Journée IXXI sur les lois de puissance

L’objectif de cette journée est de passer en revue un certain nombre de ces travaux empiriques, en testant la robustesse des ajustements par des lois de puissance (une loi log-normale ne serait-elle pas aussi pertinente?) et en explicitant l’intérêt d’un tel ajustement pour la compréhension du système étudié. Nous  espérons que les discussions ainsi générées permettront de mettre en débat l’intérêt de ces lois de puissance pour chaque discipline ainsi que l’unité qu’elles prétendent apporter à des études interdisciplinaires.

PROGRAMME (Cliquer sur les noms pour visualiser les présentations)

co-organisé avec le Laboratoire d’excellence ASLAN http://aslan.universite-lyon.fr/

A B S T R A C T S

Affiliation: GATE Lyon St Etienne (Groupe d’Analyse et de Théorie Économique) – CNRS – University of Lyon CNRS UMR 5824, christian.lebas@univ-lyon2.fr

The “long tail” is the name for a long-known feature of some statistical highly right-skewed distributions. This type of distribution often follows a power law qualitatively quite different from the « normal » or « Gaussian » type distributions. It is a matter of facts that the types of distribution exist for the technology and innovation activities. We focus our study on the different types of distributions of inventor productivity in terms of inventions patented. We utilize the properties and characteristics of power laws to represent the distribution of numbers of patents by inventors. We calculate for five countries the empirical values of the exponent of the power law. Lastly we provide some insights for interpret these type of distribution occurring in techno-economic systems.

Affiliation: Complexity & Quantitative Linguistics Lab, Universitat Politècnica de Catalunya, Barcelona (Catalonia), rferrericancho@lsi.upc.edu

Decades of research in quantitative linguistics have led to the discovery of many scaling laws of human language: Zipf’s laws for word frequencies, the law of abbreviation, Menzerath-Altmann law, Hilberg’s law, etc. However, these laws are largely unknown or seen by many as inevitable, useless or lacking mechanistic sophistication. In this talk, I will dismantle this negative view and review the abstract optimization principles that have been proposed for some of them. At least three beliefs are seriously challenged: that these laws are anecdotal, that language universals are a myth and that humans and other species are separated by a large gulf at the level of language or cognition.  The minimal assumptions required by statistical linguistics research are helping to build bridges between apparently distant disciplines such as linguistics, animal behavior and genetics.

Affiliation: Theoretical Systems Biology Group, Imperial College, London, m.stumpf@imperial.ac.uk

Scaling relationships have been important in the theory of critical phenomena, where they allow us to demarcate qualitatively different types of behaviour close to critical points. Especially for continuous phase transitions their usefulness, power and even elegance are undisputed. What is less clear, however, is the extent to which such simple relationships matter in mesoscopic or real-life systems. Here I will review the notion of power laws from the perspectives of renormalization group theory, and highlight the statistical challenges faced – but generally not properly confronted – in the empirical search for power law behaviour. Along the way I will discuss some of the more illuminating and droll examples from the recent literature. As I will argue, both the theoretical underpinnings and the challenges of the empirical analysis of real-world phenomena are sufficiently intricate that lack of awareness of either or both is central to the bulk of reports of power law behaviour in mesoscopic systems.

Affiliation: CNRS, Physics Dept. ENS Lyon, patrice.abry@ens-lyon.fr

Intrapartum fetal heart rate monitoring constitutes an important stake aiming at early acidosis detection. Measuring heart rate variability is often considered a powerful tool to assess the intrapartum health status of fetus and has been envisaged using various techniques. In this presentation, it will first be explained how and why the notion of scale invariance (or scaling, or fractal) enables to reconcile in a same perspective time variability and spectrum analysis that are classically used to evaluate fetal heart rate variability. Second, it will be shown how the Hurst and global regularity parameters enable to classify the health status of the fetuses. Comparisons against earlier classifications based on standard obstetric parameters will be shown. The impact of decelerations on the Hurst exponent will be discussed. Extensions to other scale invariance parameters, related to multifractal analysis, will also be discussed.

Work done within the ANR FETUSES project, joint work with M. Doret, MD, Hôpital Femme-Mère-Enfant, HCL, Lyon, France & P. Goncalvès, Inria, LIP ENS Lyon)

Affiliation: Laboratoire de Physique, École Normale Supérieure de Lyon, eric.bertin@ens-lyon.fr

Power laws are very common in physics, and appear in many different contexts. It is necessary to distinguish between on the one hand power-law relations between two different physical quantities (e.g., the volume of a sphere proportional to the third power of the radius), often called scaling relations, and on the other hand power-law tails in probability distributions (e.g., the Pareto distribution of income). In some cases, scaling relations are purely dimensional, and are thus rather trivial: in the example of the sphere, the exponent 3 simply comes from space dimension. However, in other situations like critical phenomena (e.g., a magnet close to the magnetization onset temperature), non-trivial scaling relations appear, governed by complex scale-invariant processes. Interestingly, the corresponding exponents depend only on a few generic characteristic of the system, and not on microscopic details, a notion called « universality » by physicists. On the other side, the frequent appearance of power-law tails in probability distributions is perhaps harder to rationalize, but in some cases, they can be understood from scale invariance arguments, or from probabilistic convergence theorems.