CNRS senior researcher, and EHESS Director of studies, I am working with both the Laboratoire de Physique Statistique (LPS), Ecole Normale Supérieure (ENS), and with the Centre d'Analyse et de Mathématique Sociales (CAMS), Ecole des Hautes Etudes en Sciences Sociales (EHESS), Paris. My research interests : computational neuroscience, complex systems in social sciences.More (with full list of my publications) on my webpage: http://www.lps.ens.fr/~nadal/
Perceptual decision-making is the subject of many experimental and theoretical studies. Most mode... more Perceptual decision-making is the subject of many experimental and theoretical studies. Most modeling analyses are based on statistical processes of accumulation of evidence. In contrast, very few works confront attractor network models' predictions with empirical data from continuous sequences of trials. Recently however, numerical simulations of a biophysical competitive attractor network model have shown that such a network can describe sequences of decision trials and reproduce repetition biases observed in perceptual decision experiments. Here we get more insights into such effects by considering an extension of the reduced attractor network model of Wong and Wang (2006), taking into account an inhibitory current delivered to the network once a decision has been made. We make explicit the conditions on this inhibitory input for which the network can perform a succession of trials, without being either trapped in the first reached attractor, or losing all memory of the past ...
Identifying genes from up–down properties of microarray expression series Vol. 21 no. 20 2005, pa... more Identifying genes from up–down properties of microarray expression series Vol. 21 no. 20 2005, pages 3859–3864 doi:10.1093/bioinformatics/bti549
Elections studied at municipality scale Table S1 gives more details about the 76 elections studie... more Elections studied at municipality scale Table S1 gives more details about the 76 elections studied in this paper at the municipality scale. There
Bien que le changement linguistique ait fait l'objet de nombreuses recherches nume-riques, le... more Bien que le changement linguistique ait fait l'objet de nombreuses recherches nume-riques, les phenomenes diachroniques de renouvellement linguistique et plus specifiquement la grammaticalisation ont ete, semble-t-il, laisses de cote. Motives par d'autres perspectives, les differents modeles s'appuient sur des representations qui, comme nous le montrons, ne per-mettent pas d'aborder efficacement la modelisation de ce type de phenomenes. Nous proposons ici un cadre de representation visant a decrire le renouvellement linguistique et se pretant bien a la simulation numerique. Nous l'illustrons par une implementation particuliere mettant en evidence le phenomene de javellisation semantique.
The cerebellum aids the learning and execution of fast coordinated movements, with acquired infor... more The cerebellum aids the learning and execution of fast coordinated movements, with acquired information being stored by plasticity of parallel fibre—Purkinje cell synapses. According to the current consensus, erroneously active parallel fibre synapses are depressed by complex spikes arising when climbing fibres signal movement errors. However, this theory cannot solve the credit assignment problem of using the limited information from a global movement evaluation to optimise behaviour by guiding the plasticity in numerous neurones. We identify the possible implementation of an algorithm solving this problem, whereby spontaneous complex spikes perturb ongoing movements, create an eligibility trace for plasticity and signal resulting error changes to guide plasticity. These error changes are extracted by adaptively cancelling the average error. This framework, stochastic gradient descent with estimated global errors, generates specific predictions for synaptic plasticity rules that co...
It is generally believed that when a linguistic item acquires a new meaning, its overall frequenc... more It is generally believed that when a linguistic item acquires a new meaning, its overall frequency of use rises with time with an S-shaped growth curve. Yet, this claim has only been supported by a limited number of case studies. In this paper, we provide the first corpus-based large-scale confirmation of the S-curve in language change. Moreover, we uncover another generic pattern, a latency phase preceding the S-growth, during which the frequency remains close to constant. We propose a usage-based model which predicts both phases, the latency and the S-growth. The driving mechanism is a random walk in the space of frequency of use. The underlying deterministic dynamics highlights the role of a control parameter which tunes the system at the vicinity of a saddle-node bifurcation. In the neighbourhood of the critical point, the latency phase corresponds to the diffusion time over the critical region, and the S-growth to the fast convergence that follows. The durations of the two phas...
