Pun and wordplay – deconstruction and reconstruction of meaning

The present study aims at analyzing puns from the front page of the newspaper Canard Enchaîné, more precisely the deconstruction of meanings and the reconstruction of new meanings by means of this linguistic process. As it is shown by the specialized literature, the nature of the pun itself actually reveals the lexical or semantic organization of all pre-constructed material. The puns used in our corpus will extend, as we shall see, from polysemy and ambiguity resulting from the multitude of meanings that a word can have, to the construction of portmanteau words: « Pour Standard et Poor’s : Cet accord Mercozy, c’est de la poudre de Berlinpimpin » (Canard enchaîné, 4754), the construction of new words : « Après l’annonce surprise du référendum le choeur des 26 européens : On s’est fait Papandréouter » (Canard enchaîné, 4749), to finally arrive at the use of defrosted structures, as in the example: « Sommet à Bruxelles pour sauver la Grèce et l’euro. L’Europe peine à reprendre du poil de la dette » (Canard enchaîné, 4734)

On the geometry of mixed states and the Fisher information tensor

In this paper, we will review the co-adjoint orbit formulation of finite dimensional quantum mechanics, and in this framework, we will interpret the notion of quantum Fisher information index (and metric). Following previous work of part of the authors, who introduced the definition of Fisher information tensor, we will show how its antisymmetric part is the pullback of the natural Kostant-Kirillov-Souriau symplectic form along some natural diffeomorphism. In order to do this, we will need to understand the symmetric logarithmic derivative as a proper 1-form, settling the issues about its very definition and explicit computation. Moreover, the fibration of co-adjoint orbits, seen as spaces of mixed states, is also discussed.Comment: 27 pages; Accepted Manuscrip

Statistical Geometry in Quantum Mechanics

A statistical model M is a family of probability distributions, characterised by a set of continuous parameters known as the parameter space. This possesses natural geometrical properties induced by the embedding of the family of probability distributions into the Hilbert space H. By consideration of the square-root density function we can regard M as a submanifold of the unit sphere in H. Therefore, H embodies the `state space' of the probability distributions, and the geometry of M can be described in terms of the embedding of in H. The geometry in question is characterised by a natural Riemannian metric (the Fisher-Rao metric), thus allowing us to formulate the principles of classical statistical inference in a natural geometric setting. In particular, we focus attention on the variance lower bounds for statistical estimation, and establish generalisations of the classical Cramer-Rao and Bhattacharyya inequalities. The statistical model M is then specialised to the case of a submanifold of the state space of a quantum mechanical system. This is pursued by introducing a compatible complex structure on the underlying real Hilbert space, which allows the operations of ordinary quantum mechanics to be reinterpreted in the language of real Hilbert space geometry. The application of generalised variance bounds in the case of quantum statistical estimation leads to a set of higher order corrections to the Heisenberg uncertainty relations for canonically conjugate observables.Comment: 32 pages, LaTex file, Extended version to include quantum measurement theor

Ubiquitin and AP180 Regulate the Abundance of GLR-1 Glutamate Receptors at Postsynaptic Elements in C. elegans

AbstractRegulated delivery and removal of α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) glutamate receptors (GluRs) from postsynaptic elements has been proposed as a mechanism for regulating synaptic strength. Here we test the role of ubiquitin in regulating synapses that contain a C. elegans GluR, GLR-1. GLR-1 receptors were ubiquitinated in vivo. Mutations that decreased ubiquitination of GLR-1 increased the abundance of GLR-1 at synapses and altered locomotion behavior in a manner that is consistent with increased synaptic strength. By contrast, overexpression of ubiquitin decreased the abundance of GLR-1 at synapses and decreased the density of GLR-1-containing synapses, and these effects were prevented by mutations in the unc-11 gene, which encodes a clathrin adaptin protein (AP180). These results suggest that ubiquitination of GLR-1 receptors regulates synaptic strength and the formation or stability of GLR-1-containing synapses

