Paris Dauphine University

About: Paris Dauphine University is a education organization based out in Paris, France. It is known for research contribution in the topics: Context (language use) & Population. The organization has 1766 authors who have published 6909 publications receiving 162747 citations. The organization is also known as: Paris Dauphine & Dauphine.

Aggregating preferences in multi-issue domains by using maximum likelihood estimators

Abstract: In this paper, we study a maximum likelihood estimation (MLE) approach to voting when the set of alternatives has a multi-issue structure, and the voters' preferences are represented by CP-nets.We first consider general multi-issue domains, and study whether and how issue-by-issue voting rules and sequential voting rules can be represented by MLEs. We first show that issue-by-issue voting rules in which each local rule is itself an MLE (resp. a candidate scoring rule) can be represented by MLEs with a weak (resp. strong) decomposability property. Then, we prove two theorems that state that if the noise model satisfies a very weak decomposability property, then no sequential voting rule that satisfies unanimity can be represented by an MLE, unless the number of voters is bounded.We then consider multi-issue domains in which each issue is binary; for these, we propose a general family of distance-based noise models, of which give an axiomatic characterization. We then propose a more specific family of natural distance-based noise models that are parameterized by a threshold. We identify the complexity of winner determination for the corresponding MLE voting rule in the two most important subcases of this framework.

Superdiffusion of Energy in a Chain of Harmonic Oscillators with Noise

Abstract: We consider a one dimensional infinite chain of harmonic oscillators whose dynamics is perturbed by a stochastic term conserving energy and momentum. We prove that in the unpinned case the macroscopic evolution of the energy converges to the solution of the fractional diffusion equation $${\partial_t u = -|\Delta|^{3/4}u}$$ . For a pinned system we prove that its energy evolves diffusively, generalizing some results of Basile and Olla (J. Stat. Phys. 155(6):1126–1142, 2014).

Ground State and Charge Renormalization in a Nonlinear Model of Relativistic Atoms

Abstract: We study the reduced Bogoliubov-Dirac-Fock (BDF) energy which allows to describe relativistic electrons interacting with the Dirac sea, in an external electrostatic potential. The model can be seen as a mean-field approximation of Quantum Electrodynamics (QED) where photons and the so-called exchange term are neglected. A state of the system is described by its one-body density matrix, an infinite rank self-adjoint operator which is a compact perturbation of the negative spectral projector of the free Dirac operator (the Dirac sea). We study the minimization of the reduced BDF energy under a charge constraint. We prove the existence of minimizers for a large range of values of the charge, and any positive value of the coupling constant α. Our result covers neutral and positively charged molecules, provided that the positive charge is not large enough to create electron-positron pairs. We also prove that the density of any minimizer is an L1 function and compute the effective charge of the system, recovering the usual renormalization of charge: the physical coupling constant is related to α by the formula αphys ≃ α(1 + 2α/(3π) log Λ)−1, where Λ is the ultraviolet cut-off. We eventually prove an estimate on the highest number of electrons which can be bound by a nucleus of charge Z. In the nonrelativistic limit, we obtain that this number is ≤ 2Z, recovering a result of Lieb. This work is based on a series of papers by Hainzl, Lewin, Sere and Solovej on the mean-field approximation of no-photon QED.

A Metric Approach to Vector-Valued Image Segmentation

Abstract: We address the issue of low-level segmentation of vector-valued images, focusing on the case of color natural images The proposed approach relies on the formulation of the problem in the metric framework, as a Voronoi tessellation of the image domain In this context, a segmentation is determined by a distance transform and a set of sites Our method consists in dividing the segmentation task in two successive sub-tasks: pre-segmentation and hierarchical representation We design specific distances for both sub-problems by considering low-level image attributes and, particularly, color and lightness information Then, the interpretation of the metric formalism in terms of boundaries allows the definition of a soft contour map that has the property of producing a set of closed curves for any threshold Finally, we evaluate the quality of our results with respect to ground-truth segmentation data

Insider trading in an equilibrium model with default: a passage from reduced-form to structural modelling

Abstract: We study an equilibrium model for the pricing of a defaultable zero coupon bond issued by a firm in the framework of Back [2]. The market consists of a risk- neutral informed agent, noise traders and a market maker who sets the price using the total order. When the insider does not trade, the default time possesses a default intensity in market's view as in reduced-form credit risk models. However, we show that, in the equilibrium, the modelling becomes structural in the sense that the default time becomes the first time that some continuous observation process falls below a certain barrier. Interestingly, the firm value is still not observable. We also establish the no expected trade theorem that the insider's trades are inconspicuous.