Intrinsic character of Stokes matrices

Two germs of linear analytic differential systems $x^{k+1}Y^\prime=A(x)Y$ with a non resonant irregular singularity are analytically equivalent if and only if they have the same eigenvalues and equivalent collections of Stokes matrices. The Stokes matrices are the transition matrices between sectors on which the system is analytically equivalent to its formal normal form. Each sector contains exactly one separating ray for each pair of eigenvalues. A rotation in $S$ allows supposing that $\mathbb R^+$ lies in the intersection of two sectors. Reordering of the coordinates of $Y$ allows ordering the real parts of the eigenvalues, thus yielding triangular Stokes matrices. However, the choice of the rotation in $x$ is not canonical. In this paper we establish how the collection of Stokes matrices depends on this rotation, and hence on a chosen order of the projection of the eigenvalues on a line through the origin.Comment: 10 pages, 3 figure

Capacity of The Discrete-Time Non-Coherent Memoryless Gaussian Channels at Low SNR

We address the capacity of a discrete-time memoryless Gaussian channel, where the channel state information (CSI) is neither available at the transmitter nor at the receiver. The optimal capacity-achieving input distribution at low signal-to-noise ratio (SNR) is precisely characterized, and the exact capacity of a non-coherent channel is derived. The derived relations allow to better understanding the capacity of non-coherent channels at low SNR. Then, we compute the non-coherence penalty and give a more precise characterization of the sub-linear term in SNR. Finally, in order to get more insight on how the optimal input varies with SNR, upper and lower bounds on the non-zero mass point location of the capacity-achieving input are given.Comment: 5 pages and 4 figures. To appear in Proceeding of International Symposium on Information Theory (ISIT 2008

Autour d’Insite : un événement discursif

Cet article effectue un retour sur l’hypothèse de renforcement des logiques prohibitionniste et thérapeutique par la logique de « périllisation ». Cette hypothèse a été émise pour expliquer l’apparent succès politique des pratiques et politiques de réduction des méfaits, celles-ci étant animées par la logique de « périllisation ». Cette réflexion s’effectue à travers un examen des énoncés produits autour d’Insite, un des deux services d’injection supervisée de Vancouver. S’inspirant de l’approche foucaldienne de l’analyse du discours, il montre comment des énoncés ont problématisé les logiques thérapeutique et prohibitionniste même s’ils les ont reconduites en partie. En conclusion, une discussion exploratoire de certains possibles ouverts par cet « événement discursif » est amorcée.This article revisits the hypothesis whereby perilization logic reinforces both the prohibitionist and the therapeutic logics. This hypothesis was put forward in order to explain the apparent political success of harm reduction practices and policies, these being grounded in the perilization logic. This reflection is realized through an examination of the statements produced around Insite, one of two safe injection services in Vancouver. Using a Foucauldian-inspired approach to discourse analysis, it shows how certain statements have problematized both the therapeutic and prohibitionist logics even as they have partly renewed them. As a conclusion, an exploratory discussion of some of the possibilities opened up by this “discursive event” is initiated.En este artículo se vuelve sobre la hipótesis del refuerzo de la lógica prohibicionista y la terapéutica por la lógica de la atribución de un riesgo. Esta hipótesis surge para explicar el éxito político aparente de las prácticas y políticas de la reducción de infracciones y delitos, prácticas que están animadas por la lógica de la atribución de un riesgo. Esta reflexión se lleva a cabo por medio de un análisis de enunciados producidos en torno a Insite, uno de los dos sitios supervisados para la inyección de drogas de Vancouver. Inspirándose en el enfoque foulcadiano de análisis del discurso, se ilustra de qué manera los enunciados han problematizado la lógica terapéutica y la prohibicionista, aun cuando han prolongado parcialmente su vigencia. En conclusión, se inicia aquí una discusión exploratoria de ciertas posibilidades abiertas por este “acontecimiento discursivo”