RESEARCH CENTRE

Inria Centre
at Université Côte d’Azur

2023
ACTIVITY REPORT

Project-Team

CRONOS

Computational modelling of brain
dynamical networks

DOMAIN

Digital Health, Biology and Earth

THEME

Computational Neuroscience and
Medicine

Contents

Project-Team CRONOS

1 Team members, visitors, external collaborators

2 Overall objectives

2.1 Main Research hypotheses

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Brain Signal Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.2 Network Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 Research program

3.1 Sensor level: the first window on brain dynamics . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Automating the detection of brain state changes from the acquired data . . . . . . .
3.1.2 Better modeling of the spatio-temporal variability of brain signals . . . . . . . . . . .
3.1.3 Adapting to new sensor modalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Source level: the integration space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Source modeling: anatomical, temporal, and numerical constraints . . . . . . . . . .
3.2.2 Unified network models explaining various brain measurements
. . . . . . . . . . .
3.2.3 Global inverse problem using all measurements altogether . . . . . . . . . . . . . . .
3.3 Group level: understanding variability to constrain network properties . . . . . . . . . . . .
3.3.1 Matching individual subject models . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Statistics over brain networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 Application domains

4.1 Clinical applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Brain Computer Interfaces

5 Highlights of the year

5.1 Awards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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6 New software, platforms, open data

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6.1 New software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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6.1.1 BCI-VIZAPP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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6.1.2 BifurcationKit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Open data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

7 New results

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7.1 Sensor Level: Brain Signal Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
7.2 Source Level: Brain Dynamic Network Modeling . . . . . . . . . . . . . . . . . . . . . . . . . 12
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
7.3 Group Level
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
7.4 Other Results

8 Bilateral contracts and grants with industry

17
8.1 Bilateral Grants with Industry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

9 Partnerships and cooperations

17
9.1 International initiatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
9.1.1 Inria associate team not involved in an IIL or an international program . . . . . . . . 17
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
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9.3 National initiatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
9.4 Regional initiatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

9.2 European initiatives

9.2.1 H2020 projects

10 Dissemination

19
10.1 Promoting scientific activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
10.1.1 Scientific events: organisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
10.1.2 Journal
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
10.1.3 Invited talks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
10.1.4 Leadership within the scientific community . . . . . . . . . . . . . . . . . . . . . . . . 21
10.1.5 Scientific expertise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
10.1.6 Research administration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
10.2 Teaching - Supervision - Juries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
10.2.1 Teaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
10.2.2 Supervision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
10.2.3 Juries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
10.3 Popularization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
10.3.1 Articles and contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
10.3.2 Interventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

11 Scientific production

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11.1 Major publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
11.2 Publications of the year
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11.3 Cited publications

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Project-Team CRONOS

Creation of the Project-Team: 2022 December 01

Keywords

Computer sciences and digital sciences

A3.4. – Machine learning and statistics

A6.1. – Methods in mathematical modeling

A9.2. – Machine learning

A9.3. – Signal analysis

Other research topics and application domains

B1. – Life sciences

B1.2. – Neuroscience and cognitive science

B1.2.1. – Understanding and simulation of the brain and the nervous system

B1.2.2. – Cognitive science

B1.2.3. – Computational neurosciences

B2.2.2. – Nervous system and endocrinology

B2.2.6. – Neurodegenerative diseases

B2.5.1. – Sensorimotor disabilities

B2.6.1. – Brain imaging

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Inria Annual Report 2023

1 Team members, visitors, external collaborators

Research Scientists

• Théodore Papadopoulo [Team leader, INRIA, Senior Researcher, HDR]

• Rachid Deriche [INRIA, Emeritus, HDR]

• Samuel Deslauriers-Gauthier [INRIA, ISFP]

• Olivier Faugeras [INRIA, Emeritus, from Oct 2023, HDR]

• Romain Veltz [INRIA, Researcher, from Oct 2023]

PhD Students

• Yanis Aeschlimann [UNIV COTE D’AZUR]

• Igor Carrara [UNIV COTE D’AZUR]

• Petru Isan [CHU NICE, from Sep 2023]

Technical Staff

• Laura Gee [INRIA, Engineer, from Dec 2023]

• Eleonore Haupaix-Birgy [INRIA, Engineer, from Apr 2023]

Interns and Apprentices

• Martin Bouchet [INRIA, Intern, from Apr 2023 until Aug 2023]

• Arturo Cabrera Vazquez [UNIV COTE D’AZUR, Intern, from Mar 2023 until May 2023]

• Tijn Logtens [UNIV COTE D’AZUR, Intern, from Mar 2023 until May 2023]

Administrative Assistant

• Claire Senica [INRIA]

External Collaborator

• Petru Isan [CHU NICE, from Mar 2023 until Aug 2023]

2 Overall objectives

The objective of CRONOS is to develop models, algorithms, and software to estimate, understand, and
quantify the whole brain dynamics. We will achieve this objective by modeling the macroscopic archi-
tecture and connectivity of the brain at three complexity levels: source, sensor, and group (see Figure 1).
These three levels, detailed in section 3, will be studied through the unifying representation of dynamic
networks.

CRONOS aims at pushing forward the state-of-the-art in computational brain imaging by developing
computational tools to integrate the dynamic and partial information provided by each measurement
modality (fMRI, dMRI, EEG, MEG, . . . )1 into a consistent global dynamic network model.

Developing the computational models, algorithms, and software to estimate, understand, and
quantify the brain’s dynamical networks is a mathematical and computational challenge. Starting from

1fMRI: functional magnetic resonance imaging, dMRI: diffusion magnetic resonance imaging, EEG: electroencephalography,

MEG:magnetoencephalography.

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Figure 1: Research axes and their interactions

several specific partial models of the brain, the overall goal is to assimilate in a single global numerical
model the diversity of observations provided by non-invasive imaging. Indeed, the observations provided
by various modalities are based on very different physical and biological principles. They thus reveal very
different but complementary aspects of the brain, including its structural organization, electrical activity,
and hemodynamic response. In addition, because of the varied nature of the physical principles used for
imaging, different modalities also have drastically different spatial and temporal resolutions making their
unification challenging. Some examples of sub-objectives we will develop are:

• Go beyond the hypothesis that brain networks are static over a given period of time.

• Study the possibility of estimating brain functional areas simultaneously with the networks.

• Study the impact on the reconstructed networks of the brain area to brain area activity transfer

model.

• Develop a complete modeling of time delays involved by long range connections.

• Develop network based regularization methods in estimating brain activity.

• Go from subject specific studies to group level studies and increase the level of abstraction implied
by the use of brain networks to open research perspectives in identifying network characteristics
and invariances.

• Study the impact of the model imperfections on the obtained results.

Finally, the software implementing our models and algorithms must be accessible to non-technical
users. They must therefore provide a level of abstraction, ease of use, and interpretability suitable for
neuroscientists, cogniticians, and clinicians.

2.1 Main Research hypotheses

To achieve our goals, we decided to make some hypotheses on the way brain signals and networks are
modeled.

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Inria Annual Report 2023

2.1.1 Brain Signal Modeling

To model brain signals, we adopt a signal processing perspective, i.e. consider that at the macroscopic
scale we look at signals, general signal modeling approaches are sufficient for the goal of describing brain
dynamics. This contrasts with many other teams, which often follow a more constructivist approach,
where brain signal models are derived from a computational neuroscience perspective, i.e. emerge from
a mathematical modeling of neurons, axons and dendrites or assemblies of those (spiking neurons,
neural mass models, . . . ). Our approach gives more freedom to model signals and allows for descriptions
with a very limited number of parameters at the cost of losing some connection with the microscopic
reality. Additionally, the reduced number of parameters simplifies the problem of parameter identific-
ation. Depending on the type of modeling, we may use rather simple phenomenological descriptions
(e.g a region is activated or not) or more or less complicated signal models (sampled signals with no
specific temporal models, various multivariate autoregressive models, integro-differential equations, . . . ).
Generally speaking, the more we will be interested in dynamical properties of the signals, the more we
will need sophisticated signal models.

2.1.2 Network Modeling

Classical – deterministic – networks only strictly exist at the microscopic level where neurons are connec-
ted together through axons. For complex neural systems, such networks are huge, currently unavailable
and too complex for a macroscopic view of the brain. At such a scale, networks are of stochastic nature.
Both nodes and edges are only defined probabilistically. We allow ourselves to work either directly with
these probablistic networks or with deterministic networks obtained by thresholding the probabilistic
ones, in which case it is important to pay attention to the amount of approximation and bias introduced
by the thresholding operation. Its is important to note that, while deterministic networks have received a
lot of attention, the domain of stochastic networks or its tranfer to computational neurosciences is still in
its infancy.

3 Research program

As described in section 2 and Figure 1, the research program of CRONOS is organized in 3 main axes
corresponding to different levels of complexity:

• The Sensor level aims at extracting information directly from sensor data, without necessarily using
the underlying brain anatomy. It can be thought of as a projection of the underlying brain networks
onto a low dimensional space thus allowing computationally efficient processing and analysis.
This provides a first window for observing and estimating brain dynamics. This sensor space is
particularly convenient for the estimation of properties that are projection invariants (e.g. number
of sources, state changes, . . . ). It is also the level that is most suitable for real time applications,
such as brain computer interfaces.

• The Source level aims at measurement integration into a unified and high dimensional spatio-
temporal space, i.e. a computational representation of dynamic brain networks. This is the level
that is understood by neuroscientists, cogniticians, and clinicians, and therefore has an essential
role to play in the visualization of brain activities.

• The Group level aims at providing tools to constrain the search space of the two previous levels.
This is the natural space to develop statistical models and tests of the functioning of the brain. It is
the level that allows the study of inter-subject variability of brain activity and the development of
data driven priors. In particular, the topic of making statistics over noisy networks is a challenging
task for this level.

These three levels closely interact with each other, as depicted by Fig. 1, towards the ultimate goal of
non-invasively and continuously localizing brain activity in the form of brain networks.

