Jean-Pierre NADAL

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Research interests

My research is in the field of the statistical physics of complex systems, with specific interests in computational neuroscience, more broadly in cognitive science, and in complex systems in social science.

Below: Main recent and current projects - My research trajectory - List of topics/key words with links to main pubications.

Main recent and current research projects

Computational neuroscience

One main line of research is on the neural correlates of perception and decision making. Making use of tools from information theory, I study the typical and optimal peroperties of neural codes, notably of population codes involved in perception tasks. Recently I have been focusing on categorical perception. This leads to the study of decision making based on ambiguous/noisy stimuli.

When dealing with a difficult categorization task, the brain has to face two independent sources of uncertainty: categorization uncertainty and neuronal uncertainty. The latter stems from neuronal noise, whereas the former is intrinsic to the category structure in stimulus space: categories like phonemes or colors typically overlap, so that a given stimulus might belong to different categories. In works done with Laurent Bonnasse-Gahot, we propose a general neural theory of category coding, in which these two sources of uncertainty are quantified by means of information theoretic tools. We derive analytical formulae which capture different psychophysical consequences of category learning - namely, a better discrimination between categories, and longer reaction times to identify the category of a stimulus lying at the category boundary. Our approach allows us to model experimental data. One main contribution of this work is to exhibit, in both quantitative and qualitative terms, the interplay between discrimination and identification.
[Publications : BGN08, BGN12]

Most experiments are based on reinforcement learning protocoles - e g a monkey learns a task through trials and errors, with rewards in case of success. An ongoing project is with the biologist Barry Richmond (NIH, Bethesda, USA) and his team on the behavioral learning of categories in monkeys (see CEHMRN13).

An other project is on the modeling of learning in the Cerebellum, in collaboration with Boris Barbour at the Biology Department of the ENS, and other physicists, Vincent Hakim at the ENS and Nicolas Brunel, Chicago University.
[Publications : BHINB04, BBHN07, CNB12].

I have also some interest in the modelling at the interface between neuro-computation and social cognition.

Complex systems in social science

My interest is on the modeling of collective phenomena in economic and social sciences, working on the effect at the population level of social influences ("externalities") on individual behaviour. Whenever customers'choices (e.g. to buy or not a given good) depend on others choices (cases coined 'positive externalities' or 'bandwagon effect' in the economic literature), the demand may be multiply valued: for a same posted price, there is either a small number of buyers, or a large one - in which case one says that the customers coordinate. This leads to a dilemma for the seller: should he sell at a high price, targeting a small number of buyers, or at low price targeting a large number of buyers? In this paper we show that the interaction between demand and supply is even more complex than expected, leading to a systemic risk for the seller, what we call the curse of coordination: the pricing strategy for the seller which aimed at maximizing his profit corresponds to posting a price which, not only assumes that the customers will coordinate, but also lies very near the critical price value at which such high demand no more exists. This is obtained by the detailed mathematical analysis of a particular model formally related to the Random Field Ising Model (RFIM) and to a model introduced in social sciences by T. C. Schelling in the 70's. Collaboration with Mirta B. Gordon (LIG, Grenoble), Denis Phan (GEMASS, Paris), and Viktoriya Semeshenko (Economics departement, Univ. of Buenos-Aires).
[Publications: NGPV05, GNPV05, SGN07, GNPS09, GNPS13]

In the 70' the social scientist Thomas Schelling has introduced a simple model of social segregation, an agent-based model considered as the paradigm of auto-organisation in social science: a global 'ordered' state - segregation - emerges from the dynamics of individual choices made by agents with only weak preferences for neighbours of similar social status or ethnic characteristics. With Laetitia Gauvin and Jean Vannimenus, we have been working on the analysis of Schelling type models, exhibiting a phase diagram and showing formal links between the models and physics models (spin-1 models used for the modeling of binary alloys with lacunes).
More recently, with Laetitia Gauvin and the economist Annick Vignes, we have introduced a new family of models coupling social and economic factors, allowing for some comparison with empirical data (housing market in Paris). A key assumption is that agents preferences for a place depend on both an intrinsic attractiveness and on the social characteristics of its neighborhood. The approach combines agent-based models and partial diffusion equations.
[Publications: GVN09, GNV10, GVN13]

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Research trajectory

With a general maths and physics background, and a specialisation in theoretical physics, my earliest research works are in the domain of the statistical physics of disordered systems. I worked mainly on the statistical physics of "lattice animals" - percolation type models studied both in physics and in combinatorics.

In the mid 80's I turned to the modelling of neural networks, following the pioneering work of J. J. Hopfield on attractor neural networks. Since then my main contributions in the domains of neural networks and computational neuroscience have been in the modelling of short term memory in the human brain, the theory of supervised and unsupervised learning, and in the study of neural coding making use of both statistical physics and information theoretic tools. In the recent years I have been involved in collaborations with biologists. Some of my most recent works are motivated by problems at the boundary between linguistics and neuroscience (in particular in collaboration with psycholinguists). This lead me to study the neural coding of phonemes, and the neural mechanisms underlying decision making in multichoices tasks.

While working on problems motivated by the modelling of human cognitive processing, I have also addressed issues in the related fields of machine learning (theoretical and practical algorithmic aspects within the supervised learning framework), statistical inference, data analysis (in particular in bioinformatics) and signal processing (notably working on blind source separation and independent component analysis). The analysis of optimal neural coding also lead me to study of the statistical properties of natural images. Finally, during about ten years I have been acting as a consultant for a private research laboratory, working on applications of machine learning techniques.

My first work in the field of economic and social science dates back to the mid 90's, a collaboration on the topic of market organization with Gérard Weisbuch at the ENS and the economist Alan Kirman, EHESS. Since 2002, I work on collective phenomena in economic and social sciences in collaboration with physicists, mathematicians, economists and other social scientists.

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List of topics/key words, with links to main publications

information processing in neural networks: { neural coding and signal processing - modeling memory}
learning algorithms for data analysis {constructive algos. - R & D}
complex systems in social science [econophysics - social cognition - linguistics ]

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