Error and attack tolerance of layered complex networks.

Many complex systems may be described by not one but a number of complex networks mapped on each other in a multi-layer structure. Because of the interactions and dependencies between these layers, the state of a single layer does not necessarily reflect well the state of the entire system. In this paper we study the robustness of five examples of two-layer complex systems: three real-life data sets in the fields of communication (the Internet), transportation (the European railway system), and biology (the human brain), and two models based on random graphs. In order to cover the whole range of features specific to these systems, we focus on two extreme policies of system's response to failures, no rerouting and full rerouting. Our main finding is that multi-layer systems are much more vulnerable to errors and intentional attacks than they appear from a single layer perspective.

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.

Synchronizability of EEG-Based Functional Networks in Early Alzheimer's Disease.

Recently graph theory and complex networks have been widely used as a mean to model functionality of the brain. Among different neuroimaging techniques available for constructing the brain functional networks, electroencephalography (EEG) with its high temporal resolution is a useful instrument of the analysis of functional interdependencies between different brain regions. Alzheimer's disease (AD) is a neurodegenerative disease, which leads to substantial cognitive decline, and eventually, dementia in aged people. To achieve a deeper insight into the behavior of functional cerebral networks in AD, here we study their synchronizability in 17 newly diagnosed AD patients compared to 17 healthy control subjects at no-task, eyes-closed condition. The cross-correlation of artifact-free EEGs was used to construct brain functional networks. The extracted networks were then tested for their synchronization properties by calculating the eigenratio of the Laplacian matrix of the connection graph, i.e., the largest eigenvalue divided by the second smallest one. In AD patients, we found an increase in the eigenratio, i.e., a decrease in the synchronizability of brain networks across delta, alpha, beta, and gamma EEG frequencies within the wide range of network costs. The finding indicates the destruction of functional brain networks in early AD.

Local optima networks of hard combinatorial landscapes

Combinatorial optimization involves finding an optimal solution in a finite set of options; many everyday life problems are of this kind. However, the number of options grows exponentially with the size of the problem, such that an exhaustive search for the best solution is practically infeasible beyond a certain problem size. When efficient algorithms are not available, a practical approach to obtain an approximate solution to the problem at hand, is to start with an educated guess and gradually refine it until we have a good-enough solution. Roughly speaking, this is how local search heuristics work. These stochastic algorithms navigate the problem search space by iteratively turning the current solution into new candidate solutions, guiding the search towards better solutions. The search performance, therefore, depends on structural aspects of the search space, which in turn depend on the move operator being used to modify solutions. A common way to characterize the search space of a problem is through the study of its fitness landscape, a mathematical object comprising the space of all possible solutions, their value with respect to the optimization objective, and a relationship of neighborhood defined by the move operator. The landscape metaphor is used to explain the search dynamics as a sort of potential function. The concept is indeed similar to that of potential energy surfaces in physical chemistry. Borrowing ideas from that field, we propose to extend to combinatorial landscapes the notion of the inherent network formed by energy minima in energy landscapes. In our case, energy minima are the local optima of the combinatorial problem, and we explore several definitions for the network edges. At first, we perform an exhaustive sampling of local optima basins of attraction, and define weighted transitions between basins by accounting for all the possible ways of crossing the basins frontier via one random move. Then, we reduce the computational burden by only counting the chances of escaping a given basin via random kick moves that start at the local optimum. Finally, we approximate network edges from the search trajectory of simple search heuristics, mining the frequency and inter-arrival time with which the heuristic visits local optima. Through these methodologies, we build a weighted directed graph that provides a synthetic view of the whole landscape, and that we can characterize using the tools of complex networks science. We argue that the network characterization can advance our understanding of the structural and dynamical properties of hard combinatorial landscapes. We apply our approach to prototypical problems such as the Quadratic Assignment Problem, the NK model of rugged landscapes, and the Permutation Flow-shop Scheduling Problem. We show that some network metrics can differentiate problem classes, correlate with problem non-linearity, and predict problem hardness as measured from the performances of trajectory-based local search heuristics.

Flippase (FLP) recombinase-mediated marker recycling in the dermatophyte Arthroderma vanbreuseghemii.

