A THEORETICAL RESULT ON PHASE-LAG

We prove a Theoretical result which relates phase-lag to the error constant of a numerical method for periodic problem y'' = f(x, y).

When long-range zero-lag synchronization is feasible in cortical networks

Many studies have reported long-range synchronization of neuronal activity between brain areas, in particular in the beta and gamma bands with frequencies in the range of 14–30 and 40–80 Hz, respectively. Several studies have reported synchrony with zero phase lag, which is remarkable considering the synaptic and conduction delays inherent in the connections between distant brain areas. This result has led to many speculations about the possible functional role of zero-lag synchrony, such as for neuronal communication, attention, memory, and feature binding. However, recent studies using recordings of single-unit activity and local field potentials report that neuronal synchronization may occur with non-zero phase lags. This raises the questions whether zero-lag synchrony can occur in the brain and, if so, under which conditions. We used analytical methods and computer simulations to investigate which connectivity between neuronal populations allows or prohibits zero-lag synchrony. We did so for a model where two oscillators interact via a relay oscillator. Analytical results and computer simulations were obtained for both type I Mirollo–Strogatz neurons and type II Hodgkin–Huxley neurons. We have investigated the dynamics of the model for various types of synaptic coupling and importantly considered the potential impact of Spike-Timing Dependent Plasticity (STDP) and its learning window. We confirm previous results that zero-lag synchrony can be achieved in this configuration. This is much easier to achieve with Hodgkin–Huxley neurons, which have a biphasic phase response curve, than for type I neurons. STDP facilitates zero-lag synchrony as it adjusts the synaptic strengths such that zero-lag synchrony is feasible for a much larger range of parameters than without STDP.

On the wake-induced vibration of tandem circular cylinders: the vortex interaction excitation mechanism

The mechanism of wake-induced vibrations (WIV) of a pair of cylinders in a tandem arrangement is investigated by experiments. A typical WIV response is characterized by a build-up of amplitude persisting to high reduced velocities; this is different from a typical vortex-induced vibration (VIV) response, which occurs in a limited resonance range. We suggest that WIV of the downstream cylinder is excited by the unsteady vortex-structure interactions between the body and the upstream wake. Coherent vortices interfering with the downstream cylinder induce fluctuations in the fluid force that are not synchronized with the motion. A favourable phase lag between the displacement and the fluid force guarantees that a positive energy transfer from the flow to the structure sustains the oscillations. If the unsteady vortices are removed from the wake of the upstream body then WIV will not be excited. An experiment performed in a steady shear flow turned out to be central to the understanding of the origin of the fluid forces acting on the downstream cylinder.

Influence of hysteresis on tidal capillary fringe dynamics in a well-sorted sand

Nielsen and Perrochet [Adv. Water Resour. 23 (2000) 503] presented experimental data for cyclic water movement in the vadose zone above an oscillating watertable. The response of the watertable to cyclic forcing was characterised by the ratios of the forcing head to watertable amplitudes and their associated phase lag. They found that their non-hysteretic Richards' equation model failed to represent the observed behaviour of these parameters. This paper explores the effect on the simulated capillary fringe dynamics (in terms of these parameters) of including varying degrees of hysteresis in the moisture retention curve used in a numerical model of their experiment. It is clear that hysteresis can indeed account for observed discrepancies between simulation and experiment and that the effect of hysteresis varies with the frequency of oscillation. The use of a single-valued mean retention curve, as advocated by some authors, fails to provide a match between the simulated and observed behaviour of the Nielsen and Perrochet parameters, but is shown to be adequate for predicting time-averaged soil moisture profiles. (C) 2003 Elsevier Ltd. All rights reserved.

