7 research outputs found
Spectral properties of Google matrix of Wikipedia and other networks
We study the properties of eigenvalues and eigenvectors of the Google matrix
of the Wikipedia articles hyperlink network and other real networks. With the
help of the Arnoldi method we analyze the distribution of eigenvalues in the
complex plane and show that eigenstates with significant eigenvalue modulus are
located on well defined network communities. We also show that the correlator
between PageRank and CheiRank vectors distinguishes different organizations of
information flow on BBC and Le Monde web sites.Comment: 10 pages, 9 figure
Centrality metrics and localization in core-periphery networks
Two concepts of centrality have been defined in complex networks. The first
considers the centrality of a node and many different metrics for it has been
defined (e.g. eigenvector centrality, PageRank, non-backtracking centrality,
etc). The second is related to a large scale organization of the network, the
core-periphery structure, composed by a dense core plus an outlying and
loosely-connected periphery. In this paper we investigate the relation between
these two concepts. We consider networks generated via the Stochastic Block
Model, or its degree corrected version, with a strong core-periphery structure
and we investigate the centrality properties of the core nodes and the ability
of several centrality metrics to identify them. We find that the three measures
with the best performance are marginals obtained with belief propagation,
PageRank, and degree centrality, while non-backtracking and eigenvector
centrality (or MINRES}, showed to be equivalent to the latter in the large
network limit) perform worse in the investigated networks.Comment: 15 pages, 8 figure
Highlighting Entanglement of Cultures via Ranking of Multilingual Wikipedia Articles
How different cultures evaluate a person? Is an important person in one
culture is also important in the other culture? We address these questions via
ranking of multilingual Wikipedia articles. With three ranking algorithms based
on network structure of Wikipedia, we assign ranking to all articles in 9
multilingual editions of Wikipedia and investigate general ranking structure of
PageRank, CheiRank and 2DRank. In particular, we focus on articles related to
persons, identify top 30 persons for each rank among different editions and
analyze distinctions of their distributions over activity fields such as
politics, art, science, religion, sport for each edition. We find that local
heroes are dominant but also global heroes exist and create an effective
network representing entanglement of cultures. The Google matrix analysis of
network of cultures shows signs of the Zipf law distribution. This approach
allows to examine diversity and shared characteristics of knowledge
organization between cultures. The developed computational, data driven
approach highlights cultural interconnections in a new perspective.Comment: Published in PLoS ONE
(http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0074554).
Supporting information is available on the same webpag
Interactions of cultures and top people of Wikipedia from ranking of 24 language editions
Wikipedia is a huge global repository of human knowledge, that can be
leveraged to investigate interwinements between cultures. With this aim, we
apply methods of Markov chains and Google matrix, for the analysis of the
hyperlink networks of 24 Wikipedia language editions, and rank all their
articles by PageRank, 2DRank and CheiRank algorithms. Using automatic
extraction of people names, we obtain the top 100 historical figures, for each
edition and for each algorithm. We investigate their spatial, temporal, and
gender distributions in dependence of their cultural origins. Our study
demonstrates not only the existence of skewness with local figures, mainly
recognized only in their own cultures, but also the existence of global
historical figures appearing in a large number of editions. By determining the
birth time and place of these persons, we perform an analysis of the evolution
of such figures through 35 centuries of human history for each language, thus
recovering interactions and entanglement of cultures over time. We also obtain
the distributions of historical figures over world countries, highlighting
geographical aspects of cross-cultural links. Considering historical figures
who appear in multiple editions as interactions between cultures, we construct
a network of cultures and identify the most influential cultures according to
this network.Comment: 32 pages. 10 figures. Submitted for publication. Supporting
information is available on
http://www.quantware.ups-tlse.fr/QWLIB/topwikipeople
Network Modeling of Motor Pathways from Neural Recordings
During cued motor tasks, for both speech and limb movement, information propagates from primary sensory areas, to association areas, to primary and supplementary motor and language areas. Through the recent advent of high density recordings at multiple scales, it has become possible to simultaneously observe activity occurring from these disparate regions at varying resolution. Models of brain activity generally used in brain-computer interface (BCI) control do not take into account the global differences in recording site function, or the interactions between them. Through the use of connectivity measures, however, it has been made possible to determine the contribution of individual recording sites to the global activity, as they vary with task progression.
