Graph theoretical approaches for the characterization of damage in hierarchical materials

We discuss the relevance of methods of graph theory for the study of damage in simple model materials described by the random fuse model. While such methods are not commonly used when dealing with regular random lattices, which mimic disordered but statistically homogeneous materials, they become relevant in materials with microstructures that exhibit complex multi-scale patterns. We specifically address the case of hierarchical materials, whose failure, due to an uncommon fracture mode, is not well described in terms of either damage percolation or crack nucleation-and-growth. We show that in these systems, incipient failure is accompanied by an increase in eigenvector localization and a drop in topological dimension. We propose these two novel indicators as possible candidates to monitor a system in the approach to failure. As such, they provide alternatives to monitoring changes in the precursory avalanche activity, which is often invoked as a candidate for failure prediction in materials which exhibit critical-like behavior at failure, but may not work in the context of hierarchical materials which exhibit scale-free avalanche statistics even very far from the critical load.Comment: 12 pages, 6 figure

Models of atypical development must also be models of normal development

Functional magnetic resonance imaging studies of developmental disorders and normal cognition that include children are becoming increasingly common and represent part of a newly expanding field of developmental cognitive neuroscience. These studies have illustrated the importance of the process of development in understanding brain mechanisms underlying cognition and including children ill the study of the etiology of developmental disorders

Are developmental disorders like cases of adult brain damage? Implications from connectionist modelling

It is often assumed that similar domain-specific behavioural impairments found in cases of adult brain damage and developmental disorders correspond to similar underlying causes, and can serve as convergent evidence for the modular structure of the normal adult cognitive system. We argue that this correspondence is contingent on an unsupported assumption that atypical development can produce selective deficits while the rest of the system develops normally (Residual Normality), and that this assumption tends to bias data collection in the field. Based on a review of connectionist models of acquired and developmental disorders in the domains of reading and past tense, as well as on new simulations, we explore the computational viability of Residual Normality and the potential role of development in producing behavioural deficits. Simulations demonstrate that damage to a developmental model can produce very different effects depending on whether it occurs prior to or following the training process. Because developmental disorders typically involve damage prior to learning, we conclude that the developmental process is a key component of the explanation of endstate impairments in such disorders. Further simulations demonstrate that in simple connectionist learning systems, the assumption of Residual Normality is undermined by processes of compensation or alteration elsewhere in the system. We outline the precise computational conditions required for Residual Normality to hold in development, and suggest that in many cases it is an unlikely hypothesis. We conclude that in developmental disorders, inferences from behavioural deficits to underlying structure crucially depend on developmental conditions, and that the process of ontogenetic development cannot be ignored in constructing models of developmental disorders

Clustering and Community Detection in Directed Networks: A Survey

Networks (or graphs) appear as dominant structures in diverse domains, including sociology, biology, neuroscience and computer science. In most of the aforementioned cases graphs are directed - in the sense that there is directionality on the edges, making the semantics of the edges non symmetric. An interesting feature that real networks present is the clustering or community structure property, under which the graph topology is organized into modules commonly called communities or clusters. The essence here is that nodes of the same community are highly similar while on the contrary, nodes across communities present low similarity. Revealing the underlying community structure of directed complex networks has become a crucial and interdisciplinary topic with a plethora of applications. Therefore, naturally there is a recent wealth of research production in the area of mining directed graphs - with clustering being the primary method and tool for community detection and evaluation. The goal of this paper is to offer an in-depth review of the methods presented so far for clustering directed networks along with the relevant necessary methodological background and also related applications. The survey commences by offering a concise review of the fundamental concepts and methodological base on which graph clustering algorithms capitalize on. Then we present the relevant work along two orthogonal classifications. The first one is mostly concerned with the methodological principles of the clustering algorithms, while the second one approaches the methods from the viewpoint regarding the properties of a good cluster in a directed network. Further, we present methods and metrics for evaluating graph clustering results, demonstrate interesting application domains and provide promising future research directions.Comment: 86 pages, 17 figures. Physics Reports Journal (To Appear

Multi-scale community organization of the human structural connectome and its relationship with resting-state functional connectivity

The human connectome has been widely studied over the past decade. A principal finding is that it can be decomposed into communities of densely interconnected brain regions. This result, however, may be limited methodologically. Past studies have often used a flawed modularity measure in order to infer the connectome's community structure. Also, these studies relied on the intuition that community structure is best defined in terms of a network's static topology as opposed to a more dynamical definition. In this report we used the partition stability framework, which defines communities in terms of a Markov process (random walk), to infer the connectome's multi-scale community structure. Comparing the community structure to observed resting-state functional connectivity revealed communities across a broad range of dynamical scales that were closely related to functional connectivity. This result suggests a mapping between communities in structural networks, models of communication processes, and brain function. It further suggests that communication in the brain is not limited to a single characteristic scale, leading us to posit a heuristic for scale-selective communication in the cerebral cortex.Comment: Corrected small typographical mistakes, changed order of authors and funding information, and also chose a more efficient compression for figure

Multi-scale community organization of the human structural connectome and its relationship with resting-state functional connectivity

The human connectome has been widely studied over the past decade. A principal finding is that it can be decomposed into communities of densely interconnected brain regions. Past studies have often used single-scale modularity measures in order to infer the connectome's community structure, possibly overlooking interesting structure at other organizational scales. In this report, we used the partition stability framework, which defines communities in terms of a Markov process (random walk), to infer the connectome's multi-scale community structure. Comparing the community structure to observed resting-state functional connectivity revealed communities across a broad range of scales that were closely related to functional connectivity. This result suggests a mapping between communities in structural networks, models of influence-spreading and diffusion, and brain function. It further suggests that the spread of influence among brain regions may not be limited to a single characteristic scal

Synchronization in complex networks

Synchronization processes in populations of locally interacting elements are in the focus of intense research in physical, biological, chemical, technological and social systems. The many efforts devoted to understand synchronization phenomena in natural systems take now advantage of the recent theory of complex networks. In this review, we report the advances in the comprehension of synchronization phenomena when oscillating elements are constrained to interact in a complex network topology. We also overview the new emergent features coming out from the interplay between the structure and the function of the underlying pattern of connections. Extensive numerical work as well as analytical approaches to the problem are presented. Finally, we review several applications of synchronization in complex networks to different disciplines: biological systems and neuroscience, engineering and computer science, and economy and social sciences.Comment: Final version published in Physics Reports. More information available at http://synchronets.googlepages.com