7.1.1 Bump attractors and waves in networks of leaky integrate-and-fire neurons

Participant: Daniele Avitabile [VU Amsterdam and external collaborator of MathNeuro], Joshua Davis [University of Nottingham, UK], Kyle Wedgwood [University of Exeter, UK].

This work was partially carried out during an invitation of Daniele Avitabile within the MathNeuro team.

Bump attractors are wandering localised patterns observed in in vivo experiments of spatially-extended neurobiological networks. They are important for the brain's navigational system and specific memory tasks. A bump attractor is characterised by a core in which neurons fire frequently, while those away from the core do not fire. We uncover a relationship between bump attractors and travelling waves in a classical network of excitable, leaky integrate-and-fire neurons. This relationship bears strong similarities to the one between complex spatiotemporal patterns and waves at the onset of pipe turbulence. Waves in the spiking network are determined by a firing set, that is, the collection of times at which neurons reach a threshold and fire as the wave propagates. We define and study analytical properties of the voltage mapping, an operator transforming a solution's firing set into its spatiotemporal profile. This operator allows us to construct localised travelling waves with an arbitrary number of spikes at the core, and to study their linear stability. A homogeneous "laminar" state exists in the network, and it is linearly stable for all values of the principal control parameter. Sufficiently wide disturbances to the homogeneous state elicit the bump attractor. We show that one can construct waves with a seemingly arbitrary number of spikes at the core; the higher the number of spikes, the slower the wave, and the more its profile resembles a stationary bump. As in the fluid-dynamical analogy, such waves coexist with the homogeneous state, are unstable, and the solution branches to which they belong are disconnected from the laminar state; we provide evidence that the dynamics of the bump attractor displays echoes of the unstable waves, which form its building blocks.

This work has been accepted for publication in SIAM Review and is available as 19.

7.2.1 Network torus canards and their mean-field limits

Participants: Emre Baspinar [Institut des Neurosciences Paris-Saclay, MathNeuro], Daniele Avitabile [VU Amsterdam and external collaborator of MathNeuro], Mathieu Desroches.

This work was partially achieved during a stay of Daniele Avitabile in MathNeuro.

We show that during the transition from and to elliptic burstings both classical and mixed-type torus canards appear in a Wilson-Cowan type neuronal network model, as well as in its corresponding mean-field framework. We show numerically the overlap between the network and mean-field dynamics. We comment on that mixed-type torus canards result from the nonsymmetric fast subsystem. This nonsymmetricity provides the dynamics linked to an associated canonical form presented in  38, and it occurs mainly due to the three-timescale nature of the Wilson-Cowan type models.

This work is available as 34.

7.2.2 Cross-scale excitability in networks of quadratic integrate-and-fire neurons

Participants: Daniele Avitabile [VU Amsterdam and external collaborator of MathNeuro], Mathieu Desroches, G. Bard Ermentrout [University of Pittsburgh, USA].

This work was partially carried out during an invitation of Daniele Avitabile within the MathNeuro team.

From the action potentials of neurons and cardiac cells to the amplification of calcium signals in oocytes, excitability is a hallmark of many biological signalling processes. In recent years, excitability in single cells has been related to multiple-timescale dynamics through canards, special solutions which determine the effective thresholds of the all-or-none responses. However, the emergence of excitability in large populations remains an open problem. We show that the mechanism of excitability in large networks and mean-field descriptions of coupled quadratic integrate-and-fire (QIF) cells mirrors that of the individual components. We initially exploit the Ott-Antonsen ansatz to derive low-dimensional dynamics for the coupled network and use it to describe the structure of canards via slow periodic forcing. We demonstrate that the thresholds for onset and offset of population firing can be found in the same way as those of the single cell. We combine theoretical analysis and numerical computations to develop a novel and comprehensive framework for excitability in large populations, applicable not only to models amenable to Ott-Antonsen reduction, but also to networks without a closed-form mean-field limit, in particular sparse networks.

This work has been published in PLoS Computational Biology and is available as 20.

7.2.3 Bursting in a next generation neural mass model with synaptic dynamics: a slow-fast approach

Participants: Halgurd Taher, Mathieu Desroches, Daniele Avitabile [VU Amsterdam and external collaborator of MathNeuro].

This work was partially achieved during a stay of Daniele Avitabile in MathNeuro.

