Temporal Networks

Workshop ILCB, Porquerolles, 10-12 May 2017
Demian Battaglia (INS), Andrea Brovelli (INT), Frederic Richard (I2M)
Graphs and networks provide powerful mathematical representations which have been increasingly used in cognitive neuroscience to represent anatomical connectivity and patterns of functional interactions. The temporal network framework provides powerful generalizations of graphs to the case of time-varying relations between network elements, which are particularly fit to model cognitive brain networks, dynamically reconfiguring over time depending on task-demands and context. Accounting for temporal variations of brain networks allow not to misinterpret averaged-out temporal fluctuations as inter-subject or inter-condition variability, thus promising a superior discriminatory power. At the same time, temporal network descriptions are better compliant with the nature of cognitive information processing in the brain which necessarily unrolls in time, alternating steps of massively parallel and serial information processing. In this Transversal Questions we will develop new methods to tackle with the challenge of extracting and characterizing brain functional connectivity networks and their temporal evolution, in strict relation with the underlying anatomy and the performed cognitive tasks. We will apply these new tools to the analysis of specific datasets, in particular about cognitive experiments involving language analysis and production. The developed tools may furthermore find applications to problems in formal linguistics, in which temporal network representations also arise. Ultimately, we will explore the possibility of describing functional connectivity dynamics itself as a "language" of brain mental processes, endowed with a combinatorial generative syntax which exhibit non-trivial hallmarks of complexity.

Researchers that may be interested in the QT

NS: Battaglia, Benar, Jirsa, Liégeois-Chauvel, Schon, Morillon, Badier
INT: Brovelli, Coulon, Lefèvre, Takerkart, Belin, Giordano
LPC: Alario, Lemaire
LIF: Kevin Perrot, Pablo Arrighi (équipe CANA), François-Xavier Dupé (équipe QARMA)
I2M: Caroline Chaux, Pierre Guillon, Bruno Torrésani, Khuyen Le, Frederic Richard

Members of the Scientific Council the may be interested in this QT

Anne-Lise Giraud; Peter Hagoort; Stanislas Dehaene; Ghislaine Dehaene-Lambertz

Topic of the QT

A temporal network is a mathematical structure used to model time-varying relations between objects organised in networks. A vast number of complex systems, from brain networks to socio-communication patterns or social networks, until recently studied as static objects, can —and should— be represented as temporal networks. A number of problematics addressed by the ILCB may profit from a QT on temporal networks. For example, cognitive brain networks dynamically reconfigure over time depending on task-demands and context. Similarly, language can be described in terms of interacting modules with a flexible organisation that evolves in time during communication. Our challenge is to develop methodological tools for the efficient analysis of brain temporal networks and to elaborate general theoretical approaches that may be applied at the bidirectional interface between brain science, language and communication. Indeed, from the methodological point of view, the routine integration of personalised and multimodal brain data for the analysis of cognitive temporal networks still represents an exceptional tour-de-force , both in terms of workload and computational demands. At the theoretical level, approaches for tracking information flow in temporal networks and for comparing networks observed are still at their infancy. The QT will have two sub-focuses. The first will deal with the development of brain connectivity tools for the characterization of brain temporal networks arising in cognition (time-resolved functional connectivity). Transversal cross-disciplinary interactions will be here crucial to improve existing signal processing and graph-extraction techniques, upgrading them to the challenge of temporally resolving the usual functional connectivity analyses. The second sub-focus will deal with more formal extensions of the temporal network framework, to describe functional connectivity dynamics as a formal language or, possibly, to apply temporal network techniques to the analysis of language itself. This will require to inaugurate a yet unprecedented cooperation between specialists of neuroimaging and systems neuroscience on one side and theoretical computer scientists and researchers in formal linguistics on the other, to enable a veritable knowledge transfer. We have furthermore already started brainstorming potential cooperations with several researchers from multiple disciplines across the labs involved in the ILCB.

