Phase transition in the R\'enyi-Shannon entropy of Luttinger liquids

The R\'enyi-Shannon entropy associated to critical quantum spins chain with central charge $c=1$ is shown to have a phase transition at some value $n_c$ of the R\'enyi parameter $n$ which depends on the Luttinger parameter (or compactification radius R). Using a new replica-free formulation, the entropy is expressed as a combination of single-sheet partition functions evaluated at $n-$ dependent values of the stiffness. The transition occurs when a vertex operator becomes relevant at the boundary. Our numerical results (exact diagonalizations for the XXZ and $J_1-J_2$ models) are in agreement with the analytical predictions: above $n_c=4/R^2$ the subleading and universal contribution to the entropy is $\ln(L)(R^2-1)/(4n-4)$ for open chains, and $\ln(R)/(1-n)$ for periodic ones (R=1 at the free fermion point). The replica approach used in previous works fails to predict this transition and turns out to be correct only for $n<n_c$. From the point of view of two-dimensional Rokhsar-Kivelson states, the transition reveals a rich structure in the entanglement spectra.Comment: 4 pages, 3 figure

R\'enyi entropy of a line in two-dimensional Ising models

We consider the two-dimensional (2d) Ising model on a infinitely long cylinder and study the probabilities $p_i$ to observe a given spin configuration $i$ along a circular section of the cylinder. These probabilities also occur as eigenvalues of reduced density matrices in some Rokhsar-Kivelson wave-functions. We analyze the subleading constant to the R\'enyi entropy $R_n=1/(1-n) \ln (\sum_i p_i^n)$ and discuss its scaling properties at the critical point. Studying three different microscopic realizations, we provide numerical evidence that it is universal and behaves in a step-like fashion as a function of $n$, with a discontinuity at the Shannon point $n=1$. As a consequence, a field theoretical argument based on the replica trick would fail to give the correct value at this point. We nevertheless compute it numerically with high precision. Two other values of the R\'enyi parameter are of special interest: $n=1/2$ and $n=\infty$ are related in a simple way to the Affleck-Ludwig boundary entropies associated to free and fixed boundary conditions respectively.Comment: 8 pages, 6 figures, 2 tables. To be submitted to Physical Review

R\'enyi entanglement entropies in quantum dimer models : from criticality to topological order

Thanks to Pfaffian techniques, we study the R\'enyi entanglement entropies and the entanglement spectrum of large subsystems for two-dimensional Rokhsar-Kivelson wave functions constructed from a dimer model on the triangular lattice. By including a fugacity $t$ on some suitable bonds, one interpolates between the triangular lattice (t=1) and the square lattice (t=0). The wave function is known to be a massive $\mathbb Z_2$ topological liquid for $t>0$ whereas it is a gapless critical state at t=0. We mainly consider two geometries for the subsystem: that of a semi-infinite cylinder, and the disk-like setup proposed by Kitaev and Preskill [Phys. Rev. Lett. 96, 110404 (2006)]. In the cylinder case, the entropies contain an extensive term -- proportional to the length of the boundary -- and a universal sub-leading constant $s_n(t)$. Fitting these cylinder data (up to a perimeter of L=32 sites) provides $s_n$ with a very high numerical accuracy ($10^{-9}$ at t=1 and $10^{-6}$ at $t=0.5$). In the topological $\mathbb{Z}_2$ liquid phase we find $s_n(t>0)=-\ln 2$, independent of the fugacity $t$ and the R\'enyi parameter $n$. At t=0 we recover a previously known result, $s_n(t=0)=-(1/2)\ln(n)/(n-1)$ for $n1$. In the disk-like geometry -- designed to get rid of the boundary contributions -- we find an entropy $s^{\rm KP}_n(t>0)=-\ln 2$ in the whole massive phase whatever $n>0$, in agreement with the result of Flammia {\it et al.} [Phys. Rev. Lett. 103, 261601 (2009)]. Some results for the gapless limit $R^{\rm KP}_n(t\to 0)$ are discussed.Comment: 33 pages, 17 figures, minor correction

Nash Region of the Linear Deterministic Interference Channel with Noisy Output Feedback

In this paper, the $\eta$-Nash equilibrium ($\eta$-NE) region of the two-user linear deterministic interference channel (IC) with noisy channel-output feedback is characterized for all $\eta > 0$. The $\eta$-NE region, a subset of the capacity region, contains the set of all achievable information rate pairs that are stable in the sense of an $\eta$-NE. More specifically, given an $\eta$-NE coding scheme, there does not exist an alternative coding scheme for either transmitter-receiver pair that increases the individual rate by more than $\eta$ bits per channel use. Existing results such as the $\eta$-NE region of the linear deterministic IC without feedback and with perfect output feedback are obtained as particular cases of the result presented in this paper.Comment: 5 pages, 2 figures, to appear in ISIT 201

