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SUMMARYNeuronal cultures are a prominent experimental tool to understand complex functional organization in neuronal assemblies. However, neurons grown on flat surfaces exhibit a strongly coherent bursting behavior with limited functionality. To approach the functional richness of naturally formed neuronal circuits, here we studied neuronal networks grown on polydimethylsiloxane (PDMS) topographical patterns shaped as either parallel tracks or square valleys. We followed the evolution of spontaneous activity in these cultures along 20 daysin vitrousing fluorescence calcium imaging. The networks were characterized by rich spatiotemporal activity patterns that comprised from small regions of the culture to its whole extent. Effective connectivity analysis revealed the emergence of spatially compact functional modules that were associated to both the underpinned topographical features and predominant spatiotemporal activity fronts. Our results show the capacity of spatial constraints to mold activity and functional organization, bringing new opportunities to comprehend the structure-function relationship in living neuronal circuits.

We propose a novel phase based analysis with the purpose of quantifying the periodic bursts of activity observed in various neuronal systems. The way bursts are intiated and propagate in a spatial network is still insufficiently characterized. In particular, we investigate here how these spatiotemporal dynamics depend on the mean connection length. We use a simplified description of a neuron's state as a time varying phase between firings. This leads to a definition of network bursts, that does not depend on the practitioner's individual judgment as the usage of subjective thresholds and time scales. This allows both an easy and objective characterization of the bursting dynamics, only depending on system's proper scales. Our approach thus ensures more reliable and reproducible measurements. We here use it to describe the spatiotemporal processes in networks of intrinsically oscillating neurons. The analysis rigorously reveals the role of the mean connectivity length in spatially embedded networks in determining the existence of "leader" neurons during burst initiation, a feature incompletely understood observed in several neuronal cultures experiments. The precise definition of a burst with our method allowed us to rigorously characterize the initiation dynamics of bursts and show how it depends on the mean connectivity length. Although presented with simulations, the methodology can be applied to other forms of neuronal spatiotemporal data. As shown in a preliminary study with MEA recordings, it is not limited to in silico modeling.

Cultures of dissociated neurons are an invaluable experimental tool in studying neuronal networks at an intermediate scale in an in vitro controlled physico-chemical environment. Moreover, current micro-fabrication techniques allow the design of a custom connectivity between subpopulations, which could make it possible to carry out computations with devices involving living cells. The quorum percolation (QP) model has been designed in the context of neurobiology to describe bursts of activity occurring in neuronal cultures from the point of view of collective phenomena rather than from a dynamical synchronization approach. Such a model is well suited to describe triggered activity in neuronal devices, and its generic character points at the necessity of heavily structured devices to go beyond collective bursting. We derive a continuous extension of the QP model, seen as information propagation on a non-metric directed graph, and discuss how its critical behavior might give insight on the connectivity of neuronal networks. The link with metric graphs, embedded in a two-dimensional space, is tackled by the introduction of a geometrical model based upon a random walk, where axon growth is constrained by obstacles such as walls and channels. This provides a starting point for the construction of neuronal devices in vitro capable of more complex behaviors. Lastly, we show how simulations of bursts with a dynamical adaptive integrate-and-fire model can be interpreted in terms of QP, confirming the robustness of this synchronized behavior.

Experimental and numerical studies have revealed that isolated populations of oscillatory neurons can spontaneously synchronize and generate periodic bursts involving the whole network. Such a behavior has notably been observed for cultured neurons in rodent's cortex or hippocampus. We show here that a sufficient condition for this network bursting is the presence of an excitatory population of oscillatory neurons which displays spike-driven adaptation. We provide an analytic model to analyze network bursts generated by coupled adaptive exponential integrate-and-fire neurons. We show that, for strong synaptic coupling, intrinsically tonic spiking neurons evolve to reach a synchronized intermittent bursting state. The presence of inhibitory neurons or plastic synapses can then modulate this dynamics in many ways but is not necessary for its appearance. Thanks to a simple self-consistent equation, our model gives an intuitive and semi-quantitative tool to understand the bursting behavior. Furthermore, it suggests that after-hyperpolarization currents are sufficient to explain bursting termination. Through a thorough mapping between the theoretical parameters and ion-channel properties, we discuss the biological mechanisms that could be involved and the relevance of the explored parameter-space. Such an insight enables us to propose experimentally-testable predictions regarding how blocking fast, medium or slow after-hyperpolarization channels would affect the firing rate and burst duration, as well as the interburst interval.