We report a detailed analysis on the emergence of bursting in a recently developed neural mass model that takes short-term synaptic plasticity into account. The one being used here is particularly important, as it represents an exact meanfield limit of synaptically coupled quadratic integrate & fire neurons, a canonical model for type I excitability. In absence of synaptic dynamics, a periodic external current with a slow frequency $\epsilon$ can lead to burst-like dynamics. The firing patterns can be understood using techniques of singular perturbation theory, specifically slow-fast dissection. In the model with synaptic dynamics the separation of timescales leads to a variety of slow-fast phenomena and their role for bursting is rendered inordinately more intricate. Canards are one of the main slow-fast elements on the route to bursting. They describe trajectories evolving nearby otherwise repelling locally invariant sets of the system and are found in the transition region from subthreshold dynamics to bursting. For values of the timescale separation nearby the singular limit $\epsilon =0$, we report peculiar jump-on canards, which block a continuous transition to bursting. In the biologically more plausible regime of $\epsilon$ this transition becomes continuous and bursts emerge via consecutive spike-adding transitions. The onset of bursting is of complex nature and involves mixed-type like torus canards, which form the very first spikes of the burst and revolve nearby fast-subsystem repelling limit cycles. We provide numerical evidence for the same mechanisms to be responsible for the emergence of bursting in the quadratic integrate & fire network with plastic synapses. The main conclusions apply for the network, owing to the exactness of the meanfield limit.

This work was published in Nonlinear Dynamics and is available as 32.

7.3.1 Projection methods for Neural Field equations

Participants: Daniele Avitabile [VU Amsterdam and external collaborator of MathNeuro].

This work was partially carried out during an invitation of the author within the MathNeuro team.

We propose a numerical analysis framework for the study of the numerical approximation of nonlinear integro-differential equations for the evolution of neuronal activity. Neural fields are often simulated heuristically and, in spite of their popularity in mathematical neuroscience, their numerical analysis is not yet fully established. We introduce generic projection methods for neural fields, and derive a priori error bounds for these schemes. We extend an existing framework for stationary integral equations to the time-dependent case, which is relevant for neuroscience applications. We find that the convergence rate of a projection scheme for a neural field is determined to a great extent by the convergence rate of the projection operator. This abstract analysis, which unifies the treatment of collocation and Galerkin schemes, is carried out in operator form, without resorting to quadrature rules for the integral term, which are introduced only at a later stage, and whose choice is enslaved by the choice of the projector.

This work has been accepted for publication in SIAM Journal on Numerical Analysis and is available as 21.

7.4.1 Classification of bursting patterns: A tale of two ducks

Participants: Mathieu Desroches, John Rinzel [Courant Institute of Mathematical Sciences and Center for Neural Science, New York University, New York, USA], Serafim Rodrigues [BCAM, Bilbao, and external collaborator of MathNeuro].

This work has been partially done during a stay of Serafim Rodrigues in MathNeuro.

Bursting is one of the fundamental rhythms that excitable cells can generate either in response to incoming stimuli or intrinsically. It has been a topic of intense research in computational biology for several decades. The classification of bursting oscillations in excitable systems has been the subject of active research since the early 1980s and is still ongoing. As a by-product, it establishes analytical and numerical foundations for studying complex temporal behaviors in multiple timescale models of cellular activity. In this review, we first present the seminal works of Rinzel and Izhikevich in classifying bursting patterns of excitable systems. We recall a complementary mathematical classification approach by Bertram and colleagues, and then by Golubitsky and colleagues, which, together with the Rinzel-Izhikevich proposals, provide the state-of-the-art foundations to these classifications. Beyond classical approaches, we review a recent bursting example that falls outside the previous classification systems. Generalizing this example leads us to propose an extended classification, which requires the analysis of both fast and slow subsystems of an underlying slow-fast model and allows the dissection of a larger class of bursters. Namely, we provide a general framework for bursting systems with both subthreshold and superthreshold oscillations. A new class of bursters with at least 2 slow variables is then added, which we denote folded-node bursters , to convey the idea that the bursts are initiated or annihilated via a folded-node singularity. Key to this mechanism are so-called canard or duck orbits, organizing the underpinning excitability structure. We describe the 2 main families of folded-node bursters, depending upon the phase (active/spiking or silent/nonspiking) of the bursting cycle during which folded-node dynamics occurs. We classify both families and give examples of minimal systems displaying these novel bursting patterns. Finally, we provide a biophysical example by reinterpreting a generic conductance-based episodic burster as a folded-node burster, showing that the associated framework can explain its subthreshold oscillations over a larger parameter region than the fast subsystem approach.

