arXiv subjects

Daniele Marinazzo

Publications and source records attributed to Daniele Marinazzo.

At least 55 records · Page 3Linked to original sources

arXiv2017

Multiscale Granger causality analysis by à trous wavelet transform

Since interactions in neural systems occur across multiple temporal scales, it is likely that information flow will exhibit a multiscale structure, thus requiring a multiscale generalization of classical temporal precedence causality analysis like Granger's approach. However, the computation of multiscale measures of information dynamics is complicated by theoretical and practical issues such as filtering and undersampling: to overcome these problems, we propose a wavelet-based approach for multiscale Granger causality (GC) analysis, which is characterized by the following properties: (i) only the candidate driver variable is wavelet transformed (ii) the decomposition is performed using the à trous wavelet transform with cubic B-spline filter. We measure GC, at a given scale, by including the wavelet coefficients of the driver times series, at that scale, in the regression model of the target. To validate our method, we apply it to publicly available scalp EEG signals, and we find that the condition of closed eyes, at rest, is characterized by an enhanced GC among channels at slow scales w.r.t. eye open condition, whilst the standard Granger causality is not significantly different in the two conditions.

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arXiv2017

Consensus clustering approach to group brain connectivity matrices

A novel approach rooted on the notion of consensus clustering, a strategy developed for community detection in complex networks, is proposed to cope with the heterogeneity that characterizes connectivity matrices in health and disease. The method can be summarized as follows: (i) define, for each node, a distance matrix for the set of subjects by comparing the connectivity pattern of that node in all pairs of subjects; (ii) cluster the distance matrix for each node; (iii) build the consensus network from the corresponding partitions; (iv) extract groups of subjects by finding the communities of the consensus network thus obtained. Differently from the previous implementations of consensus clustering, we thus propose to use the consensus strategy to combine the information arising from the connectivity patterns of each node. The proposed approach may be seen either as an exploratory technique or as an unsupervised pre-training step to help the subsequent construction of a supervised classifier. Applications on a toy model and two real data sets, show the effectiveness of the proposed methodology, which represents heterogeneity of a set of subjects in terms of a weighted network, the consensus matrix.

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arXiv2017

Conserved Ising Model on the Human Connectome

Dynamical models implemented on the large scale architecture of the human brain may shed light on how function arises from the underlying structure. This is the case notably for simple abstract models, such as the Ising model. We compare the spin correlations of the Ising model and the empirical functional brain correlations, both at the single link level and at the modular level, and show that their match increases at the modular level in anesthesia, in line with recent results and theories. Moreover, we show that at the peak of the specific heat (the \it{critical state}) the spin correlations are minimally shaped by the underlying structural network, explaining how the best match between structure and function is obtained at the onset of criticality, as previously observed. These findings confirm that brain dynamics under anesthesia shows a departure from criticality and could open the way to novel perspectives when the conserved magnetization is interpreted in terms of an homeostatic principle imposed to neural activity.

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arXiv2016

Evolutionary Dynamics of Group Formation

We introduce a model, based on the Evolutionary Game Theory, for studying the dynamics of group formation. The latter constitutes a relevant phenomenon observed in different animal species, whose individuals tend to cluster together forming groups of different size. Results of previous investigations suggest that this phenomenon might have similar reasons across different species, such as improving the individual safety (e.g. from predators), and increasing the probability to get food resources. Remarkably, the group size might strongly vary from species to species, and sometimes even within the same species. In the proposed model, an agent population tries to form homogeneous groups. The homogeneity of a group is computed according to a spin vector, that characterizes each agent, and represents a set a features (e.g. physical traits). We analyze the formation of groups of different size, on varying a parameter named 'individual payoff'. The latter represents the gain one agent would receive acting individually. In particular, the agents choose whether to form a group (receiving a 'group payoff'), or if to play individually (receiving an 'individual payoff'). The phase diagram representing the equilibria of our population shows a sharp transition between the 'group phase' and the 'individual phase', in correspondence of a critical 'individual payoff'. In addition, we found that forming (homogeneous) small groups is easier than forming big groups. To conclude, we deem that our model and the related results supports the hypothesis that the phenomenon of group formation has evolutionary roots.

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arXiv2016

Critical comments on EEG sensor space dynamical connectivity analysis

Many different analysis techniques have been developed and applied to EEG recordings that allow one to investigate how different brain areas interact. One particular class of methods, based on the linear parametric representation of multiple interacting time series, is widely used to study causal connectivity in the brain. However, the results obtained by these methods should be interpreted with great care. The goal of this paper is to show, both theoretically and using simulations, that results obtained by applying causal connectivity measures on the sensor (scalp) time series do not allow interpretation in terms of interacting brain sources. This is because 1) the channel locations cannot be seen as an approximation of a source's anatomical location and 2) spurious connectivity can occur between sensors. Although many measures of causal connectivity derived from EEG sensor time series are affected by the latter, here we will focus on the well-known time domain index of Granger causality (GC) and on the frequency domain directed transfer function (DTF). Using the state-space framework and designing two simulation studies we show that mixing effects caused by volume conduction can lead to spurious connections, detected either by time domain GC or by DTF. Therefore, GC/DTF causal connectivity measures should be computed at the source level, or derived within analysis frameworks that model the effects of volume conduction. Since mixing effects can also occur in the source space, it is advised to combine source space analysis with connectivity measures that are robust to mixing.

