The Early Toarcian anoxia, a synchronous event in the Western Tethys? An approach by quantitative biochronology (Unitary Associations), applied on calcareous nannofossils

During the Early Toarcian, major paleoenvironnemental and paleoceanographical changes occurred, leading to an oceanic anoxic event (OAE) and to a perturbation of the carbon isotope cycle. Although the standard biochronology of the Lower Jurassic is essentially based upon ammonites, in recent years biostratigraphy based on calcareous nannofossils and dinoflagellate cysts is increasingly used to date Jurassic rocks. However, the precise dating and correlation of the Early Toarcian OAE, and of the associated delta C-13 anomaly in different settings of the western Tethys, are still partly problematic, and it is still unclear whether these events are synchronous or not. In order to allow more accurate correlations of the organic rich levels recorded in the Lower Toarcian OAE, this account proposes a new biozonation based on a quantitative biochronology approach, the Unitary Associations (UA), applied to calcareous nannofossils. This study represents the first attempt to apply the UA method to Jurassic nannofossils. The study incorporates eighteen sections distributed across western Tethys and ranging from the Pliensbachian to Aalenian, comprising 1220 samples and 72 calcareous nannofossil taxa. The BioGraph [Savary, J., Guex, J., 1999. Discrete biochronological scales and unitary associations: description of the Biograph Computer program. Memoires de Geologie de Lausanne 34, 282 pp] and UA-Graph (Copyright Hammer O., Guex and Savary, 2002) softwares provide a discrete biochronological framework based upon multi-taxa concurrent range zones in the different sections. The optimized dataset generates nine UAs using the co-occurrences of 56 taxa. These UAs are grouped into six Unitary Association Zones (UA-Z), which constitute a robust biostratigraphic synthesis of all the observed or deduced biostratigraphic relationships between the analysed taxa. The UA zonation proposed here is compared to ``classic'' calcareous nannofossil biozonations, which are commonly used for the southern and the northern sides of Tethys. The biostratigraphic resolution of the UA-Zones varies from one nannofossil subzone or part of it to several subzones, and can be related to the pattern of calcareous nannoplankton originations and extinctions during the studied time interval. The Late Pliensbachian - Early Toarcian interval (corresponding to the UA-Z II) represents a major step in the Jurassic nannoplankton radiation. The recognized UA-Zones are also compared to the carbon isotopic negative excursion and TOC maximum in five sections of central Italy, Germany and England, with the aim of providing a more reliable correlation tool for the Early Toarcian OAE, and of the associated isotopic anomaly, between the southern and northern part of western Tethys. The results of this work show that the TOC maximum and delta C-13 negative excursion correspond to the upper part of the UA-Z II (i.e., UA 3) in the sections analysed. This suggests that the Early Toarcian OAE was a synchronous event within the western Tethys. (c) 2006 Elsevier B.V. All rights reserved.

Constructing brain functional networks from EEG: partial and unpartial correlations.

We consider electroencephalograms (EEGs) of healthy individuals and compare the properties of the brain functional networks found through two methods: unpartialized and partialized cross-correlations. The networks obtained by partial correlations are fundamentally different from those constructed through unpartial correlations in terms of graph metrics. In particular, they have completely different connection efficiency, clustering coefficient, assortativity, degree variability, and synchronization properties. Unpartial correlations are simple to compute and they can be easily applied to large-scale systems, yet they cannot prevent the prediction of non-direct edges. In contrast, partial correlations, which are often expensive to compute, reduce predicting such edges. We suggest combining these alternative methods in order to have complementary information on brain functional networks.

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.

Is spinal stenosis assessment dependent on slice orientation? A magnetic resonance imaging study.