This work has been published in PLoS Computational Biology and is available as 23.

7.4.2 Multiple-timescale dynamics, mixed mode oscillations and mixed affective states in a model of Bipolar Disorder

Participants: Efstathios Pavlidis [Neuromod Institute, UCA and Inria MathNeuro], Fabien Campillo, Albert Goldbeter [Free University Brussels, Belgium], Mathieu Desroches.

Mixed affective states in bipolar disorder (BD) is a common psychiatric condition that occurs when symptoms of the two opposite poles coexist during an episode of mania or depression. A four-dimensional model by A. Goldbeter [27, 28] rests upon the notion that manic and depressive symptoms are produced by two competing and auto-inhibited neural networks. Some of the rich dynamics that this model can produce, include complex rhythms formed by both small-amplitude (subthreshold) and large-amplitude (suprathreshold) oscillations and could correspond to mixed bipolar states. These rhythms are commonly referred to as mixed mode oscillations (MMOs) and they have already been studied in many different contexts [7, 50]. In order to accurately explain these dynamics one has to apply a mathematical apparatus that makes full use of the timescale separation between variables. Here we apply the framework of multiple-timescale dynamics to the model of BD in order to understand the mathematical mechanisms underpinning the observed dynamics of changing mood. We show that the observed complex oscillations can be understood as MMOs due to a so-called folded-node singularity. Moreover, we explore the bifurcation structure of the system and we provide possible biological interpretations of our findings. Finally, we show the robustness of the MMOs regime to stochastic noise and we propose a minimal three- dimensional model which, with the addition of noise, exhibits similar yet purely noise-driven dynamics. The broader significance of this work is to introduce mathematical tools that could be used to analyse and potentially control future, more biologically grounded models of BD.

This work was published in Cognitive Neurodynamics and is available as 29.

7.4.3 Slow passage through a Hopf-like bifurcation in piecewise linear systems: Application to elliptic bursting

Participant: Jordi Penalva Vadell [University of the Balearic Islands, Spain], Mathieu Desroches, Antonio E. Teruel [University of the Balearic Islands, Spain], Catalina Vich [University of the Balearic Islands, Spain].

The phenomenon of slow passage through a Hopf bifurcation is ubiquitous in multiple-timescale dynamical systems, where a slowly varying quantity replacing a static parameter induces the solutions of the resulting slow–fast system to feel the effect of the Hopf bifurcation with a delay. This phenomenon is well understood in the context of smooth slow–fast dynamical systems; in the present work, we study it for the first time in piecewise linear (PWL) slow–fast systems. This special class of systems is indeed known to reproduce all features of their smooth counterpart while being more amenable to quantitative analysis and offering some level of simplification, in particular, through the existence of canonical (linear) slow manifolds. We provide conditions for a PWL slow–fast system to exhibit a slow passage through a Hopf-like bifurcation, in link with possible connections between canonical attracting and repelling slow manifolds. In doing so, we fully describe the so-called way-in/way-out function. Finally, we investigate this slow passage effect in the Doi–Kumagai model, a neuronal PWL model exhibiting elliptic bursting oscillations.

This work was published in Chaos and is available as 30.

7.4.4 A Generalization of Lanchester's Model of Warfare

Participant: Nicolò Cangiotti [Polytechnic University of Milan, Italy], Marco Capolli [Polish Academy of Sciences, Poland], Mattia Sensi.

The classical Lanchester's model is shortly reviewed and analysed, with particular attention to the critical issues that intrinsically arise from the mathematical formalization of the problem. We then generalize a particular version of such a model describing the dynamics of warfare when three or more armies are involved in the conflict. Several numerical simulations are provided.

This work has been submitted for publication and is available as 35.

7.4.5 Entry-exit functions in fast-slow systems with intersecting eigenvalues

Participant: Panagiotis Kaklamanos [Maxwell Institute for Mathematical Sciences, University of Edinburgh, UK], Christian Kuehn [TU Munich, Germany], Nikola Popović [Maxwell Institute for Mathematical Sciences, University of Edinburgh, UK], Mattia Sensi.