We study the modifications induced in the behavior of the quorum percolation model on neural networks with Gaussian in-degree by taking into account an uncorrelated Gaussian thresholds variability. We derive a mean-field approach and show its relevance by carrying out explicit Monte Carlo simulations. It turns out that such a disorder shifts the position of the percolation transition, impacts the size of the giant cluster, and can even destroy the transition. Moreover, we highlight the occurrence of disorder independent fixed points above the quorum critical value. The mean-field approach enables us to interpret these effects in terms of activation probability. A finite-size analysis enables us to show that the order parameter is weakly self-averaging with an exponent independent on the thresholds disorder. Last, we show that the effects of the thresholds and connectivity disorders cannot be easily discriminated from the measured averaged physical quantities.

We start from a continuous extension of a mean field approach of the quorum percolation model, accounting for the response of in vitro neuronal cultures, to carry out a normal form analysis of the critical behavior. We highlight the effects of nonlinearities associated with this mean field approach even in the close vicinity of the critical point. Statistical properties of random networks with Gaussian in-degree are related to the outcoming links distribution. Finite size analysis of explicit Monte Carlo simulations enables us to confirm the relevance of the mean field approach on such networks and to show that the order parameter is weakly self-averaging; dynamical relaxation is investigated. Furthermore we derive a mean field equation taking into account the effect of inhibitory neurons and discuss the equivalence with a purely excitatory network.

We provide a direct quantitative evidence that the critical behavior of the Ising model on self-similar lattices depends upon the geometrical features of the underlying structure. Intensive Monte Carlo simulations enable to show that the values of the ratio of exponents γ / ν depend upon the lacunarity of the structure, which measures the deviation from the translational symmetry. Finally, the topological character of the scaling corrections when the fractal dimension is smaller than 2 is discussed.

International audience; We study the cluster size distributions generated by the Wolff algorithm in the framework of the Ising model on Sierpinski fractals with Hausdorff dimension Df between 1 and 2. We show that these distributions exhibit a scaling property involving the magnetic exponent yh associated with one of the eigendirection of the renormalization flows. We suggest that a single cluster tends to invade the whole lattice as Df tends towards the lower critical dimension of the Ising model, namely 1. The autocorrelation times associated with the Wolff and Swendsen-Wang algorithms enable us to calculate dynamical exponents; the cluster algorithms are shown to be more efficient in reducing the critical slowing down when Df is lowered.

We examine a simplified approach to the classical scattering of a particle by a neutral atom, first for a Thomson-like model and then for different screened Coulomb potentials. As an application we discuss in detail why, in the experiments of Geiger and Marsden on the scattering of α particles by matter, screening effects are negligible. On the way we encounter several unusual phenomena in classical scattering theory.

The Quorum Percolation model has been designed in the context of neurobiology to describe bursts of activity occurring in neuronal cultures from the point of view of statistical physics rather than from a dynamical synchronization approach. It is based upon information propagation on a directed graph with a threshold activation rule; this leads to a phase diagram which exhibits a giant percolation cluster below some critical value mC of the excitability. We describe the main characteristics of the original model and derive extensions according to additional relevant biological features. Firstly, we investigate the effects of an excitability variability on the phase diagram and show that the percolation transition can be destroyed by a sufficient amount of such a disorder; we stress the weakly averaging character of the order parameter and show that connectivity and excitability can be seen as two overlapping aspects of the same reality. Secondly, we elaborate a discrete time stochastic model taking into account the decay originating from ionic leakage through the membrane of neurons and synaptic depression; we give evidence that the decay softens and shifts the transition, and conjecture than decay destroys the transition in the thermodynamical limit. We were able to develop mean-field theories associated with each of the two effects; we discuss the framework of their agreement with Monte Carlo simulations. It turns out that the the critical point mC from which information on the connectivity of the network can be inferred is affected by each of these additional effects. Lastly, we show how dynamical simulations of bursts with an adaptive exponential integrateand- fire model can be interpreted in terms of Quorum Percolation. Moreover, the usefulness of the percolation model including the set of sophistication we investigated can be extended to many scientific fields involving information propagation, such as the spread of rumors in sociology, ethology, ecology.

International audience; We investigate a model derived from bootstrap percolation on a directed random graph with Gaussian in-degree useful in describing the collective behavior of dissociated neuronal networks. By developing a continuous version of the model, we were able to provide accurate values of the critical thresholds and exponents associated with the occurrence of a giant cluster. As a main result, it turns out that the values of the exponents calculated over a numerical accessible range covering more than two orders of magnitude below the critical point exhibit a slight dependence upon the connectivity of the graph.

