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Estimating composite functions by model selection

Yannick Baraud, Lucien Birgé (2014)

Annales de l'I.H.P. Probabilités et statistiques

We consider the problem of estimating a function s on [ - 1 , 1 ] k for large values of k by looking for some best approximation of s by composite functions of the form g u . Our solution is based on model selection and leads to a very general approach to solve this problem with respect to many different types of functions g , u and statistical frameworks. In particular, we handle the problems of approximating s by additive functions, single and multiple index models, artificial neural networks, mixtures of Gaussian...

Estudio de algunas secuencias pseudoaleatorias de aplicación criptográfica.

P. Caballero Gil, A. Fúster Sabater (1998)

Revista Matemática Complutense

Pseudorandom binary sequences are required in stream ciphers and other applications of modern communication systems. In the first case it is essential that the sequences be unpredictable. The linear complexity of a sequence is the amount of it required to define the remainder. This work addresses the problem of the analysis and computation of the linear complexity of certain pseudorandom binary sequences. Finally we conclude some characteristics of the nonlinear function that produces the sequences...

EuDML—Towards the European Digital Mathematics Library

Sylwestrzak, Wojtek, Borbinha, José, Bouche, Thierry, Nowiński, Aleksander, Sojka, Petr (2010)

Towards a Digital Mathematics Library. Paris, France, July 7-8th, 2010

The paper describes the background, the expected functionalities, and the architecture design goals of the European Digital Mathematics Library (Eu-DML), an infrastructure system aimed to integrate the mathematical contents available online throughout Europe, allowing for both extensive and specialized mathematics resource discovery. The three years long project to build the EuDML, partially funded by the European Commission, started in February 2010.

Euler's Polyhedron Formula

Jesse Alama (2008)

Formalized Mathematics

Euler's polyhedron theorem states for a polyhedron p, thatV - E + F = 2,where V, E, and F are, respectively, the number of vertices, edges, and faces of p. The formula was first stated in print by Euler in 1758 [11]. The proof given here is based on Poincaré's linear algebraic proof, stated in [17] (with a corrected proof in [18]), as adapted by Imre Lakatos in the latter's Proofs and Refutations [15].As is well known, Euler's formula is not true for all polyhedra. The condition on polyhedra considered...

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