University of Marne-la-Vallée

About: University of Marne-la-Vallée is a based out in . It is known for research contribution in the topics: Estimator & Context (language use). The organization has 831 authors who have published 1855 publications receiving 55316 citations.

An explicit formula for the characters of the symmetric group

Abstract: We give an explicit expression of the normalized characters of the symmetric group in terms of the “contents” of the partition labelling the representation.

Sandpile group on the graph D n of the dihedral group

Abstract: In this paper we study the structure of the Abelian sandpile group on the Cayley graph Dn of the dihedral group Dn = 〈a, b | an = b2 = (ab)2 = 1〉. We prove that the Smith normal form of the sandpile group is not cyclic as one can generally expect but is always the direct product of two or three cyclic groups. We conclude by considering some particular cases.

Higher genus Riemann minimal surfaces

Abstract: Riemann surfaces constitute a one parameter family of embedded minimal surfaces which are periodic and have infinitely many horizontal planar ends. The surfaces in this family are foliated by circles (or straight lines). In this paper, we prove the existence of a one parameter family of embeded minimal surfaces which have infinitely many horizontal planar ends and have genus k, for k = 1, ... , 37. Riemann surfaces, as their flux is nearly vertical, can be understood as a sequence of parallel planes connected by slightly bent catenoidal neks. The surfaces we construct are obtained by replacing one of these catenoidal necks by a member of the family of minimal surfaces discovered by C. Costa, D. Hoffman and W. Meek.

Optimal learning with $Q$-aggregation

Abstract: We consider a general supervised learning problem with strongly convex and Lipschitz loss and study the problem of model selection aggregation. In particular, given a finite dictionary functions (learners) together with the prior, we generalize the results obtained by Dai, Rigollet and Zhang [Ann. Statist. 40 (2012) 1878-1905] for Gaussian regression with squared loss and fixed design to this learning setup. Specifically, we prove that the $Q$-aggregation procedure outputs an estimator that satisfies optimal oracle inequalities both in expectation and with high probability. Our proof techniques somewhat depart from traditional proofs by making most of the standard arguments on the Laplace transform of the empirical process to be controlled.