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3.1 Sensor level: the first window on brain dynamics

Sensor level mostly concerns MEG and EEG measurements. These serve as a support not only for
experiments aimed at understanding the functioning of the brain when it performs certain tasks, but also
for the characterization of certain pathologies (such as epilepsy). As an inexpensive modality, EEG is also
widely used for the development of brain-computer interfaces (BCI). EEG and MEG are characterized
by a high temporal resolution (up to 1000Hz or more), by a poor spatial resolution (measurable events
involve several centimers-square portions of the cortex) and by a rather poor signal-to-noise ratio (SNR)2.
For both EEG and MEG, the obtained measurements are linear mixtures of the “true” electrical sources
that are at a distance of the sensors. MEG and EEG temporal resolution characteristics allow them to
reveal changes in the dynamic of the brain activity. This “sensor space” has two main advantages: 1) its
relatively small dimension (from a few to several hundreds sensors) compared to that of the “source space”
(tens of thousands of degrees of freedom) and 2) its ease-of-use3. It is thus opportune to extract as much
information as possible from this lower dimensional space, which already contains all the dynamical
information of the functioning brain available from these modalities. This involves a better understanding
of the invariants between source and sensor levels, which can lead to better Brain Computer Interfaces
(BCI) classification algorithms. BCI not only clearly is an applicative domain that will benefit from this
research, but will also help in validation of algorithms and methods. Our ambition is also to study how
BCI-like techniques can be used for constraining the reconstruction of brain networks, for detecting
some brain events in real time for clinical applications for creating improved cognitive protocols using
real time responses to dynamically adapt stimulations.

This axis relies on three major ideas, which are necessary steps towards the ultimate goal of using
MEG or EEG systems to non-invasively and continuously localize brain activity in the form of brain
networks (i.e. without averaging multiple trials signals).

3.1.1 Automating the detection of brain state changes from the acquired data

Experimental practice in MEG, EEG, and BCI shows that very valuable information can be obtained
directly from the “sensor space”. This encompasses estimating the number [43] or the time courses of
sources [38, 37] or the detection of changes in the brain dynamical activity. This type of information
can be an indication of a “brain state change”. In particular, automating the detection of changes in
brains states would allow the splitting of the incoming functional data into segments in which the brain
network can be considered as stationary. During such stationary segments of data, the sources and their
locations remains fixed, which offers a means to regularize the solution of the inverse problem of source
reconstruction. Furthermore, any improvement on EEG signal classification has direct applications for
Brain Computer Interfaces. One approach that we will explore is the use of autoregressive spatio-temporal
models or lagged correlation measurements as a means to improve classification of MEG/EEG signals.
These autoregressive spatio-temporal models are a possible first step towards using more sophisticated
causality modeling.

3.1.2 Better modeling of the spatio-temporal variability of brain signals

Hand in hand with the previous sub-goal, there is the need to better understand the spatio-temporal
variability of brain signals. This variability originates from several factors ranging from the intrinsic
variability of the brain sources (even in a same subject) to important differences in the spatial organization
of the cortex across subjects or to variations in the way sensors are setup by experimenters. Thus,
variability occurs not only across subjects, but also across sessions or even trials for a same subject.

The most common approach developed to cope with the noisy MEG and EEG signals is commonly
referred to as evoked potentials: the signal is “clocked” on some stimulus or reaction of the subject and
the low amplitude signals – almost completely hidden by background activity – are then averaged over
multiple repetitions (trials) of the experiment to improve the SNR. But, because of variability, such an

2The SNR further depends on several factors such as the technology used in the sensor (dry/wet, active/passive electrodes, ...),

on the quality of the amplifier, on the quality of the setup, etc.

3Going to source space needs to create a head model which, for better efficiency, requires to be adapted to the subject. In turn,

this means acquiring MR data and apply complex processes to it.

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Inria Annual Report 2023

averaging distorts the overall activity and hides specific activities such as high frequency components. It
is thus advisable to improve models so that they can work in single event mode (i.e without averaging).
Relying on multiple trials to obtain better statistical models of individual signals (with techniques such
as dictionary learning, autoregressive models, deep-neural networks, etc) would be an important im-
provement over the current state of the art as it would provide a more objective and systematic way
of characterizing single trial data. Events will be extracted separately for each trial without relying on
averaging, but with the knowledge of the “group” model. This will allow the study of the variability of
brain activity across trials (attention, habituation are e.g. known to change activity). This is a difficult
long term challenge with possible short-middle term advances for some specific cases such as epileptic
spikes. This research path is grounded by some of our previous work [5, 2]. Understanding variability
is particularly important for Brain Computer Interfaces as it is often necessary to “learn” a classifier to
detect the subject’s brain state with a limited dataset (because of time constraint). At the sensor level,
spatial patterns of activity are often described by covariance/correlation matrices. Using Riemannian
metric over the space of symmetric definite positive matrices is a powerful technique that has been used
these last years by the BCI community. Extending and improving these techniques as well as finding
proper low dimensional spaces that characterize brain activity are other research paths we will follow.

3.1.3 Adapting to new sensor modalities

During the last few years, tremendous improvements have been made on means to acquire functional
brain data. Yet, novelty in this domain continues and new sensors are regularly proposed. These sensors
can offer more accurate measurements with improved signal-to-noise ratio (SNR) and/or some ease-of-
use improvements. For example, the use of room temperature MEG sensors (such as those developed by
Mag4Health) promise improvements in both aspects. EEG dry electrodes hold the promises to simplify
the setup of BCI systems, but are difficult to master. MR machines are also more and more powerful
with either higher fields (better signal quality and/or better spatial resolution) or, on the contrary, lower
fields (easier to use and better contrasts in some cases). It is important to continually adapt processing
methods to exploit the specificities of these new sensors as they become available to the community.

3.2 Source level: the integration space

Magnetic Resonance (MR) images of the brain offer different views of its organization and function via
diffusion MRI tractography and functional MRI connectivity. When combined with MEG and EEG, we
obtain complementary, but highly heterogeneous perspectives on brain networks and their dynamics.
The natural space to integrate this complex information is the space of brain sources, allowing a unified
model of imaging data. This axis is built over our past research (in the team ATHENA) in modeling the
propagation of the electromagnetic field from brain sources to sensors [6], brain structural connectivity [3]
or mapping different brain imaging modalities [4]. Our plan for fusing the data originating from different
modalities into a single network based model can be described in 3 sub-topics.

3.2.1 Source modeling: anatomical, temporal, and numerical constraints

Brain sources refer to regions of interests whose properties link brain activity to the observed measure-
ments. For example, in EEG, brain sources can be modeled as dipoles representing the superposition
of many synchronous and parallel neurons. The combination of the electric fields generated by these
dipoles gives rise to the potential differences measured at the surface of the scalp in EEG. The magnetic
fields generated by these same dipoles give rise to MEG signals. Regardless of the modality, the task of
recovering brain sources from imaging data is an inverse problem. This inverse problem is ill–posed,
either because of the limited number of sensors (EEG and MEG), because of poor signal to noise ratio
(EEG, MEG, fMRI), or because of the limited spatial (dMRI, EEG, MEG) or temporal resolution (fMRI,
dMRI). To recover a unique and stable solution, simple mathematical criteria (minimum norm, sparsity)
are used to constrain the source space. However, these regularization approaches do not correspond to
any specific anatomical or physiological properties of the brain and are therefore quite arbitrary. The
challenge we address here is to increase the amount of subject specific anatomical and physiological con-
straints taken into acount for the recovery of brain activity from non–invasive imaging. More specifically,

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we will investigate how brain networks, and in particular their associated delays, can be used to constrain
the inverse problem. Previous work has already shown the potential of temporal regularization based
on brain connectivity [3], but the topic remains largely open to identifying new models grounded in
physiological data. Another difficulty is the dynamic aspect of brain networks: we will first assume that a
stationary brain state has been identified (e.g. using methods from section 3.1). Eventually (as a long term
objective), transitions between stationary brain state models could be directly modeled in the networks
themselves and estimated from the data. The validation of the proposed models is both challenging and
essential and will be explored with our clinical partners (see section 9). Finally, non-traditional imaging
modalities will also be considered. For example, accurate modeling of electromyography, in collaboration
with Neurodec, can provide important timing information of sources.

3.2.2 Unified network models explaining various brain measurements

In the previous section, brain activity is estimated from one modality using information from the others
as constraints or priors. This obviously favors one modality over the others and propagates errors of
processing pipelines via the constraints. This modus operandi, while suboptimal, is justified historically:
analysis pipelines have been developed independently for each modality by different communities. Given
the complementary nature of the different modalities, it seems relevant to instead construct one global
pipeline encompassing all brain measurement modalities into a single unified framework. With brain
networks arising as a central concept in the neuroscientific community, we propose to make it the basis
of such a global model. Doing so will enable the recovery of brain network dynamics from non–invasive
multi–modal data, an important open problem in neuroscience. To achieve this objective, we propose
to devise forward models describing the link between brain networks and each of the various imaging
modalities. Specifically, work is needed to evaluate different formalisms describing brain networks that
differ in the way nodes and their interactions are defined. For example, we will investigate the relationship
between electrical (EEG/MEG), architectural (diffusion MRI) and metabolic (functional MRI) activities.
Separated models – either electric or hemodynamic – have been devised for some time, but coupling
them is an important challenge all the more that the role of some neural constituents (such as glia) is
currently not well understood. Such models have already been – at least partly as in [35] – devised. The
main challenge is to define one sufficiently simple and well spatialized (in particular to incorporate
connectivity) in order to be useful for our purpose. We will also consider electromyography in this context,
extending brain networks to the peripherial nervous system.

3.2.3 Global inverse problem using all measurements altogether

Models established in the previous section can be used in a global inverse problem involving all the
sources of measurements to recover the specific brain network involved in a task. In all cases, we need to
solve an inverse problem over a complex network model with a sparse prior as we need to find "simple"
networks that can explain our data. Depending on the way networks are modeled, some difficulties may
arise. For example, the model defined in [41, 40] leads to combinatorial explosion when used for source
localization. Finding appropriate models that facilitate the resolution of the inverse problem may require
some iterations between this sub-task and the previous one.

3.3 Group level: understanding variability to constrain network properties

Given the high intra- or inter-subject variability of brain activity, it is particularly interesting to be able to
characterize the part of the activity that remains invariant (over time for one subject or across different
subjects). This will allow a better understanding of brain processes as well as a better understanding
of their variability across time or subjects. It also opens the possibility to constrain network models
to reduce their complexity and improve their identifiability. The following description mostly refers to
group statistics at the source level, but similar techniques are also relevant for the sensor level axis (see
section 3.1). This research axis is a longer term research effort as it builds upon previous axes.

