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We derive generalization and excess risk bounds for neural networks using a family of complexity measures based on a multilevel relative entropy. The bounds are obtained by introducing the notion of generated hierarchical coverings of neural networks and b ...
In [8] we introduced the notion of multi-Koszul algebra: it is an extension of the definition of generalized Koszul algebra given by R. Berger in [1] for homogeneous algebras (see also [7]) that can be applied to any nonnegatively graded connected algebra ...
The aim of this article is to provide explicit formulas for the cup product on the Hochschild cohomology of any nonnegatively graded connected algebra and for the cap products on the Hochschild homology of with coefficients in any graded bimodule at the le ...
Magnetic resonance imaging is widely used in medical diagnosis to obtain anatomical details of the human body in a non-invasive way. Clinical MR scanners typically operate at a static magnetic field strength (B0) of 1.5T or 3T. However, going to higher fie ...
We consider a divergence-form elliptic difference operator on the lattice Zd, with a coefficient matrix that is an i.i.d. perturbation of the identity matrix. Recently, Bourgain introduced novel techniques from harmonic analysis to prove the convergence of ...
We study the evolution equation where is the Dirichlet-Neumann operator of a decreasing family of Riemannian manifolds with boundary . We derive a lower bound for the solution of such an equation, and apply it to a quantitative density estimate for the res ...
Cakoni and Nguyen recently proposed very general conditions on the coefficients of Maxwell equations for which they established the discreten ess of the set of eigenvalues of the transmission problem and studied their locations. In this paper, we establish ...
For the application of discomfort glare metrics, a categorisation is used, dividing the metric scale into categories of perception. These categories are separated by borderline values, or so-called cut-off values. Recent literature shows that these cut-off ...
This work studies the problem of statistical inference for Fréchet means in the Wasserstein space of measures on Euclidean spaces, W2(Rd). This question arises naturally from the problem of separating amplitude and phase variation i ...
The problem of control synthesis to maximize the probability of satisfying automata specifications for systems with uncertainty is addressed. Two types of uncertainty are considered; stochasticity in the dynamical system and in the sets defining the specif ...