Soil thermal diffusivity estimated from data of soil temperature and single soil component properties

Under field conditions, thermal diffusivity can be estimated from soil temperature data but also from the properties of soil components together with their spatial organization. We aimed to determine soil thermal diffusivity from half-hourly temperature measurements in a Rhodic Kanhapludalf, using three calculation procedures (the amplitude ratio, phase lag and Seemann procedures), as well as from soil component properties, for a comparison of procedures and methods. To determine thermal conductivity for short wave periods (one day), the phase lag method was more reliable than the amplitude ratio or the Seemann method, especially in deeper layers, where temperature variations are small. The phase lag method resulted in coherent values of thermal diffusivity. The method using properties of single soil components with the values of thermal conductivity for sandstone and kaolinite resulted in thermal diffusivity values of the same order. In the observed water content range (0.26-0.34 m³ m-3), the average thermal diffusivity was 0.034 m² d-1 in the top layer (0.05-0.15 m) and 0.027 m² d-1 in the subsurface layer (0.15-0.30 m).

Timing and climatic imprint of Greenland interstadials recorded in stalagmites from Northern Turkey

A 50 kyr-long exceptionally well-dated and highly resolved stalagmite oxygen (δ 18O) and carbon (δ 13C) isotope record from Sofular Cave in northwestern Turkey helps to further improve the dating of Greenland Interstadials (GI) 1, and 3–12. Timing of most GI in the Sofular record is consistent within ±10 to 300 years with the “iconic” Hulu Cave record. Larger divergences (>500 years) between Sofular and Hulu are only observed for GI 4 and 7. The Sofular record differs from the most recent NGRIP chronology by up to several centuries, whereas age offsets do not increase systematically with depth. The Sofular record also reveals a rapid and sensitive climate and ecosystem response in the eastern Mediterranean to GI, whereas a phase lag of ∼100 years between climate and full ecosystem response is evident. Finally, results of spectral analyses of the Sofular isotope records do not support a 1,470-year pacing of GI.

Ionospheric Signatures of Pulsed Magnetopause Reconnection

The concept of zero-flow equilibria of the magnetosphere-ionosphere system leads to a large number of predictions concerning the ionospheric signatures of pulsed magnetopause reconnection. These include: poleward-moving F-region electron temperature enhancements and associated transient 630nm emission; associated poleward plasma flow which, compared to the pulsed variation of the reconnection rate, is highly smoothed by induction effects; oscillatory latitudinal motion of the open/closed field line boundary; phase lag of plasma flow enhancements after equatorward motions of the boundary; azimuthal plasma flow bursts, coincident in time and space with the 630nm-dominant auroral transients, only when the magnitude of the By component of the interplanetary magnetic field (IMF) is large; azimuthal-then-poleward motion of 630nm-dominant transients at a velocity which at all times equals the internal plasma flow velocity; 557.7nm-dominant transients on one edge of the 630nm-dominant transient (initially, and for large |By|, on the poleward or equatorward edge depending on the polarity of IMF By); tailward expansion of the flow response at several km s-1; and discrete steps in the cusp ion dispersion signature between the polewardmoving structures. This paper discusses these predictions and how all have recently been confirmed by combinations of observations by optical instruments on the Svalbard Islands, the EISCAT radars and the DMSP and DE satellites.

Orbital and millenial-scale environmental changes between 64 and 25 ka BP recorded in Black Sea sediments

High-resolution pollen and dinoflagellate cyst records from sediment core M72/5-25-GC1 were used to reconstruct vegetation dynamics in northern Anatolia and surface conditions of the Black Sea between 64 and 20 ka BP. During this period, the dominance of Artemisia in the pollen record indicates a steppe landscape and arid climate conditions. However, the concomitant presence of temperate arboreal pollen suggests the existence of glacial refugia in northern Anatolia. Long-term glacial vegetation dynamics reveal two major arid phases ~64–55 and 40–32 ka BP, and two major humid phases ~54–45 and 28–20 ka BP, correlating with higher and lower summer insolation, respectively. Dansgaard–Oeschger (D–O) cycles are clearly indicated by the 25-GC1 pollen record. Greenland interstadials are characterized by a marked increase in temperate tree pollen, indicating a spread of forests due to warm/wet conditions in northern Anatolia, whereas Greenland stadials reveal cold and arid conditions as indicated by spread of xerophytic biomes. There is evidence for a phase lag of ~500 to 1500 yr between initial warming and forest expansion, possibly due to successive changes in atmospheric circulation in the North Atlantic sector. The dominance of Pyxidinopsis psilata and Spiniferites cruciformis in the dinocyst record indicates brackish Black Sea conditions during the entire glacial period. The decrease of marine indicators (marine dinocysts, acritarchs) at ~54 ka BP and increase of freshwater algae (Pediastrum, Botryococcus) from 32 to 25 ka BP reveals freshening of the Black Sea surface water. This freshening is possibly related to humid phases in the region, to connection between Caspian Sea and Black Sea, to seasonal freshening by floating ice, and/or to closer position of river mouths due to low sea level. In the southern Black Sea, Greenland interstadials are clearly indicated by high dinocyst concentrations and calcium carbonate content, as a result of an increase in primary productivity. Heinrich events show a similar impact on the environment in the northern Anatolia/Black Sea region as Greenland stadials.