International audienceIn this paper, we consider a discrete choice model where heterogeneous agen... more International audienceIn this paper, we consider a discrete choice model where heterogeneous agents are subject to mutual influences. We explore some consequences on the market's behaviour, in the simplest case of a uniform willingness to pay distribution. We exhibit a first-order phase transition in the profit optimization by the monopolist: if the social influence is strong enough, there is a regime where, if the mean willingness to pay increases, or if the production costs decrease, the optimal solution for the monopolist jumps from a solution with a high price and a small number of buyers, to a solution with a low price and a large number of buyers. Depending on the path of prices adjustments by the monopolist, simulations show hysteretic effects on the fraction of buyers
Emergence dans les systemes complexes : des cas reels aux modeles formels anime par Michel Morvan... more Emergence dans les systemes complexes : des cas reels aux modeles formels anime par Michel Morvan et Henri Berestycki, directeurs d’etudes et Modelisation de comportements collectifs en sciences sociales anime par Henri Berestycki, directeur d’etudes, et Jean-Pierre Nadal, directeur de recherche au CNRS Ces deux seminaires developpent des approches du type « systemes complexes » en sciences sociales, le premier en abordant la question de l’emergence (emergence de normes, de comportements...),...
Systeme (22) pour la synthese d'images texturees qui comprend un analyseur de textures (24) e... more Systeme (22) pour la synthese d'images texturees qui comprend un analyseur de textures (24) et un synthetiseur de textures (28). L'analyseur de textures (24) comprend un reseau de neurones d'analyse (30) qui apprend a caracteriser une texture en calculant des coefficients synaptiques (C ab ) en mettant en oeuvre au moins une fonction de voisinage caracterisant un voisinage autour des pixels de ladite texture. Le synthetiseur de textures (28) comprend un reseau de neurones de synthese (40) qui recoit les coefficients synaptiques (C ab ) ainsi calcules et qui, par un mecanisme de relaxation, synthetise une replique de la texture apprise. Les reseaux de neurones (30) (40) peuvent avoir une structure en arbre. Applications : a un televiseur, a un visiophone, a un compact disque video.
We study social organizations with possible coexistence at equilibrium of cooperating individuals... more We study social organizations with possible coexistence at equilibrium of cooperating individuals and pure consumers (free-riders). We investigate this polymorphic equilibrium using a game-theoretic approach and a statistical physics analysis of a simple model. The agents face a binary decision problem: whether to contribute or not to the public good, through the maximization of an additive utility that has two competing terms, a fixed cost for cooperating and an idiosyncratic moral cost for free-riding proportional to the fraction of cooperators. We study the equilibria regimes of this model. We show that there is a fraction of expected cooperators below which cooperation fails to emerge. Besides the homogeneous stable equilibria (everybody cooperates or everybody free-rides), it exists a solution in which cooperators coexist with free-riders. This polymorphic equilibrium is a consequence of the heterogeneous (idiosyncratic) perceptions of the social reproval by the different indiv...
Monkeys can learn discrete categories (such as ‘cat ’ / ‘dog’) while performing a behavioral task... more Monkeys can learn discrete categories (such as ‘cat ’ / ‘dog’) while performing a behavioral task without explicit instruction related to the categories [1]. The reward pro-tocol is such that the monkey always gains some reward if it performs correctly an easy learnable task, but it can considerably increase its cumulative reward if it can make a proper use of categorical cues, which requires being able to distinguish between the two categories. These experiments have not allowed to compare the acquired knowledge of categories with the standard phe-nomenon of categorical perception [2]. Notably, the main characteristic features of categorical perception show up in the psychophysics when the stimuli are ambiguous, near the boundary between categories in stimulus space. On the theoretical side, these features have been shown
As a large-scale instance of dramatic collective behaviour, the 2005 French riots started in a po... more As a large-scale instance of dramatic collective behaviour, the 2005 French riots started in a poor suburb of Paris, then spread in all of France, lasting about three weeks. Remarkably, although there were no displacements of rioters, the riot activity did travel. Access to daily national police data has allowed us to explore the dynamics of riot propagation. Here we show that an epidemic-like model, with just a few parameters and a single sociological variable characterizing neighbourhood deprivation, accounts quantitatively for the full spatio-temporal dynamics of the riots. This is the first time that such data-driven modelling involving contagion both within and between cities (through geographic proximity or media) at the scale of a country, and on a daily basis, is performed. Moreover, we give a precise mathematical characterization to the expression "wave of riots", and provide a visualization of the propagation around Paris, exhibiting the wave in a way not describ...
