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The aim of this work is to provide a new Linearization Principle approach particularly suited for problems in fluid–structure stability. The complexity here, and the main difference with respect to the classical approach, comes from the fact that the full ...
We provide necessary and sufficient conditions for stochastic invariance of finite dimensional submanifolds with boundary in Hilbert spaces for stochastic partial differential equations driven by Wiener processes and Poisson random measures. ...
In this paper we propose a novel dimensionality reduction method that is based on successive Laplacian SVM projections in orthogonal deflated subspaces. The proposed method, called Laplacian Support Vector Analysis, produces projection vectors, which captu ...
We study a driven-dissipative array of coupled nonlinear optical resonators by numerically solving the von Neumann equation for the density matrix. We demonstrate that quantum correlated states of many photons can also be generated in the limit where the n ...
Institute of Physics (IoP) and Deutsche Physikalische Gesellschaft2013
This project offers a rigorous introduction to the tools needed to construct a continuous stochastic process. Among other things, we give a very detailed proof of the Kolmogorov continuity criterion. We then construct a Brownian Motion following the formal ...
We present complex rotation-covariant multiresolution families aimed for image analysis. Since they are complex-valued functions, they provide the important phase information, which is missing in the discrete wavelet transform with real wavelets. Our basis ...
David Hilbert discovered in 1895 an important metric that is canonically associated to any convex domain Ω in the Euclidean (or projective) space. This metric is known to be Finslerian, and the usual proof assumes a certain degree of smoothness of t ...
We present a detailed discussion of the evolution of a statistical ensemble of quantum mechanical systems coupled weakly to a bath. The Hilbert space of the full system is given by the tensor product between the Hilbert spaces associated with the bath and ...
This brief presents a methodology to develop recursive filters in reproducing kernel Hilbert spaces. Unlike previous approaches that exploit the kernel trick on filtered and then mapped samples, we explicitly define the model recursivity in the Hilbert spa ...
The set of solutions of a parameter-dependent linear partial differential equation with smooth coefficients typically forms a compact manifold in a Hilbert space. In this paper we review the generalized reduced basis method as a fast computational tool for ...