Tidal friction in close-in satellites and exoplanets: The Darwin theory re-visited

This report is a review of Darwin`s classical theory of bodily tides in which we present the analytical expressions for the orbital and rotational evolution of the bodies and for the energy dissipation rates due to their tidal interaction. General formulas are given which do not depend on any assumption linking the tidal lags to the frequencies of the corresponding tidal waves (except that equal frequency harmonics are assumed to span equal lags). Emphasis is given to the cases of companions having reached one of the two possible final states: (1) the super-synchronous stationary rotation resulting from the vanishing of the average tidal torque; (2) capture into the 1:1 spin-orbit resonance (true synchronization). In these cases, the energy dissipation is controlled by the tidal harmonic with period equal to the orbital period (instead of the semi-diurnal tide) and the singularity due to the vanishing of the geometric phase lag does not exist. It is also shown that the true synchronization with non-zero eccentricity is only possible if an extra torque exists opposite to the tidal torque. The theory is developed assuming that this additional torque is produced by an equatorial permanent asymmetry in the companion. The results are model-dependent and the theory is developed only to the second degree in eccentricity and inclination (obliquity). It can easily be extended to higher orders, but formal accuracy will not be a real improvement as long as the physics of the processes leading to tidal lags is not better known.

Chawla-Numerov method revisited

The well-known two-step fourth-order Numerov method was shown to have better interval of periodicity when made explicit, see Chawla (1984). It is readily verifiable that the improved method still has phase-lag of order 4. We suggest a slight modification from which linear problems could benefit. Phase-lag of any order can be achieved, but only order 6 is derived. © 1991.

Variability of mesospheric water vapor above Bern in relation to the 27-day solar rotation cycle

Many studies investigated solar–terrestrial responses (thermal state, O₃ , OH, H₂O) with emphasis on the tropical upper atmosphere. In this paper the Focus is switched to water vapor in the mesosphere at a mid-latitudinal location. Eight years of water vapor profile measurements above Bern (46.88°N/7.46°E) are investigated to study oscillations with the Focus on periods between 10 and 50 days. Different spectral analyses revealed prominent features in the 27-day oscillation band, which are enhanced in the upper mesosphere (above 0.1 hPa, ∼64 km) during the rising sun spot activity of solar cycle 24. Local as well as zonal mean Aura MLS observations Support these results by showing a similar behavior. The relationship between mesospheric water and the solar Lyman-α flux is studied by comparing thesi-milarity of their temporal oscillations. The H₂O oscillation is negatively correlated to solar Lyman-α oscillation with a correlation coefficient of up to −0.3 to −0.4, and the Phase lag is 6–10 days at 0.04 hPa. The confidence level of the correlation is ≥99%. This finding supports the assumption that the 27-day oscillation in Lyman-α causes a periodical photo dissociation loss in mesospheric water. Wavelet power spectra, cross-wavelet transform and wavelet coherence analysis (WTC)complete our study. More periods of high common wavelet power of H₂O and solar Lyman-α are present when amplitudes of the Lyman-α flux increase. Since this is not a measure of physical correlation a more detailed view on WTC is necessary, where significant (two sigma level)correlations occur intermittently in the 27 and 13-day band with variable Phase lock behavior. Large Lyman-α oscillations appeared after the solar super storm in July 2012 and the H₂O oscillations show a well pronounced anticorrelation. The competition between advective transport and photo dissociation loss of mesospheric water vapor may explain the sometimes variable Phase relationship of mesospheric H₂O and solar Lyman-α oscillations. Generally, the WTC analysis indicates that solar variability causes observable photochemical and dynamical processes in the mid-latitude mesosphere.