I give a review of recent results obtained on the associative properties of a simple perceptron i... more I give a review of recent results obtained on the associative properties of a simple perceptron in the sparse coding limit : simple Hebbian rules allow to reach optimal or near optimal performances, and these performances may be obtained in the regime where the network makes errors.
Perceptual decision-making is the subject of many experimental and theoretical studies. Most mode... more Perceptual decision-making is the subject of many experimental and theoretical studies. Most modeling analyses are based on statistical processes of accumulation of evidence. In contrast, very few works confront attractor network models' predictions with empirical data from continuous sequences of trials. Recently however, numerical simulations of a biophysical competitive attractor network model have shown that such a network can describe sequences of decision trials and reproduce repetition biases observed in perceptual decision experiments. Here we get more insights into such effects by considering an extension of the reduced attractor network model of Wong and Wang (2006), taking into account an inhibitory current delivered to the network once a decision has been made. We make explicit the conditions on this inhibitory input for which the network can perform a succession of trials, without being either trapped in the first reached attractor, or losing all memory of the past ...
Identifying genes from up–down properties of microarray expression series Vol. 21 no. 20 2005, pa... more Identifying genes from up–down properties of microarray expression series Vol. 21 no. 20 2005, pages 3859–3864 doi:10.1093/bioinformatics/bti549
Elections studied at municipality scale Table S1 gives more details about the 76 elections studie... more Elections studied at municipality scale Table S1 gives more details about the 76 elections studied in this paper at the municipality scale. There
Bien que le changement linguistique ait fait l'objet de nombreuses recherches nume-riques, le... more Bien que le changement linguistique ait fait l'objet de nombreuses recherches nume-riques, les phenomenes diachroniques de renouvellement linguistique et plus specifiquement la grammaticalisation ont ete, semble-t-il, laisses de cote. Motives par d'autres perspectives, les differents modeles s'appuient sur des representations qui, comme nous le montrons, ne per-mettent pas d'aborder efficacement la modelisation de ce type de phenomenes. Nous proposons ici un cadre de representation visant a decrire le renouvellement linguistique et se pretant bien a la simulation numerique. Nous l'illustrons par une implementation particuliere mettant en evidence le phenomene de javellisation semantique.
The cerebellum aids the learning and execution of fast coordinated movements, with acquired infor... more The cerebellum aids the learning and execution of fast coordinated movements, with acquired information being stored by plasticity of parallel fibre—Purkinje cell synapses. According to the current consensus, erroneously active parallel fibre synapses are depressed by complex spikes arising when climbing fibres signal movement errors. However, this theory cannot solve the credit assignment problem of using the limited information from a global movement evaluation to optimise behaviour by guiding the plasticity in numerous neurones. We identify the possible implementation of an algorithm solving this problem, whereby spontaneous complex spikes perturb ongoing movements, create an eligibility trace for plasticity and signal resulting error changes to guide plasticity. These error changes are extracted by adaptively cancelling the average error. This framework, stochastic gradient descent with estimated global errors, generates specific predictions for synaptic plasticity rules that co...
It is generally believed that when a linguistic item acquires a new meaning, its overall frequenc... more It is generally believed that when a linguistic item acquires a new meaning, its overall frequency of use rises with time with an S-shaped growth curve. Yet, this claim has only been supported by a limited number of case studies. In this paper, we provide the first corpus-based large-scale confirmation of the S-curve in language change. Moreover, we uncover another generic pattern, a latency phase preceding the S-growth, during which the frequency remains close to constant. We propose a usage-based model which predicts both phases, the latency and the S-growth. The driving mechanism is a random walk in the space of frequency of use. The underlying deterministic dynamics highlights the role of a control parameter which tunes the system at the vicinity of a saddle-node bifurcation. In the neighbourhood of the critical point, the latency phase corresponds to the diffusion time over the critical region, and the S-growth to the fast convergence that follows. The durations of the two phas...