INTRODUCTION: Lumbar spinal stenosis (LSS) treatment is based primarily on the clinical criteria providing that imaging confirms radiological stenosis. The radiological measurement more commonly used is the dural sac cross-sectional area (DSCA). It has been recently shown that grading stenosis based on the morphology of the dural sac as seen on axial T2 MRI images, better reflects severity of stenosis than DSCA and is of prognostic value. This radiological prospective study investigates the variability of surface measurements and morphological grading of stenosis for varying degrees of angulation of the T2 axial images relative to the disc space as observed in clinical practice. MATERIALS AND METHODS: Lumbar spine TSE T2 three-dimensional (3D) MRI sequences were obtained from 32 consecutive patients presenting with either suspected spinal stenosis or low back pain. Axial reconstructions using the OsiriX software at 0°, 10°, 20° and 30° relative to the disc space orientation were obtained for a total of 97 levels. For each level, DSCA was digitally measured and stenosis was graded according to the 4-point (A-D) morphological grading by two observers. RESULTS: A good interobserver agreement was found in grade evaluation of stenosis (k = 0.71). DSCA varied significantly as the slice orientation increased from 0° to +10°, +20° and +30° at each level examined (P < 0.0001) (-15 to +32% at 10°, -24 to +143% at 20° and -29 to +231% at 30° of slice orientation). Stenosis definition based on the surface measurements changed in 39 out of the 97 levels studied, whereas the morphology grade was modified only in two levels (P < 0.01). DISCUSSION: The need to obtain continuous slices using the classical 2D MRI acquisition technique entails often at least a 10° slice inclination relative to one of the studied discs. Even at this low angulation, we found a significantly statistical difference between surface changes and morphological grading change. In clinical practice, given the above findings, it might therefore not be necessary to align the axial cuts to each individual disc level which could be more time-consuming than obtaining a single series of axial cuts perpendicular to the middle of the lumbar spine or to the most stenotic level. In conclusion, morphological grading seems to offer an alternative means of assessing severity of spinal stenosis that is little affected by image acquisition technique.

Evolutionary games on complex networks : the emergence and maintenance of cooperation