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3.3.1 Matching individual subject models

Reconstructions obtained in section 3.2 will certainly differ even for different measurement sessions
obtained for a same subject. An important problem to solve is the matching of instances of such
reconstructions (whether they consist in brain networks or spatio-temporal autoregressive models). In
general, the relative positions of functional brain areas are fairly well known. However, timing variations
(lag, duration) in these models make the matching problem rather complicated. Finding and using some
invariants of the models is one path to find a good compromise that would allow enough flexibility in
the matching process while avoiding the combinatorial complexity that e.g. graph matching problems
usually exhibit. Another – long term – possibility would be to directly solve “group problems”, but this
would complexify even more the modeling problem and might have the same drawbacks as averaging if
not done properly (i.e. hiding some activity or the intrinsic variability of the studied phenomenon).

3.3.2 Statistics over brain networks

Once the matching of single subject models has been solved, statistics will be necessary to assess the
significance of the various model elements (e.g. in the case of dynamic network models, brain areas
and their connections). Such statistics can also be used as a basis to derive “group statistical models”
describing a family of task-related models that can in turn be used to constrain models used in section 3.2
and, through a forward model to reduce search space at sensor level 3.1. The BCI community is still
divided on the actual benefits in terms of accuracy on going to source space for classifying brain signals.
The statistical tools developed in this sub-axis may help to address this problem.

4 Application domains

4.1 Clinical applications

CRONOS research has a strong clinical potential impact for brain diseases like epilepsy, brain cancer
surgery, phantom pains, traumatic brain injuries, . . . We work closely with several hospital teams and
research groups (Pasteur hospital in Nice, La Timone hospital in Marseille, CRNL – Centre de Recherche
en Neuroscience in Lyon –) towards exporting our research in their contexts. Example of applications are:

• Better understanding brain stimulation used in awake brain surgery and its relation with brain

anatomy and in particular fibers as measured by dMRI.

• Real time detection of epileptic spikes from new generation MEG data and the visualization of their

associated brain sources in real time.

• Use of BCI (see section 4.2) for helping disabled people to communicate (e.g. for patients suffering
from Amyotrophic Lateral Sclerosis) or for helping epileptic patients to learn how to control the
occurence of seizures.

• Understand the somatotopy of the thalamus and its relation with the efficiency of the deep brain

stimulation therapy.

4.2 Brain Computer Interfaces

Brain Computer Interface is a closely related domain to both the ‘Signal Processing‘ and ‘Network
Modeling‘ aspects. It typically extracts from the signal a ’brain state’ that is a correlate of the ‘brain
network’. While traditional MEG/EEG studies have been extensively exploited by the BCI community, the
opposite nourishing of the former field by BCI has been much less explored. There is a continuing dispute
in the BCI community on the advantages of going to source space or not (see e.g. [42]). By studying the
invariants between source and sensor space, we hope to not only provide clues on the above dispute
but also to open the opportunity of using BCI-like techniques to ease the more traditional brain signal
processing. In some sense, it is such invariants that BCI exploits in doing classification on sensor data. BCI
also has the advantage of providing a more quantitative way (in term of classification quality) to evaluate
methods. A strong BCI concern is also on the resources (computer power, number and quality of the

Project CRONOS

9

sensors, . . . ) needed to achieve a given classification accuracy. This point of view is also complementary
to that of more traditional brain signal modeling and can have a significant impact in terms of cost and
ease of use in the clinical context.

5 Highlights of the year

5.1 Awards

• Rachid Deriche has been elected as a member of Academia Europaea in the section Informatics

[May. 2023].

• Rachid Deriche has obtained the position of Inria Emeritus Research Director [Jan. 2023].

• The article [15] has been selected by the “Société des Neurosciences” to be in the "Highlights 2023"

of the works of the community.

6 New software, platforms, open data

6.1 New software

6.1.1 BCI-VIZAPP

Name: Real time EEG applications

Keywords: Health, Brain-Computer Interface, GUI (Graphical User Interface)

Functional Description: BCI-VIZAPP is a software suite for designing real-time EEG applications such
as BCIs or neurofeedback applications. It has been been developed to build a virtual keyboard
for typing text and a photodiode monitoring application for checking timing issues, but can
now be also used in other tasks such as EEG monitoring. Originally, it was designed to delegate
signal acquisition and processing to OpenViBE but has recently been extended to get some of
these capabilities. This allows for more integrated and robust applications but also opens up new
algorithmic opportunities, such as real time parameter modification, more controlled interfaces, . . .

News of the Year: Bci-Vizapp has been enriched with numerous features, notably to read and save
certain files created with OpenViBE or with MNE-python, thus allowing an easier communication
with them. Bci-Vizapp is also the software base used (or which we aim to use it in the long term) for
different contracts (Demagus, EPIFEED, EPINFB, Techicopa and ConnectTC) and has integrated
different elements to support them.

Contact: Théodore Papadopoulo

Participants: Nathanaël Foy, Romain Lacroix, Maureen Clerc Gallagher, Théodore Papadopoulo, Yang Ji,

Come Le Breton

6.1.2 BifurcationKit

Name: Automatic computation of numerical bifurcation diagrams

Keywords: Bifurcation, GPU

Functional Description: This Julia package aims at performing automatic bifurcation analysis of pos-
sibly large dimensional equations function of a real parameter by taking advantage of iterative
methods, dense / sparse formulation and specific hardware (e.g. GPU).

It incorporates continuation algorithms (PALC, deflated continuation, ...) based on a Newton-
Krylov method to correct the predictor step and a Matrix-Free/Dense/Sparse eigensolver is used to
compute stability and bifurcation points.

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Inria Annual Report 2023

The package can also seek for periodic orbits of Cauchy problems. It is by now one of the few
software programs which provide shooting methods and methods based on finite differences or
collocation to compute periodic orbits.

The current package focuses on large-scale, multi-hardware nonlinear problems and is able to use
both Matrix and Matrix Free methods on GPU.

News of the Year: The package was complemented with methods for computing curves of Neimark-
Sacker or period-doubling bifurcations in two parameters. The corresponding normal forms have
also been implemented. Additionally, a package HclinicBifurcationKit.jl has been added to the
github organisation bifurcationkit. It allows computations of homoclinic orbits.

URL: https://github.com/rveltz/BifurcationKit.jl

Publication: hal-02902346

Contact: Romain Veltz

Participant: Romain Veltz

6.2 Open data

Temporal Brain Networks Dataset

Participants:

Samuel Deslauriers-Gauthier, Aurora Rossi
Emanuele Natale (COATI, Inria).

(COATI,

Inria),

One of the first step in our study of null models for dynamic brain networks [16, 33, 24] was to
process a significant amount of the data from the Human Connectome Project (HCP). The result of
this work is the dynamic brain networks of 1047 subjects at various resolutions (number of nodes).
Recognizing that few teams have the expertise and computational resources to reproduce this dataset,
we decided to make it publicly accessible [32]. It is our hope that this dataset will not only allow other
researchers in network neuroscience to reproduce our results, but also allow researchers in other fields
(e.g. graph theory) access to real world networks. This dataset is available in an easy-to-read format from
entrepot.recherche.data.gouv.fr.

7 New results

7.1 Sensor Level: Brain Signal Modeling

Augmented Covariance Approaches for BCI

Participants:

Igor Carrara, Théodore Papadopoulo.

EEG signals are complex and difficult to characterize, in particular because of their variability, whether
in the same subject through the repetition of the same experiment or a fortiori when one wants to carry
out multi-subject analyses. They therefore require the use of specific and adapted signal processing
methods. In a recent approach [34], sources were modeled as an autoregressive model which explains a
portion of a signal. This approach works at the level of the source space (i.e. the cortex), which requires
modeling of the head and makes it quite expensive. However, EEG measurements can be considered as a
linear mixture of sources and therefore it is possible to estimate an autoregressive model directly at the
measurement level. The objectives of this line of work is to explore the possibility of exploiting EEG/MEG
autoregressive models to extract as much information as possible without requiring the complex head
modeling required for source reconstruction.

Project CRONOS

11

A first result in this line of research is the use of Augmented Covariance Matrices (ACMs) for BCI
classification. These ACMs appear naturally in the Yule-Walker equations that were derived to recover
autoregressive models from data. ACMs being symmetric positive definite matrices, it is natural to
apply Riemannian Geometry based classification approaches on these objects, as those are the current
state-of-the-art for such matrix types. Using these ACMs noticeably improves classification performance
on several BCI benchmarks both in the within-session or in the cross-session evaluation protocols. This is
due to the fact that ACMs incorporate not only spatial (the classical covariance matrix) but also temporal
information. As such, it contains information on the nonlinear components of the signal through the
embedding procedure, which allows the leveraging of dynamical systems algorithms. This comes at the
cost of introducing two hyper-parameters: the order of the autoregressive model and a delay that controls
the time resolution at which the signal is considered, which have to be estimated. This work is described
in the preprint [18], which is currently under evaluation.

The improvements related above are made with a grid search hyper-parameter selection, which can
be quite costly. As an ACM can be seen as the standard spatial covariance matrix of an extended signal
created from the original one using a multidimensional embedding, there is an obvious link with the
delay embedding theorem proposed by Takens[45] for the study of dynamical systems. This view provides
an alternate path for estimating the hyper-parameters using methods proposed for dynamical systems
such as the MDOP (Maximizing Derivatives On Projection) algorithm [44]. This method is evaluated in
the above preprint.

Finally, ACM approaches also allow better classification of "reduced signals" with typically only a few

EEG channels [31].

Augmented methods with SPDNet

Participants:

Igor Carrara, Bruno Aristimunha (Universidade Federal do ABC,
Santo André, Brazil and Université Paris-Saclay, Paris, France),
Marie-Constance Corsi (ARAMIS, Inria, Paris Brain Institute, France),
Raphael Yokoingawa De Camargo (Universidade Federal do ABC,
Santo André, Brazil), Sylvain Chevallier (Université Paris-Saclay, Paris,
France), Théodore Papadopoulo.

