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This thesis concerns the theory of positive-definite completions and its mutually beneficial connections to the statistics of function-valued or continuously-indexed random processes, better known as functional data analysis. In particular, it dwells upon ...
In this paper, we analyze the recently proposed stochastic primal-dual hybrid gradient (SPDHG) algorithm and provide new theoretical results. In particular, we prove almost sure convergence of the iterates to a solution and linear convergence with standard ...
This paper is devoted to the study of the behavior of the unique solution u delta is an element of H-0(1)(Omega), as delta -> 0, to the equation div(s(delta)A del u(delta)) + k(2)s(0)Sigma u(delta) = s0 f in Omega, where Omega is a smooth connected bounded ...
A simple characterisation of topological amenability in terms of bounded cohomology is proved, following Johnson's formulation of amenability. The connection to injective Banach modules is established. ...
In this paper, we provide a Banach-space formulation of supervised learning with generalized total-variation (gTV) regularization. We identify the class of kernel functions that are admissible in this framework. Then, we propose a variation of supervised l ...
We present new results concerning the approximation of the total variation, integral(Omega)vertical bar del u vertical bar, of a function u by non-local, non-convex functionals of the form Lambda delta(u) = integral(Omega)integral(Omega)delta phi(vertical ...
The well-known "necklace splitting theorem" of Alon (1987) asserts that every k-colored necklace can be fairly split into q parts using at most t cuts, provided k(q - 1)
The present invention relates system for planning and/or providing neuromodulation (10), especially neurostimulation, comprising - a neurostimulator (24) comprising a least one electrode (22), - functional mapping module (38) configured and arranged such t ...
We study the Gowers uniformity norms of functions over Z/pZ which are trace functions of l-adic sheaves. On the one hand, we establish a strong inverse theorem for these functions, and on the other hand this gives many explicit examples of functions with G ...
In this note we show that, for any proper action of a Banach-Lie group G on a Banach manifold M, the corresponding tangent maps g -> T-x(M) have closed range for each x is an element of M, i.e., the tangent spaces of the orbits are closed. As a consequence ...