Biological processes can be elucidated by investigating complex networks of relevant factors and genes. However, this is not possible in species for which dominant selectable markers for genetic studies are unavailable. To overcome the limitation in selectable markers for the dermatophyte Arthroderma vanbreuseghemii (anamorph: Trichophyton mentagrophytes), we adapted the flippase (FLP) recombinase-recombination target (FRT) site-specific recombination system from the yeast Saccharomyces cerevisiae as a selectable marker recycling system for this fungus. Taking into account practical applicability, we designed FLP/FRT modules carrying two FRT sequences as well as the flp gene adapted to the pathogenic yeast Candida albicans (caflp) or a synthetic codon-optimized flp (avflp) gene with neomycin resistance (nptII) cassette for one-step marker excision. Both flp genes were under control of the Trichophyton rubrum copper-repressible promoter (PCTR4). Molecular analyses of resultant transformants showed that only the avflp-harbouring module was functional in A. vanbreuseghemii. Applying this system, we successfully produced the Ku80 recessive mutant strain devoid of any selectable markers. This strain was subsequently used as the recipient for sequential multiple disruptions of secreted metalloprotease (fungalysin) (MEP) or serine protease (SUB) genes, producing mutant strains with double MEP or triple SUB gene deletions. These results confirmed the feasibility of this system for broad-scale genetic manipulation of dermatophytes, advancing our understanding of functions and networks of individual genes in these fungi.

Arbuscular mycorrhizal fungi mediate below-ground plant-herbivore interactions: a phylogenetic study

Ecological interactions are complex networks, but have typically been studied in a pairwise fashion. Examining how third-party species can modify the outcome of pairwise interactions may allow us to better predict their outcomes in realistic systems. For instance, arbuscular mycorrhizal fungi (AMF) can affect plant interactions with other organisms, including below-ground herbivores, but the mechanisms underlying these effects remain unclear. Here, we use a comparative, phylogenetically controlled approach to test the relative importance of mycorrhizal colonization and plant chemical defences (cardenolides) in predicting plant survival and the abundance of a generalist below-ground herbivore across 14 species of milkweeds (Asclepias spp.). Plants were inoculated with a mixture of four generalist AMF species or left uninoculated. After 1month, larvae of Bradysia sp. (Diptera: Sciaridae), a generalist below-ground herbivore, colonized plant roots. We performed phylogenetically controlled analyses to assess the influence of AMF colonization and toxic cardenolides on plant growth, mortality and infestation by fungus gnats. Overall, plants inoculated with AMF exhibited greater survival than did uninoculated plants. Additionally, surviving inoculated plants had lower numbers of larvae in their roots and fewer non-AM fungi than surviving uninoculated plants. In phylogenetic controlled regressions, gnat density in roots was better predicted by the extent of root colonized by AMF than by root cardenolide concentration. Taken as a whole, AMF modify the effect of below-ground herbivores on plants in a species-specific manner, independent of changes in chemical defence. This study adds to the growing body of literature demonstrating that mycorrhizal fungi may improve plant fitness by conferring protection against antagonists, rather than growth benefits. In addition, we advocate using comparative analyses to disentangle the roles of shared history and ecology in shaping trait expression and to better predict the outcomes of complex multitrophic interactions.

A high-resolution anatomical atlas of the transcriptome in the mouse embryo.

Ascertaining when and where genes are expressed is of crucial importance to understanding or predicting the physiological role of genes and proteins and how they interact to form the complex networks that underlie organ development and function. It is, therefore, crucial to determine on a genome-wide level, the spatio-temporal gene expression profiles at cellular resolution. This information is provided by colorimetric RNA in situ hybridization that can elucidate expression of genes in their native context and does so at cellular resolution. We generated what is to our knowledge the first genome-wide transcriptome atlas by RNA in situ hybridization of an entire mammalian organism, the developing mouse at embryonic day 14.5. This digital transcriptome atlas, the Eurexpress atlas (http://www.eurexpress.org), consists of a searchable database of annotated images that can be interactively viewed. We generated anatomy-based expression profiles for over 18,000 coding genes and over 400 microRNAs. We identified 1,002 tissue-specific genes that are a source of novel tissue-specific markers for 37 different anatomical structures. The quality and the resolution of the data revealed novel molecular domains for several developing structures, such as the telencephalon, a novel organization for the hypothalamus, and insight on the Wnt network involved in renal epithelial differentiation during kidney development. The digital transcriptome atlas is a powerful resource to determine co-expression of genes, to identify cell populations and lineages, and to identify functional associations between genes relevant to development and disease.

Spatial prediction of monthly wind speeds in complex terrain with adaptive general regression neural networks

This paper presents the general regression neural networks (GRNN) as a nonlinear regression method for the interpolation of monthly wind speeds in complex Alpine orography. GRNN is trained using data coming from Swiss meteorological networks to learn the statistical relationship between topographic features and wind speed. The terrain convexity, slope and exposure are considered by extracting features from the digital elevation model at different spatial scales using specialised convolution filters. A database of gridded monthly wind speeds is then constructed by applying GRNN in prediction mode during the period 1968-2008. This study demonstrates that using topographic features as inputs in GRNN significantly reduces cross-validation errors with respect to low-dimensional models integrating only geographical coordinates and terrain height for the interpolation of wind speed. The spatial predictability of wind speed is found to be lower in summer than in winter due to more complex and weaker wind-topography relationships. The relevance of these relationships is studied using an adaptive version of the GRNN algorithm which allows to select the useful terrain features by eliminating the noisy ones. This research provides a framework for extending the low-dimensional interpolation models to high-dimensional spaces by integrating additional features accounting for the topographic conditions at multiple spatial scales. Copyright (c) 2012 Royal Meteorological Society.