A list of possible concrete projects that could be undertaken within the transversal question on temporal networks we are proposing are listed at the end of this document.
Methodological sub-focus #1 Brain connectivity tools for cognitive temporal networks We propose to frame the analysis of cognitive temporal networks within the field of Brain Connectivity. Brain Connectivity is a field of research that unites computational neuroscience, neuroscience methodology and experimental neuroscience with a common interest in understanding the tripartite relationship between anatomical connectivity, brain dynamics and cognitive function. Brain connectivity investigates the interplay between structural , functional and effective connectivity between distinct units within a nervous system, such as brain areas. Structural connectivity (SC) is the pattern of anatomical links, such as fibre pathways, and represents the anatomical scaffolding onto which neural dynamics evolves. Functional Connectivity (FC) is defined as the set of statistical dependences that are observed at the level of neural signals. Effective Connectivity (EC) represents the set of causal relations neural populations or brain areas. On time scales relevant for cognition and behavior, both FC and EC networks can be described as temporally evolving networks. Uplifting their description to the level of temporal rather than static graphs will allow to better render the fact that FC and EC are the emergent manifestation of brain dynamics, constrained, but not fully determined, by the underlying SC.Usually, FC analysis has relied on averaging networks of interaction over long times, or over trials temporally aligned according to some external reference cue.

However the existence of an intrinsic reorganization of FC networks across time is radically inconsistent with these widespread averaging approaches, which unavoidably destroy information about brain dynamics. An initial step of the QT towards a coherent analysis of brain temporal networks will be to organise the competences of the ILCB members regarding the existing tools for the estimation of both anatomical and functional connectivity. Anatomical information plays a key role in the identification of the “nodes” that will constitute the brain networks. A standard approach is to create a brain atlas containing a cortical and subcortical parcellation scheme. A variety of atlases are provided by the main neuroimaging software such as the Desikan-Killiany (Desikan et al., 2006; Destrieux et al., 2010) and Destrieux (Destrieux et al., 2010) , as well as a segmentation of subcortical structures (Fischl et al., 2002). A made-in-Marseille brain atlas has recently been developed and optimized for functional mapping, named MarsAtlas (Auzias et al., 2016) , based on the parcellation of the cortical surface defined by principal sulci (Auzias et al., 2013) . Brain atlases implicitly provide single-subject representations and allow inter-subject analyses. Thus, they provide a useful framework for analysing SC and FC. SC can be inferred in humans from diffusion MRI (dMRI). FC analysis includes various forms of statistical dependences between neural signals that allow the estimate of directional influences between brain regions, such as Granger causality (Brovelli et al., 2004, 2015) . Bayesian inference of actual causal links is performed in EC approaches, as the DCM framework (Friston et al., 2003). Most recent approaches to FC Dynamics (FCD) rely on sliding window approaches in which FC graphs are extracted within each window separately. Such strategies allow the analysis of FC temporal networks both along a task (Brovelli et al., 2017) , studying how the schedule of FC networks recruitment is affected by learning, and in the resting-state (Hansen et al., 2015) , in which the flexibility of FCD correlate with “cognitive flexibility” (Bassett et al., 2011; Shine et al., 2016) and in which the intrinsic speed of FCD slows down with aging (Battaglia et al., 2017). FC can be computed using neural signals from multiple functional imaging techniques such as EEG, MEG, fMRI and intracranial EEG. The tools for the estimation of FC depend on the type of imaging modality and requires the integration of different softwares and pipelines. The first objective of the QT may thus be methodological. We would organise and structure existing pipelines at ILCB, and develop novel ones when needed, for the routine integration of multimodal brain data for the characterization of Functional Connectivity (FC) and its Dynamics (FCD), and possibly of dynamic Effective Connectivity (EC) as well, always in comparison and strict alignment with Structural Connectivity (SC). The resulting temporal network metrics will quantify how the couplings between brain regions fluctuates over time and during cognitive tasks (i.e., across-trials,experimental conditions or even through learning). All the developed tools will be thoroughly documented and shared for open use (at least) within the ILCB consortium. This will allow us to set the bases for detailed connectivity analyses of cognitive temporal networks in specific scientific problems, including language-related tasks, beyond the usual “complex network mantra”.

