6,571 research outputs found
A Graph Algorithmic Approach to Separate Direct from Indirect Neural Interactions
Network graphs have become a popular tool to represent complex systems
composed of many interacting subunits; especially in neuroscience, network
graphs are increasingly used to represent and analyze functional interactions
between neural sources. Interactions are often reconstructed using pairwise
bivariate analyses, overlooking their multivariate nature: it is neglected that
investigating the effect of one source on a target necessitates to take all
other sources as potential nuisance variables into account; also combinations
of sources may act jointly on a given target. Bivariate analyses produce
networks that may contain spurious interactions, which reduce the
interpretability of the network and its graph metrics. A truly multivariate
reconstruction, however, is computationally intractable due to combinatorial
explosion in the number of potential interactions. Thus, we have to resort to
approximative methods to handle the intractability of multivariate interaction
reconstruction, and thereby enable the use of networks in neuroscience. Here,
we suggest such an approximative approach in the form of an algorithm that
extends fast bivariate interaction reconstruction by identifying potentially
spurious interactions post-hoc: the algorithm flags potentially spurious edges,
which may then be pruned from the network. This produces a statistically
conservative network approximation that is guaranteed to contain non-spurious
interactions only. We describe the algorithm and present a reference
implementation to test its performance. We discuss the algorithm in relation to
other approximative multivariate methods and highlight suitable application
scenarios. Our approach is a tractable and data-efficient way of reconstructing
approximative networks of multivariate interactions. It is preferable if
available data are limited or if fully multivariate approaches are
computationally infeasible.Comment: 24 pages, 8 figures, published in PLOS On
Model-free reconstruction of neuronal network connectivity from calcium imaging signals
A systematic assessment of global neural network connectivity through direct
electrophysiological assays has remained technically unfeasible even in
dissociated neuronal cultures. We introduce an improved algorithmic approach
based on Transfer Entropy to reconstruct approximations to network structural
connectivities from network activity monitored through calcium fluorescence
imaging. Based on information theory, our method requires no prior assumptions
on the statistics of neuronal firing and neuronal connections. The performance
of our algorithm is benchmarked on surrogate time-series of calcium
fluorescence generated by the simulated dynamics of a network with known
ground-truth topology. We find that the effective network topology revealed by
Transfer Entropy depends qualitatively on the time-dependent dynamic state of
the network (e.g., bursting or non-bursting). We thus demonstrate how
conditioning with respect to the global mean activity improves the performance
of our method. [...] Compared to other reconstruction strategies such as
cross-correlation or Granger Causality methods, our method based on improved
Transfer Entropy is remarkably more accurate. In particular, it provides a good
reconstruction of the network clustering coefficient, allowing to discriminate
between weakly or strongly clustered topologies, whereas on the other hand an
approach based on cross-correlations would invariantly detect artificially high
levels of clustering. Finally, we present the applicability of our method to
real recordings of in vitro cortical cultures. We demonstrate that these
networks are characterized by an elevated level of clustering compared to a
random graph (although not extreme) and by a markedly non-local connectivity.Comment: 54 pages, 8 figures (+9 supplementary figures), 1 table; submitted
for publicatio
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EEG-Based Quantification of Cortical Current Density and Dynamic Causal Connectivity Generalized across Subjects Performing BCI-Monitored Cognitive Tasks.