Stable isotope record and distribution of foraminifera in sediment core GeoB3004-1

Fluctuations in the abundance of selected foraminiferal indicator species and diversity allowed the reconstruction of changes in deepwater oxygenation and monsoon-driven organic matter fluxes in the deep western Arabian Sea during the last 190 kyr. Times of maximum surface production coincide with periods of intensified SW monsoon as shown by the abundance of Globigerina bulloides and enhanced carbonate corrosion. Benthic ecosystem variability in the deep Arabian Sea is not exclusively driven by variations in monsoonal upwelling and related organic matter supply to the seafloor but also by changes in deepwater ventilation. Deepening of the base of the oxygen minimum zone (OMZ) below 1800 m water depth is strongly coherent on the precessional band but lags proxies of SW monsoon strength by 4 to 6 kyr. The "out-of-phase" relationship between OMZ deepening and maximum SW monsoon strength is explained by temporal changes in the advection of oxygen-rich deepwater masses of North Atlantic and Antarctic origin. This process affected the remineralization and burial efficiency of organic matter in the deep Arabian Sea, resulting in the observed phase lag between maximum monsoon strength and organic carbon preservation.

Functional and effective connectivity in MEG. Application to the study of epilepsy

Nuestro cerebro contiene cerca de 1014 sinapsis neuronales. Esta enorme cantidad de conexiones proporciona un entorno ideal donde distintos grupos de neuronas se sincronizan transitoriamente para provocar la aparición de funciones cognitivas, como la percepción, el aprendizaje o el pensamiento. Comprender la organización de esta compleja red cerebral en base a datos neurofisiológicos, representa uno de los desafíos más importantes y emocionantes en el campo de la neurociencia. Se han propuesto recientemente varias medidas para evaluar cómo se comunican las diferentes partes del cerebro a diversas escalas (células individuales, columnas corticales, o áreas cerebrales). Podemos clasificarlos, según su simetría, en dos grupos: por una parte, la medidas simétricas, como la correlación, la coherencia o la sincronización de fase, que evalúan la conectividad funcional (FC); mientras que las medidas asimétricas, como la causalidad de Granger o transferencia de entropía, son capaces de detectar la dirección de la interacción, lo que denominamos conectividad efectiva (EC). En la neurociencia moderna ha aumentado el interés por el estudio de las redes funcionales cerebrales, en gran medida debido a la aparición de estos nuevos algoritmos que permiten analizar la interdependencia entre señales temporales, además de la emergente teoría de redes complejas y la introducción de técnicas novedosas, como la magnetoencefalografía (MEG), para registrar datos neurofisiológicos con gran resolución. Sin embargo, nos hallamos ante un campo novedoso que presenta aun varias cuestiones metodológicas sin resolver, algunas de las cuales trataran de abordarse en esta tesis. En primer lugar, el creciente número de aproximaciones para determinar la existencia de FC/EC entre dos o más señales temporales, junto con la complejidad matemática de las herramientas de análisis, hacen deseable organizarlas todas en un paquete software intuitivo y fácil de usar. Aquí presento HERMES (http://hermes.ctb.upm.es), una toolbox en MatlabR, diseñada precisamente con este fin. Creo que esta herramienta será de gran ayuda para todos aquellos investigadores que trabajen en el campo emergente del análisis de conectividad cerebral y supondrá un gran valor para la comunidad científica. La segunda cuestión practica que se aborda es el estudio de la sensibilidad a las fuentes cerebrales profundas a través de dos tipos de sensores MEG: gradiómetros planares y magnetómetros, esta aproximación además se combina con un enfoque metodológico, utilizando dos índices de sincronización de fase: phase locking value (PLV) y phase lag index (PLI), este ultimo menos sensible a efecto la conducción volumen. Por lo tanto, se compara su comportamiento al estudiar las redes cerebrales, obteniendo que magnetómetros y PLV presentan, respectivamente, redes más densamente conectadas que gradiómetros planares y PLI, por los valores artificiales que crea el problema de la conducción de volumen. Sin embargo, cuando se trata de caracterizar redes epilépticas, el PLV ofrece mejores resultados, debido a la gran dispersión de las redes obtenidas con PLI. El análisis de redes complejas ha proporcionado nuevos conceptos que mejoran caracterización de la interacción de sistemas dinámicos. Se considera que una red está compuesta por nodos, que simbolizan sistemas, cuyas interacciones se representan por enlaces, y su comportamiento y topología puede caracterizarse por un elevado número de medidas. Existe evidencia teórica y empírica de que muchas de ellas están fuertemente correlacionadas entre sí. Por lo tanto, se ha conseguido seleccionar un pequeño grupo que caracteriza eficazmente estas redes, y condensa la información redundante. Para el análisis de redes funcionales, la selección de un umbral adecuado para decidir si un determinado valor de conectividad de la matriz de FC es significativo y debe ser incluido para un análisis posterior, se convierte en un paso crucial. En esta tesis, se han obtenido resultados más precisos al utilizar un test de subrogadas, basado en los datos, para evaluar individualmente cada uno de los enlaces, que al establecer a priori un umbral fijo para la densidad de conexiones. Finalmente, todas estas cuestiones se han aplicado al estudio de la epilepsia, caso práctico en el