Theoretical sub-focus #2 General approaches for temporal networks and potential applications to language and communication Temporal networks provide a powerful abstract framework which transcend brain connectivity applications. In fact, the notion of functional connectivity can be used to represent any abstract graph with interacting modules. For example, the use of temporal network representations may be explored in formal linguistics. For instance, graph rewriting grammars (Ehrig et al., 1990), which are non-linear generalization of traditional formal grammars and produce languages adapted to parallel computations, naturally produce temporal network structures, instead of strings of alphabet symbols. Temporal networks also naturally emerge in the field of semantic web search, where dynamic ontologies allow metadata navigation across time (Gutierrez et al., 2005). In a second and more explorative part of QT, we propose to investigate fields of applicability to language and communication by developing novel approaches for the analysis of temporal networks. A first goal would be to improve current methods for the comparison of networks observed at different times, which may differ in their number of nodes and links or links (weaker or stronger interactions, transient correlations, etc). Secondly, a key element would be to devise general approaches for tracking information flow in temporal networks. Third, it would be interesting to identify the relevant temporal scales of network reconfigurations, so to better isolate FC states independently from external cues. Identification of a “dictionary” of prototypical FC states emerging across time could be tackled in a statistical setting by developing appropriate tests of network similarity. In the static setting, there are already promising tests for analyzing the graph connectivity based on regularization approaches (Bien et al., 2013) , which we plan to extend in a temporal setting. We will then study how these FC states concatenate into sequences (i.e. strings of FC network states, whose catalogue is seen as an “alphabet of states”) with a structured combinatorial syntax, providing a potential “assembler language”. FCD streams, neither fully regular nor random, will be parsed to extract statistical generative models as Hidden Markov Models, Hidden Context Trees, dynamic stochastic block models or even, directly, cellular automata approximations (“ε-machines”) or causal graph dynamics descriptions (Arrighi & Dowek, 2012). This may open the possibility to infer generative models that will allow assessing how large is the FCD flux’ statistical complexity (Feldman & Crutchfield, 1998), and how it changes across brain states or conditions. Thus, a second objective of the QT would be to tackle theoretical questions revolving around temporal networks which are transversal to both brain science and formal linguistics and coordinate the competences and synergies of members of the ILCB. Examples of concrete collaborations and contributions We have been contacting in the last weeks several researchers interested by the topic of temporal networks, to explore potential transversal cooperations. The results of this brainstorming, to be further perfected before the meeting at Porquerolles are summarized below. Methodological questions and developments The study of dynamic functional connectivity networks is not going to be immune from technical problems already important for “classic” static network analyses. Introducing novel methods for the extraction and characterization of functional networks, in relation to the underlying anatomy and task performance, will thus profit to both standard functional connectivity analyses and their temporal network level generalization.

● Novel functional connectivity metrics for time-resolved analyses. Andrea Brovelli (INT) has recently developed tools for the estimation of Granger causality on short neural signals (Brovelli et al., 2015). This opens up the possibility for the use of these techniques for a single-trial and time-resolved analyses of directional interactions. Demian Battaglia (INS) has strong experience in information theory and dynamic functional connectivity measures. The will lead to the development of a novel branch called information dynamics, which aims at combining these fields of research.. Bruno Giordano of the BANCO team at INT is involved in the development of novel measures of generalized functional connectivity based on information theoretic approaches (transfer entropy, directed feature information, … also actively explored in the past by the QT co-leader Battaglia). He is currently applying those metrics to MEG datasets. These metrics and their generalizations to temporally-resolved generalized functional connectivity could be used to analyze, in cooperation with Pascal Belin (at the BANCO team), multi-electrode recordings in macaque auditory cortex realized in the framework of the ANR project PRIMAVOICE.

● Analysis of structural-to-functional connectivity relation. The study of both static and dynamic functional connectivity relies necessarily on a better description of the underlying anatomy, in order to better localize the involved functionally-relevant areas. Julien Lefèvre and Olivier Coulon at the MeCA team at INT intend to contribute in this field, making progress in two directions:

○ Optimizing the cortical parcellations used as a spatial support to define nodes of connectivity networks. It has been shown (e.g. Basset et al., 2011) that the number of regions in such parcellations has a strong impact on the graph metrics, but also on the inter and intra-subject variability. While it is recommended to use a number of regions of at least n=200 , it is also known that when n increases the inter-subject correspondences are challenged and the impact of the noise is larger, therefore imposing a necessary tradeoff. Besides, the functional homogeneity of regions must be as good as possible, as it influences the measures of connectivity and the global properties of networks (Park et al., 2013), which is a reason to favor anatomically defined parcellations schemes compared to random ones. Finally, it is also known that regions must be as homogeneous in size as possible (Achard et al., 2011). We intend to propose a new cortical parcellation scheme, specifically designed for functional connectivity inference, based on subdivisions of the existing MarsAtlas model (Auzias et al., 2016), in order to optimize these various constraints. While profiting to standard “static connectivity” estimation, these developments will also be crucial to assess the relative advantage of upgrading to dynamical connectivity analysis, allowing to better disambiguate from potential confounders the fraction of the inter-subject variability which is really due to a different temporal dynamics of networks.

