Paris, France
Paris, France

Télécom ParisTech is one of the most selective grandes écoles in France. Located in Paris, it is also a member of prestigious ParisTech and Institut Telecom.It has established a school named Institut Eurécom in collaboration with EPFL at Sophia-Antipolis. Wikipedia.


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Bianchi P.,Telecom ParisTech | Jakubowicz J.,Orange S.A.
IEEE Transactions on Automatic Control | Year: 2013

We introduce a new framework for the convergence analysis of a class of distributed constrained non-convex optimization algorithms in multi-agent systems. The aim is to search for local minimizers of a non-convex objective function which is supposed to be a sum of local utility functions of the agents. The algorithm under study consists of two steps: a local stochastic gradient descent at each agent and a gossip step that drives the network of agents to a consensus. Under the assumption of decreasing stepsize, it is proved that consensus is asymptotically achieved in the network and that the algorithm converges to the set of Karush-Kuhn-Tucker points. As an important feature, the algorithm does not require the double-stochasticity of the gossip matrices. It is in particular suitable for use in a natural broadcast scenario for which no feedback messages between agents are required. It is proved that our results also holds if the number of communications in the network per unit of time vanishes at moderate speed as time increases, allowing potential savings of the network's energy. Applications to power allocation in wireless ad-hoc networks are discussed. Finally, we provide numerical results which sustain our claims. © 2012 IEEE.


Wang Z.,Telecom ParisTech | Markham D.,Telecom ParisTech
Physical Review Letters | Year: 2012

In this Letter we study the nonlocal properties of permutation symmetric states of n qubits. We show that all these states are nonlocal, via an extended version of the Hardy paradox and associated inequalities. Natural extensions of both the paradoxes and the inequalities are developed which relate different entanglement classes to different nonlocal features. Belonging to a given entanglement class will guarantee the violation of associated Bell inequalities which see the persistence of correlations to subsets of players, whereas there are states outside that class which do not violate. © 2012 American Physical Society.


Bloch I.,Telecom ParisTech
Information Sciences | Year: 2011

Mathematical morphology is based on the algebraic framework of complete lattices and adjunctions, which endows it with strong properties and allows for multiple extensions. In particular, extensions to fuzzy sets of the main morphological operators, such as dilation and erosion, can be done while preserving all properties of these operators. Another extension concerns bipolar fuzzy sets, where both positive information and negative information are handled, along with their imprecision. We detail these extensions from the point of view of the underlying lattice structure. In the case of bipolarity, its two-components nature raises the question of defining a proper partial ordering. In this paper, we consider Pareto (component-wise) and lexicographic orderings. © 2010 Elsevier Inc. All rights reserved.


Rioul O.,Telecom ParisTech
IEEE Transactions on Information Theory | Year: 2011

While most useful information theoretic inequalities can be deduced from the basic properties of entropy or mutual information, up to now Shannon's entropy power inequality (EPI) is an exception: Existing information theoretic proofs of the EPI hinge on representations of differential entropy using either Fisher information or minimum mean-square error (MMSE), which are derived from de Bruijn's identity. In this paper, we first present an unified view of these proofs, showing that they share two essential ingredients: 1) a data processing argument applied to a covariance-preserving linear transformation; 2) an integration over a path of a continuous Gaussian perturbation. Using these ingredients, we develop a new and brief proof of the EPI through a mutual information inequality, which replaces Stam and Blachman's Fisher information inequality (FII) and an inequality for MMSE by Guo, Shamai, and Verd used in earlier proofs. The result has the advantage of being very simple in that it relies only on the basic properties of mutual information. These ideas are then generalized to various extended versions of the EPI: Zamir and Feder's generalized EPI for linear transformations of the random variables, Takano and Johnson's EPI for dependent variables, Liu and Viswanath's covariance- constrained EPI, and Costa's concavity inequality for the entropy power. © 2006 IEEE.


Markham D.J.H.,Telecom ParisTech
Physical Review A - Atomic, Molecular, and Optical Physics | Year: 2011

We investigate the relationship between multipartite entanglement and symmetry, focusing on permutation symmetric states. We give a highly intuitive geometric interpretation to entanglement via the Majorana representation, where these states correspond to points on a unit sphere. We use this to show how various entanglement properties are determined by the symmetry properties of the states. The geometric measure of entanglement is thus phrased entirely as a geometric optimization and a condition for the equivalence of entanglement measures written in terms of point symmetries. Finally, we see that different symmetries of the states correspond to different types of entanglement with respect to interconvertibility under stochastic local operations and classical communication. © 2011 American Physical Society.


