Polynomial systems supported on circuits and dessins d'enfants

We study polynomial systems whose equations have as common support a set C of n+2 points in Z^n called a circuit. We find a bound on the number of real solutions to such systems which depends on n, the dimension of the affine span of the minimal affinely dependent subset of C, and the "rank modulo 2" of C. We prove that this bound is sharp by drawing so-called dessins d'enfant on the Riemann sphere. We also obtain that the maximal number of solutions with positive coordinates to systems supported on circuits in Z^n is n+1, which is very small comparatively to the bound given by the Khovanskii fewnomial theorem.Comment: 19 pages, 5 figures, Section 3.1 revised, minor changes in other section

Quatre indicateurs d'inflation sous-jacente: application et interpretation.

Dans ce papier, nous comparons quatre indicateurs de l'inflation sous-jacente: l'approche par exclusion de postes, les estimateurs "a influence limitee" comme l'inflation mediane, les mesures issues d'un VAR structurel et une mesure tiree d'un modele a composantes inobservables. Ces indicateurs sont discutes du point de vue de leur interpretation et de leur utilisation a des fins conjoncturelles.Econometrie ; Inflation ; Instruments de mesure

Hardy type spaces on certain noncompact manifolds and applications

In this paper we consider a complete connected noncompact Riemannian manifold M with Ricci curvature bounded from below, positive injectivity radius and spectral gap b. We introduce a sequence X^1(M), X^2(M), ... of new Hardy spaces on M, the sequence Y^1(M/, Y^2(M), ... of their dual spaces, and show that these spaces may be used to obtain endpoint estimates for purely imaginary powers of the Laplace-Beltrami operator and for more general spectral multipliers associated to the Laplace--Beltrami operator L on M. Under the additional condition that the volume of the geodesic balls of radius r is controlled by C r^a e^{2\sqrt{b} r} for some real number a and for all large r, we prove also an endpoint result for first order Riesz transforms D L^{-1/2}. In particular, these results apply to Riemannian symmetric spaces of the noncompact type.Comment: 27 pages, v2: the first version has been revised and rearranged, with additions, in two papers, of which this new version is the first. The second paper is posted as arXiv:1002.1161v

Automatic analysis of facial actions: a survey

As one of the most comprehensive and objective ways to describe facial expressions, the Facial Action Coding System (FACS) has recently received significant attention. Over the past 30 years, extensive research has been conducted by psychologists and neuroscientists on various aspects of facial expression analysis using FACS. Automating FACS coding would make this research faster and more widely applicable, opening up new avenues to understanding how we communicate through facial expressions. Such an automated process can also potentially increase the reliability, precision and temporal resolution of coding. This paper provides a comprehensive survey of research into machine analysis of facial actions. We systematically review all components of such systems: pre-processing, feature extraction and machine coding of facial actions. In addition, the existing FACS-coded facial expression databases are summarised. Finally, challenges that have to be addressed to make automatic facial action analysis applicable in real-life situations are extensively discussed. There are two underlying motivations for us to write this survey paper: the first is to provide an up-to-date review of the existing literature, and the second is to offer some insights into the future of machine recognition of facial actions: what are the challenges and opportunities that researchers in the field face

Modelisation et prevision des indices de prix sectoriels.

Ce papier presente une modelisation de l'indice des prix francais. L'objectif est de permettre une analyse rapide et detaillee des tendances de court terme de l'inflation ainsi que de realiser des previsions a intervalles rapproches. Les caracteristiques de cet outil sont les suivantes: un petit nombre d'equations, une frequence mensuelle, un detail sectoriel assez fin et la publication d'intervalles de confiance relatifs a la prevision.Modèles economiques ; Prevision ; Instrument de mesure ; Prix

Optimized diffusion gradient orientation schemes for corrupted clinical DTI data sets

