1,806 research outputs found
Measuring autonomy and emergence via Granger causality
Concepts of emergence and autonomy are central to artificial life and related cognitive and behavioral sciences. However, quantitative and easy-to-apply measures of these phenomena are mostly lacking. Here, I describe quantitative and practicable measures for both autonomy and emergence, based on the framework of multivariate autoregression and specifically Granger causality. G-autonomy measures the extent to which the knowing the past of a variable helps predict its future, as compared to predictions based on past states of external (environmental) variables. G-emergence measures the extent to which a process is both dependent upon and autonomous from its underlying causal factors. These measures are validated by application to agent-based models of predation (for autonomy) and flocking (for emergence). In the former, evolutionary adaptation enhances autonomy; the latter model illustrates not only emergence but also downward causation. I end with a discussion of relations among autonomy, emergence, and consciousness
Multivariate Granger Causality and Generalized Variance
Granger causality analysis is a popular method for inference on directed
interactions in complex systems of many variables. A shortcoming of the
standard framework for Granger causality is that it only allows for examination
of interactions between single (univariate) variables within a system, perhaps
conditioned on other variables. However, interactions do not necessarily take
place between single variables, but may occur among groups, or "ensembles", of
variables. In this study we establish a principled framework for Granger
causality in the context of causal interactions among two or more multivariate
sets of variables. Building on Geweke's seminal 1982 work, we offer new
justifications for one particular form of multivariate Granger causality based
on the generalized variances of residual errors. Taken together, our results
support a comprehensive and theoretically consistent extension of Granger
causality to the multivariate case. Treated individually, they highlight
several specific advantages of the generalized variance measure, which we
illustrate using applications in neuroscience as an example. We further show
how the measure can be used to define "partial" Granger causality in the
multivariate context and we also motivate reformulations of "causal density"
and "Granger autonomy". Our results are directly applicable to experimental
data and promise to reveal new types of functional relations in complex
systems, neural and otherwise.Comment: added 1 reference, minor change to discussion, typos corrected; 28
pages, 3 figures, 1 table, LaTe
Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System
Peer reviewedPublisher PD
A Toolbox to Analyze Emergence in Multiagent Simulations
The field of complexity science often employs multiagent simulations to investigate complex and emergent behavior. Authors in complexity science have suggested that the discussion of complex systems could benefit from a more systematic approach and a more compact mathematical way to describe the behavior of such systems in addition to the common observations and interpretations taking place today. Regarding quantitative measures to capture emergent phenomena, several approaches have been published, but have not yet been put to wide systematic use in the research community. One reason for this could be the manual effort required to investigate multiagent systems in a quantitatively accurate form. Toward this end, there has so far been a lack of appropriate and easy-to-use IT-based tools. To eliminate this deficiency, we present a software library, which enables researchers to integrate emergence measurements into experiments with multiagent modeling tools such as Repast and NetLogo. The major benefit for researchers is that this toolbox enables them to make comparable, quantitatively well-grounded statements about the emergent behavior of the model at hand. The toolbox therefore provides researchers with a standardized artifact that can be employed in a systematic methodological approach to the analysis of multiagent systems
Causal connectivity of evolved neural networks during behavior
To show how causal interactions in neural dynamics are modulated by behavior, it is valuable to analyze these interactions without perturbing or lesioning the neural mechanism. This paper proposes a method, based on a graph-theoretic extension of vector autoregressive modeling and 'Granger causality,' for characterizing causal interactions generated within intact neural mechanisms. This method, called 'causal connectivity analysis' is illustrated via model neural networks optimized for controlling target fixation in a simulated head-eye system, in which the structure of the environment can be experimentally varied. Causal connectivity analysis of this model yields novel insights into neural mechanisms underlying sensorimotor coordination. In contrast to networks supporting comparatively simple behavior, networks supporting rich adaptive behavior show a higher density of causal interactions, as well as a stronger causal flow from sensory inputs to motor outputs. They also show different arrangements of 'causal sources' and 'causal sinks': nodes that differentially affect, or are affected by, the remainder of the network. Finally, analysis of causal connectivity can predict the functional consequences of network lesions. These results suggest that causal connectivity analysis may have useful applications in the analysis of neural dynamics
Information flow between resting state networks
The resting brain dynamics self-organizes into a finite number of correlated
patterns known as resting state networks (RSNs). It is well known that
techniques like independent component analysis can separate the brain activity
at rest to provide such RSNs, but the specific pattern of interaction between
RSNs is not yet fully understood. To this aim, we propose here a novel method
to compute the information flow (IF) between different RSNs from resting state
magnetic resonance imaging. After haemodynamic response function blind
deconvolution of all voxel signals, and under the hypothesis that RSNs define
regions of interest, our method first uses principal component analysis to
reduce dimensionality in each RSN to next compute IF (estimated here in terms
of Transfer Entropy) between the different RSNs by systematically increasing k
(the number of principal components used in the calculation). When k = 1, this
method is equivalent to computing IF using the average of all voxel activities
in each RSN. For k greater than one our method calculates the k-multivariate IF
between the different RSNs. We find that the average IF among RSNs is
dimension-dependent, increasing from k =1 (i.e., the average voxels activity)
up to a maximum occurring at k =5 to finally decay to zero for k greater than
10. This suggests that a small number of components (close to 5) is sufficient
to describe the IF pattern between RSNs. Our method - addressing differences in
IF between RSNs for any generic data - can be used for group comparison in
health or disease. To illustrate this, we have calculated the interRSNs IF in a
dataset of Alzheimer's Disease (AD) to find that the most significant
differences between AD and controls occurred for k =2, in addition to AD
showing increased IF w.r.t. controls.Comment: 47 pages, 5 figures, 4 tables, 3 supplementary figures. Accepted for
publication in Brain Connectivity in its current for
Econometric Measures of Connectedness and Systemic Risk in the Finance and Insurance Sectors
We propose several econometric measures of connectedness based on principal-components analysis and Granger-causality networks, and apply them to the monthly returns of hedge funds, banks, broker/dealers, and insurance companies. We find that all four sectors have become highly interrelated over the past decade, likely increasing the level of systemic risk in the finance and insurance industries through a complex and time-varying network of relationships. These measures can also identify and quantify financial crisis periods, and seem to contain predictive power in out-of-sample tests. Our results show an asymmetry in the degree of connectedness among the four sectors, with banks playing a much more important role in transmitting shocks than other financial institutions.Systemic Risk; Financial Institutions; Liquidity; Financial Crises
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
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