Bloch I.,Telecom ParisTech
International Journal of Approximate Reasoning | Year: 2012

In many domains of information processing, bipolarity is a core feature to be considered: positive information represents what is possible or preferred, while negative information represents what is forbidden or surely false. If the information is moreover endowed with vagueness and imprecision, as is the case for instance in spatial information processing, then bipolar fuzzy sets constitute an appropriate knowledge representation framework. In this paper, we focus on mathematical morphology as a tool to handle such information and reason on it. Applying mathematical morphology to bipolar fuzzy sets requires defining an appropriate lattice. We extend previous work based on specific partial orderings to any partial ordering leading to a complete lattice. We address the case of algebraic operations and of operations based on a structuring element, and show that they have good properties for any partial ordering, and that they can be useful for processing in particular spatial information, but also other types of bipolar information such as preferences and constraints. Particular cases using Pareto and lexicographic orderings are illustrated. Operations derived from fuzzy bipolar erosion and dilation are proposed as well. © 2012 Elsevier Inc. All rights reserved.


Randriambololona H.,Telecom ParisTech
IEEE Transactions on Information Theory | Year: 2013

If C is a binary linear code, let C(2) be the linear code spanned by intersections of pairs of codewords of C. We construct an asymptotically good family of binary linear codes such that, for $C$ ranging in this family, C(2) also form an asymptotically good family. For this, we use algebraic-geometry codes, concatenation, and a fair amount of bilinear algebra. More precisely, the two main ingredients used in our construction are, first, a description of the symmetric square of an odd degree extension field in terms only of field operations of small degree, and second, a recent result of Garcia-Stichtenoth- Bassa-Beelen on the number of points of curves on such an odd degree extension field. © 1963-2012 IEEE.


Patent
Telecom ParisTech | Date: 2013-06-26

The invention relates to a speech recognition system (1) for creating an output text from input speech signals, comprising a dictionary (6) including in-vocabulary words and fillers,said fillers being formed by a predetermined number of language elements arranged in a combinatorial manner, each filler enabling treatment of input speech signals not corresponding to in-vocabulary words by representation as a predetermined string of language elements.


The present invention is related to a method for providing with a score an object represented by a target item from a multidimensional space, said score being representative of the probability that the object satisfies a given binary property, said method being performed in a computer environment comprising processing means connected to memory means, comprising the following steps: (a) providing and storing in the memory means data representative of a set of sample items from said multidimensional space, each sample item being associated with a multi-value label representative of the probability that an object represented by said sample item satisfies the given binary property; (b) storing in the memory means data representative of the target item; (c) with said processing means, generating and storing in said memory means data representative of an oriented binary tree with a given height, said binary tree being defined by a plurality of nodes having index values in relation with their position in the binary tree, said nodes comprising a root node, intermediate nodes and terminal nodes, and each node being associated with a subspace of the multidimensional space according to the following rules: if the node is a root node, the associated subspace is the whole multidimensional subspace; if the node is a non-terminal node, its associated subspace is split into two disjoint subspaces _(+) and _() and respectively associated with a first child node and a second child node of said non-terminal node, said splitting being performed by the processing unit according to a classifier minimizing the number of sample items associated with a first given label value to belong to the subspace _(+), and/or the number of sample items associated with a second given label value to belong to the subspace _(), said second label value being representative of a higher probability that an object represented by said sample item satisfies the given binary property than said first given label value; (d) with said processing means, associating with at least each terminal node of the binary tree a score depending on its index value in the binary tree, and storing the score value in the memory means; (e) with said processing means, identifying a target node, the target node being a teminal node whose associated subspace comprises the target item; and (f) outputting the score value associated with said target node. The invention is also related to a decision-support system.


An optical network comprising a plurality of nodes connected via two or more optical links (a, b, c, d, e, f, g). It comprises means to generate a supervisory optical signal transmitted through the optical links, means to duplicate and forward (401, 403, 405) the supervisory optical signal received by a node towards one or several other nodes, a plurality of optical monitors (402, 404, 406, 407), the said monitors being arranged in order to detect disruptions of the supervisory optical signal and to determine an alarm code (408) allowing to localize network failures.

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