This conference poster [29] studies whether the combination of phase space reconstruction and
deep-learning methods can enhance the performance of BCI decoding for motor imagery (MI-BCI) in a
low number of electrodes situation. This work relies on the combination of the Augmented Covariance
method (ACM) explained in the previous paragraph, but implemented in the deep learning framework
of SPDNet. The results show that the combination of ACM and SPDNet improves the classification
performance of MI-BCI in a low number of electrodes regimes over the deep learning state-of-the-art.
Moreover the Augmented SPDNet is explainable (using GadCam++[36]), with a low number of trainable
parameters and a reduced carbon footprint.

In another work [28], we propose a contrastive learning approach to learn discriminative represent-
ations of EEG signals in the context of motor imagery (MI) BCI tasks. Specifically, we investigate the
use of SPDNet with different EEG signal representations based on symmetric positive definite (SPD)
matrix: covariance matrix, augmented covariance matrix, and coherence matrix. The main advantage of
contrastive learning is that it can learn representations that are invariant to irrelevant variations, such
as differences in electrode placement, noise, and individual differences in brain activity. By learning
to contrast similar and dissimilar examples, contrastive learning can discover patterns that are shared
across subjects and generalize well to new data. We validate our approach using the MOABB framework
(Mother of All BCI Benchmarks), focusing on Cross Subject evaluation. The study is in its initial stages
and further research is required to fully explore the potential of contrastive learning and SPDNet in the
context of EEG-BCI.

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Inria Annual Report 2023

Pseudo-online framework for BCI evaluation

Participants:

Igor Carrara, Théodore Papadopoulo.

BCI (Brain-Computer Interface) technology operates in three modes: online, offline, and pseudo-
online. In the online mode, real-time EEG data is constantly analyzed. In offline mode, the signal is
acquired and processed afterwards. The pseudo-online mode processes collected data as if they were
received in real-time, but without the real-time constraints. The main difference is that the offline
mode often analyzes the whole data, while the online and pseudo-online modes only analyze data in
short time windows, which is more flexible and realistic for real-life applications. Consequently, offline
processing tends to be more accurate, but biases the comparison of classification methods towards
methods requiring more dataset. In this work, we extended the current MOABB framework [39], that
used to operate in offline mode only, with pseudo-online capabilities using overlapping sliding windows.
This requires the introduction of an idle state event in the dataset to account for non task related signal
portions. We analyzed the state-of-the-art algorithms of the last 15 years over several Motor Imagery (MI)
datasets composed by several subjects, showing the differences between the two approaches (offline,
and pseudo-online) and show that the adoption of the pseudo-online strategy modifies the hierarchy
of classification methods. The publications related to this work are [30, 19]. The second reference is a
preprint of an accepted article that will appear in 2024.

Familiarity and mind wandering in neural tracking of music

Participants:

Joan Belo, Maureen Clerc (Inria), Daniele Schön (ILCB, Aix-Marseille
University).

One way to investigate the cortical tracking of continuous auditory stimuli is to use the stimulus recon-
struction approach. However, the cognitive and behavioral factors impacting this cortical representation
remain largely overlooked. Two possible candidates are familiarity with the stimulus and the ability to
resist internal distractions. To explore the possible impacts of these two factors on the cortical represent-
ation of natural music stimuli, forty-one participants listened to monodic natural music stimuli while
we recorded their neural activity. Using the stimulus reconstruction approach and linear mixed models,
we found that familiarity positively impacted the reconstruction accuracy of music stimuli and that this
effect of familiarity was modulated by mind wandering. This work is published in [10].

7.2 Source Level: Brain Dynamic Network Modeling

Null models of dynamic brain networks

Participants:

Samuel Deslauriers-Gauthier, Aurora Rossi
Emanuele Natale (COATI, Inria).

(COATI,

Inria),

Null models are crucial for determining the degree of significance when testing hypotheses about
brain dynamics modeled as a temporal complex network. The comparison between the hypotheses being
tested on empirical data and on the null model enables us to assess the extent to which an apparently
remarkable feature of the former can be attributed to randomness. In [16, 33, 24], we consider networks
generated from resting-state functional magnetic resonance imaging (fMRI) signals from the Human
Connectome Project using standard processing techniques. The network nodes correspond to brain
regions while the edges represent the presence of a correlation greater than a certain value between
the signals of two regions. Over time, edges may appear and disappear, indicating that the associated
correlation may jump above and below a certain value. While null models for static networks have been
studied extensively, there is a lack of attention to temporal networks. Therefore, our investigation focuses
on the study of temporal null models. In doing so, we focus on the ability of the null models to reproduce

Project CRONOS

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the temporal small-worldness present in the empirical data, a property associated with the efficient
exchange of information at local and global scales over time.
The networks used in this work are publicly available [32].

Challenge on the estimation of structural connectivity from dMRI

Participants:

Samuel Deslauriers-Gauthier, Rachid Deriche, and many other re-
searchers from the dMRI community.

Estimating structural connectivity from diffusion-weighted magnetic resonance imaging is a challen-
ging task, partly due to the presence of false-positive connections and the misestimation of connection
weights. Building on previous efforts, the MICCAI-CDMRI Diffusion-Simulated Connectivity (DiSCo) chal-
lenge was carried out to evaluate state-of-the-art connectivity methods using novel large-scale numerical
phantoms [13]. The diffusion signal for the phantoms was obtained from Monte Carlo simulations. The
results of the challenge suggest that methods selected by the 14 teams participating in the challenge
can provide high correlations between estimated and ground-truth connectivity weights, in complex
numerical environments. Additionally, the methods used by the participating teams were able to accur-
ately identify the binary connectivity of the numerical dataset. However, specific false positive and false
negative connections were consistently estimated across all methods. Although the challenge dataset
does not capture the complexity of a real brain, it provided unique data with known macrostructure
and microstructure ground-truth properties to facilitate the development of connectivity estimation
methods.

Brain surgery: Free-water correction DTI-based tractography in brain

Participants:

Fabien Almairac (Pasteur Hospital, UR2CA, Nice), Drew Parker (Univer-
sity of Pennyslvania), Lydiane Mondot (UR2CA, Nice), Petru Isan (Pas-
teur Hospital, UR2CA, Nice), Marie Onno (Pasteur Hospital, Nice),
Théodore Papadopoulo, Patryk Filipiak (NYU Langone Health),
Denys Fontaine (Pasteur Hospital, UR2CA, Nice), Ragini Verma (Uni-
versity of Pennyslvania).

Peritumoral edema prevents fiber tracking from diffusion tensor imaging (DTI). A free-water correc-
tion may overcome this drawback, as illustrated in the case of a patient undergoing awake surgery for
brain metastasis. The anatomical plausibility and accuracy of tractography with and without free-water
correction were assessed with functional mapping and axono-cortical evoked-potentials (ACEPs) as
reference methods. The results suggest a potential synergy between corrected DTI-based tractography
and ACEPs to reliably identify and preserve white matter tracts during brain tumor surgery. This work has
been published in [9].

Brain surgery: identifying subcortical connectivity

Participants:

Fabien Almairac (Pasteur Hospital, UR2CA, Nice), Petru Isan (Pas-
teur Hospital, UR2CA, Nice), Marie Onno (Pasteur Hospital,
Nice), Théodore Papadopoulo, Lydiane Mondot (UR2CA, Nice),
Stéphane Chanalet (UR2CA, Nice), Chalotte Fernandez (Pasteur Hos-
pital, Nice), Maureen Clerc (Inria), Rachid Deriche, Denys Fon-
taine (Pasteur Hospital, UR2CA, Nice), Patryk Filipiak (NYU Langone
Health).

Bipolar direct electrical stimulation (DES) of an awake patient is the reference technique for identifying
brain structures to achieve maximal safe tumor resection. Unfortunately, DES cannot be performed in all

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Inria Annual Report 2023

cases. Alternative surgical tools are, therefore, needed to aid identification of subcortical connectivity
during brain tumor removal. In this pilot study, we sought to (i) evaluate the combined use of evoked
potential (EP) and tractography for identification of white matter (WM) tracts under the functional
control of DES, and (ii) provide clues to the electrophysiological effects of bipolar stimulation on neural
pathways. We included 12 patients (mean age of 38.4 years) who had had a dMRI-based tractography
and a functional brain mapping under awake craniotomy for brain tumor removal. Electrophysiological
recordings of subcortical evoked potentials (SCEPs) were acquired during bipolar low frequency (2
Hz) stimulation of the WM functional sites identified during brain mapping. SCEPs were successfully
triggered in 11 out of 12 patients. The median length of the stimulated fibers was 43.24 ± 19.55 mm,
belonging to tracts of median lengths of 89.84 ± 24.65 mm. The electrophysiological (delay, amplitude,
and speed of propagation) and structural (number and lengths of streamlines, and mean fractional
anisotropy) measures were correlated. In our experimental conditions, SCEPs were essentially limited to
a subpart of the bundles, suggesting a selectivity of action of the DES on the brain networks. Correlations
between functional, structural, and electrophysiological measures portend the combined use of EPs and
tractography as a potential intraoperative tool to achieve maximum safe resection in brain tumor surgery.
This work is published in [8].

Connectivity in the rat brain

Participants:

Samuel Deslauriers-Gauthier, Joana Gomes-Ribeiro (Instituto de Medi-
cina Molecular, Portugal), João Martins (Instituto de Ciências Nucleares
Aplicadas à Saúde and University of Coimbra, Portual), Teresa Sum-
mavielle (Instituto de Investigação e Inovação em Saúde, Portugal),
Joana E. Coelho (Instituto de Medicina Molecular, Portugal), Miguel Re-
mondes (Instituto de Medicina Molecular, Portugal), Miguel Castelo
Branco (Instituto de Ciências Nucleares Aplicadas à Sa’de and Uni-
versity of Coimbra, Portual), Luísa V. Lopes (Instituto de Medicina
Molecular, Portugal).