○ Using diffusion MRI to infer local, short range, connectivity networks. It is likely that the functional connectivity dynamics more tightly associated to cognition is the one of local subsystems, e.g. within selected regions or region groups related to language processing. Functional connectivity and its dynamics are critically constrained by the underlying anatomy, however, due to a large inter-subject variability, it is often difficult to describe anatomo-functional organization locally, for instance around a specific sulcus or functional area, at the individual level. Structural connectivity could help deciphering local functional organization, build local functional networks and better extract their dynamics. Such short range connectivity is nevertheless difficult to infer due to acquisition and algorithmic limitations, and we are investigating how to overcome these limitations and understand the structure of white matter connectivity around important sulci such as the central sulcus or the superior temporal sulcus.

● Comparison and classification of functional connectivity networks. In order to follow network changes across time and extract the functionally-relevant ones. A further methodological goal is thus to define new graph metrics in order to characterize populations and to investigate their ability to detect changes in brain networks. We will explore two classes of methods with this goal in mind: ○ Julien Lefèvre (LSIS / INT) will be using spectral graph theory . Spectral methods for graphs have been introduced by M.Fiedler in the 1970's but in spite of their solid mathematical foundations (algebraic graph theory - Merris, 1994), they have not been fully explored to study brain networks, in comparison to more popular but also more empirical metrics. Thus it would be interesting: 1 - to study how spectral descriptors can provide information on brain network topology and geometry, for instance by looking at graph Laplacian eigenvalues and eigenvectors (in particular, but not only, the second ones, so called algebraic connectivity and Fiedler vector); 2 - to investigate theoretically how topological and geometrical perturbations of networks affect spectral descriptors (Poignard et al., 2017). ○ Sylvain Takerkart (INT) and François-Xavier Dupé (LIF) will design new graph kernels suited for dynamical graphs. Graph kernels are mathematical objects which provide similarity measures between graphs, and which open a vast array of possibilities as they can be exploited in the general framework of kernel methods to perform classification, regression, dimensionality reduction etc. (which creates a link with the QT Machine Learning). Overall, we hope that these two classes of methods will allow to determine the range of subtle changes in brain networks that such methods can detect. Also it will allow discriminating which changes of networks occurring across time are “fluctuations”, e.g. small quantitative alterations of edge strengths without real impact on the graph properties, or actual “reconfigurations”, with an impact on the graph and thus their information processing-relevant properties. Cognitive neuroscience questions In terms of applications of Functional Connectivity Dynamics analyses to questions related to the cognitive neurosciences of brain processes and language for which the spatio-temporal dynamics of functional interactions is highly relevant:

● Aging ( Demian Battaglia at INS ). Cognitive psychology studies have shown that aging slows down the ‘clock’ of information processing (Salthouse, 1996; Lemaire, 2010) and even more radically transforms the strategic steps followed in cognitive tasks (Lemaire 2016). However brain imaging studies of these changes have traditionally relied on averaged activity and FC patterns, in such a way that they have failed to render the distinctly temporal nature of cognitive aging effects. Here is where the study of time-dependent functional connectivity could rescue mental chronometry and beyond, helping to temporally unfold the structured flux of Functional Connectivity Dynamics (FCD) that indirectly manifests —or directly provides the functional substrate for— ongoing mental computations. In Battaglia et al. (2017), we have used this new approach to start characterizing how FCD evolves through development, and, notably, through the human adult lifespan (18-80 yrs). Introducing a rigorous measure of the speed at which the brain-wide FC networks spontaneously reconfigure in time along a rs fMRI imaging session, we have found that the speed of FCD slows-down through the human adult lifespan . If we cannot yet directly link the cognitive psychology notion of ‘speed of processing’ with the ‘speed of FCD’ inferred from brain imaging, we have nevertheless shown already that FCD speed and other metrics correlate with the score achieved in the MoCA test, a screening tool commonly used for the diagnosis of Mild Cognitive Impairment, highly significantly even when the common declining trend with age is regressed out. In collaboration with Patrick Lemaire at LPC we plan to further investigate the variations along aging of these FCD-to-cognition interrelations.