Object:A method is proposed for generating schemes of diffusion gradient orientations which allow the diffusion tensor to be reconstructed from partial data sets in clinical DT-MRI, should the acquisition be corrupted or terminated before completion because of patient motion. Materials and methods: A general energy-minimization electrostatic model was developed in which the interactions between orientations are weighted according to their temporal order during acquisition. In this report, two corruption scenarios were specifically considered for generating relatively uniform schemes of 18 and 60 orientations, with useful subsets of 6 and 15 orientations. The sets and subsets were compared to conventional sets through their energy, condition number and rotational invariance. Schemes of 18 orientations were tested on a volunteer. Results: The optimized sets were similar to uniform sets in terms of energy, condition number and rotational invariance, whether the complete set or only a subset was considered. Diffusion maps obtained in vivo were close to those for uniform sets whatever the acquisition time was. This was not the case with conventional schemes, whose subset uniformity was insufficient. Conclusion: With the proposed approach, sets of orientations responding to several corruption scenarios can be generated, which is potentially useful for imaging uncooperative patients or infant

Duality and ontology

A ‘duality’ is a formal mapping between the spaces of solutions of two empirically equivalent theories. In recent times, dualities have been found to be pervasive in string theory and quantum field theory. Naïvely interpreted, duality-related theories appear to make very different ontological claims about the world—differing in e.g. space-time structure, fundamental ontology, and mereological structure. In light of this, duality-related theories raise questions familiar from discussions of underdetermination in the philosophy of science: in the presence of dual theories, what is one to say about the ontology of the world? In this paper, we undertake a comprehensive and non-technical survey of the landscape of possible ontological interpretations of duality-related theories. We provide a significantly enriched and clarified taxonomy of options—several of which are novel to the literature

Counting and computing regions of DD-decomposition: algebro-geometric approach

New methods for $D$-decomposition analysis are presented. They are based on topology of real algebraic varieties and computational real algebraic geometry. The estimate of number of root invariant regions for polynomial parametric families of polynomial and matrices is given. For the case of two parametric family more sharp estimate is proven. Theoretic results are supported by various numerical simulations that show higher precision of presented methods with respect to traditional ones. The presented methods are inherently global and could be applied for studying $D$-decomposition for the space of parameters as a whole instead of some prescribed regions. For symbolic computations the Maple v.14 software and its package RegularChains are used.Comment: 16 pages, 8 figure

Monitoring of ultrafine particles in French regional air quality network

Monitoring of ultrafine particles (UFP) in the ambient air is ongoing since 2012 in France. A national working group was created in 2014, including nowadays five French regional air quality monitoring networks. The main instrument selected to monitor UFP is the particle sizer “UFP-3031” (TSI Inc.). It measures the particle number concentration between 20 and 800 nm with six size channels. Two intercomparisons were organized in 2014 and 2015, which evaluated the accuracy of this instrument through a comparison with other techniques (such as Scanning Mobility Particle Sizer, SMPS), and through uncertainty calculations. Recently, several networks have been also equipped with CPC (condensation particle counter) to be able to measure the total UFP number concentration from 7 nm. This work presents the main results of short and long-term measurement of UFP which have been carried out in various environments: urban/traffic sites, near heavy industry zones (Dunkerque and Fos-sur-Mer in northern and southern France, respectively), near harbor area (Nice)… For urban/ traffic environment, the number concentration and size distribution are compared at the national level; it appears that they vary significantly depending on the influence of road traffic around the site. The concentration levels near traffic sites are at least twice than in the urban area, especially for UFP smaller than 50 nm. Additionally, the UFP measurement also makes it possible to improve the identification of specific sources and to understand the atmospheric physicochemical phenomena. The relationship between UFP and industrial emissions, ferries, forest fires was clearly identified in different places in France. During summer, the UFP monitoring also shows the formation of new particles (between 20-30 nm or smaller) in the afternoon, due to photochemical reactions. From 2019, the French national strategy on UFP will start putting a particular emphasis on the impact of UFP on human health