que se analizan las redes funcionales MEG, en estado de reposo, de dos grupos de pacientes epilépticos (generalizada idiopática y focal frontal) en comparación con sujetos control sanos. La epilepsia es uno de los trastornos neurológicos más comunes, con más de 55 millones de afectados en el mundo. Esta enfermedad se caracteriza por la predisposición a generar ataques epilépticos de actividad neuronal anormal y excesiva o bien síncrona, y por tanto, es el escenario perfecto para este tipo de análisis al tiempo que presenta un gran interés tanto desde el punto de vista clínico como de investigación. Los resultados manifiestan alteraciones especificas en la conectividad y un cambio en la topología de las redes en cerebros epilépticos, desplazando la importancia del ‘foco’ a la ‘red’, enfoque que va adquiriendo relevancia en las investigaciones recientes sobre epilepsia. ABSTRACT There are about 1014 neuronal synapses in the human brain. This huge number of connections provides the substrate for neuronal ensembles to become transiently synchronized, producing the emergence of cognitive functions such as perception, learning or thinking. Understanding the complex brain network organization on the basis of neuroimaging data represents one of the most important and exciting challenges for systems neuroscience. Several measures have been recently proposed to evaluate at various scales (single cells, cortical columns, or brain areas) how the different parts of the brain communicate. We can classify them, according to their symmetry, into two groups: symmetric measures, such as correlation, coherence or phase synchronization indexes, evaluate functional connectivity (FC); and on the other hand, the asymmetric ones, such as Granger causality or transfer entropy, are able to detect effective connectivity (EC) revealing the direction of the interaction. In modern neurosciences, the interest in functional brain networks has increased strongly with the onset of new algorithms to study interdependence between time series, the advent of modern complex network theory and the introduction of powerful techniques to record neurophysiological data, such as magnetoencephalography (MEG). However, when analyzing neurophysiological data with this approach several questions arise. In this thesis, I intend to tackle some of the practical open problems in the field. First of all, the increase in the number of time series analysis algorithms to study brain FC/EC, along with their mathematical complexity, creates the necessity of arranging them into a single, unified toolbox that allow neuroscientists, neurophysiologists and researchers from related fields to easily access and make use of them. I developed such a toolbox for this aim, it is named HERMES (http://hermes.ctb.upm.es), and encompasses several of the most common indexes for the assessment of FC and EC running for MatlabR environment. I believe that this toolbox will be very helpful to all the researchers working in the emerging field of brain connectivity analysis and will entail a great value for the scientific community. The second important practical issue tackled in this thesis is the evaluation of the sensitivity to deep brain sources of two different MEG sensors: planar gradiometers and magnetometers, in combination with the related methodological approach, using two phase synchronization indexes: phase locking value (PLV) y phase lag index (PLI), the latter one being less sensitive to volume conduction effect. Thus, I compared their performance when studying brain networks, obtaining that magnetometer sensors and PLV presented higher artificial values as compared with planar gradiometers and PLI respectively. However, when it came to characterize epileptic networks it was the PLV which gives better results, as PLI FC networks where very sparse. Complex network analysis has provided new concepts which improved characterization of interacting dynamical systems. With this background, networks could be considered composed of nodes, symbolizing systems, whose interactions with each other are represented by edges. A growing number of network measures is been applied in network analysis. However, there is theoretical and empirical evidence that many of these indexes are strongly correlated with each other. Therefore, in this thesis I reduced them to a small set, which could more efficiently characterize networks. Within this framework, selecting an appropriate threshold to decide whether a certain connectivity value of the FC matrix is significant and should be included in the network analysis becomes a crucial step, in this thesis, I used the surrogate data tests to make an individual data-driven evaluation of each of the edges significance and confirmed more accurate results than when just setting to a fixed value the density of connections. All these methodologies were applied to the study of epilepsy, analysing resting state MEG functional networks, in two groups of epileptic patients (generalized and focal epilepsy) that were compared to matching control subjects. Epilepsy is one of the most common neurological disorders, with more than 55 million people affected worldwide, characterized by its predisposition to generate epileptic seizures of abnormal excessive or synchronous neuronal activity, and thus, this scenario and analysis, present a great interest from both the clinical and the research perspective. Results revealed specific disruptions in connectivity and network topology and evidenced that networks’ topology is changed in epileptic brains, supporting the shift from ‘focus’ to ‘networks’ which is gaining importance in modern epilepsy research.