International audience; The critical temperature and the set of critical exponents (β,γ,ν) of the Ising model on a fractal structure, namely the Sierpiński carpet, are calculated from a Monte Carlo simulation based on the Wolff algorithm together with the histogram method and finite-size scaling. Both cases of periodic boundary conditions and free edges are investigated. The calculations have been done up to the seventh iteration step of the fractal structure. The results show that, although the structure is not translationally invariant, the scaling behavior of thermodynamical quantities is conserved, which gives a meaning to the finite-size analysis. Although some discrepancies in the values of the critical exponents occur between periodic boundary conditions and free edges, the effective dimension obtained through the Rushbrooke and Josephson's scaling law have the same value in both cases. This value is slightly but significantly different from the fractal dimension.

International audience; In this paper, we present the effects of memory decay on a bootstrap percolation model applied to randomdirected graphs (quorum percolation). The addition of decay was motivated by its natural occurrence in physicalsystems previously described by percolation theory, such as cultured neuronal networks, where decay originatesfrom ionic leakage through the membrane of neurons and/or synaptic depression. Surprisingly, this featurealone appears to change the critical behavior of the percolation transition, where discontinuities are replacedby steep but finite slopes. Using different numerical approaches, we show evidence for this qualitative changeeven for very small decay values. In experiments where the steepest slopes can not be resolved and still appearas discontinuities, decay produces nonetheless a quantitative difference on the location of the apparent criticalpoint. We discuss how this shift impacts network connectivity previously estimated without considering decay.In addition to this particular example, we believe that other percolation models are worth reinvestigating, takinginto account similar sorts of memory decay.

International audience; The effects of disorder on the critical behavior of the q-state Potts model in noninteger dimensions are studied by comparison of deterministic and random fractals sharing the same dimensions in the framework of a discrete scale invariance. We carried out intensive Monte Carlo simulations. In the case of a fractal dimension slightly smaller than two df 1.974 636, we give evidence that the disorder structured by discrete scale invariance does not change the first order transition associated with the deterministic case when q = 7. Furthermore the study of the high value q = 14 shows that the transition is a second order one both for deterministic and random scale invariance, but that their behavior belongs to different university classes.

International audience; The properties of magnon spectra in low dimensional random Sierpinski fractals, deterministic fractals, and percolation clusters are calculated and compared. While deterministic scale invariance leads to singular continuous spectra with gaps and degenerated levels, random scale invariance leads to continuous density of states which enables to define low frequency exponents; the exponents associated to random percolation clusters and to Sierpinski fractals are significantly different, even if their fractal dimensions are very close. The study of spacing levels shows quantitatively that the degeneracy is linked to geometrical symmetry in deterministic fractals while it is strongly reduced by random discrete scale invariance.

We study the critical behavior of the Ising model in the case of quenched disorder constrained by fractality on random Sierpinski fractals with a Hausdorff dimension ${d}_{f}\ensuremath{\simeq}1.8928$. This is a first attempt to study a situation between the borderline cases of deterministic self-similarity and quenched randomness. Intensive Monte Carlo simulations were carried out. Scaling corrections are much weaker than in the deterministic cases, so that our results enable us to ensure that finite-size scaling holds, and that the critical behavior is described by a new universality class. The hyperscaling relation is compatible with an effective dimension equal to the Hausdorff one; moreover the two eigenvalues exponents of the renormalization flows are shown to be different from the ones calculated from $\ensuremath{\epsilon}$ expansions, and from the ones obtained for fourfold symmetric deterministic fractals. Although the space dimensionality is not integer, lack of self-averaging properties exhibits some features very close to the ones of a random fixed point associated with a relevant disorder.

International audience; We calculate spin wave spectra of low-dimensional self-similar nanostructures, namely deterministic Sierpinski carpets, in the framework of short ranged ferromagnetic exchange. The integrated density of states of magnetic excitations are shown to exhibit singularities resulting in devil's staircase spectra which remain at all iteration steps; the spectra are found to be singular continuous functions of the frequency with numerous gaps and plateaux linked to symmetry and degeneracy of the associated eigen-modes. These spin wave spectra are shown to be sensitive not only to the fractal dimension, but to additional connectivity properties of the structures as already pointed out in the study of critical properties of fractals. This result is closely linked to the fractal subdimensions arising from the set of eigenvalues of the connectivity matrix describing the construction of the fractal structure; our set of results strongly suggests that the link between the integrated density of states and fractal subdimensions is a much more general feature of deterministic fractals; connectivity marks mode localization. Lastly, magnetic fractals are shown to be able to filter radiofrequencies.