Quantification of dynamic causal interactions among brain regions constitutes an important component of conducting research and developing applications in experimental and translational neuroscience. Furthermore, cortical networks with dynamic causal connectivity in brain-computer interface (BCI) applications offer a more comprehensive view of brain states implicated in behavior than do individual brain regions. However, models of cortical network dynamics are difficult to generalize across subjects because current electroencephalography (EEG) signal analysis techniques are limited in their ability to reliably localize sources across subjects. We propose an algorithmic and computational framework for identifying cortical networks across subjects in which dynamic causal connectivity is modeled among user-selected cortical regions of interest (ROIs). We demonstrate the strength of the proposed framework using a "reach/saccade to spatial target" cognitive task performed by 10 right-handed individuals. Modeling of causal cortical interactions was accomplished through measurement of cortical activity using (EEG), application of independent component clustering to identify cortical ROIs as network nodes, estimation of cortical current density using cortically constrained low resolution electromagnetic brain tomography (cLORETA), multivariate autoregressive (MVAR) modeling of representative cortical activity signals from each ROI, and quantification of the dynamic causal interaction among the identified ROIs using the Short-time direct Directed Transfer function (SdDTF). The resulting cortical network and the computed causal dynamics among its nodes exhibited physiologically plausible behavior, consistent with past results reported in the literature. This physiological plausibility of the results strengthens the framework's applicability in reliably capturing complex brain functionality, which is required by applications, such as diagnostics and BCI
Distinguishing Cause and Effect via Second Order Exponential Models
We propose a method to infer causal structures containing both discrete and
continuous variables. The idea is to select causal hypotheses for which the
conditional density of every variable, given its causes, becomes smooth. We
define a family of smooth densities and conditional densities by second order
exponential models, i.e., by maximizing conditional entropy subject to first
and second statistical moments. If some of the variables take only values in
proper subsets of R^n, these conditionals can induce different families of
joint distributions even for Markov-equivalent graphs.
We consider the case of one binary and one real-valued variable where the
method can distinguish between cause and effect. Using this example, we
describe that sometimes a causal hypothesis must be rejected because
P(effect|cause) and P(cause) share algorithmic information (which is untypical
if they are chosen independently). This way, our method is in the same spirit
as faithfulness-based causal inference because it also rejects non-generic
mutual adjustments among DAG-parameters.Comment: 36 pages, 8 figure
Deep learning systems as complex networks
Thanks to the availability of large scale digital datasets and massive
amounts of computational power, deep learning algorithms can learn
representations of data by exploiting multiple levels of abstraction. These
machine learning methods have greatly improved the state-of-the-art in many
challenging cognitive tasks, such as visual object recognition, speech
processing, natural language understanding and automatic translation. In
particular, one class of deep learning models, known as deep belief networks,
can discover intricate statistical structure in large data sets in a completely
unsupervised fashion, by learning a generative model of the data using
Hebbian-like learning mechanisms. Although these self-organizing systems can be
conveniently formalized within the framework of statistical mechanics, their
internal functioning remains opaque, because their emergent dynamics cannot be
solved analytically. In this article we propose to study deep belief networks
using techniques commonly employed in the study of complex networks, in order
to gain some insights into the structural and functional properties of the
computational graph resulting from the learning process.Comment: 20 pages, 9 figure
Synergetic and redundant information flow detected by unnormalized Granger causality: application to resting state fMRI
Objectives: We develop a framework for the analysis of synergy and redundancy
in the pattern of information flow between subsystems of a complex network.
Methods: The presence of redundancy and/or synergy in multivariate time series
data renders difficult to estimate the neat flow of information from each
driver variable to a given target. We show that adopting an unnormalized
definition of Granger causality one may put in evidence redundant multiplets of
variables influencing the target by maximizing the total Granger causality to a
given target, over all the possible partitions of the set of driving variables.
Consequently we introduce a pairwise index of synergy which is zero when two
independent sources additively influence the future state of the system,
differently from previous definitions of synergy. Results: We report the
application of the proposed approach to resting state fMRI data from the Human
Connectome Project, showing that redundant pairs of regions arise mainly due to
space contiguity and interhemispheric symmetry, whilst synergy occurs mainly
between non-homologous pairs of regions in opposite hemispheres. Conclusions:
Redundancy and synergy, in healthy resting brains, display characteristic
patterns, revealed by the proposed approach. Significance: The pairwise synergy
index, here introduced, maps the informational character of the system at hand
into a weighted complex network: the same approach can be applied to other
complex systems whose normal state corresponds to a balance between redundant
and synergetic circuits.Comment: 6 figures. arXiv admin note: text overlap with arXiv:1403.515
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