439,636 research outputs found
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
A Study of Brain Networks Associated with Swallowing Using Graph-Theoretical Approaches
Functional connectivity between brain regions during swallowing tasks is still not well understood. Understanding these complex interactions is of great interest from both a scientific and a clinical perspective. In this study, functional magnetic resonance imaging (fMRI) was utilized to study brain functional networks during voluntary saliva swallowing in twenty-two adult healthy subjects (all females, 23.1±1.52 years of age). To construct these functional connections, we computed mean partial correlation matrices over ninety brain regions for each participant. Two regions were determined to be functionally connected if their correlation was above a certain threshold. These correlation matrices were then analyzed using graph-theoretical approaches. In particular, we considered several network measures for the whole brain and for swallowing-related brain regions. The results have shown that significant pairwise functional connections were, mostly, either local and intra-hemispheric or symmetrically inter-hemispheric. Furthermore, we showed that all human brain functional network, although varying in some degree, had typical small-world properties as compared to regular networks and random networks. These properties allow information transfer within the network at a relatively high efficiency. Swallowing-related brain regions also had higher values for some of the network measures in comparison to when these measures were calculated for the whole brain. The current results warrant further investigation of graph-theoretical approaches as a potential tool for understanding the neural basis of dysphagia. © 2013 Luan et al
Extracting the Groupwise Core Structural Connectivity Network: Bridging Statistical and Graph-Theoretical Approaches
Finding the common structural brain connectivity network for a given
population is an open problem, crucial for current neuro-science. Recent
evidence suggests there's a tightly connected network shared between humans.
Obtaining this network will, among many advantages , allow us to focus
cognitive and clinical analyses on common connections, thus increasing their
statistical power. In turn, knowledge about the common network will facilitate
novel analyses to understand the structure-function relationship in the brain.
In this work, we present a new algorithm for computing the core structural
connectivity network of a subject sample combining graph theory and statistics.
Our algorithm works in accordance with novel evidence on brain topology. We
analyze the problem theoretically and prove its complexity. Using 309 subjects,
we show its advantages when used as a feature selection for connectivity
analysis on populations, outperforming the current approaches
A PAC-Bayesian Analysis of Graph Clustering and Pairwise Clustering
We formulate weighted graph clustering as a prediction problem: given a
subset of edge weights we analyze the ability of graph clustering to predict
the remaining edge weights. This formulation enables practical and theoretical
comparison of different approaches to graph clustering as well as comparison of
graph clustering with other possible ways to model the graph. We adapt the
PAC-Bayesian analysis of co-clustering (Seldin and Tishby, 2008; Seldin, 2009)
to derive a PAC-Bayesian generalization bound for graph clustering. The bound
shows that graph clustering should optimize a trade-off between empirical data
fit and the mutual information that clusters preserve on the graph nodes. A
similar trade-off derived from information-theoretic considerations was already
shown to produce state-of-the-art results in practice (Slonim et al., 2005;
Yom-Tov and Slonim, 2009). This paper supports the empirical evidence by
providing a better theoretical foundation, suggesting formal generalization
guarantees, and offering a more accurate way to deal with finite sample issues.
We derive a bound minimization algorithm and show that it provides good results
in real-life problems and that the derived PAC-Bayesian bound is reasonably
tight
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