Addiction to psychoactive substances is a maladaptive learned behavior. Contexts surrounding drug
use integrate this aberrant mnemonic process and hold strong relapse triggering ability. In [21], we
asked where context and salience might be concurrently represented in the brain, and found circuitry
hubs specific to morphine-related contextual information storage. Starting with a classical rodent
morphine-conditioned place preference (CPP) apparatus, we developed a CPP protocol that allows
stimuli presentation inside a magnetic resonance imaging scanner, to allow the investigation of whole
brain activity during retrieval of drug-context paired associations, as well as resting state functional
connectivity under the effect of morphine conditioning. Using fMRI, we found context-specific responses
to stimulus onset in multiple brain regions, namely limbic, sensory, and striatal. Furthermore, we found
increased functional connectivity of lateral septum with regions within and beyond a proposed limbic
network, and of the lateral habenula with hippocampal CA1 region, in response to repeated pairings
of drug and context. Subsequent exposure to either morphine or saline-conditioned contexts led to
significant, context-specific, functional interconnectivity among amygdala, lateral habenula, and lateral
septum. Resting-state connectivity of the lateral habenula and amygdala, and that during saline-paired
context presentation significantly predicted inter-individual CPP score differences. In sum, our findings
show that drug- and saline-paired contexts form distinct memory traces in overlapping functional
brain microcircuits, and intrinsic connectivity of habenula, septum, and amygdala likely influences the
maladaptive contextual learning in response to opioids. We identify functional mechanisms involved in
the acquisition and retrieval of drug-related memories that might be behind the relapse-triggering ability
of opioid-associated sensory/contextual cues.

Project CRONOS

15

7.3 Group Level

Alignment of brain networks

Participants:

Yanis Aeschlimann, Samuel Deslauriers-Gauthier, Théodore Papado-
poulo, Anna Calissano (Inria EPIONE), Xavier Pennec (Inria EPIONE).

Every brain is unique, having its structural and functional organization shaped by both genetic and
environmental factors over the course of its development. Brain image studies tend to produce results
by averaging across a group of subjects, under a common assumption that it is possible to subdivide
the cortex into homogeneous areas while maintaining a correspondence across subjects. This project
questions such assumption: can the structural and functional properties of a specific region of an atlas be
assumed to be the same across subjects? In [27, 11], this question is addressed by looking at the network
representation of the brain, with nodes corresponding to brain regions and edges to their structural
relationships. We perform graph matching on a set of control patients and on parcellations of different
granularity to understand which is the connectivity misalignment between regions. The graph matching
is unsupervised and reveals interesting insight on local misalignment of brain regions across subjects.

Structural connectivity is one view of brain networks provided by diffusion MRI, but these networks
can also be observed from a functional point of view via functional MRI. In [26] and [17], we propose to
simultaneously exploit structural and functional information in the alignment process. This allows us
to explore multiple perspective of brain networks. Our results show the permutations induced by one
type of connectivity (structural, functional) are not always supported by the other connectivity network,
but when considering combined alignment, it is possible to find permutations of regions which are
supported by both connectome modalities, leading to an increased similarity of functional and structural
connectivity across subjects.

7.4 Other Results
Realistic simulation of Electromyogram (EMG) data

Participants:

Samuel Deslauriers-Gauthier, Kostiantyn Maksymenko (Neurodec,
Sophia Antipolis, France), Alexander Kenneth Clarke (Imperial College
London, United Kingdom), Irene Mendez Guerra (Imperial College Lon-
don, United Kingdom), Dario Farina (Imperial College London, United
Kingdom).

In [14], we introduce the concept of a Myoelectric Digital Twin: a highly realistic and fast computa-
tional model tailored for the training of deep learning algorithms. It enables the simulation of arbitrary
large and perfectly annotated datasets of realistic electromyographic signals, allowing new approaches to
muscular signal decoding, accelerating the development of human-machine interfaces.

While the myoelectric digital twin is highly accurate, it is computationally expensive and thus is
generally limited to modeling static systems such as isometrically contracting limbs. As a solution to
this problem, we propose a transfer learning approach, in which a conditional generative model is
trained to mimic the output of an advanced numerical model. To this end, we present BioMime in [22], a
conditional generative neural network trained adversarially to generate motor unit activation potential
waveforms under a wide variety of volume conductor parameters. We demonstrate the ability of such a
model to predictively interpolate between a much smaller number of numerical model’s outputs with a
high accuracy. Consequently, the computational load is dramatically reduced, which allows the rapid
simulation of EMG signals during truly dynamic and naturalistic movements.

Together, the myoelectric digital twin and BioMime provide a fast and accurate simulation of elec-
tromyography. However, the input to these systems is abstract: a percentage of voluntary contraction
per muscle. A more intuitive and natural input would be a movement description, from which muscle
contractions could be extracted. To this end, we propose in [23] NeuroMotion, an open-source simulator
that provides a full-spectrum synthesis of EMG signals during voluntary movements. NeuroMotion is

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Inria Annual Report 2023

comprised of three modules. The first module is an upper-limb musculoskeletal model with OpenSim
API to estimate the muscle fibre lengths and muscle activations during movements. The second module
is BioMime, a deep neural network-based EMG generator that receives nonstationary physiological para-
meter inputs, such as muscle fibre lengths, and efficiently outputs motor unit action potentials (MUAPs).
The third module is a motor unit pool model that transforms the muscle activations into discharge
timings of motor units. The discharge timings are convolved with the output of BioMime to simulate
EMG signals during the movement. NeuroMotion is the first full-spectrum EMG generative model to
simulate human forearm electrophysiology during voluntary hand, wrist, and forearm movements.

Analysis of large size networks of Hopfield neurones

Participants: Olivier Faugeras, Etienne Tanré (LJAD, Nice, France).

We revisit the problem of characterizing the thermodynamic limit of a fully connected network of
Hopfield-like neurons. Our contributions are that we provide a) a complete description of the mean-field
equations as a set of stochastic differential equations depending on a mean and covariance functions, b)
a provably convergent method for estimating these functions, and c) numerical results of this estimation
as well as examples of the resulting dynamics. The mathematical tools are the theory of Large Deviations,
Itô stochastic calculus, and the theory of Volterra equations.

An abstract has been submitted to the 2024 International Conference on Mathematical Neuroscience,

deposited onto HAL and a manuscript is almost ready for submission to a Journal.

Pros and cons of mean field representations of large size networks of spiking neurons

Participants: Olivier Faugeras, Romain Veltz.

We have laid out a roadmap for classifying the behaviors of large ensembles of networks of spiking
neurons through the analysis of the corresponding Nonlinear Fokker-Planck equation. Rather than
using this equation to simulate the network equations, we apply advanced methods for analyzing the
bifurcations of its solutions. This analysis can then be used to predict the behaviors of the original
network. We have used the example of a fully connected network of N Fitzhugh-Nagumo neurons with
electrical and chemical synapses to convey the interest of our approach.

An abstract has been submitted to the 2024 International Conference on Mathematical Neuroscience

and a manuscript is almost ready for submission to a Journal.

Modeling of pain processing in spinal cord

Participants:

Romain Veltz, Emmanuel Deval (IPMC).

In a recent publication [12], we finalized a work concerning the modeling of processing of pain in-
formation by deep projection neurons and more specifically the implication of ASIC1a channels. This
involved experiments in rats with single neuron modeling done at the Institute of Molecular and Cellular
Pharmacology (IPMC).

Project CRONOS

17

Modeling of excitatory synapse in rat hippocampus

Participants:

Romain Veltz, Hélène Marie (IPMC).

In the publication [15], a stochastic model of hippocampal and excitatory synaptic plasticity has been
finalized. It is the current state of the art model for such synapse. More precisely, we provide a multi-
timescale model of hippocampal synaptic plasticity induction that includes electrical dynamics, calcium,
CaMKII and calcineurin, and accurate representation of intrinsic noise sources. Using a single set of
model parameters, we demonstrate the robustness of this plasticity rule by reproducing nine published ex
vivo experiments covering various spike-timing and frequency-dependent plasticity induction protocols,
animal ages, and experimental conditions. This is an on-going collaboration with H. Marie.

8 Bilateral contracts and grants with industry

8.1 Bilateral Grants with Industry

Demagus: BPI Grant April 2022–September 2024

Participants:

Laura Gee,
Théodore Papadopoulo, Julien Wintz.

Éléonore Haupaix-Birgy,

Côme

Le Breton,

This grant has been obtained with the startup Mag4Health (other partners are CNRS and INSERM).
This company develops a new MEG machine working with optically pumped magnetometers (magnetic
sensors), which potentially means lower costs and better measurements. CRONOS is in charge of develop-
ing a real time interface for signal visualization, source reconstruction and epileptic spikes detection. The
initial funding was for 2 years, but an extension of 6 months has been obtained.

9 Partnerships and cooperations

9.1 International initiatives

9.1.1 Inria associate team not involved in an IIL or an international program

MUSCULAR

Participants:

Samuel Deslauriers-Gauthier, Théodore Papadopoulo, Yanis Aeschli-
mann, Igor Carrara, Dario Farina (Imperial College London, United
Kingdom), Shihan Ma (Imperial College London, United Kingdom),
Bruno Grandi Sgambato (Imperial College London, United Kingdom).

Surface electromyography (EMG) is the non-invasive recording of electrical activity produced by
skeletal muscle contractions. Surface electroencephalography (EEG) is the recording of electrical activity
produced by the activity of neural assemblies in the brain. In both modalities, there is a strong interest
in recovering the underlying physiological sources, either the motor unit spike trains or the activity of
cortical neural assemblies, that explain the recordings. In addition, the underlying physics of EMG and
EEG which relates sources to measurements are identical and governed by Maxwell’s equations. Despite
their obvious similarities, the methodological landscapes of EMG and EEG have very little intersection
and there is little bandwidth between the two scientific communities.

Recognizing the need for an increase in exchange and collaboration between the EEG and EMG
communities, we proposed the associated team MUSCULAR between CRONOS and Dario Farina’s lab
at Imperial College. The nature and objective of the MUSCULAR associated team is to increase the
bandwidth between the EEG and EMG communities and promote a mutually beneficial exchange of

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Inria Annual Report 2023

methodology and knowledge. The CRONOS team has a longstanding history in forward modeling and
inverse problem in electroencephalography and magnetoencephalography. The Imperial College London
team has extensive expertise in the processing and analysis of EMG signals for neurorehabilitation and
the control of movements. By collaborating via the MUSCULAR associated team, the two research labs
will rapidly move forward both the EMG and the EEG communities.

Because of our early work on the hyper-realistic simulation of EMG, published in Nature Commu-
nications in March 2023 [14], the associated team was able to move quickly and has proposed two new
methods to model EMG signals. The first contribution is the development of BioMime,conditional gener-
ative neural network trained adversarially to generate motor unit activation potential waveforms [22].
The second contribution is the development of NeuroMotion, an open-source simulator that provides a
full-spectrum synthesis of EMG signals [23]. These contributions are further detailed in section 7.4.