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arXiv2016

Mapping the functional connectome traits of levels of consciousness

Examining task-free functional connectivity (FC) in the human brain offers insights on how spontaneous integration and segregation of information relate to human cognition, and how this organization may be altered in different conditions, and neurological disorders. This is particularly relevant for patients in disorders of consciousness (DOC) following severe acquired brain damage and coma, one of the most devastating conditions in modern medical care. We present a novel data-driven methodology, connICA, which implements Independent Component Analysis (ICA) for the extraction of robust independent FC patterns (FC-traits) from a set of individual functional connectomes, without imposing any a priori data stratification into groups. We here apply connICA to investigate associations between network traits derived from task-free FC and cognitive/clinical features that define levels of consciousness. Three main independent FC-traits were identified and linked to consciousness-related clinical features. The first one represents the functional configuration it is associated to a sedative (sevoflurane), the overall effect of the pathology and the level of arousal. The second FC-trait reflects the disconnection of the visual and sensory-motor connectivity patterns. It also relates to the time since the insult and to the ability of communicating with the external environment. The third FC-trait isolates the connectivity pattern encompassing the fronto-parietal and the default-mode network areas as well as the interaction between left and right hemispheres, which are also associated to the awareness of the self and its surroundings. Each FC-trait represents a distinct functional process with a role in the degradation of conscious states of functional brain networks, shedding further light on the functional subcircuits that get disrupted in severe brain-damage.

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arXiv2016

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.

cs.IT↗

arXiv2016

Multiscale Analysis of Information Dynamics for Linear Multivariate Processes

In the study of complex physical and physiological systems represented by multivariate time series, an issue of great interest is the description of the system dynamics over a range of different temporal scales. While information-theoretic approaches to the multiscale analysis of complex dynamics are being increasingly used, the theoretical properties of the applied measures are poorly understood. This study introduces for the first time a framework for the analytical computation of information dynamics for linear multivariate stochastic processes explored at different time scales. After showing that the multiscale processing of a vector autoregressive (VAR) process introduces a moving average (MA) component, we describe how to represent the resulting VARMA process using state-space (SS) models and how to exploit the SS model parameters to compute analytical measures of information storage and information transfer for the original and rescaled processes. The framework is then used to quantify multiscale information dynamics for simulated unidirectionally and bidirectionally coupled VAR processes, showing that rescaling may lead to insightful patterns of information storage and transfer but also to potentially misleading behaviors.

cs.IT↗

arXiv2015

Identification of redundant and synergetic circuits in triplets of electrophysiological data

Neural systems are comprised of interacting units, and relevant information regarding their function or malfunction can be inferred by analyzing the statistical dependencies between the activity of each unit. Whilst correlations and mutual information are commonly used to characterize these dependencies, our objective here is to extend interactions to triplets of variables to better detect and characterize dynamic information transfer. Our approach relies on the measure of interaction information (II). The sign of II provides information as to the extent to which the interaction of variables in triplets is redundant (R) or synergetic (S). Here, based on this approach, we calculated the R and S status for triplets of electrophysiological data recorded from drug-resistant patients with mesial temporal lobe epilepsy in order to study the spatial organization and dynamics of R and S close to the epileptogenic zone (the area responsible for seizure propagation). In terms of spatial organization, our results show that R matched the epileptogenic zone while S was distributed more in the surrounding area. In relation to dynamics, R made the largest contribution to high frequency bands (14-100Hz), whilst S was expressed more strongly at lower frequencies (1-7Hz). Thus, applying interaction information to such clinical data reveals new aspects of epileptogenic structure in terms of the nature (redundancy vs. synergy) and dynamics (fast vs. slow rhythms) of the interactions. We expect this methodology, robust and simple, can reveal new aspects beyond pair-interactions in networks of interacting units in other setups with multi-recording data sets (and thus, not necessarily in epilepsy, the pathology we have approached here).

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arXiv2015

Neural Networks with Non-Uniform Embedding and Explicit Validation Phase to Assess Granger Causality

A challenging problem when studying a dynamical system is to find the interdependencies among its individual components. Several algorithms have been proposed to detect directed dynamical influences between time series. Two of the most used approaches are a model-free one (transfer entropy) and a model-based one (Granger causality). Several pitfalls are related to the presence or absence of assumptions in modeling the relevant features of the data. We tried to overcome those pitfalls using a neural network approach in which a model is built without any a priori assumptions. In this sense this method can be seen as a bridge between model-free and model-based approaches. The experiments performed will show that the method presented in this work can detect the correct dynamical information flows occurring in a system of time series. Additionally we adopt a non-uniform embedding framework according to which only the past states that actually help the prediction are entered into the model, improving the prediction and avoiding the risk of overfitting. This method also leads to a further improvement with respect to traditional Granger causality approaches when redundant variables (i.e. variables sharing the same information about the future of the system) are involved. Neural networks are also able to recognize dynamics in data sets completely different from the ones used during the training phase.

physics.data-an↗

arXiv2015

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.

