9,337 research outputs found
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 is shown to have a phase transition at some value of
the R\'enyi parameter 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
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 models) are in agreement with the
analytical predictions: above the subleading and universal
contribution to the entropy is for open chains, and
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 . 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 to observe a given spin
configuration 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
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 , with a discontinuity at the Shannon point . 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: and 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 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 topological liquid for
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 . Fitting these cylinder data (up to a perimeter of L=32
sites) provides with a very high numerical accuracy ( at t=1 and
at ). In the topological liquid phase we find
, independent of the fugacity and the R\'enyi parameter
. At t=0 we recover a previously known result,
for . In the disk-like geometry --
designed to get rid of the boundary contributions -- we find an entropy in the whole massive phase whatever , in agreement with
the result of Flammia {\it et al.} [Phys. Rev. Lett. 103, 261601 (2009)]. Some
results for the gapless limit 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 -Nash equilibrium (-NE) region of the two-user
linear deterministic interference channel (IC) with noisy channel-output
feedback is characterized for all . The -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 -NE. More specifically, given an
-NE coding scheme, there does not exist an alternative coding scheme for
either transmitter-receiver pair that increases the individual rate by more
than bits per channel use. Existing results such as the -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 - and -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 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 and 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
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