9.2 European initiatives

9.2.1 H2020 projects

HBP SGA3

Participants:

Romain Veltz.

Coordinator Name : Victor Jirsa

Partner Institutions: 117 partner institutions in 19 countries across Europe

Date/Duration: ended in September 2023

Web site

Within the SGA3 component of HBP, we develop mean field models of stochastic and spiking neural
networks with heterogenous connections.

9.3 National initiatives
ANR ChaMaNe, Mathematical Challenges in Neurosciences

Participants:

Romain Veltz.

Coordinator Name : Delphine Salort

Partner Institutions:

• Partner 1: Biologie Computationnelle et Quantitative (CQB), France

• Partner 2: LJAD, Université Nice, France

Date/Duration: 2020-2025

Web site

This project aims at a mathematical study, on the one hand, of the intrinsic dynamics of a neuron and
their consequences, and on the other hand, of the qualitative dynamics of large neural networks with
respect to the intrinsic behavior of the individual neurons, the interactions between them, memory
effects, spatial structure, etc.

19

Project CRONOS

FHU InnovPain 2

Participants:

Théodore Papadopoulo.

Coordinator Name : Denys Fontaine (Pasteur Hospital)

Date/Duration: 2023–2027

Web site

The FHU INOVPAIN is a Hospital-University Federation focused on chronic refractory pain and innovative
therapeutic solutions. It involves 6 hospital facilities, 13 academic research teams and 12 platforms and
core facilities.

9.4 Regional initiatives

Project NeuroKoopman - AAP neuromod GP

Participants:

Samuel Deslauriers-Gauthier, Théodore Papadopoulo, Romain Veltz.

Coordinator Name : Patricia Reynaud-Bouret (UniCA).

Partner Institutions:

• Partner 1: Neuromod

• Partner 2: IIT of Genova

• Partner 3: Ecole Polytechnique Paris

Date/Duration: 2024

This project aims at exploring Koopman’s theory for characterizing dynamical system in the context of
brain data. This grant is obtained to get first results and use them for applying to a bigger one (ANR or
European grant).

Cooperation with clinical partners The team CRONOS also has some long-term cooperations with
several clinical partners:

Awake brain surgery: Institution: Pasteur Hospital in Nice

Collaborators: F. Almairac, P. Isan

Study name: ConnectTC

Using dry electrodes for the P300 speller BCI: Institution: Pasteur Hospital in Nice

Collaborators: M.-H. Soriani, M. Bruno, E. Guichard

Study name: TechIcopa

Neurorehabilitation for epileptic patients: Institution: La Timone Hospital in Marseille

Collaborators: F. Bartolomei, C. Bénar, R. Guex, . . .

Study names: EPIFEED and NFBEPI

10 Dissemination

Participants: Rachid Deriche, Samuel Deslauriers-Gauthier, Olivier Faugeras,

Théodore Papadopoulo, Romain Veltz.

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Inria Annual Report 2023

10.1 Promoting scientific activities

10.1.1 Scientific events: organisation

Member of the conference program committees

• O. Faugeras is a member of the Scientific Committee of the International Conference on Mathemat-

ical Neuroscience, Dublin, June 2024

• O. Faugeras is a member of the Scientific Committee Random processes in the brain: From experi-

mental data to Math and back, IHP, Paris, February-April

Reviewer

• T. Papadopoulo served several international and national conferences (ISBI, GRETSI, CORTICO

days)4.

• S. Deslauriers-Gauthier served several international and national conferences (ISBI, IABM)4 and

an international workshop (MICCAI-CDMRI)4.

• R. Deriche served several international conferences (ISBI, MICCAI)4 and an international workshop

(MICCAI-CDMRI)4.

10.1.2 Journal

Member of the editorial boards

• T. Papadopoulo serves as Associate Editor in “Frontiers: Brain Imaging Methods” and as Review

Editor for “Frontiers: Artificial Intelligence in Radiology”.

• R. Veltz is in the Editorial Board of the journal Mathematical Neuroscience and Applications.

• S. Deslauriers-Gauthier serves as Guest Associate Editor in Frontiers: Brain Imaging Methods and

as Review Editor for Frontiers: Frontiers in Computational Neuroscience.

• R. Deriche is member of the Editorial Boards of the Journal of Neural Engineering and of the Medical
Image Analysis Journal. He is also an editorial board member at Springer for the book series entitled
Computational Imaging and Vision.

• O. Faugeras is the Editor in Chief of the journal Mathematical Neuroscience and Applications.

Reviewer - reviewing activities

• R. Deriche serves several international journals (NeuroImage, IEEE Transactions on Medical Ima-
ging, Magnetic Resonance in Medicine, Medical Image Analysis Journal, Journal of Neural Engin-
eering, . . . ).

• S. Deslauriers-Gauthier served several international journals (Medical Image Analysis, Nature

Machine Intelligence, Network Neuroscience).

• O. Faugeras does reviews for several international Journals including Science, SIAM Journal on
Applied Mathematics, SIAM Journal on Applied Dynamical Systems, Journal of Mathematical
Biology, Journal of Mathematical Neuroscience and Applications.

• T. Papadopoulo served several international journals (Journal of Neural Engineering, Physics &
Medicine in Biology, Inverse Problems, IEEE Transactions on Biomedical Engineering, Frontiers in
Neurosciences, Frontiers in Human Neurosciences, Brain Topography, Computers in Biology and
Medicine, IEEE Transactions on Medical Imaging).

4 ISBI: International Symposium on Biomedical Imaging, GRETSI: Colloque Francophone de Traitement du Signal et des
Images, MICCAI: Medical Image Computing and Computer Assisted Intervention, MICCAI-CDMRI: International Workshop on
Computational Diffusion MRI, CORTICO: COllectif pour la Recherche Transdisciplinaire sur les Interfaces Cerveau-Ordinateur,
IABM: Colloque Français d’Intelligence Artificielle en Imagerie Biomédicale.

Project CRONOS

21

• R. Veltz served several international journals (Chaos, Theory in Biosciences, SIAM for Mathematical

Analysis, Physica D, Nonlinear Dynamics, Kyungpook Mathematical Journal).

10.1.3 Invited talks

• R. Deriche, From Computational Imaging to Brain Connectomics: A Geometrical Perspective, key-
note speech at the Workshop of Informatics Section at Academia Europaea - Munich - Germany -
Oct 2023.

• O. Faugeras, Two examples of thermodynamic limits in neuroscience, One World Dynamics seminar,

Dec 5th, 2023.

• O. Faugeras, Mathematical Neuroscience: A personal perspective, Structural learning by the Brain,

IHP workshop.

• O. Faugeras, Des mathématiques au chevet des neurones et des astrocytes, Semaine du cerveau, Paris.

• O. Faugeras, Two examples of thermodynamic limits in neuroscience, A Random Walk in the Land of

Stochastic Analysis and Numerical Probability, CIRM.

• T. Papadopoulo, Improving BCI classification accuracy using tools from autoregressive models, ISAE-

SUPAERO.

• T. Papadopoulo and I. Carrara, Toward everyday BCI: Augmented Covariance Method in a reduced

dataset setting, 10th International BCI Meeting.

• R. Veltz, Some results concerning a mean field of a network of 2d spiking neurons, Oxford.

• R. Veltz, Theoretical / numerical study of modulated traveling pulses in inhibition stabilized networks,

NFW Paris.

• R. Veltz, Study of a mean field of a network of 2d spiking neurons. One world dynamics seminar.

• R. Veltz, Theoretical study of a mean-field model of two-dimensional nonlinear integrate-and-fire

neurons, ANR Chamane.

• R. Veltz, Theoretical / numerical study of modulated traveling pulses in inhibition stabilized networks,

Workshop: Networks of spiking neurons, IHP Paris.

10.1.4 Leadership within the scientific community

• O. Faugeras is a member of the French Academy of Sciences and of the French Academy of Techno-

logies.

• R. Veltz and J.B. Caillau, organization of a half day conference Julia at Inria, 50 attendees, January

2023.

10.1.5 Scientific expertise

• R. Deriche served several national and international institutions in reviewing applications : 3IA

UniCA Chairs, ANR and ERC Grants.

• T. Papadopoulo served in reviewing applications for the Neuromod institute of Université Côte

d’Azur.

• T. Papadopoulo served in reviewing for several internal programs of Université Côte d’Azur (see

membership in academic council below).

• T. Papadopoulo served as an internal proof-reader for a PEPR proposal.

• T. Papadopoulo served in reviewing a proposal for an INRIA associate team.

• R. Veltz served in reviewing for the PhD grant program in Neuromod.

22

Inria Annual Report 2023

10.1.6 Research administration

• T. Papadopoulo is elected member in the academic council of University of Côte d’Azur (UniCA).

• T. Papadopoulo is the head of the Technological Development Committee of Inria Sophia Antipolis

Méditerranée.

• T. Papadopoulo is a member of the Neuromod scientific council and represents Neuromod in the
EUR Healthy (EUR: Universitary Research School) and in the Maison de la Simulation of UniCA.

10.2 Teaching - Supervision - Juries

10.2.1 Teaching

• Master: T. Papadopoulo, Inverse problems for brain functional imaging, 24 ETD, M2, Mathématiques,

Vision et Apprentissage, ENS Cachan, France.

• Master: T. Papadopoulo and S. Deslauriers-Gauthier Functional Brain Imaging, each 15 ETD,

M1,M2 in the MSc Mod4NeuCog of Université Côte d’Azur.

• Master: T. Papadopoulo and S. Deslauriers-Gauthier, Application of machine learning to MRI,
electophysiology & brain computer interfaces, each 10 ETD, M1,M2 in the MSc Data Science and
Artificial Intelligence of Université Côte d’Azur.

• PSL Graduate Program: T. Papadopoulo, Brain-Computer interfaces, 3 ETD, Advanced Course in

Computational Neuroscience, Ecole Normale Supérieure, Paris, France.

• Master: R. Veltz, Mathematical methods for neuroscience, 24 ETD, M2, Mathématiques, Vision et

Apprentissage, ENS Cachan, France.

• Automn School, EITN Paris, France. R. Veltz has been invited for a lecture on mean fields of neural

networks.