We study delayed loss of stability in a class of fast-slow systems with two fast variables and one slow one, where the linearization of the fast vector field along a one-dimensional critical manifold has two real eigenvalues which intersect before the accumulated contraction and expansion are balanced along any individual eigendirection. That interplay between eigenvalues and eigendirections renders the use of known entry-exit relations unsuitable for calculating the point at which trajectories exit neighborhoods of the given manifold. We illustrate the various qualitative scenarios that are possible in the class of systems considered here, and we propose novel formulae for the entry-exit functions that underlie the phenomenon of delayed loss of stability therein.

This work has been submitted for publication and is available as 36.

7.5.1 A phenomenological model for interfacial water near hydrophilic polymers

Participants: Ashley Earls [BCAM, Bilbao, Spain], Maria-Carme Calderer [University of Minnesota, USA], Mathieu Desroches, Arghir Zarnescu [BCAM, Bilbao, Spain], Serafim Rodrigues [BCAM, Bilbao, and external collaborator of MathNeuro].

This work was partially done during a stay of Serafim Rodrigues in MathNeuro.

We propose a minimalist phenomenological model for the 'interfacial water' phenomenon that occurs near hydrophilic polymeric surfaces. We achieve this by combining a Ginzburg–Landau approach with Maxwell's equations which leads us to a well-posed model providing a macroscopic interpretation of experimental observations. From the derived governing equations, we estimate the unknown parameters using experimental measurements from the literature. The resulting profiles of the polarization and electric potential show exponential decay near the surface, in qualitative agreement with experiments. Furthermore, the model's quantitative prediction of the electric potential at the hydrophilic surface is in excellent agreement with experiments. The proposed model is a first step towards a more complete parsimonious macroscopic model that will, for example, help to elucidate the effects of interfacial water on cells (e.g. neuronal excitability, the effects of infrared neural stimulation or the effects of drugs mediated by interfacial water.

This work was published in Journal of Physics: Condensed Matter and is available as 24.

7.6.1 Dynamic branching in a neural network model for probabilistic prediction of sequences

Participant: Elif Köksal Ersöz [LTSI, Inserm, Rennes], Pascal Chossat, Martin Krupa [LJAD, UCA and Inria MathNeuro], Frédéric Lavigne [BCL, UCA].

An important function of the brain is to predict which stimulus is likely to occur based on the perceived cues. The present research studied the branching behavior of a computational network model of populations of excitatory and inhibitory neurons, both analytically and through simulations. Results show how synaptic efficacy, retroactive inhibition and short-term synaptic depression determine the dynamics of selection between different branches predicting sequences of stimuli of different probabilities. Further results show that changes in the probability of the different predictions depend on variations of neuronal gain. Such variations allow the network to optimize the probability of its predictions to changing probabilities of the sequences without changing synaptic efficacy.

This work was published in Journal of Computational Neuroscience and is available as 28.

7.7.1 Spatial and color hallucinations in a mathematical model of primary visual cortex

Participant: Olivier Faugeras.

In collaboration with Anna Song (Imperial College London, The Francis Crick Institute) and Romain Veltz (on secondment to Inria).

We study a simplified model of the representation of colors in the primate primary cortical visual area V1. The model is described by an initial value problem related to a Hammerstein equation. The solutions to this problem represent the variation of the activity of populations of neurons in V1 as a function of space and color. The two space variables describe the spatial extent of the cortex while the two color variables describe the hue and the saturation represented at every location in the cortex. We prove the well-posedness of the initial value problem. We focus on its stationary and periodic in space solutions. We show that the model equation is equivariant with respect to the direct product G of the group of the Euclidean transformations of the planar lattice determined by the spatial periodicity and the group of color transformations, isomorphic to O(2), and study the equivariant bifurcations of its stationary solutions when some parameters in the model vary. Their variations may be caused by the consumption of drugs and the bifurcated solutions may represent visual hallucinations in space and color. Some of the bifurcated solutions can be determined by applying the Equivariant Branching Lemma (EBL) by determining the axial subgroups of G. These define bifurcated solutions which are invariant under the action of the corresponding axial subgroup. We compute analytically these solutions and illustrate them as color images. Using advanced methods of numerical bifurcation analysis we then explore the persistence and stability of these solutions when varying some parameters in the model. We conjecture that we can rely on the EBL to predict the existence of patterns that survive in large parameter domains but not to predict their stability. On our way we discover the existence of spatially localized stable patterns through the phenomenon of "snaking".

This work has been published in Compte Rendus Mathématique and is available as 25.