The study of random configurations of Sierpinski carpets enables us to observe the fluctuations and mean values of local connectedness. The law of variation of these mean values with the order of iteration is deduced numerically in exact agreement with analytical considerations where new “simplex” statistical subdimensions appear.

On presente ici les cliches de diffraction optique de tapis de Sierpinski aleatoires de differentes dimensions fractales, pris a des niveaux d'iteration differents. Au moyen du formalisme de la matrice de transfert dans les fractals, on montre la sensibilite de cette analyse experimentale aux correlations a moyenne et longue portee. Ainsi la relation entre les sous-dimensions fractales du F.M.T. et les rapports d'intensite entre les cliches de diffraction de figures fractales a des niveaux d'iteration differents est soulignee

We present an experimental and theoretical investigation of the Generalized Einstein Relation (GER), a particular form of a fluctuation-dissipation relation, in an out-of-equilibrium visco-elastic fluid. Micrometer beads, used as thermometers, are immersed in an aging colloidal glass to provide both fluctuation and dissipation measurements. The deviations from the Generalized Einstein Relation are derived as a function of frequency and aging time. The observed deviations from GER are interpreted as directly related to the change in the glass relaxation times with aging time. In our scenario, deviations are observed in the regime where the observation time scale is of the order of a characteristic relaxation time of the glass., Comment: 20 pages, 6 figures; revised version

International audience; The phase diagram of the q-state Potts model in fractal dimensions is studied with the help of Wang–Landau Monte Carlo simulations on Sierpinski and Menger fractal structures. A particular attention is paid to first order transitions just above the border separating the second order phase transition regime from the first order one. Although the translation invariance is strongly broken in deterministic fractals, evidence is given that such a deviation from the translational symmetry is not able to induce second order transitions for large values of q when the dimension lies between 1:9746 and 3. Moreover, the occurrence of second order transitions for very large values of q in the case of hierarchically weakly connected systems, that is when the fractal dimension is significantly smaller than 2, is pointed out. At last, the evolution of first order physical averages such as the latent heats and the interfacial free energies with the space dimensionality and the number of spin states is discussed.

The extension of the phase diagram of the q-state Potts model to noninteger dimension is investigated by means of Monte Carlo simulations on Sierpinski and Menger fractal structures. Both multicanonical and canonical simulations have been carried out with the help of the Wang-Landau and the Wolff cluster algorithms. Lower bounds are provided for the critical values qc of q where a first-order transition is expected in the cases of two structures whose fractal dimension is smaller than 2: The transitions associated with the sevenstate and ten-state Potts models on Sierpinski carpets with fractal dimensions df1.8928 and df1.7925, respectively, are shown to be second-order ones, the renormalization eigenvalue exponents yh are calculated, and bounds are provided for the renormalization eigenvalue exponents yt and the critical temperatures. Moreover, the results suggest that second-order transitions are expected to occur for very large values of q when the fractal dimension is lowered below 2—that is, in the case of hierarchically weakly connected systems with an infinite ramification order. At last, the transition associated with the four-state Potts model on a fractal structure with a dimension df2.631 is shown to be a weakly first-order one.

International audience; We provide a Monte Carlo analysis of the moments of the cluster size distributions built up from random occupation of deterministic Sierpinski fractals. Features of the site percolation transition in non-integer dimensions are investigated for two fractal dimensions lying between 1 and 2. Data collapses of the moments when going from an iteration step of the fractal to the next are associated with a real space renormalization procedure and show that a constant gap scaling hypothesis is satisfied. Nevertheless, scaling corrections occuring in the behavior of the thresholds with the size of the lattices are stronger that in the standard percolation case; we point out that, in the case of fractals, a contribution to these corrections can be interpreted as a topological effect of the convergence towards the thermodynamical limit and described by a size dependent shift of the percolation threshold. The bounds of the infinite limit thresholds that we are able to provide are in disagreement with the predictions of Galam and Mauger in the case of translationally invariant lattices, and suggest a new behavior in the case of percolation in non-integer dimension

We study the scaling properties of the clusters grown by the Wolff algorithm on seven different Sierpinski-type fractals of Hausdorff dimension $1 < d_f \le 3$ in the framework of the Ising model. The mean absolute value of the surface energy of Wolff cluster follows a power law with respect to the lattice size. Moreover, we investigate the probability density distribution of the surface energy of Wolff cluster and are able to establish a new scaling relation. It enables us to introduce a new exponent associated to the surface energy of Wolff cluster. Finally, this new exponent is linked to a dynamical exponent via an inequality., 12 pages, 3 figures. To appear in PRB