10.2.2 Supervision

• PhD in progress: I. Carrara, "Auto-regressive models for MEG/EEG processing", started in Oct. 2021.

Supervisor: Théodore Papadopoulo.

• PhD in progress: Y. Aeschlimann, "Brain networks from simultaneous modelling of functional MRI
and diffusion MRI", started in Oct. 2022. Supervisors: Samuel Deslauriers-Gauthier, Théodore
Papadopoulo.

• PhD in progress: P. Isan, "Cerebral eletrophysiological exploitation of in vivo evoked potentials
to guide the resection of adult brain tumors", started in Oct. 2023. Supervisor: F. Almairac. Co-
Supervisors: T. Papadopoulo, S. Deslauriers-Gauthier.

• Postdoc ended in December 2023: N. Vattuone "Study subject with the title Dynamics of spiking
neural networks with connectivity represented by random graphs". Student co-supervised by R.
Veltz and E. Tanré (Inria) since December 2021.

• Postdoc: O. Senkevich "Study subject with the title Fluctuations of synaptic connections’ strengths
due to the randomness in synaptic protein counts caused by the stochasticity of gene expression
and protein transport in neurons.", Student co-supervised by R. Veltz and C. O’Donnell (University
of Ulster) since June 2022.

Project CRONOS

10.2.3 Juries

23

• R. Deriche participated in the Ph.D. jury of T. Durantel at University of Rennes on Dec. 15th, 2023.

• T. Papadopoulo participated in the Ph.D. jury of X. XU at University of Toulouse on Jan. 27th, 2023

as a reviewer.

• T. Papadopoulo participated in the Ph.D. jury of V. d. R. Hernández Catañón at Université of

Lorraine on Feb. 8th, 2023.

• T. Papadopoulo participated in the Ph.D. thesis committees of G. Girier and V. Strizhkova for

Université Côte d’Azur.

• T. Papadopoulo and S. Deslauriers-Gauthier participated in the Msc Neuromod first year training

jury, 2023.

• R. Veltz participated in the jury of N. Vadot’s master 2 defense at EPFL on June 2023. N. Vadot was

supervised by Wulfram Gerstner.

• R. Veltz participated in the Ph.D. jury of S. Ebert at Université of Cote d’Azur on Dec. 13th, 2023 as

an examiner.

10.3 Popularization

10.3.1 Articles and contents

• T. Papadopoulo has been interviewed for an article published in the magazine Science&Vie.

10.3.2 Interventions

• R. Veltz participated at "Semaine du numérique" at Terra Numerica in May 2023.

• R. Veltz participated at "Robotique MathC2+" in June 2023.

11 Scientific production

11.1 Major publications

[1] B. Belaoucha and T. Papadopoulo. ‘Structural connectivity to reconstruct brain activation and
effective connectivity between brain regions’. In: Journal of Neural Engineering 17.3 (1st June 2020),
p. 035006. DOI: 10.1088/1741-2552/ab8b2b. URL: https://inria.hal.science/hal-02945
585.

[2] C. Bénar, T. Papadopoulo, B. Torrésani and M. Clerc. ‘Consensus Matching Pursuit for multi-trial
EEG signals’. In: Journal of Neuroscience Methods 180.1 (May 2009), pp. 161–170. DOI: 10.1016/j
.jneumeth.2009.03.005. URL: https://inria.hal.science/hal-04391937.

[3] S. Deslauriers-Gauthier, J.-M. Lina, R. Butler, K. Whittingstall, P.-M. Bernier, R. Deriche and M.
Descoteaux. ‘White Matter Information Flow Mapping from Diffusion MRI and EEG’. In: NeuroIm-
age (15th July 2019). DOI: 10.1016/j.neuroimage.2019.116017. URL: https://inria.hal.sc
ience/hal-02187859.

[4] S. Deslauriers-Gauthier, M. Zucchelli, M. Frigo and R. Deriche. ‘A Unified Framework for Mul-
timodal Structure-function Mapping Based on Eigenmodes’. In: Medical Image Analysis (20th Aug.
2020), p. 22. DOI: 10.1016/j.media.2020.101799. URL: https://inria.hal.science/hal-0
2925913.

[5] S. Hitziger, M. Clerc, S. Saillet, C. Bénar and T. Papadopoulo. ‘Adaptive Waveform Learning: A
Framework for Modeling Variability in Neurophysiological Signals’. In: IEEE Transactions on Signal
Processing 65 (15th Aug. 2017), pp. 4324–4338. DOI: 10.1109/TSP.2017.2698415. URL: https:
//inria.hal.science/hal-01548428.

24

[6]

Inria Annual Report 2023

J. Kybic, M. Clerc, T. Abboud, O. Faugeras, R. Keriven and T. Papadopoulo. ‘A common formalism for
the Integral formulations of the forward EEG problem’. In: IEEE Transactions on Medical Imaging
24.1 (Jan. 2005), pp. 12–28. DOI: 10.1109/tmi.2004.837363. URL: https://inria.hal.scienc
e/hal-04389249.

[7] K. Maksymenko, A. K. Clarke, I. Mendez Guerra, S. Deslauriers-Gauthier and D. Farina. ‘A Myoelec-
tric Digital Twin for Fast and Realistic Modelling in Deep Learning’. In: Nature Communications
14.1 (23rd Mar. 2023), p. 1600. DOI: 10.1038/s41467-023-37238-w. URL: https://inria.hal
.science/hal-04390364.

11.2 Publications of the year

International journals

[8] F. Almairac, P. Isan, M. Onno, T. Papadopoulo, L. Mondot, S. Chanalet, C. Fernandez, M. Clerc,
R. Deriche, D. Fontaine and P. Filipiak. ‘Identifying subcortical connectivity during brain tumor
surgery: a multimodal study’. In: Brain Structure and Function 228.3-4 (25th Feb. 2023), pp. 815–830.
DOI: 10.1007/s00429-023-02623-0. URL: https://inria.hal.science/hal-04391976.

[9] F. Almairac, D. Parker, L. Mondot, P. Isan, M. Onno, T. Papadopoulo, P. Filipiak, D. Fontaine and
R. Verma. ‘Free-water correction DTI-based tractography in brain tumor surgery: assessment with
functional and electrophysiological mapping of the white matter’. In: Acta Neurochirurgica 165.6
(2nd May 2023), pp. 1675–1681. DOI: 10.1007/s00701-023-05608-4. URL: https://inria.hal
.science/hal-04391965.

[10]

J. Belo, M. Clerc and D. Schön. ‘The effect of familiarity on neural tracking of music stimuli is
modulated by mind wandering’. In: AIMS Neuroscience 10.4 (2023), pp. 319–331. DOI: 10.3934/Ne
uroscience.2023025. URL: https://inria.hal.science/hal-04357054.

[11] A. Calissano, T. Papadopoulo, X. Pennec and S. Deslauriers-Gauthier. ‘Graph Alignment Exploiting
the Spatial Organisation Improves the Similarity of Brain Networks’. In: Human Brain Mapping
(28th Dec. 2023). DOI: 10.1002/hbm.26554. URL: https://inria.hal.science/hal-0391076
1.

[12] M. Chafaï, A. Delrocq, P. Inquimbert, L. Pidoux, K. Delanoe, M. Toft, F. Brau, E. Lingueglia, R. Veltz
and E. Deval. ‘Dual contribution of ASIC1a channels in the spinal processing of pain information
by deep projection neurons revealed by computational modeling’. In: PLoS Computational Biology
19.4 (17th Apr. 2023), e1010993. DOI: 10.1371/journal.pcbi.1010993. URL: https://hal.sci
ence/hal-04077155.

[13] G. Girard, J. Rafael-Patiño, R. Truffet, D. B. Aydogan, N. Adluru, V. A. Nair, V. Prabhakaran, B. B.
Bendlin, A. L. Alexander, S. Bosticardo et al. ‘Tractography passes the test: Results from the diffusion-
simulated connectivity (disco) challenge’. In: NeuroImage 277 (16th June 2023). DOI: 10.1016/j.n
euroimage.2023.120231. URL: https://inria.hal.science/hal-04390592.

[14] K. Maksymenko, A. K. Clarke, I. Mendez Guerra, S. Deslauriers-Gauthier and D. Farina. ‘A Myoelec-
tric Digital Twin for Fast and Realistic Modelling in Deep Learning’. In: Nature Communications
14.1 (23rd Mar. 2023), p. 1600. DOI: 10.1038/s41467-023-37238-w. URL: https://inria.hal
.science/hal-04390364.

[15] Y. E. Rodrigues, C. Tigaret, H. Marie, C. O’Donnell and R. Veltz. ‘A stochastic model of hippocampal
synaptic plasticity with geometrical readout of enzyme dynamics’. In: eLife 12 (17th Aug. 2023).
DOI: 10.7554/eLife.80152. URL: https://hal.science/hal-04275554.

International peer-reviewed conferences

[16] A. Rossi, S. Deslauriers-Gauthier and E. Natale. ‘Temporal Hyperbolic Graphs as Null Models for
Brain Dynamics’. In: Temporal Hyperbolic Graphs as Null Models for Brain Dynamics. The 12th
International Conference on Complex Networks and their Applications - CNA 2023. Menton, France,
28th Nov. 2023. URL: https://hal.science/hal-04343066.

Project CRONOS

Reports & preprints

25

[17] Y. Aeschlimann, A. Calissano, A. Abildtrup Hansen, T. Papadopoulo and S. Deslauriers-Gauthier.
GRAPH MATCHING OF STRUCTURAL AND FUNCTIONAL BRAIN NETWORKS. 11th Jan. 2024. URL:
https://hal.science/hal-04387986.

[18]

[19]

I. Carrara and T. Papadopoulo. Classification of BCI-EEG based on augmented covariance matrix.
2023. URL: https://hal.science/hal-03977680.

I. Carrara and T. Papadopoulo. Pseudo-online framework for BCI evaluation : a MOABB perspective.
2023. DOI: 10.1088/1741-2552/ad171a. URL: https://hal.science/hal-04182027.

[20] O. Faugeras and E. Tanré. A new twist on the large size limit behaviour of networks of Hopfield-like

neurons. 12th Jan. 2024. URL: https://hal.science/hal-04391216.