7.7.2 Geometry of spiking patterns in early visual cortex: a topological data analytic approach

Participants: Andrea Guidolin [BCAM, Bilbao, and KTH, Sweden], Mathieu Desroches, Jonathan Victor [Feil Family Brain and Mind Research Institute, Weill Cornell Medical College, New York, USA], Keith Purpura [Feil Family Brain and Mind Research Institute, Weill Cornell Medical College, New York, USA], Serafim Rodrigues [BCAM Bilbao and external collaborator of MathNeuro].

This work was partially achieved during a stay of Serafim Rodrigues in MathNeuro.

In the brain, spiking patterns live in a high-dimensional space of neurons and time. Thus, determining the intrinsic structure of this space presents a theoretical and experimental challenge. To address it, we introduce a new framework for applying topological data analysis (TDA) to spike train data and use it to determine the geometry of spiking patterns in the visual cortex. Key to our approach is a parametrized family of distances based on the timing of spikes that quantifies the dissimilarity between neuronal responses. We applied TDA to visually driven single-unit and multiple single-unit spiking activity in macaque V1 and V2. TDA across timescales reveals a common geometry for spiking patterns in V1 and V2 which, among simple models, is most similar to that of a low-dimensional space endowed with Euclidean or hyperbolic geometry with modest curvature. Remarkably, the inferred geometry depends on timescale and is clearest for the timescales that are important for encoding contrast, orientation and spatial correlations.

This work was published in Journal of the Royal Society Interface and is available as 27.

7.8.1 Interaction Mechanism Between the HSV-1 Glycoprotein B and the Antimicrobial Peptide Amyloid-beta

Participants: Mathieu Desroches, Serafim Rodrigues [BCAM Bilbao and external collaborator of MathNeuro].

This work was notably done in collaboration with Tamás Fülöp (Centre de recherche sur le vieillissement, CSSS-UIGS, Université de Sherbrooke). This work was partially done during a stay of Serafim Rodrigues in MathNeuro.

Unravelling the mystery of Alzheimer’s disease (AD) requires urgent resolution given the worldwide increase of the aging population. There is a growing concern that the current leading AD hypothesis, the amyloid cascade hypothesis, does not stand up to validation with respect to emerging new data. Indeed, several paradoxes are being discussed in the literature, for instance, both the deposition of the amyloid-β peptide (Aβ) and the intracellular neurofibrillary tangles could occur within the brain without any cognitive pathology. Thus, these paradoxes suggest that something more fundamental is at play in the onset of the disease and other key and related pathomechanisms must be investigated. The present study follows our previous investigations on the infectious hypothesis, which posits that some pathogens are linked to late onset AD. Our studies also build upon the finding that Aβ is a powerful antimicrobial agent, produced by neurons in response to viral infection, capable of inhibiting pathogens as observed in in vitro experiments. Herein, we ask what are the molecular mechanisms in play when Aβ neutralizes infectious pathogens? Methods: To answer this question, we probed at nanoscale lengths with FRET (Förster Resonance Energy Transfer), the interaction between Aβ peptides and glycoprotein B (responsible of virus-cell binding) within the HSV-1 virion Results: The experiments show an energy transfer between Aβ peptides and glycoprotein B when membrane is intact. No energy transfer occurs after membrane disruption or treatment with blocking antibody. Conclusion: We concluded that Aβ insert into viral membrane, close to glycoprotein B, and participate in virus neutralization.

This work have been published in Journal of Alzheimer's Disease Reports and is available as 22.

7.8.2 Immunosenescence and Altered Vaccine Efficiency in Older Subjects: A Myth Difficult to Change

Participants: Mathieu Desroches, Serafim Rodrigues [BCAM, Bilbao, and external collaborator of MathNeuro].

Notably with Tamás Fulop (Centre de recherche sur le vieillissement - CSSS-UIGS, Université de Sherbrooke). This work was partially achieved during a stay of Serafim Rodrigues in MathNeuro.