We perform a Monte Carlo Renormalization Group analysis of the critical behavior of the ferromagnetic Ising model on a Sierpi\'nski fractal with Hausdorff dimension $d_f\simeq 1.8928$. This method is shown to be relevant to the calculation of the critical temperature $T_c$ and the magnetic eigen-exponent $y_h$ on such structures. On the other hand, scaling corrections hinder the calculation of the temperature eigen-exponent $y_t$. At last, the results are shown to be consistent with a finite size scaling analysis., Comment: 16 pages, 7 figures

International audience; We study the Wolff cluster size distributions obtained from Monte Carlo simulations of the Ising phase transition on Sierpinski fractals with Hausdorff dimensions Df between 2 and 3. These distributions are shown to be invariant when going from an iteration step of the fractal to the next under a scaling of the cluster sizes involving the exponent (b/n )1(g /n ). Moreover, the decay of the autocorrelation functions at the critical points enables us to calculate the Wolff dynamical critical exponents z for three different values of Df . The Wolff algorithm is more efficient in reducing the critical slowing down when Df is lowered.

International audience; We provide an overall picture of the magnetic critical behavior of the Ising and three-state Potts models on fractal structures. The results brought out fromMonte Carlo simulations for several Hausdorff dimensions between 1 and 3 show that this behavior can be understood in the framework of weak universality. Moreover, the maxima of the susceptibility follow power laws in a very reliable way, which allows us to calculate the ratio of the exponents γ/ν and the anomalous dimension exponent η in a reliable way. At last, the evolution of these exponents with the Hausdorff dimension is discussed.

We study the critical behavior of the 3-state Potts model, where the spins arelocated at the centers of the occupied squares of the deterministic Sierpinski car-pet. A finite-size scaling analysis is performed from Monte Carlo simulations, fora Hausdorff dimension d f ≃ 1.8928. The phase transition is shown to be a secondorder one. The maxima of the susceptibility of the order parameter follow a powerlaw in a very reliable way, which enables us to calculate the ratio of the exponentsγ/ν. We find that the scaling corrections affect the behavior of most of the thermo-dynamical quantities. However, the sequence of intersection points extracted fromthe Binder’s cumulant provides bounds for the critical temperature. We are able togive the bounds for the exponent 1/ν as well as for the ratio of the exponents β/ν,which are compatible with the results calculated from the hyperscaling relation. Keywords: phase transitions, fractal, Potts model, finite size scaling, Monte Carlo.PACS:68.35.Rh: Phase transitions andcritical phenomena, 05.45.Df: Fractals, 75.10.Hk:Classical spin models, 75.40.Mg: Numerical simulation studies, 89.75.Da: Systems obey-ing scaling laws.

The magnetic critical behavior of Ising spins located at the sites of deterministic Sierpinski carpets is studied within the framework of a ferromagnetic Ising model. A finite-size scaling analysis is performed from Monte Carlo simulations. We investigate four different fractal dimensions between 1.9746 and 1.7227, up to the sixth and eighth iteration step of the fractal structure in one case. It turns out that the finite-size scaling behavior of most thermodynamical quantities is affected by scaling corrections increasing as the fractal dimension decreases, tending towards the lower critical dimension of the Ising model. These corrections are related to the topology of the fractal structure and to the scale invariance. Nevertheless the maxima of the susceptibility follow power laws in a very reliable way, which allows us to calculate the ratio of the exponents γ/ν. Moreover, the fixed point of the fourth order cumulant at Tc exhibited by Binder on translation invariant lattices is replaced by a decreasing sequence of intersection points converging towards the critical temperature. The convergence towards the thermodynamical limit as the size of the networks increases is slowed down as the fractal dimension decreases. At last, the evolution of the discrepancies between Monte Carlo simulations and e expansions with the fractal dimension is set out.

