Bernat Corominas-Murtra

Resting-brain functional connectivity predicted by analytic measures of network communication

Significance Patterns of distributed brain activity are thought to underlie virtually all aspects of cognition and behavior. In this paper, we explore the degree to which it is possible to predict such functional patterns from the network of anatomical connections that link brain regions. To this end, we use three separately acquired neuroimaging datasets recording anatomical and functional connections in the human brain. We apply several measures of network communication that are derived analytically from the brain’s anatomical network. Our principal finding is that such network measures can predict empirically measured functional connectivity at levels that exceed other modeling approaches. Our study sheds light on the important role of anatomical networks and communication processes in shaping the brain’s functional activity. The complex relationship between structural and functional connectivity, as measured by noninvasive imaging of the human brain, poses many unresolved challenges and open questions. Here, we apply analytic measures of network communication to the structural connectivity of the human brain and explore the capacity of these measures to predict resting-state functional connectivity across three independently acquired datasets. We focus on the layout of shortest paths across the network and on two communication measures—search information and path transitivity—which account for how these paths are embedded in the rest of the network. Search information is an existing measure of information needed to access or trace shortest paths; we introduce path transitivity to measure the density of local detours along the shortest path. We find that both search information and path transitivity predict the strength of functional connectivity among both connected and unconnected node pairs. They do so at levels that match or significantly exceed path length measures, Euclidean distance, as well as computational models of neural dynamics. This capacity suggests that dynamic couplings due to interactions among neural elements in brain networks are substantially influenced by the broader network context adjacent to the shortest communication pathways.

Robustness of the European power grids under intentional attack

The power grid defines one of the most important technological networks of our times and sustains our complex society. It has evolved for more than a century into an extremely huge and seemingly robust and well understood system. But it becomes extremely fragile as well, when unexpected, usually minimal, failures turn into unknown dynamical behaviours leading, for example, to sudden and massive blackouts. Here we explore the fragility of the European power grid under the effect of selective node removal. A mean field analysis of fragility against attacks is presented together with the observed patterns. Deviations from the theoretical conditions for network percolation (and fragmentation) under attacks are analysed and correlated with non topological reliability measures.

On the origins of hierarchy in complex networks

Hierarchy seems to pervade complexity in both living and artificial systems. Despite its relevance, no general theory that captures all features of hierarchy and its origins has been proposed yet. Here we present a formal approach resulting from the convergence of theoretical morphology and network theory that allows constructing a 3D morphospace of hierarchies and hence comparing the hierarchical organization of ecological, cellular, technological, and social networks. Embedded within large voids in the morphospace of all possible hierarchies, four major groups are identified. Two of them match the expected from random networks with similar connectivity, thus suggesting that nonadaptive factors are at work. Ecological and gene networks define the other two, indicating that their topological order is the result of functional constraints. These results are consistent with an exploration of the morphospace, using in silico evolved networks.

Universality of Zipf’s law

Zipfs law is the most common statistical distribution displaying scaling behavior. Cities, populations or firms are just examples of this seemingly universal law. Although many different models have been proposed, no general theoretical explanation has been shown to exist for its universality. Here, we show that Zipfs law is, in fact, an inevitable outcome of a very general class of stochastic systems. Borrowing concepts from Algorithmic Information Theory, our derivation is based on the properties of the symbolic sequence obtained through successive observations over a system with an ubounded number of possible states. Specifically, we assume that the complexity of the description of the system provided by the sequence of observations is the one expected for a system evolving to a stable state between order and disorder. This result is obtained from a small set of mild, physically relevant assumptions. The general nature of our derivation and its model-free basis would explain the ubiquity of such a law in real systems.

The semantic organization of the animal category: evidence from semantic verbal fluency and network theory

Semantic memory is the subsystem of human memory that stores knowledge of concepts or meanings, as opposed to life-specific experiences. How humans organize semantic information remains poorly understood. In an effort to better understand this issue, we conducted a verbal fluency experiment on 200 participants with the aim of inferring and representing the conceptual storage structure of the natural category of animals as a network. This was done by formulating a statistical framework for co-occurring concepts that aims to infer significant concept–concept associations and represent them as a graph. The resulting network was analyzed and enriched by means of a missing links recovery criterion based on modularity. Both network models were compared to a thresholded co-occurrence approach. They were evaluated using a random subset of verbal fluency tests and comparing the network outcomes (linked pairs are clustering transitions and disconnected pairs are switching transitions) to the outcomes of two expert human raters. Results show that the network models proposed in this study overcome a thresholded co-occurrence approach, and their outcomes are in high agreement with human evaluations. Finally, the interplay between conceptual structure and retrieval mechanisms is discussed.