Organismal ageing is associated with many physiological changes, including differences in the immune system of most animals. These differences are often considered to be a key cause of age-associated diseases as well as decreased vaccine responses in humans. The most often cited vaccine failure is seasonal influenza, but, while it is usually the case that the efficiency of this vaccine is lower in older than younger adults, this is not always true, and the reasons for the differential responses are manifold. Undoubtedly, changes in the innate and adaptive immune response with ageing are associated with failure to respond to the influenza vaccine, but the cause is unclear. Moreover, recent advances in vaccine formulations and adjuvants, as well as in our understanding of immune changes with ageing, have contributed to the development of vaccines, such as those against herpes zoster and SARS-CoV-2, that can protect against serious disease in older adults just as well as in younger people. In the present article, we discuss the reasons why it is a myth that vaccines inevitably protect less well in older individuals, and that vaccines represent one of the most powerful means to protect the health and ensure the quality of life of older adults.

This work was published in Vaccines and is available as 26.

7.9.1 The one step fixed-lag particle smoother as a strategy to improve the prediction step of particle filtering

Participant: Samuel Nyobe [University of Yaoundé, Cameroon], Fabien Campillo, Serge Moto [University of Yaoundé, Cameroon], Vivien Rossi [Cirad and University of Yaoundé, Cameroon].

We have considerably revised and improved a preprint from last year. This work consists in improving the prediction step in the particle filter. This step is still delicate since if the particles explore areas of the state space that will not match the next observation via the likelihood function, the filter will lose the state track and the filter will be inoperative. We have improved this prediction step by using a simple technique, which may be close to a smoothing technique, that uses the next observation.

This work has been submitted for publication and is available as  54.

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

Participants: Mathieu Desroches, Fabien Campillo.

8.2.1 Visits of international scientists

8.2.2 Visits to international teams

8.2.3 H2020 projects

Member of the organizing committees

• Olivier Faugeras was co-organiser of the Workshop on Mathematical modeling and statistical analysis in Neuroscience, 31 January - 4 February 2022, Henri Poincaré Institute, Paris.

9.1.1 Journal

9.1.2 Invited talks

• Pascal Chossat gave a talk entitled “A neural network model for production and dynamic branching of sequences of learned items” at the French Regional Conference on Complex Systems - FRCCS 2022, 21 June 2022, Paris.
• Pascal Chossat and Frédéric Lavigne (BCL, UCA) gave a joint talk entitled “Dynamic branching of sequences for probabilistic prediction: A neural network model and behavioral experiment” at the Neuromod Institute annual meeting, 1 June 2022, Antibes.
• Mathieu Desroches and Afia B. Ali (University College London, UK) gave a joint online talk entitled “Understanding Synaptic Mechanisms: Why a Multi-disciplinary Approach is Important?” at the Workshop on Mathematical modeling and statistical analysis in Neuroscience, 3 February 2022, Henri Poincaré Institute, Paris.
• Mathieu Desroches gave a talk entitled “Cross-scale excitability in networks of synaptically-coupled quadratic integrate-and-fire neurons” at the 40th congress of the francophone society for theoretical biology (SFBT), 28 June 2022, Poitiers.
• Mathieu Desroches gave an online talk entitled “Classification of Bursting Patterns: A Tale of Two Ducks” in the Mini-Symposium on Multiscale Oscillations in Biological Systems, at the SIAM Life Science conference, 14 July 2022, Pittsburgh, USA.
• Mathieu Desroches gave a webinar talk entitled “Classification of Bursting Patterns: A Tale of Two Ducks” at the Mathematical Biology Seminar of the Mathematics Dept, University of Iowa, 12 September 2022, Iowa City, USA.
• Mattia Sensi gave a seminar talk entitled “Entry-exit functions: beyond eigenvalue separation” at the Edinburgh Dynamical Systems Study Group, 11 March 2022, University of Edinburgh, UK.
• Mattia Sensi gave a talk entitled “A Geometric Singular Perturbation approach to epidemic compartmental models” at the 100 UMI 800 UniPD conference, 24 May 2022, University of Padova, Italy.
• Mattia Sensi gave a talk entitled “Delayed loss of stability in multiple time scale models of natural phenomena” in the Mini-Symposium on Slow-Fast Systems and Phenomena, at the ENOC 2022 Conference, 19 July 2022, Lyon.
• Mattia Sensi gave a talk entitled “A generalization of the full SNARE-SM model”, in the minisymposium on “Recent advances in mathematical modelling in neuroscience”, at the ECMTB 2022 Conference, 23 September 2022, Heidelberg, Germany.
• Mattia Sensi gave a seminar talk entitled “A Geometric Singular Perturbation approach to epidemic compartmental models” at the Dynamics Seminar, Maths Dept, VU Amsterdam, Netherlands, 21 November 2022.
• Mattia Sensi gave a seminar talk entitled “Entry-exit functions in fast-slow systems with intersecting eigenvalues” at the Floris Takens Seminar, University of Groningen, Netherlands, 23 November 2022.
• Mattia Sensi gave a seminar talk entitled “Delayed loss of stability in multiple time scale models of natural phenomena” at the Mathematics Seminar, University of Trento, Italy, 7 December 2022.