We report the critical exponent values of the Ising model, ${\ensuremath{\nu}}^{\ensuremath{-}1},$ $\ensuremath{\gamma}/\ensuremath{\nu},$ and $\ensuremath{\beta}/\ensuremath{\nu},$ and the critical temperatures of three Sierp\'{\i}nski fractals with Hausdorff dimensions ${d}_{f}$ equal to $2.966,$ $2.904,$ and $2.631.$ The results are calculated from finite-size scaling analysis by Monte Carlo simulations. They are precise enough to show that the hyperscaling relation ${d}_{f}=2\ensuremath{\beta}/\ensuremath{\nu}+\ensuremath{\gamma}/\ensuremath{\nu}$ is satisfied. Furthermore, the discrepancy between the values provided by $\ensuremath{\epsilon}$ expansions and by Monte Carlo simulations shows that the critical behavior of fractals cannot be fully understood in the framework of strong universality.

Recent developments [3] in the construction of coherent states for an arbitrary quantum system with Hamiltonian H are presented here. These CS families {|J,γ〉} are required to solve the unity, to be temporally stable, e -iHt/ħ |J,γ〉 =| J,γ+ ωt〉, and the J functional dependence of the energy mean value 〈J, γ | H |J,γ〉 = E(J) is assigned possibly along lines which are classically meaningful. Further extensions are finally proposed.

Apres avoir simule numeriquement l'etirement d'un reseau aleatoire de sites relies par des forces centrales entre sites occupes et par des forces proportionnelles aux ecarts angulaires entre liaisons realisees, la concentration en site etant proche de celle au seuil de percolation, on etudie analytiquement et experimentalement la diffraction optique d'un tel reseau deforme. Aux bords du reseau, les atomes sont solidaires du deplacement impose, tandis qu'a l'interieur differentes rotations apparaissent et sont detectees par diffraction. Ces regions internes, independantes, sont limitees par des pivots dont l'observation est usuelle dans les phenomenes de percolation. Les mesures dans l'espace direct, comme dans l'espace reciproque, de l'amplitude de ces rotations correspondent aux deductions theoriques qu'on peut mener a partir du modele. L'etirement global resulte de la coordination de multiples rotations locales et donc la rigidite effective du milieu est tres faible.

A network of randomly occupied sites connected by springs is submitted to an external stretch; the optical diffraction pattern of the distorted network is experimentally and analytically studied. Some regions are just shifted as a whole and related shifts are measured by means of diffraction, some regions are uniformly distorted and this distortion is optically detected. The techniques of pattern reconstruction in real space by filtering in Fourier space enable typical defects to be localized. Fractal random media are also considered.

In this thesis, I provide models and numerical tools to better understand and predict the behavior and development of neuronal cultures and devices.Neuronal cultures have proven invaluable in improving our understanding of how the brain processes information, by enabling researchers to investigate neuronal and network response functions to various perturbations and stimuli.Furthermore, recent progress in microfluidics have opened the gate towards more elaborated neuronal devices, bringing us one step closer to complex signal processing with living in vitro neurons.In a first part, I propose a mechanism to explain the epileptiform bursts of activity present in cultures, mechanism which I formulate as a concise theoretical model. I subsequently test the predictions of this model on cultures and show that they are indeed compatible with the behavior observed in vitro.I further develop this description in the second part of the thesis, where I analyze its spatiotemporal dynamics and the fact that burst nucleate in specific areas in the network.Since predictions and analysis of these nucleation centers strongly depends on the network structure, I develop a simulation platform to enable efficient modeling of the network development. This software takes into account the interactions between the neurons and their environment and is the first platform to provide versatile and complete models to simulate the entire growth process of neurons. I demonstrate that this simulator is able to generate valid neuronal morphologies, then use it to propose new network topologies to describe neuronal cultures, as well as to reproduce existing neuronal devices. I then show that the activities sustained by these structures are compatible with the experimental recordings.Eventually, I discuss several future directions for which the use of neuronal devices would enable to circumvent current limitations of neuronal cultures, thus providing new information on the processes which underlie brain development and plasticity., Dans cette thèse, je propose plusieurs modèles et outils numériques afin de mieux comprendre et prédire le comportement et le développement de cultures et dispositifs neuronaux.Les cultures de neurones ont en effet été un outil précieux durant les 20 dernières années : elles ont permis de mieux comprendre la manière dont le cerveau traite les différentes informations qui lui parviennent en donnant aux scientifiques la possibilité de tester les effets de médicaments sur les neurones, ainsi que d'obtenir leurs réponses détaillées à diverses perturbations et stimuli.De plus, de récentes avancées en microfluidiques ont ouvert la voie à la conception de dispositifs neuronaux plus élaborés, rapprochant encore un peu plus la perspective du traitement de signaux complexes via des neurones in vitro.Dans une première partie, je propose un mécanisme pour expliquer les bouffées d'activité épileptiformes présentes dans les cultures, mécanisme que je formule via un modèle théorique concis. J'effectue ensuite une vérification expérimentale des prédictions du modèle sur des cultures et montre que celles-ci sont effectivement compatibles avec le comportement observé in vitro.Dans une seconde partie, je décris plus en détail la description de la dynamique spatio-temporelle du phénomène, notamment le fait que les bursts nucléent en des zones bien précises du réseau neuronal.Comme les prédictions et analyses effectuées dépendent fortement de la structure de ce réseau, je présente ensuite la réalisation d'une plateforme de simulation afin de permettre de modéliser efficacement le développement des réseaux neuronaux. Ce logiciel prend en compte les interactions entre les neurones et leur environnement et constitue la première plateforme à fournir des modèles polyvalents et complets pour décrire l'intégralité du processus de croissance neuronal. Je montre ensuite que ce simulateur est capable de générer des morphologies valides et l'utilise pour proposer des nouvelles topologies de réseaux afin de décrire les cultures de neurones. Je reproduis également des dispositifs neuronaux existants et montre que les activités entretenues par ces structures sont compatibles avec les observations expérimentales. Enfin, je discute plusieurs directions de recherche possibles, pour lesquelles l'utilisation de dispositifs neuronaux spécifiques permettrait de contourner les limitations des cultures neuronales et fournirait ainsi de nouvelles informations sur les processus sous-tendant le développement et la plasticité cérébrale

