctuate widely in seconds, either in parallel or independently. Scalp EEG coherence cannot be predicted from subdural or deep recordings, or vice versa, and intracortical microelectrodes show still greater coherence fluctuation in space and time. Widely used computations of chaos and dimensionality made upon data from scalp or even subdural or depth electrodes, even when reproducible in successive samples, cannot be considered representative of the brain or the given structure or brain state but only of the scale or view (receptive field) of the electrodes used. Relevant to the evolution of more complex brains, which is an outstanding fact of animal evolution, we believe that measures of cooperativity are likely to be among the dynamic features by which major evolutionary grades of brains differ.

Biopacemaker acceleration without increased synchronization by chronic exposure to phorbol myristate acetate

L'activité électrique du coeur est initiée par la génération spontanée de potentiels d'action venant des cellules pacemaker du noeud sinusal (SN). Toute dysfonction au niveau de cette région entraîne une instabilité électrique du coeur. La majorité des patients souffrant d'un noeud sinusal déficient nécessitent l'implantation chirurgicale d'un pacemaker électronique; cependant, les limitations de cette approche incitent à la recherche d'une alternative thérapeutique. La base moléculaire des courants ioniques jouant un rôle crucial dans l'activité du noeud sinusal sont de plus en plus connues. Une composante importante de l'activité des cellules pacemakers semble être le canal HCN, responsable du courant pacemaker If. Le facteur T-box 3 (Tbx3), un facteur de transcription conservé durant le processus de l'évolution, est nécessaire au développement du système de conduction cardiaque. De précédentes études ont démontré que dans différentes lignées cellulaires le Phorbol 12-myristate 13-acetate (PMA) active l'expression du gène codant Tbx3 via des réactions en cascade partant de la protéine kinase C (PKC). L'objectif principal de cette étude est de tester si le PMA peut augmenter la fréquence et la synchronisation de l'activité spontanée du pacemaker biologique en culture. Plus précisément, nous avons étudié les effets de l'exposition chronique au PMA sur l'expression du facteur de transcription Tbx3, sur HCN4 et l'activité spontanée chez des monocouches de culture de myocytes ventriculaires de rats néonataux (MVRN). Nos résultats démontrent que le PMA augmente significativement le facteur transcription de Tbx3 et l'expression ARNm de HCN4, favorisant ainsi l'augmentation du rythme et de la stabilité de l'activité autonome. De plus, une diminution significative de la vitesse de conduction a été relevée et est attribuée à la diminution du couplage intercellulaire. La diminution de la vitesse de conduction pourrait expliquer l'effet négatif du PMA sur la synchronisation de l'activité autonome du pacemaker biologique. Ces résultats ont été confirmés par un modèle mathématique multicellulaire suggérant que des fréquences et résistances intercellulaires plus élevée pourraient induire une activité plus stable et moins synchrone. Cette étude amène de nouvelles connaissances très importantes destinées à la production d'un pacemaker biologique efficient et robuste.

Measuring the intermittent synchronicity of macroeconomic growth in Europe. ACES Cases No. 2010.1

Synchronization of growth rates are an important feature of international business cycles, particularly in relation to regional integration projects such as the single currency in Europe. Synchronization of growth rates clearly enhances the effectiveness of European Central Bank monetary policy, ensuring that policy changes are attuned to the dynamics of growth and business cycles in the majority of member states. In this paper a dissimilarity metric is constructed by measuring the topological differences between the GDP growth patterns in recurrence plots for individual countries. The results show that synchronization of growth rates were higher among the Euro area member states during the second half of the 1980s and from 1997 to roughly 2002. Apart from these two time periods, Euro area member states do not appear to be more synchronized than a group of major international countries, signifying that globalization was the major cause of international business cycle synchronization.

Experimental tests of quantum nonlinear dynamics in atom optics

Cold atoms in optical potentials provide an ideal test bed to explore quantum nonlinear dynamics. Atoms are prepared in a magneto-optic trap or as a dilute Bose-Einstein condensate and subjected to a far detuned optical standing wave that is modulated. They exhibit a wide range of dynamics, some of which can be explained by classical theory while other aspects show the underlying quantum nature of the system. The atoms have a mixed phase space containing regions of regular motion which appear as distinct peaks in the atomic momentum distribution embedded in a sea of chaos. The action of the atoms is of the order of Planck's constant, making quantum effects significant. This tutorial presents a detailed description of experiments measuring the evolution of atoms in time-dependent optical potentials. Experimental methods are developed providing means for the observation and selective loading of regions of regular motion. The dependence of the atomic dynamics on the system parameters is explored and distinct changes in the atomic momentum distribution are observed which are explained by the applicable quantum and classical theory. The observation of a bifurcation sequence is reported and explained using classical perturbation theory. Experimental methods for the accurate control of the momentum of an ensemble of atoms are developed. They use phase space resonances and chaotic transients providing novel ensemble atomic beamsplitters. The divergence between quantum and classical nonlinear dynamics is manifest in the experimental observation of dynamical tunnelling. It involves no potential barrier. However a constant of motion other than energy still forbids classically this quantum allowed motion. Atoms coherently tunnel back and forth between their initial state of oscillatory motion and the state 180 out of phase with the initial state.