● Learning ( Andrea Brovelli at INT ). Learning abilities, such as goal-directed and habit formation, rely on the activity fronto-striatal circuits (Brovelli et al., 2011; 2008). These abilities form the building blocks of behavioral flexibility and automaticity, processes which are crucial for more complex cognitive functions, such as language acquisition and consolidation. The underlying dynamic interplay between cortical and subcortical regions is, however, unclear. The goal will be to apply FCD tools for the study how cortico-cortical and cortical-subcortical interactions change during learning, by combining multiple experimental methodologies such as fMRI, MEG and intracranial EEG, that give access to brain dynamics at complementary spatial and temporal scales. Some open questions concern the role of interactions between: i) the medial and lateral prefrontal cortices in explorative choices and the encoding of conditional probabilities about relevant events such as stimuli, actions and outcomes; ii) the ventromedial, orbitofrontal striatal regions in action’s outcome processing and update of internal beliefs (reward circuit). The first objective will be to investigate whether and how learning-related processes are encoded in directed interactions between brain regions. A second goal will be to study the dynamics of brain interactions as they evolve during single trials (e.g., to mediate visuomotor processes from hundreds of milliseconds to seconds) and across trials duringlearning (seconds to minutes).

● Temporal attention and audition ( Benjamin Morillon at INS ). There is interest in applying functional connectivity dynamics techniques to better separate three concomitant processes all contributing to perception and processing of temporally-organized auditory inputs, but each one endowed with characteristic dynamic time-courses of activation which are lost when averaging functional connectivity in time: temporal attention, acoustic information processing and update of the internal temporal model. Study of these processes, e.g. based on MEG experiments, will require spectrally resolving functional connectivity dynamics analysis, studying how functional connectivities in different frequency bands are coupled and inter-related (on the line of a temporal network generalization of Florin & Baillet, 2015). This would allow also putting Functional Connectivity Dynamics analyses in the broader context of the theory of the involvement of oscillations at different frequencies in predictive coding (Fontolan et al., 2014; Bastos et al., 2012) or in the hierarchical parsing of nested phonemes, syllables, prosodic elements (Giraud & Poeppel, 2012).

● Rhythm perception in music and speech ( Daniele Schon at INS ). On a related topic, one interesting application would be to better understand the brain dynamics underlying rhythm perception in music and speech, known to be entrained by the temporal rhythmicity of auditory inputs (Fujioka et al., 2012). More precisely, to track the spatio-temporal dynamics of how temporal expectations emerge, become stable and decay once during and after stimulation. An interesting approach would be to study the dynamics of the coherence (i.e., frequency-dependent large-scale synchronization of oscillatory activity) between the auditory and motor systems and the extent to which these are modulated by the presence of a rhythmic stimulus, be it music or speech. In particular, the study of the transitions between more and less stable states (the dynamics of entrainment) will be valuable to study the predictive features of brain functions.

● Language ( François-Xavier Alario at LPN and Cathérine Liégeois-Chauvel at INS ). Study how blocks associated to the execution of different language-related tasks can be distinguished in an unsupervised manner between them and from resting state based on the estimated static functional connectivity. In collaboration with the WT co-leader Battaglia they are now extending their analysis to the inspection of the temporal variability of the extracted functional networks, to see whether the coordinated variability patterns of functional links are better predictors of task type (and task performance as well) than averaged link strengths. Findings in this direction would hint at the fact that temporal variability of FC is playing a (direct or indirect) functional role in the implementation of the information processing steps underlying language-related cognition.
Cooperations on more formal aspects.

From a very general perspective (Church, 1932; Turing, 1937), a computation can be defined as a string manipulation, lasting a finite number of steps, and eventually itself describable… as a symbolic string. The intrinsic signature of any computation or formal language (Chomsky, 1957) is thus the existence of a structured grammar in which the probability of producing the next system state combinatorially depends on context and system history. This is precisely what we think may be happening in Functional Connectivity Dynamics, where the “next graph” in the sequence of time-resolved functional networks is definitely not random but may be at least in part expected according to yet unknown rules of graph rewriting.

● The QT co-leader Battaglia already plans to chase for combinatorial structure (FCD syntax) in streams of Functional Connectivity Dynamics using a variety of different approaches. It is promising in this context to team up with researchers at the CANA team of the LIF , such as Kevin Perrot or, in particular, Pablo Arrighi , who are developing Causal Graph Dynamics models (Arrighi & Dowek, 2012) which combine aspects of cellular automata dynamics and graph rewriting grammars in a novel and original way and which seem particularly suitable to capture the statistically complex organization of temporal streams of brain functional graphs.


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