Being able to harness the processing power of biological neurons will openthe door to ground breaking applications in many scientific fields. Glucosepoweredneural implants could repair or enhance cerebral functions in thefield of medicine, in vitro cognitive assays could foster drug screening in thepharmaceutical industry, and biological processors could lead to new kinds ofartificial intelligence.Any neuronal culture assigned with a computable function (actual or intended)can go under the name of a neuronal device. This thesis representsa multi-frontal effort towardsmaking this concept a more tangible thing, withoutholding to firmly onto preconceptions of what might and might not berelevant for computation. Our strategy is based on the exploitation of culturedneuronal networks’ properties that are both resilient and experimentally easilyaccessible rather than on the urge to reproduce the machinery of the brain.This seemingly naive engineering approach is disputable in the same waychance and necessity are in general disputable in biology. In spite of their mindbogglingcapabilities, one can argue that brains are the product of historicalcontingency and are therefore not necessarily optimal for the functions theysupport in vivo. This would be evenmore so the case for alternative functionsonly relevant to disembodied cultures.Whereas it might then be defendable to distance ourselves from naturalbrains, there are several benefits to the use of living components in the firstplace. Living cells have evolved to be energetically very efficient, they can repairthemselves and adapt to environmental changes. On a more fundamentallevel, in vitro discoveries, originating from the making and characterizationof neuronal devices, might be transposable to processes at play in vivo butdifficult to access ; such undertaking is therefore also relevant to the field ofneurosciences in general. Finally and most importantly, this work could help todefine the kind of computations that can be performed by neuronal assembliesand bring new elements to the field of artificial intelligence, which is bound tobe determinant in our future., La possibilité d'exploiter la puissance de calcul des neurones biologiques ouvrira la porte à des applications pionnières dans plusieurs champs scientifiques. Des implants neuronaux alimentés par le glucose pourraient réparer ou renforcer des fonctions cérébrales dans le domaine médical; des essais cognitifs in vitro pourraient permettre le criblage de remèdes dans l'industrie pharmaceutique. Enfin des processeurs biologiques pourraient conduire à de nouveaux types d'intelligence artificielle.On peut appeler dispositif neuronal toute culture de neurones affectée d'une fonction calculatoire. Cette thèse constitue un effort dans différentes directions pour rendre ce concept plus tangible, sans s'en tenir fermement à des idées préconçues sur ce qui pourrait être pertinent ou pas pour le calcul. Notre stratégie est basée sur l'exploitation des propriétés des réseaux de neurones en culture qui soient à la fois résilientes et facilement accessibles expérimentalement plutôt que sur la reproduction de la machinerie du cerveau.cette approche d'ingénieur en apparence naïve est discutable de la même façon que hasard et nécessité sont discutables en biologie de manière générale. En dépit de leurs faramineuses capacités, on peut défendre l'idée que le cerveau est le produit de contingences historiques et donc non nécessairement optimal pour les fonctions qu'il assure in vivo. Cela pourrait être encore plus le cas pour des fonctions alternatives seulement pertinentes dans le cas de cultures désincarnées.Alors qu'on pourrait défendre l'idée de se distancier du cerveau naturel, il y a de nombreux avantages à utiliser directement des éléments vivants. Les cellules vivantes ont évolué pour être énergétiquement très efficaces, elles peuvent se réparer elles mêmes et s'adapter aux changements d'environnement. A un niveau plus fondamental, les découvertes in vitro issues de la fabrication et de la caractérisation de dispositifs neuronaux pourraient être transposables à des processus en jeu in vivo mais difficiles à atteindre.Une telle entreprise fait donc sens dans le champ des neurosciences en général. Finalement, et de manière plus importante, ce travail pourrait contribuer à définir le genre de calcul qui pourrait être effectué par des assemblées de neurones et apporter des éléments nouveaux au domaine de l'intelligence artificielle, ce qui est voué à être déterminant dans l'avenir.

