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- J-M Loubes, P Rochet
- 2009

We tackle the inverse problem of reconstructing an unknown finite measure µ from a noisy observation of a generalized moment of µ defined as the integral of a continuous and bounded operator Φ with respect to µ. When only a quadratic approximation Φ m of the operator is known, we introduce the L 2 approximate maximum entropy solution as a minimizer of a… (More)

In this paper, we aim at recovering an undirected weighted graph of N vertices from the knowledge of a perturbed version of the eigenspaces of its adjacency matrix W. Our approach is based on minimizing a cost function given by the Frobenius norm of the commutator AB−BA between symmetric matrices A and B. In the Erdős-Rényi model with no self-loops, we show… (More)

A well-known combinatorial theorem says that a set of n non-collinear points in the plane determines at least n distinct lines. Chen and Chvátal conjectured that this theorem extends to metric spaces, with an appropriated definition of line. In this work we prove a slightly stronger version of Chen and Chvátal conjecture for a family of graphs containing… (More)

The characterization of a graph via the variable adjacency matrix enables to dene a partially ordered relation on the walks. Studying the incidence algebra on this poset reveals unsuspected relations between connected and self-avoiding walks on the graph. These relations are derived by considering truncated versions of the characteristic polynomial of… (More)

Calibration methods have been widely studied in survey sampling over the last decades. Viewing calibration as an inverse problem, we extend the calibration technique by using a maximum entropy method. Finding the optimal weights is achieved by considering random weights and looking for a discrete distribution which maximizes an entropy under the calibration… (More)

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