26,253 research outputs found
Graph analysis of functional brain networks: practical issues in translational neuroscience
The brain can be regarded as a network: a connected system where nodes, or
units, represent different specialized regions and links, or connections,
represent communication pathways. From a functional perspective communication
is coded by temporal dependence between the activities of different brain
areas. In the last decade, the abstract representation of the brain as a graph
has allowed to visualize functional brain networks and describe their
non-trivial topological properties in a compact and objective way. Nowadays,
the use of graph analysis in translational neuroscience has become essential to
quantify brain dysfunctions in terms of aberrant reconfiguration of functional
brain networks. Despite its evident impact, graph analysis of functional brain
networks is not a simple toolbox that can be blindly applied to brain signals.
On the one hand, it requires a know-how of all the methodological steps of the
processing pipeline that manipulates the input brain signals and extract the
functional network properties. On the other hand, a knowledge of the neural
phenomenon under study is required to perform physiological-relevant analysis.
The aim of this review is to provide practical indications to make sense of
brain network analysis and contrast counterproductive attitudes
Time-Varying Graphs and Dynamic Networks
The past few years have seen intensive research efforts carried out in some
apparently unrelated areas of dynamic systems -- delay-tolerant networks,
opportunistic-mobility networks, social networks -- obtaining closely related
insights. Indeed, the concepts discovered in these investigations can be viewed
as parts of the same conceptual universe; and the formal models proposed so far
to express some specific concepts are components of a larger formal description
of this universe. The main contribution of this paper is to integrate the vast
collection of concepts, formalisms, and results found in the literature into a
unified framework, which we call TVG (for time-varying graphs). Using this
framework, it is possible to express directly in the same formalism not only
the concepts common to all those different areas, but also those specific to
each. Based on this definitional work, employing both existing results and
original observations, we present a hierarchical classification of TVGs; each
class corresponds to a significant property examined in the distributed
computing literature. We then examine how TVGs can be used to study the
evolution of network properties, and propose different techniques, depending on
whether the indicators for these properties are a-temporal (as in the majority
of existing studies) or temporal. Finally, we briefly discuss the introduction
of randomness in TVGs.Comment: A short version appeared in ADHOC-NOW'11. This version is to be
published in Internation Journal of Parallel, Emergent and Distributed
System
Metrics for Graph Comparison: A Practitioner's Guide
Comparison of graph structure is a ubiquitous task in data analysis and
machine learning, with diverse applications in fields such as neuroscience,
cyber security, social network analysis, and bioinformatics, among others.
Discovery and comparison of structures such as modular communities, rich clubs,
hubs, and trees in data in these fields yields insight into the generative
mechanisms and functional properties of the graph.
Often, two graphs are compared via a pairwise distance measure, with a small
distance indicating structural similarity and vice versa. Common choices
include spectral distances (also known as distances) and distances
based on node affinities. However, there has of yet been no comparative study
of the efficacy of these distance measures in discerning between common graph
topologies and different structural scales.
In this work, we compare commonly used graph metrics and distance measures,
and demonstrate their ability to discern between common topological features
found in both random graph models and empirical datasets. We put forward a
multi-scale picture of graph structure, in which the effect of global and local
structure upon the distance measures is considered. We make recommendations on
the applicability of different distance measures to empirical graph data
problem based on this multi-scale view. Finally, we introduce the Python
library NetComp which implements the graph distances used in this work
Perspective: network-guided pattern formation of neural dynamics
The understanding of neural activity patterns is fundamentally linked to an
understanding of how the brain's network architecture shapes dynamical
processes. Established approaches rely mostly on deviations of a given network
from certain classes of random graphs. Hypotheses about the supposed role of
prominent topological features (for instance, the roles of modularity, network
motifs, or hierarchical network organization) are derived from these
deviations. An alternative strategy could be to study deviations of network
architectures from regular graphs (rings, lattices) and consider the
implications of such deviations for self-organized dynamic patterns on the
network. Following this strategy, we draw on the theory of spatiotemporal
pattern formation and propose a novel perspective for analyzing dynamics on
networks, by evaluating how the self-organized dynamics are confined by network
architecture to a small set of permissible collective states. In particular, we
discuss the role of prominent topological features of brain connectivity, such
as hubs, modules and hierarchy, in shaping activity patterns. We illustrate the
notion of network-guided pattern formation with numerical simulations and
outline how it can facilitate the understanding of neural dynamics
A blind deconvolution approach to recover effective connectivity brain networks from resting state fMRI data
A great improvement to the insight on brain function that we can get from
fMRI data can come from effective connectivity analysis, in which the flow of
information between even remote brain regions is inferred by the parameters of
a predictive dynamical model. As opposed to biologically inspired models, some
techniques as Granger causality (GC) are purely data-driven and rely on
statistical prediction and temporal precedence. While powerful and widely
applicable, this approach could suffer from two main limitations when applied
to BOLD fMRI data: confounding effect of hemodynamic response function (HRF)
and conditioning to a large number of variables in presence of short time
series. For task-related fMRI, neural population dynamics can be captured by
modeling signal dynamics with explicit exogenous inputs; for resting-state fMRI
on the other hand, the absence of explicit inputs makes this task more
difficult, unless relying on some specific prior physiological hypothesis. In
order to overcome these issues and to allow a more general approach, here we
present a simple and novel blind-deconvolution technique for BOLD-fMRI signal.
Coming to the second limitation, a fully multivariate conditioning with short
and noisy data leads to computational problems due to overfitting. Furthermore,
conceptual issues arise in presence of redundancy. We thus apply partial
conditioning to a limited subset of variables in the framework of information
theory, as recently proposed. Mixing these two improvements we compare the
differences between BOLD and deconvolved BOLD level effective networks and draw
some conclusions
On Directed Feedback Vertex Set parameterized by treewidth
We study the Directed Feedback Vertex Set problem parameterized by the
treewidth of the input graph. We prove that unless the Exponential Time
Hypothesis fails, the problem cannot be solved in time on general directed graphs, where is the treewidth of
the underlying undirected graph. This is matched by a dynamic programming
algorithm with running time .
On the other hand, we show that if the input digraph is planar, then the
running time can be improved to .Comment: 20
Transport Processes on Homogeneous Planar Graphs with Scale-Free Loops
We consider the role of network geometry in two types of diffusion processes:
transport of constant-density information packets with queuing on nodes, and
constant voltage-driven tunneling of electrons. The underlying network is a
homogeneous graph with scale-free distribution of loops, which is constrained
to a planar geometry and fixed node connectivity . We determine properties
of noise, flow and return-times statistics for both processes on this graph and
relate the observed differences to the microscopic process details. Our main
findings are: (i) Through the local interaction between packets queuing at the
same node, long-range correlations build up in traffic streams, which are
practically absent in the case of electron transport; (ii) Noise fluctuations
in the number of packets and in the number of tunnelings recorded at each node
appear to obey the scaling laws in two distinct universality classes; (iii) The
topological inhomogeneity of betweenness plays the key role in the occurrence
of broad distributions of return times and in the dynamic flow. The
maximum-flow spanning trees are characteristic for each process type.Comment: 14 pages, 5 figure
- …