In this thesis, I provide models and numerical tools to better understand and predict the behavior and development of neuronal cultures and devices.Neuronal cultures have proven invaluable in improving our understanding of how the brain processes information, by enabling researchers to investigate neuronal and network response functions to various perturbations and stimuli.Furthermore, recent progress in microfluidics have opened the gate towards more elaborated neuronal devices, bringing us one step closer to complex signal processing with living in vitro neurons.In a first part, I propose a mechanism to explain the epileptiform bursts of activity present in cultures, mechanism which I formulate as a concise theoretical model. I subsequently test the predictions of this model on cultures and show that they are indeed compatible with the behavior observed in vitro.I further develop this description in the second part of the thesis, where I analyze its spatiotemporal dynamics and the fact that burst nucleate in specific areas in the network.Since predictions and analysis of these nucleation centers strongly depends on the network structure, I develop a simulation platform to enable efficient modeling of the network development. This software takes into account the interactions between the neurons and their environment and is the first platform to provide versatile and complete models to simulate the entire growth process of neurons. I demonstrate that this simulator is able to generate valid neuronal morphologies, then use it to propose new network topologies to describe neuronal cultures, as well as to reproduce existing neuronal devices. I then show that the activities sustained by these structures are compatible with the experimental recordings.Eventually, I discuss several future directions for which the use of neuronal devices would enable to circumvent current limitations of neuronal cultures, thus providing new information on the processes which underlie brain development and plasticity.; Dans cette thèse, je propose plusieurs modèles et outils numériques afin de mieux comprendre et prédire le comportement et le développement de cultures et dispositifs neuronaux.Les cultures de neurones ont en effet été un outil précieux durant les 20 dernières années : elles ont permis de mieux comprendre la manière dont le cerveau traite les différentes informations qui lui parviennent en donnant aux scientifiques la possibilité de tester les effets de médicaments sur les neurones, ainsi que d'obtenir leurs réponses détaillées à diverses perturbations et stimuli.De plus, de récentes avancées en microfluidiques ont ouvert la voie à la conception de dispositifs neuronaux plus élaborés, rapprochant encore un peu plus la perspective du traitement de signaux complexes via des neurones in vitro.Dans une première partie, je propose un mécanisme pour expliquer les bouffées d'activité épileptiformes présentes dans les cultures, mécanisme que je formule via un modèle théorique concis. J'effectue ensuite une vérification expérimentale des prédictions du modèle sur des cultures et montre que celles-ci sont effectivement compatibles avec le comportement observé in vitro.Dans une seconde partie, je décris plus en détail la description de la dynamique spatio-temporelle du phénomène, notamment le fait que les bursts nucléent en des zones bien précises du réseau neuronal.Comme les prédictions et analyses effectuées dépendent fortement de la structure de ce réseau, je présente ensuite la réalisation d'une plateforme de simulation afin de permettre de modéliser efficacement le développement des réseaux neuronaux. Ce logiciel prend en compte les interactions entre les neurones et leur environnement et constitue la première plateforme à fournir des modèles polyvalents et complets pour décrire l'intégralité du processus de croissance neuronal. Je montre ensuite que ce simulateur est capable de générer des morphologies valides et l'utilise pour proposer des nouvelles topologies de réseaux afin de décrire les cultures de neurones. Je reproduis également des dispositifs neuronaux existants et montre que les activités entretenues par ces structures sont compatibles avec les observations expérimentales. Enfin, je discute plusieurs directions de recherche possibles, pour lesquelles l'utilisation de dispositifs neuronaux spécifiques permettrait de contourner les limitations des cultures neuronales et fournirait ainsi de nouvelles informations sur les processus sous-tendant le développement et la plasticité cérébrale