Statistical modelling by neural networks in gamma-spectrometry

International audienceLayered Neural Networks are a class of models based on neural computation and have been applied to the measurement of uranium enrichment. The usual methods consider a limited number of $X$- and $\gamma$-ray peaks, and require calibrated instrumentation for each sample. Since the source-detector ensemble geometry conditions critically differ between such measurements, the spectral region of interest is normally reduced to improve the accuracy of such conventional methods by focusing on the $K_{\alpha}X$ region where the three elementary components are present. Such measurements lead to the desired ratio. Experimental data have been used to study the performance of neural networks involving a Maximum-Likelihood Method. The encoding of the data by a Neural Network approach is a promising method for the measurement of uranium ${}^{235}U$ and ${}^{238}U$ in infinitely thick samples

Spectral Dimensionality Reduction

In this paper, we study and put under a common framework a number of non-linear dimensionality reduction methods, such as Locally Linear Embedding, Isomap, Laplacian Eigenmaps and kernel PCA, which are based on performing an eigen-decomposition (hence the name 'spectral'). That framework also includes classical methods such as PCA and metric multidimensional scaling (MDS). It also includes the data transformation step used in spectral clustering. We show that in all of these cases the learning algorithm estimates the principal eigenfunctions of an operator that depends on the unknown data density and on a kernel that is not necessarily positive semi-definite. This helps to generalize some of these algorithms so as to predict an embedding for out-of-sample examples without having to retrain the model. It also makes it more transparent what these algorithm are minimizing on the empirical data and gives a corresponding notion of generalization error. Dans cet article, nous étudions et développons un cadre unifié pour un certain nombre de méthodes non linéaires de réduction de dimensionalité, telles que LLE, Isomap, LE (Laplacian Eigenmap) et ACP à noyaux, qui font de la décomposition en valeurs propres (d'où le nom "spectral"). Ce cadre inclut également des méthodes classiques telles que l'ACP et l'échelonnage multidimensionnel métrique (MDS). Il inclut aussi l'étape de transformation de données utilisée dans l'agrégation spectrale. Nous montrons que, dans tous les cas, l'algorithme d'apprentissage estime les fonctions propres principales d'un opérateur qui dépend de la densité inconnue de données et d'un noyau qui n'est pas nécessairement positif semi-défini. Ce cadre aide à généraliser certains modèles pour prédire les coordonnées des exemples hors-échantillons sans avoir à réentraîner le modèle. Il aide également à rendre plus transparent ce que ces algorithmes minimisent sur les données empiriques et donne une notion correspondante d'erreur de généralisation.non-parametric models, non-linear dimensionality reduction, kernel models, modèles non paramétriques, réduction de dimensionalité non linéaire, modèles à noyau

La Théorie critique n'a pas dit son dernier mot (2004)

L’Institut de recherche en science sociale (Institut für Sozialforschung, IfS) de Francfort a été fondé en février 1923, mais le véritable acte de naissance de ce que l’on appellera plus tard l’Ecole de Francfort date de la nomination de Max Horkheimer à la tête de l’Institut, et de son programme de février 1931 : « La situation actuelle de la philosophie sociale et les tâches d’un Institut de recherches sociales. » Il y trace les grandes lignes de recherches empiriques des- tinées à renouvel..

Treatment deviating from guidelines does not influence status epilepticus prognosis

Status epilepticus (SE) prognosis is related to nonmodifiable factors (age, etiology), but the exact role of drug treatment is unclear. This study was undertaken to address the prognostic role of treatment adherence to guidelines (TAG). We prospectively studied over 26months a cohort of adults with incident SE (excluding postanoxic). TAG was assessed in terms of drug doses (±30% of recommendations) and medication sequence; its prognostic impact on mortality and return to baseline conditions was adjusted for etiology, SE severity [Status Epilepticus Severity Score (STESS)], and comorbidities. Of 225 patients, 26 (12%) died and 82 (36%) were discharged with a new handicap; TAG was observed in 142 (63%). On univariate analysis, age, etiology, SE severity, and comorbidities were significantly related to outcome, while TAG was associated with neither outcome nor likelihood of SE control. Logistic regression for mortality identified etiology [odds ratio (OR) 18.8, 95% confidence interval (CI) 4.3-82.8] and SE severity (STESS ≥3; OR 1.7, 95% CI 1.2-2.4) as independent predictors, and for lack of return to baseline, again etiology (OR 7.4, 95% CI 3.9-14.0) and STESS ≥3 (OR 1.7, 95% CI 1.4-2.2). Similar results were found for the subgroup of 116 patients with generalized-convulsive SE. Receiver operator characteristic (ROC) analyses confirmed that TAG did not improve outcome prediction. This study of a large SE cohort suggests that treatment adherence to recommendations using current medications seems to play a negligible prognostic role (classIII), confirming the importance of the biological background. Awaiting further treatment trials, it appears mandatory to apply resources towards identification of new therapeutic approache