9.2.1 Scientific expertise

• Mathieu Desroches has been reviewing grant proposals for the Complex Systems Academy of the UCA JEDI Idex.

9.4.1 Teaching

• Master:
  Mathieu Desroches, Modèles Mathématiques et Computationnels en Neuroscience (Lectures, example classes and computer labs), 18 hours (Feb. 2022), M1 (BIM), Sorbonne Université, Paris, France.
• Master:
  Mathieu Desroches, Dynamical Systems in the context of neuron models, (Lectures, example classes and computer labs), 9 hours (Jan. 2022) and 9 hours (Nov.-Dec. 2022), M1 (Mod4NeuCog), Université Côte d'Azur, Sophia Antipolis, France.
• Masters and Engineer schools:
  With the project to write a book, Fabien Campillo propose a set of applications of particle filtering in tracking developed in the context of lectures given during many years in Masters and Engineer schools. See the associated web page and git repository.

9.4.2 Supervision

• PhD:
  Guillaume Girier, Basque Center for Applied Mathematics (BCAM, Bilbao, Spain) is doing a PhD on “A mathematical, computational and experimental study of neuronal excitability”, co-supervised by S. Rodrigues (BCAM) and M. Desroches.
• PhD:
  Jordi Penalva Vadell, University of the Balearic Islands (UIB, Palma, Spain) is doing a PhD on “Neuronal piecewise linear models reproducing bursting dynamics”, co-supervised by A. E. Teruel (UIB), C. Vich (UIB) and M. Desroches.
• PhD:
  Samuel Nyobe, University of Yaoundé, is doing a PhD on Particle Filtering, co-supervised with Vivien Rossi (CIRAD – UMMISCO, University Yaoundé).
• Master 2 internship:
  Efstathios Pavlidis (Université Côte d'Azur - UCA, Nice), “Multiple-timescale dynamics and mixed states in a model of Bipolar Disorder”, supervised by Mathieu Desroches, September 2021 - February 2022. An article was published, see 29.
• Master 2 internship:
  Alihan Kayabas (Sorbonne Université, Paris), “Slow-fast dissection of a theta-gamma neural oscillator: single neuron and networks”, co-supervised by Mathieu Desroches and Boris Gutkin (ENS, Paris), March - June 2022.
• Master 1 internship:
  Lyna Bouikni (UCA, Nice),“Latching dynamics in biologically inspired neural networks”, co-supervised by Pascal Chossat and Frédéric Lavigne (BCL, UCA), March - May 2022.
• Master 1 internship:
  Ufuk Cem Birbiri (UCA, Nice), “Topological data analysis of human brain data”, supervised by M. Desroches, June - September 2022.

9.4.3 Juries

• Fabien Campillo was member of the jury and reviewer of the PhD of Gaëtan Vignoud entitled “Synaptic plasticity in stochastic neuronal networks”, supervised by Philipe Robert (Inria Paris Research Centre), 8 April 2022.
• Mathieu Desroches was member of the jury of the PhD of Evgenia Kartsaki entitled “How specific classes of retinal cells contribute to vision: a computational model”, supervised by Bruno Cessac (Inria at UCA, France) and Evelyne Sernagor (University of Newcastle, UK), 17 March 2022.
• Mathieu Desroches was member of the jury and president of the jury of the PhD of Côme Le Breton entitled “Usability of phase synchrony neuromarkers in neurofeedback protocols for epileptic seizures reduction”, supervised by Theodore Papadopoulo and Maureen Clerc (Inria at UCA, France), 18 October 2022.