[21]

J. Gomes-Ribeiro, J. Martins, J. Sereno, S. Deslauriers-Gauthier, T. Summavielle, J. E. Coelho, M.
Remondes, M. C. Branco and L. V. Lopes. Mapping functional traces of opioid memories in the rat
brain. 8th Aug. 2023. DOI: 10.1101/2023.08.07.552221. URL: https://inria.hal.science
/hal-04389077.

[22] S. Ma, A. K. Clarke, K. Maksymenko, S. Deslauriers-Gauthier, X. Sheng, X. Zhu and D. Farina.
Conditional Generative Models for Simulation of EMG During Naturalistic Movements. 12th Jan.
2024. URL: https://inria.hal.science/hal-04390148.

[23] S. Ma, I. M. Guerra, A. H. Caillet, J. Zhao, A. K. Clarke, K. Maksymenko, S. Deslauriers-Gauthier,
X. Sheng, X. Zhu and D. Farina. NeuroMotion: Open-source Simulator with Neuromechanical and
Deep Network Models to Generate Surface EMG signals during Voluntary Movement. 9th Oct. 2023.
DOI: 10.1101/2023.10.05.560588. URL: https://inria.hal.science/hal-04390169.

[24] A. Rossi, S. Deslauriers-Gauthier and E. Natale. On null models for temporal small-worldness in

brain dynamics. 11th Jan. 2024. URL: https://hal.science/hal-04389639.

Other scientific publications

[25] A. Abildtrup Hansen, Y. Aeschlimann, S. Deslauriers-Gauthier and A. Calissano. ‘Permutation
equivariant structure-function mapping’. In: Organization for Human Brain Mapping 2023. Montreal
(Canada), Canada, 22nd July 2023. URL: https://hal.science/hal-04390750.

[26] Y. Aeschlimann, A. Calissano, S. Deslauriers-Gauthier, T. Papadopoulo and A. Hansen. ‘Preliminary
results on the graph matching of structural and functional brain networks’. In: Neuromod Yearly
Meeting 2023. Antibes, France, 28th June 2023. URL: https://inria.hal.science/hal-041652
09.

[27] A. Calissano, T. Papadopoulo, X. Pennec and S. Deslauriers-Gauthier. ‘Graph Matching improves the
Similarity of Structural Brain Networks’. In: OHBM 2023 - Organization for Human Brain Mapping.
Montreal (Canada), Canada, 22nd July 2023. URL: https://hal.science/hal-04390489.

[28]

[29]

[30]

[31]

I. Carrara, B. Aristimunha, S. Chevallier, M.-C. Corsi, T. Papadopoulo and M.-C. Corsi. ‘Holographic
EEG: multi-view deep learning for BCI’. In: Journée CORTICO 2023 - COllectif pour la Recherche
Transdisciplinaire sur les Interfaces Cerveau-Ordinateur. Paris, France, 9th May 2023. URL: https:
//hal.science/hal-04095900.

I. Carrara, B. Aristimunha, M.-C. Corsi, R. Y. D. Camargo, S. Chevallier and T. Papadopoulo. ‘Augmen-
ted SPDNet: Second-Order Neural Network for Motor Imagery-Based BCI’. In: Soph.IA summit 2023.
Sophia Antipolis, France, 22nd Nov. 2023. URL: https://inria.hal.science/hal-04308549.

I. Carrara and T. Papadopoulo. ‘Pseudo Online Framework’. In: BCI Society Meeting 2023. Bruxelles
(BE), Belgium, 6th June 2023. URL: https://hal.science/hal-04128689.

I. Carrara and T. Papadopoulo. ‘Toward everyday BCI: Augmented Covariance Method in a reduced
dataset settings’. In: Neuromod Meeting 2023. Antibes, France, 28th June 2023. URL: https://hal
.science/hal-04161475.

[32] A. Rossi, S. Deslauriers-Gauthier and E. Natale. Temporal Brain Networks Database. 2nd Mar. 2023.

DOI: 10.57745/PR8VUV. URL: https://hal.science/hal-04011895.

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Inria Annual Report 2023

[33] A. Rossi, E. Natale and S. Deslauriers-Gauthier. ‘Temporal Brain Networks Dataset’. In: NeuroMod

meeting 2023. Antibes, France, 28th June 2023. URL: https://hal.science/hal-04130380.

11.3 Cited publications

[34] B. Belaoucha and T. Papadopoulo. ‘Structural connectivity to reconstruct brain activation and
effective connectivity between brain regions’. In: Journal of Neural Engineering 17.3 (June 2020),
p. 035006. DOI: 10.1088/1741-2552/ab8b2b. URL: https://hal.inria.fr/hal-02945585.

[35]

S. Blanchard, T. Papadopoulo, C. Bénar, N. Voges, M. Clerc, H. Benali, J. Warnking, O. David and F.
Wendling. ‘Relationship Between Flow and Metabolism in BOLD Signals: Insights from Biophysical
Models’. In: Brain Topography 24.1 (2011), pp. 40–53. DOI: 10.1007/s10548-010-0166-6. URL:
http://dx.doi.org/10.1007/s10548-010-0166-6.

[36] A. Chattopadhyay, A. Sarkar, P. Howlader and V. N. Balasubramanian. ‘Grad-CAM++: Generalized
Gradient-Based Visual Explanations for Deep Convolutional Networks’. In: 2018 IEEE Winter
Conference on Applications of Computer Vision (WACV) (2017), pp. 839–847. URL: https://api.s
emanticscholar.org/CorpusID:13678776.

[37] T. Dupré la Tour, T. Moreau, M. Jas and A. Gramfort. ‘Multivariate Convolutional Sparse Coding
for Electromagnetic Brain Signals’. In: Advances in Neural Information Processing Systems. Ed. by
S. Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa-Bianchi and R. Garnett. Vol. 31. Curran
Associates, Inc., 2018. URL: https://proceedings.neurips.cc/paper/2018/file/64f1f27b
f1b4ec22924fd0acb550c235-Paper.pdf.

[38] S. Hitziger, M. Clerc, S. Saillet, C. Bénar and T. Papadopoulo. ‘Adaptive Waveform Learning: A
Framework for Modeling Variability in Neurophysiological Signals’. In: IEEE Transactions on Signal
Processing 65.16 (Apr. 2017), pp. 4324–4338. DOI: 10.1109/TSP.2017.2698415. URL: http://dx
.doi.org/10.1109/TSP.2017.2698415.

[39] V. Jayaram and A. Barachant. ‘MOABB: trustworthy algorithm benchmarking for BCIs’. In: Journal

of neural engineering 15.6 (2018), p. 066011.

[40]

[41]

[42]

[43]

I. Kojˇci´c, T. Papadopoulo, R. Deriche and S. Deslauriers-Gauthier. ‘Connectivity-informed M/EEG
inverse problem’. In: GRAIL 2020 - MICCAI Workshop on GRaphs in biomedicAl Image anaLysis.
Lima, Peru, Oct. 2020. URL: https://hal.inria.fr/hal-02986430.

I. Kojˇci´c, T. Papadopoulo, R. Deriche and S. Deslauriers-Gauthier. ‘Incorporating transmission
delays supported by diffusion MRI in MEG source reconstruction’. In: ISBI 2021 - IEEE International
Symposium on Biomedical Imaging. Nice, France, Apr. 2021. URL: https://hal.inria.fr/hal-
03143148.

J. T. Lindgren. ‘As above, so below? Towards understanding inverse models in BCI’. In: Journal of
Neural Engineering 15.1 (Dec. 2017).

J. C. Mosher and R. M. Leahy. ‘Source localization using recursively applied and projected (RAP)
MUSIC’. In: IEEE Transactions on Signal Processing 47.2 (Feb. 1988), pp. 332–340. DOI: 10.1109/78
.740118.

[44] C. Nichkawde. ‘Optimal state-space reconstruction using derivatives on projected manifold’. In:

Physical Review E 87.2 (2013), p. 022905.

[45] F. Takens. ‘Detecting strange attractors in turbulence’. In: Dynamical systems and turbulence,

Warwick 1980. Springer, 1981, pp. 366–381.
<scratchpad>
- Main topic: CRONOS project, focusing on computational modeling of brain dynamics
- Key points:
  - Develop models, algorithms, and software to estimate, understand, and quantify brain dynamics
  - Three levels of complexity: source, sensor, and group
  - Sensor level: extracting information from sensor data without considering brain anatomy
  - Source level: integrating sensor data into a unified, high-dimensional spatio-temporal space
  - Group level: constraining the search space of the two previous levels
  - Applications: clinical applications (e.g., epilepsy, brain cancer surgery), brain-computer interfaces
- Structure: The document is organized into sections, including activity report, project-team, overall objectives, research program, application domains, and more
- Potential artifacts to ignore: web-related elements, such as links, HTML tags, and unnecessary text
</scratchpad>

After analyzing the document, I have identified the following key points:

- The CRONOS project aims to develop models, algorithms, and software to estimate, understand, and quantify brain dynamics.
- The project focuses on three levels of complexity: source, sensor, and group.
- The sensor level involves extracting information from sensor data without considering brain anatomy.
- The source level integrates sensor data into a unified, high-dimensional spatio-temporal space.
- The group level constrains the search space of the two previous levels.
- The project has various applications, including clinical applications and brain-computer interfaces.

<final_summary>
The CRONOS project is an interdisciplinary research initiative focused on computational modeling of brain dynamics. The project aims to develop models, algorithms, and software to estimate, understand, and quantify brain dynamics, with a focus on three levels of complexity: source, sensor, and group. The sensor level involves extracting information from sensor data without considering brain anatomy, while the source level integrates sensor data into a unified, high-dimensional spatio-temporal space. The group level constrains the search space of the two previous levels. The project has various applications, including clinical applications and brain-computer interfaces, and is organized into sections covering activity report, project-team, overall objectives, research program, and more.
The CRONOS project is an interdisciplinary research initiative focused on computational modeling of brain dynamics. The project aims to develop models, algorithms, and software to estimate, understand, and quantify brain dynamics, with a focus on three levels of complexity: source, sensor, and group. The sensor level involves extracting information from sensor data without considering brain anatomy, while the source level integrates sensor data into a unified, high-dimensional spatio-temporal space. The group level constrains the search space of the two previous levels. The project has various applications, including clinical applications and brain-computer interfaces, and is organized into sections covering activity report, project-team, overall objectives, research program, and more.