Interest Rates and Information Geometry

The space of probability distributions on a given sample space possesses natural geometric properties. For example, in the case of a smooth parametric family of probability distributions on the real line, the parameter space has a Riemannian structure induced by the embedding of the family into the Hilbert space of square-integrable functions, and is characterised by the Fisher-Rao metric. In the nonparametric case the relevant geometry is determined by the spherical distance function of Bhattacharyya. In the context of term structure modelling, we show that minus the derivative of the discount function with respect to the maturity date gives rise to a probability density. This follows as a consequence of the positivity of interest rates. Therefore, by mapping the density functions associated with a given family of term structures to Hilbert space, the resulting metrical geometry can be used to analyse the relationship of yield curves to one another. We show that the general arbitrage-free yield curve dynamics can be represented as a process taking values in the convex space of smooth density functions on the positive real line. It follows that the theory of interest rate dynamics can be represented by a class of processes in Hilbert space. We also derive the dynamics for the central moments associated with the distribution determined by the yield curve.Comment: 20 pages, 3 figure

A simple probabilistic construction yielding generalized entropies and divergences, escort distributions and q-Gaussians

We give a simple probabilistic description of a transition between two states which leads to a generalized escort distribution. When the parameter of the distribution varies, it defines a parametric curve that we call an escort-path. The R\'enyi divergence appears as a natural by-product of the setting. We study the dynamics of the Fisher information on this path, and show in particular that the thermodynamic divergence is proportional to Jeffreys' divergence. Next, we consider the problem of inferring a distribution on the escort-path, subject to generalized moments constraints. We show that our setting naturally induces a rationale for the minimization of the R\'enyi information divergence. Then, we derive the optimum distribution as a generalized q-Gaussian distribution

The Bregman chord divergence

Distances are fundamental primitives whose choice significantly impacts the performances of algorithms in machine learning and signal processing. However selecting the most appropriate distance for a given task is an endeavor. Instead of testing one by one the entries of an ever-expanding dictionary of {\em ad hoc} distances, one rather prefers to consider parametric classes of distances that are exhaustively characterized by axioms derived from first principles. Bregman divergences are such a class. However fine-tuning a Bregman divergence is delicate since it requires to smoothly adjust a functional generator. In this work, we propose an extension of Bregman divergences called the Bregman chord divergences. This new class of distances does not require gradient calculations, uses two scalar parameters that can be easily tailored in applications, and generalizes asymptotically Bregman divergences.Comment: 10 page

Evolution of the global inequality in greenhouse gases emissions using multidimensional generalized entropy measures.

Given the cumulative consequences of climate change, global concentration of greenhouse gases (GHGs) must be reduced; being inequality in per-capita emissions levels a problem to achieve a commitment by all countries. Thus, the evolution of carbon dioxide (CO2) emissions inequality has received special attention because CO2 is the most abundant GHG in the atmosphere. However, it is necessary to consider other gases to provide a real illustration of our starting point to achieve a multilateral agreement. In this paper, we study the evolution of global inequality in GHGs emissions during the period 1990–2011, considering the four main gases: CO2, methane (CH4), nitrous oxide (N2O) and fluorinated gases (F-gases). The data used in this analysis is taken from the World Resources Institute (2014) and the groups of countries are constructed according to the quantity of emissions that each country released into the atmosphere in the first year of study. For this purpose we use the multidimensional generalized entropy measures proposed by Maasoumi (1986) that can be decomposable into the between- and within-group inequality components. The biggest fall in inequality is observed when we attach more weight to the emissions transfers between the most polluting countries and assume a low substitution degree among pollutants. Finally, some economic policy implications are commented.The authors thank the Ministerio de Economía y Competitividad (Project ECO2013- 48326-C2-2-P) and the Ministerio de Educación, Cultura y Deporte (FPU13/02155) for the partial support of this work

Boundary regularity of rotating vortex patches

We show that the boundary of a rotating vortex patch (or V-state, in the terminology of Deem and Zabusky) is of class C^infinity provided the patch is close enough to the bifurcation circle in the Lipschitz norm. The rotating patch is convex if it is close enough to the bifurcation circle in the C^2 norm. Our proof is based on Burbea's approach to V-states. Thus conformal mapping plays a relevant role as well as estimating, on H\"older spaces, certain non-convolution singular integral operators of Calder\'on-Zygmund type.Comment: Various proofs have been shortened. One added referenc