Abstract The object of game theory lies in the analysis of situations where different social actors have conflicting requirements and where their individual decisions will all influence the global outcome. In this framework, several games have been invented to capture the essence of various dilemmas encountered in many common important socio-economic situations. Even though these games often succeed in helping us understand human or animal behavior in interactive settings, some experiments have shown that people tend to cooperate with each other in situations for which classical game theory strongly recommends them to do the exact opposite. Several mechanisms have been invoked to try to explain the emergence of this unexpected cooperative attitude. Among them, repeated interaction, reputation, and belonging to a recognizable group have often been mentioned. However, the work of Nowak and May (1992) showed that the simple fact of arranging the players according to a spatial structure and only allowing them to interact with their immediate neighbors is sufficient to sustain a certain amount of cooperation even when the game is played anonymously and without repetition. Nowak and May's study and much of the following work was based on regular structures such as two-dimensional grids. Axelrod et al. (2002) showed that by randomizing the choice of neighbors, i.e. by actually giving up a strictly local geographical structure, cooperation can still emerge, provided that the interaction patterns remain stable in time. This is a first step towards a social network structure. However, following pioneering work by sociologists in the sixties such as that of Milgram (1967), in the last few years it has become apparent that many social and biological interaction networks, and even some technological networks, have particular, and partly unexpected, properties that set them apart from regular or random graphs. Among other things, they usually display broad degree distributions, and show small-world topological structure. Roughly speaking, a small-world graph is a network where any individual is relatively close, in terms of social ties, to any other individual, a property also found in random graphs but not in regular lattices. However, in contrast with random graphs, small-world networks also have a certain amount of local structure, as measured, for instance, by a quantity called the clustering coefficient. In the same vein, many real conflicting situations in economy and sociology are not well described neither by a fixed geographical position of the individuals in a regular lattice, nor by a random graph. Furthermore, it is a known fact that network structure can highly influence dynamical phenomena such as the way diseases spread across a population and ideas or information get transmitted. Therefore, in the last decade, research attention has naturally shifted from random and regular graphs towards better models of social interaction structures. The primary goal of this work is to discover whether or not the underlying graph structure of real social networks could give explanations as to why one finds higher levels of cooperation in populations of human beings or animals than what is prescribed by classical game theory. To meet this objective, I start by thoroughly studying a real scientific coauthorship network and showing how it differs from biological or technological networks using divers statistical measurements. Furthermore, I extract and describe its community structure taking into account the intensity of a collaboration. Finally, I investigate the temporal evolution of the network, from its inception to its state at the time of the study in 2006, suggesting also an effective view of it as opposed to a historical one. Thereafter, I combine evolutionary game theory with several network models along with the studied coauthorship network in order to highlight which specific network properties foster cooperation and shed some light on the various mechanisms responsible for the maintenance of this same cooperation. I point out the fact that, to resist defection, cooperators take advantage, whenever possible, of the degree-heterogeneity of social networks and their underlying community structure. Finally, I show that cooperation level and stability depend not only on the game played, but also on the evolutionary dynamic rules used and the individual payoff calculations. Synopsis Le but de la théorie des jeux réside dans l'analyse de situations dans lesquelles différents acteurs sociaux, avec des objectifs souvent conflictuels, doivent individuellement prendre des décisions qui influenceront toutes le résultat global. Dans ce cadre, plusieurs jeux ont été inventés afin de saisir l'essence de divers dilemmes rencontrés dans d'importantes situations socio-économiques. Bien que ces jeux nous permettent souvent de comprendre le comportement d'êtres humains ou d'animaux en interactions, des expériences ont montré que les individus ont parfois tendance à coopérer dans des situations pour lesquelles la théorie classique des jeux prescrit de faire le contraire. Plusieurs mécanismes ont été invoqués pour tenter d'expliquer l'émergence de ce comportement coopératif inattendu. Parmi ceux-ci, la répétition des interactions, la réputation ou encore l'appartenance à des groupes reconnaissables ont souvent été mentionnés. Toutefois, les travaux de Nowak et May (1992) ont montré que le simple fait de disposer les joueurs selon une structure spatiale en leur permettant d'interagir uniquement avec leurs voisins directs est suffisant pour maintenir un certain niveau de coopération même si le jeu est joué de manière anonyme et sans répétitions. L'étude de Nowak et May, ainsi qu'un nombre substantiel de travaux qui ont suivi, étaient basés sur des structures régulières telles que des grilles à deux dimensions. Axelrod et al. (2002) ont montré qu'en randomisant le choix des voisins, i.e. en abandonnant une localisation géographique stricte, la coopération peut malgré tout émerger, pour autant que les schémas d'interactions restent stables au cours du temps. Ceci est un premier pas en direction d'une structure de réseau social. Toutefois, suite aux travaux précurseurs de sociologues des années soixante, tels que ceux de Milgram (1967), il est devenu clair ces dernières années qu'une grande partie des réseaux d'interactions sociaux et biologiques, et même quelques réseaux technologiques, possèdent des propriétés particulières, et partiellement inattendues, qui les distinguent de graphes réguliers ou aléatoires. Entre autres, ils affichent en général une distribution du degré relativement large ainsi qu'une structure de "petit-monde". Grossièrement parlant, un graphe "petit-monde" est un réseau où tout individu se trouve relativement près de tout autre individu en termes de distance sociale, une propriété également présente dans les graphes aléatoires mais absente des grilles régulières. Par contre, les réseaux "petit-monde" ont, contrairement aux graphes aléatoires, une certaine structure de localité, mesurée par exemple par une quantité appelée le "coefficient de clustering". Dans le même esprit, plusieurs situations réelles de conflit en économie et sociologie ne sont pas bien décrites ni par des positions géographiquement fixes des individus en grilles régulières, ni par des graphes aléatoires. De plus, il est bien connu que la structure même d'un réseau peut passablement influencer des phénomènes dynamiques tels que la manière qu'a une maladie de se répandre à travers une population, ou encore la façon dont des idées ou une information s'y propagent. Ainsi, durant cette dernière décennie, l'attention de la recherche s'est tout naturellement déplacée des graphes aléatoires et réguliers vers de meilleurs modèles de structure d'interactions sociales. L'objectif principal de ce travail est de découvrir si la structure sous-jacente de graphe de vrais réseaux sociaux peut fournir des explications quant aux raisons pour lesquelles on trouve, chez certains groupes d'êtres humains ou d'animaux, des niveaux de coopération supérieurs à ce qui est prescrit par la théorie classique des jeux. Dans l'optique d'atteindre ce but, je commence par étudier un véritable réseau de collaborations scientifiques et, en utilisant diverses mesures statistiques, je mets en évidence la manière dont il diffère de réseaux biologiques ou technologiques. De plus, j'extrais et je décris sa structure de communautés en tenant compte de l'intensité d'une collaboration. Finalement, j'examine l'évolution temporelle du réseau depuis son origine jusqu'à son état en 2006, date à laquelle l'étude a été effectuée, en suggérant également une vue effective du réseau par opposition à une vue historique. Par la suite, je combine la théorie évolutionnaire des jeux avec des réseaux comprenant plusieurs modèles et le réseau de collaboration susmentionné, afin de déterminer les propriétés structurelles utiles à la promotion de la coopération et les mécanismes responsables du maintien de celle-ci. Je mets en évidence le fait que, pour ne pas succomber à la défection, les coopérateurs exploitent dans la mesure du possible l'hétérogénéité des réseaux sociaux en termes de degré ainsi que la structure de communautés sous-jacente de ces mêmes réseaux. Finalement, je montre que le niveau de coopération et sa stabilité dépendent non seulement du jeu joué, mais aussi des règles de la dynamique évolutionnaire utilisées et du calcul du bénéfice d'un individu.