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arXiv2014

Synergy and redundancy in the Granger causal analysis of dynamical networks

We analyze by means of Granger causality the effect of synergy and redundancy in the inference (from time series data) of the information flow between subsystems of a complex network. Whilst we show that fully conditioned Granger causality is not affected by synergy, the pairwise analysis fails to put in evidence synergetic effects. In cases when the number of samples is low, thus making the fully conditioned approach unfeasible, we show that partially conditioned Granger causality is an effective approach if the set of conditioning variables is properly chosen. We consider here two different strategies (based either on informational content for the candidate driver or on selecting the variables with highest pairwise influences) for partially conditioned Granger causality and show that depending on the data structure either one or the other might be valid. On the other hand, we observe that fully conditioned approaches do not work well in presence of redundancy, thus suggesting the strategy of separating the pairwise links in two subsets: those corresponding to indirect connections of the fully conditioned Granger causality (which should thus be excluded) and links that can be ascribed to redundancy effects and, together with the results from the fully connected approach, provide a better description of the causality pattern in presence of redundancy. We finally apply these methods to two different real datasets. First, analyzing electrophysiological data from an epileptic brain, we show that synergetic effects are dominant just before seizure occurrences. Second, our analysis applied to gene expression time series from HeLa culture shows that the underlying regulatory networks are characterized by both redundancy and synergy.

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arXiv2013

Point-process deconvolution of fMRI reveals effective connectivity alterations in chronic pain patients

It is now recognized that important information can be extracted from the brain spontaneous activity, as exposed by recent analysis using a repertoire of computational methods. In this context a novel method, based on a blind deconvolution technique, is used in this paper to analyze potential changes due to chronic pain in the brain pain matrix's effective connectivity. The approach is able to deconvolve the hemodynamic response function to spontaneous neural events, i.e., in the absence of explicit onset timings, and to evaluate information transfer between two regions as a joint probability of the occurrence of such spontaneous events. The method revealed that the chronic pain patients exhibit important changes in the Insula's effective connectivity which can be relevant to understand the overall impact of chronic pain on brain function.

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arXiv2013

Information transfer of an Ising model on a brain network

We implement the Ising model on a structural connectivity matrix describing the brain at a coarse scale. Tuning the model temperature to its critical value, i.e. at the susceptibility peak, we find a maximal amount of total information transfer between the spin variables. At this point the amount of information that can be redistributed by some nodes reaches a limit and the net dynamics exhibits signature of the law of diminishing marginal returns, a fundamental principle connected to saturated levels of production. Our results extend the recent analysis of dynamical oscillators models on the connectome structure, taking into account lagged and directional influences, focusing only on the nodes that are more prone to became bottlenecks of information. The ratio between the outgoing and the incoming information at each node is related to the number of incoming links.

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arXiv2012

Information flow in a network model and the law of diminishing marginal returns

We analyze a simple dynamical network model which describes the limited capacity of nodes to process the input information. For a suitable choice of the parameters, the information flow pattern is characterized by exponential distribution of the incoming information and a fat-tailed distribution of the outgoing information, as a signature of the law of diminishing marginal returns. The analysis of a real EEG data-set shows that similar phenomena may be relevant for brain signals.

physics.data-an↗

arXiv2012

Causal information approach to partial conditioning in multivariate data sets

When evaluating causal influence from one time series to another in a multivariate dataset it is necessary to take into account the conditioning effect of the other variables. In the presence of many variables, and possibly of a reduced number of samples, full conditioning can lead to computational and numerical problems. In this paper we address the problem of partial conditioning to a limited subset of variables, in the framework of information theory. The proposed approach is tested on simulated datasets and on an example of intracranial EEG recording from an epileptic subject. We show that, in many instances, conditioning on a small number of variables, chosen as the most informative ones for the driver node, leads to results very close to those obtained with a fully multivariate analysis, and even better in the presence of a small number of samples. This is particularly relevant when the pattern of causalities is sparse.

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arXiv2011

Abnormal effective connectivity in migraine with aura under photic stimulation

Migraine patients with aura show a peculiar pattern of visual reactivity compared with those of migraine patients without aura: an increased effective connectivity, connected to a reduced synchronization among EEG channels, for frequencies in the beta band. The effective connectivity is evaluated in terms of the Granger causality. This anomalous response to visual stimuli may play a crucial role in the progression of spreading depression and clinical evidences of aura symptoms.

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arXiv2010

Grouping time series by pairwise measures of redundancy

A novel approach is proposed to group redundant time series in the frame of causality. It assumes that (i) the dynamics of the system can be described using just a small number of characteristic modes, and that (ii) a pairwise measure of redundancy is sufficient to elicit the presence of correlated degrees of freedom. We show the application of the proposed approach on fMRI data from a resting human brain and gene expression profiles from HeLa cell culture.

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