A review of load models for the prediction of footfall-induced vibration in structures

Crowd induced dynamic loading in large structures, such as gymnasiums or stadium, is usually modelled as a series of harmonic loads which are defined in terms of their Fourier coefficients. Different values of these coefficients that were obtained from full scale measurements can be found in codes. Recently, an alternative has been proposed, based on random generation of load time histories that take into account phase lag among individuals inside the crowd. This paper presents the testing done on a structure designed to be a gymnasium. Two series of dynamic test were performed on the gym slab. For the first test an electrodynamic shaker was placed at several locations and during the second one people located inside a marked area bounced and jumped guided by different metronome rates. A finite element model (FEM) is presented and a comparison of numerically predicted and experimentally observed vibration modes and frequencies has been used to assess its validity. The second group of measurements will be compared with predictions made using the FEM model and three alternatives for crowd induced load modelling.

Cognitive reserve is associated with the functional organization of brain networks in healthy aging: a MEG study

The proportion of elderly people in the population has increased rapidly in the last century and consequently "healthy aging" is expected to become a critical area of research in neuroscience. Evidence reveals how healthy aging depends on three main behavioral factors: social lifestyle, cognitive activity and physical activity. In this study, we focused on the role of cognitive activity, concentrating specifically on educational and occupational attainment factors, which were considered two of the main pillars of cognitive reserve. 21 subjects with similar rates of social lifestyle, physical and cognitive activity were selected from a sample of 55 healthy adults. These subjects were divided into two groups according to their level of cognitive reserve; one group comprised subjects with high cognitive reserve (9 members) and the other contained those with low cognitive reserve (12 members). To evaluate the cortical brain connectivity network, all participants were recorded by Magnetoencephalography (MEG) while they performed a memory task (modified version of the Sternberg¿s Task). We then applied two algorithms (Phase Locking Value & Phase-Lag Index) to study the dynamics of functional connectivity. In response to the same task, the subjects with lower cognitive reserve presented higher functional connectivity than those with higher cognitive reserve. These results may indicate that participants with low cognitive reserve needed a greater 'effort' than those with high cognitive reserve to achieve the same level of cognitive performance. Therefore, we conclude that cognitive reserve contributes to the modulation of the functional connectivity patterns of the aging brain.