This dissertation extends those connectivity models to provide summary information about the importance of individual sites. This is achieved through the application of network measures on the adjacency structure determined by connectivity measures. Similarly, by analyzing the coordinated activity of all of the electrode sites simultaneously during task performance, it is possible to elucidate discrete functional units through clustering analysis of the electrode recordings.
In this dissertation, I first describe a BCI system using simple motor movement imagination at single recording sites. I then incorporate connectivity through the use of TV-DBN modeling on higher resolution electrode recordings, specifically electrocorticography (ECoG). I show that PageRank centrality reveals information about task progression and regional specificity which was obscured by direct application of the connectivity measures, due to the combinatorial increase in feature dimensionality. I then show that clustering of ECoG recordings using a method to determine the inherent cluster count algorithmically provides insight into how network involvement in task execution evolves, though in a manner dependent on grid coverage. Finally, I extend clustering analysis to show how individual neurons in motor cortex form distinct functional communities. These communities are shown to be task-specific, suggesting that neurons can form functional units with distinct neural populations across multiple recording sites in a context dependent impermanent manner.
This work demonstrates that network measures of connectivity models of neurophysiological recordings are a rich source of information relevant to the field of neuroscience, as well as offering the promise of improved degree-of-freedom and naturalness possible through direct BCI control. These models are shown to be useful at multiple recording scales, from cortical-area level ECoG, to highly localized single unit microelectrode recordings
Réduire la dimension des systèmes complexes : un regard sur l'émergence de la synchronisation
Les systèmes complexes se caractérisent par l’émergence de phénomènes macroscopiques qui ne s’expliquent pas uniquement par les propriétés de leurs composantes de base. La synchronisation est l’un de ces phénomènes par lequel les interactions entre des oscillateurs engendrent des mouvements collectifs coordonnés. Une représentation sous forme de graphe permet de modéliser précisément les interactions, alors que les oscillations se décrivent par des dynamiques non linéaires. Étant donné le lien subtil entre le graphe et la dynamique des oscillateurs, il est difficile de prédire l’émergence de la synchronisation. L’objectif de ce mémoire est de développer de nouvelles méthodes pour simplifier les systèmes complexes d’oscillateurs afin de révéler les mécanismes engendrant la synchronisation. À cette fin, nous introduisons des notions de la théorie des graphes et des systèmes dynamiques pour définir la synchronisation sur des bases mathématiques. Nous présentons ensuite des approches existantes sophistiquées pour réduire la dimension de dynamiques d’oscillateurs. Ces techniques sont toutefois limitées lorsque les dynamiques évoluent sur des graphes plus complexes. Nous développons alors une technique originale—spécialement adaptée pour les graphes aux propriétés plus hétérogènes—pour réduire la dimension de dynamiques non linéaires. En plus de généraliser des approches récentes, notre méthode dévoile plusieurs défis théoriques reliés à la simplification d’un système complexe. Entre autres, la réduction de la dimension du système se bute à une trichotomie : il faut favoriser la conservation des paramètres dynamiques, des propriétés locales du graphe ou des propriétés globales du graphe. Finalement, notre méthode permet de caractériser mathématiquement et numériquement l’émergence d’états exotiques de synchronisation.Complex systems are characterized by the emergence of macroscopic phenomena that cannot be explained by the properties of their basic constituents. Synchronization is one of these phenomena in which the interactions between oscillators generate coordinate collective behaviors. Graphs allow a precise representation of the interactions, while nonlinear dynamics describe the oscillations. Because of the subtle relationship between graphs and dynamics of oscillators, it is challenging to predict the emergence of synchronization. The goal of this master’s thesis is to develop new methods for simplifying complex systems of oscillators in order to reveal the mechanism causing synchronization. To this end, we introduce notions of graph theory and dynamical systems to define synchronization on sound mathematical basis. We then present existing sophisticated approaches for reducing the dimension of oscillator dynamics. Yet, the efficiency of these techniques is limited for dynamics on complex graphs. We thus develop an original method—specially adapted for graphs with heterogeneous properties—for reducing the dimensions of nonlinear dynamics. Our method generalizes previous approaches and uncovers multiple challenges related to the simplification of complex systems. In particular, the dimension reduction of a system comes up against a trichotomy: one must choose to conserve either the dynamical parameters, the local properties of the graph, or the global properties of the graph. We finally use our method to characterize mathematically and numerically the emergence of exotic synchronization states