Using active learning for monitoring networks design: The example of wind power plants sites evaluation

Locating new wind farms is of crucial importance for energy policies of the next decade. To select the new location, an accurate picture of the wind fields is necessary. However, characterizing wind fields is a difficult task, since the phenomenon is highly nonlinear and related to complex topographical features. In this paper, we propose both a nonparametric model to estimate wind speed at different time instants and a procedure to discover underrepresented topographic conditions, where new measuring stations could be added. Compared to space filling techniques, this last approach privileges optimization of the output space, thus locating new potential measuring sites through the uncertainty of the model itself.

Dynamical modeling and analysis of large cellular regulatory networks.

The dynamical analysis of large biological regulatory networks requires the development of scalable methods for mathematical modeling. Following the approach initially introduced by Thomas, we formalize the interactions between the components of a network in terms of discrete variables, functions, and parameters. Model simulations result in directed graphs, called state transition graphs. We are particularly interested in reachability properties and asymptotic behaviors, which correspond to terminal strongly connected components (or "attractors") in the state transition graph. A well-known problem is the exponential increase of the size of state transition graphs with the number of network components, in particular when using the biologically realistic asynchronous updating assumption. To address this problem, we have developed several complementary methods enabling the analysis of the behavior of large and complex logical models: (i) the definition of transition priority classes to simplify the dynamics; (ii) a model reduction method preserving essential dynamical properties, (iii) a novel algorithm to compact state transition graphs and directly generate compressed representations, emphasizing relevant transient and asymptotic dynamical properties. The power of an approach combining these different methods is demonstrated by applying them to a recent multilevel logical model for the network controlling CD4+ T helper cell response to antigen presentation and to a dozen cytokines. This model accounts for the differentiation of canonical Th1 and Th2 lymphocytes, as well as of inflammatory Th17 and regulatory T cells, along with many hybrid subtypes. All these methods have been implemented into the software GINsim, which enables the definition, the analysis, and the simulation of logical regulatory graphs.

Comparison of early cortical networks in efficient and inefficient visual search: an event-related potential study.

Functional magnetic resonance imaging studies have indicated that efficient feature search (FS) and inefficient conjunction search (CS) activate partially distinct frontoparietal cortical networks. However, it remains a matter of debate whether the differences in these networks reflect differences in the early processing during FS and CS. In addition, the relationship between the differences in the networks and spatial shifts of attention also remains unknown. We examined these issues by applying a spatio-temporal analysis method to high-resolution visual event-related potentials (ERPs) and investigated how spatio-temporal activation patterns differ for FS and CS tasks. Within the first 450 msec after stimulus onset, scalp potential distributions (ERP maps) revealed 7 different electric field configurations for each search task. Configuration changes occurred simultaneously in the two tasks, suggesting that contributing processes were not significantly delayed in one task compared to the other. Despite this high spatial and temporal correlation, two ERP maps (120-190 and 250-300 msec) differed between the FS and CS. Lateralized distributions were observed only in the ERP map at 250-300 msec for the FS. This distribution corresponds to that previously described as the N2pc component (a negativity in the time range of the N2 complex over posterior electrodes of the hemisphere contralateral to the target hemifield), which has been associated with the focusing of attention onto potential target items in the search display. Thus, our results indicate that the cortical networks involved in feature and conjunction searching partially differ as early as 120 msec after stimulus onset and that the differences between the networks employed during the early stages of FS and CS are not necessarily caused by spatial attention shifts.

The challenge of modeling nuclear receptor regulatory networks in mammalian cells.

Nuclear receptors are a major component of signal transduction in animals. They mediate the regulatory activities of many hormones, nutrients and metabolites on the homeostasis and physiology of cells and tissues. It is of high interest to model the corresponding regulatory networks. While molecular and cell biology studies of individual promoters have provided important mechanistic insight, a more complex picture is emerging from genome-wide studies. The regulatory circuitry of nuclear receptor regulated gene expression networks, and their response to cellular signaling, appear highly dynamic, and involve long as well as short range chromatin interactions. We review how progress in understanding the kinetics and regulation of cofactor recruitment, and the development of new genomic methods, provide opportunities but also a major challenge for modeling nuclear receptor mediated regulatory networks.