International journals

• 19 articleD.D. Avitabile, J. L.J. L. Davis and K. C.K. C. A. Wedgwood. Bump attractors and waves in networks of leaky integrate-and-fire neurons.SIAM ReviewDecember 2022
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• 20 articleD.Daniele Avitabile, M.Mathieu Desroches and G.G Bard Ermentrout. Cross-scale excitability in networks of quadratic integrate-and-fire neurons.PLoS Computational Biology1810October 2022, e1010569
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• 21 articleD.Daniele Avitabile. Projection methods for Neural Field equations.SIAM Journal on Numerical AnalysisDecember 2022
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• 22 articleK.Karine Bourgade, E.Eric Frost, G.Gilles Dupuis, J.Jacek Witkowski, B.Benoit Laurent, C.Charles Calmettes, C.Charles Ramassamy, M.Mathieu Desroches, S.Serafim Rodrigues and T.Tamás Fülöp. Interaction Mechanism Between the HSV-1 Glycoprotein B and the Antimicrobial Peptide Amyloid-β.Journal of Alzheimer's Disease Reports61September 2022, 599-606
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• 23 articleM.Mathieu Desroches, J.John Rinzel and S.Serafim Rodrigues. Classification of bursting patterns: A tale of two ducks.PLoS Computational Biology182February 2022, e1009752
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• 24 articleA.A Earls, M.-C.M-C Calderer, M.Mathieu Desroches, A.A Zarnescu and S.S Rodrigues. A phenomenological model for interfacial water near hydrophilic polymers.Journal of Physics: Condensed Matter3435June 2022, 355102
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• 25 articleO. C.Olivier C Faugeras, A.Anna Song and R.Romain Veltz. Spatial and color hallucinations in a mathematical model of primary visual cortex.Comptes Rendus. Mathématique3602022, 59-87
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• 26 articleT.Tamas Fulop, A.Anis Larbi, G.Graham Pawelec, A.Alan Cohen, G.Guillaume Provost, A.Abedelouahed Khalil, G.Guy Lacombe, S.Serafim Rodrigues, M.Mathieu Desroches, K.Katsuiku Hirokawa, C.Claudio Franceschi and J.Jacek Witkowski. Immunosenescence and Altered Vaccine Efficiency in Older Subjects: A Myth Difficult to Change.Vaccines104April 2022, 607
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• 27 articleA.Andrea Guidolin, M.Mathieu Desroches, J.Jonathan Victor, K.Keith Purpura and S.Serafim Rodrigues. Geometry of spiking patterns in early visual cortex: a topological data analytic approach.Journal of the Royal Society Interface19196November 2022
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• 28 articleE.Elif Köksal Ersöz, P.Pascal Chossat, M.Martin Krupa and F.Frédéric Lavigne. Dynamic branching in a neural network model for probabilistic prediction of sequences.Journal of Computational NeuroscienceAugust 2022
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• 29 articleE.Efstathios Pavlidis, F.Fabien Campillo, A.Albert Goldbeter and M.Mathieu Desroches. Multiple-timescale dynamics, mixed mode oscillations and mixed affective states in a model of Bipolar Disorder.Cognitive Neurodynamics2022
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• 30 articleJ.Jordi Penalva, M.Mathieu Desroches, A. E.Antonio E. Teruel and C.Catalina Vich. Slow passage through a Hopf-like bifurcation in piecewise linear systems: Application to elliptic bursting.Chaos: An Interdisciplinary Journal of Nonlinear Science3212December 2022, 123109
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• 31 articleS.Sara Sottile, O.Ozan Kahramanoğulları and M.Mattia Sensi. How network properties and epidemic parameters influence stochastic SIR dynamics on scale-free random networks.Journal of SimulationAugust 2022, 1-14
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• 32 articleH.Halgurd Taher, M.Mathieu Desroches and D.Daniele Avitabile. Bursting in a next generation neural mass model with synaptic dynamics: a slow-fast approach.Nonlinear DynamicsApril 2022
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Reports & preprints

• 33 miscM. A.Massimo A. Achterberg and M.Mattia Sensi. A minimal model for adaptive SIS epidemics.November 2022
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• 34 miscE.Emre Baspinar, D.Daniele Avitabile and M.Mathieu Desroches. Network torus canards and their mean-field limits.February 2022
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• 35 miscN.Nicolò Cangiotti, M.Marco Capolli and M.Mattia Sensi. A Generalization of Lanchester's Model of Warfare.November 2022
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• 36 miscP.Panagiotis Kaklamanos, C.Christian Kuehn, N.Nikola Popović and M.Mattia Sensi. Entry-exit functions in fast-slow systems with intersecting eigenvalues.November 2022
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• 37 miscS.Stefania Ottaviano, M.Mattia Sensi and S.Sara Sottile. Global stability of multi-group SAIRS epidemic models.November 2022
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