International audienceIn this paper, we consider a discrete choice model where heterogeneous agen... more International audienceIn this paper, we consider a discrete choice model where heterogeneous agents are subject to mutual influences. We explore some consequences on the market's behaviour, in the simplest case of a uniform willingness to pay distribution. We exhibit a first-order phase transition in the profit optimization by the monopolist: if the social influence is strong enough, there is a regime where, if the mean willingness to pay increases, or if the production costs decrease, the optimal solution for the monopolist jumps from a solution with a high price and a small number of buyers, to a solution with a low price and a large number of buyers. Depending on the path of prices adjustments by the monopolist, simulations show hysteretic effects on the fraction of buyers
Emergence dans les systemes complexes : des cas reels aux modeles formels anime par Michel Morvan... more Emergence dans les systemes complexes : des cas reels aux modeles formels anime par Michel Morvan et Henri Berestycki, directeurs d’etudes et Modelisation de comportements collectifs en sciences sociales anime par Henri Berestycki, directeur d’etudes, et Jean-Pierre Nadal, directeur de recherche au CNRS Ces deux seminaires developpent des approches du type « systemes complexes » en sciences sociales, le premier en abordant la question de l’emergence (emergence de normes, de comportements...),...
Systeme (22) pour la synthese d'images texturees qui comprend un analyseur de textures (24) e... more Systeme (22) pour la synthese d'images texturees qui comprend un analyseur de textures (24) et un synthetiseur de textures (28). L'analyseur de textures (24) comprend un reseau de neurones d'analyse (30) qui apprend a caracteriser une texture en calculant des coefficients synaptiques (C ab ) en mettant en oeuvre au moins une fonction de voisinage caracterisant un voisinage autour des pixels de ladite texture. Le synthetiseur de textures (28) comprend un reseau de neurones de synthese (40) qui recoit les coefficients synaptiques (C ab ) ainsi calcules et qui, par un mecanisme de relaxation, synthetise une replique de la texture apprise. Les reseaux de neurones (30) (40) peuvent avoir une structure en arbre. Applications : a un televiseur, a un visiophone, a un compact disque video.
We study social organizations with possible coexistence at equilibrium of cooperating individuals... more We study social organizations with possible coexistence at equilibrium of cooperating individuals and pure consumers (free-riders). We investigate this polymorphic equilibrium using a game-theoretic approach and a statistical physics analysis of a simple model. The agents face a binary decision problem: whether to contribute or not to the public good, through the maximization of an additive utility that has two competing terms, a fixed cost for cooperating and an idiosyncratic moral cost for free-riding proportional to the fraction of cooperators. We study the equilibria regimes of this model. We show that there is a fraction of expected cooperators below which cooperation fails to emerge. Besides the homogeneous stable equilibria (everybody cooperates or everybody free-rides), it exists a solution in which cooperators coexist with free-riders. This polymorphic equilibrium is a consequence of the heterogeneous (idiosyncratic) perceptions of the social reproval by the different indiv...
Monkeys can learn discrete categories (such as ‘cat ’ / ‘dog’) while performing a behavioral task... more Monkeys can learn discrete categories (such as ‘cat ’ / ‘dog’) while performing a behavioral task without explicit instruction related to the categories [1]. The reward pro-tocol is such that the monkey always gains some reward if it performs correctly an easy learnable task, but it can considerably increase its cumulative reward if it can make a proper use of categorical cues, which requires being able to distinguish between the two categories. These experiments have not allowed to compare the acquired knowledge of categories with the standard phe-nomenon of categorical perception [2]. Notably, the main characteristic features of categorical perception show up in the psychophysics when the stimuli are ambiguous, near the boundary between categories in stimulus space. On the theoretical side, these features have been shown
As a large-scale instance of dramatic collective behaviour, the 2005 French riots started in a po... more As a large-scale instance of dramatic collective behaviour, the 2005 French riots started in a poor suburb of Paris, then spread in all of France, lasting about three weeks. Remarkably, although there were no displacements of rioters, the riot activity did travel. Access to daily national police data has allowed us to explore the dynamics of riot propagation. Here we show that an epidemic-like model, with just a few parameters and a single sociological variable characterizing neighbourhood deprivation, accounts quantitatively for the full spatio-temporal dynamics of the riots. This is the first time that such data-driven modelling involving contagion both within and between cities (through geographic proximity or media) at the scale of a country, and on a daily basis, is performed. Moreover, we give a precise mathematical characterization to the expression "wave of riots", and provide a visualization of the propagation around Paris, exhibiting the wave in a way not describ...
I give a review of recent results obtained on the associative properties of a simple perceptron i... more I give a review of recent results obtained on the associative properties of a simple perceptron in the sparse coding limit : simple Hebbian rules allow to reach optimal or near optimal performances, and these performances may be obtained in the regime where the network makes errors.
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