THE ONTOGENY OF SCALE-FREE SYNTAX NETWORKS: PHASE TRANSITIONS IN EARLY LANGUAGE ACQUISITION

Language development in children provides a window to understand the transition from protolanguage to language. Here we present the first analysis of the emergence of syntax in terms of complex networks. A previously unreported, sharp transition is shown to occur around two years of age from a (pre-syntactic) tree-like structure to a scale-free, small world syntax network. The development of these networks thus reveals a nonlinear dynamical pattern where the global topology of syntax graphs shifts from a hierarchical, tree-like pattern, to a scale-free organization. Such change seems difficult to be explained under a self-organization framework. Instead, it actually supports the presence of some underlying innate component, as early suggested by some authors.

Diversity, competition, extinction: the ecophysics of language change

As indicated early by Charles Darwin, languages behave and change very much like living species. They display high diversity, differentiate in space and time, emerge and disappear. A large body of literature has explored the role of information exchanges and communicative constraints in groups of agents under selective scenarios. These models have been very helpful in providing a rationale on how complex forms of communication emerge under evolutionary pressures. However, other patterns of large-scale organization can be described using mathematical methods ignoring communicative traits. These approaches consider shorter time scales and have been developed by exploiting both theoretical ecology and statistical physics methods. The models are reviewed here and include extinction, invasion, origination, spatial organization, coexistence and diversity as key concepts and are very simple in their defining rules. Such simplicity is used in order to catch the most fundamental laws of organization and those universal ingredients responsible for qualitative traits. The similarities between observed and predicted patterns indicate that an ecological theory of language is emerging, supporting (on a quantitative basis) its ecological nature, although key differences are also present. Here, we critically review some recent advances and outline their implications and limitations as well as highlight problems for future research.

Emergence of Zipf’s law in the evolution of communication

Zipfs law seems to be ubiquitous in human languages and appears to be a universal property of complex communicating systems. Following the early proposal made by Zipf concerning the presence of a tension between the efforts of speaker and hearer in a communication system, we introduce evolution by means of a variational approach to the problem based on Kullbacks Minimum Discrimination of Information Principle. Therefore, using a formalism fully embedded in the framework of information theory, we demonstrate that Zipfs law is the only expected outcome of an evolving communicative system under a rigorous definition of the communicative tension described by Zipf.

Understanding scaling through history-dependent processes with collapsing sample space

Significance Many complex systems reduce their flexibility over time in the sense that the number of options (possible states) diminishes over time. We show that rank distributions of the visits to these states that emerge from such processes are exact power laws with an exponent −1 (Zipf’s law). When noise is added to such processes, meaning that from time to time they can also increase the number of their options, the rank distribution remains a power law, with an exponent that is related to the noise level in a remarkably simple way. Sample-space-reducing processes provide a new route to understand the phenomenon of scaling and provide an alternative to the known mechanisms of self-organized criticality, multiplicative processes, or preferential attachment. History-dependent processes are ubiquitous in natural and social systems. Many such stochastic processes, especially those that are associated with complex systems, become more constrained as they unfold, meaning that their sample space, or their set of possible outcomes, reduces as they age. We demonstrate that these sample-space-reducing (SSR) processes necessarily lead to Zipf’s law in the rank distributions of their outcomes. We show that by adding noise to SSR processes the corresponding rank distributions remain exact power laws, p(x)∼x−λ, where the exponent directly corresponds to the mixing ratio of the SSR process and noise. This allows us to give a precise meaning to the scaling exponent in terms of the degree to which a given process reduces its sample space as it unfolds. Noisy SSR processes further allow us to explain a wide range of scaling exponents in frequency distributions ranging from α=2 to ∞. We discuss several applications showing how SSR processes can be used to understand Zipf’s law in word frequencies, and how they are related to diffusion processes in directed networks, or aging processes such as in fragmentation processes. SSR processes provide a new alternative to understand the origin of scaling in complex systems without the recourse to multiplicative, preferential, or self-organized critical processes.

Detection of the Elite Structure in a Virtual Multiplex Social System by Means of a Generalised K-Core

Elites are subgroups of individuals within a society that have the ability and means to influence, lead, govern, and shape societies. Members of elites are often well connected individuals, which enables them to impose their influence to many and to quickly gather, process, and spread information. Here we argue that elites are not only composed of highly connected individuals, but also of intermediaries connecting hubs to form a cohesive and structured elite-subgroup at the core of a social network. For this purpose we present a generalization of the -core algorithm that allows to identify a social core that is composed of well-connected hubs together with their ‘connectors’. We show the validity of the idea in the framework of a virtual world defined by a massive multiplayer online game, on which we have complete information of various social networks. Exploiting this multiplex structure, we find that the hubs of the generalised -core identify those individuals that are high social performers in terms of a series of indicators that are available in the game. In addition, using a combined strategy which involves the generalised -core and the recently introduced -core, the elites of the different ’nations’ present in the game are perfectly identified as modules of the generalised -core. Interesting sudden shifts in the composition of the elite cores are observed at deep levels. We show that elite detection with the traditional -core is not possible in a reliable way. The proposed method might be useful in a series of more general applications, such as community detection.