This paper reviews the functional aspects of statistical learning theory. The main point under consideration is the nature of the hypothesis set when no prior information is available but data. Within this framework we first discuss about the hypothesis set: it is a vectorial space, it is a set of pointwise defined functions, and the evaluation functional on this set is a continuous mapping. Ba...

<p style='text-indent:20px;'>Many recurrent neural network machine learning paradigms can be formulated using state-space representations. The classical notion of canonical realization is adapted in this paper to accommodate semi-infinite inputs so that it used as a dimension reduction tool the networks setup. so-called input forgetting property identified key hypothesis guarantees existe...

Stochastic analysis of random heterogeneous media provides useful information only if realistic input models of the material property variations are used. These input models are often constructed from a set of experimental samples of the underlying random field. To this end, the Karhunen-Loève (K-L) expansion, also known as principal component analysis (PCA), is the most popular model reduction...

In this brief note, it is shown that the random hyperbolicity of a random linear cocycle is equivalent to having the Lipschitz shadowing property.

In this paper we investigate how the short-time Fourier transform can be extended in a Clifford setting. We prove some of main properties such as orthogonality relation, reconstruction property and reproducing kernel formula. Moreover, show effects modulating translating signal window function, respectively. Finally, demonstrate Lieb’s uncertainty principle for transform.

Since meshless methods have been introduced to alleviate the difficulties arising in conventional finite element method, many papers on applications of meshless methods to boundary element method have been published. However, most of these papers use moving least squares approximation functions that have difficulties in prescribing essential boundary conditions. Recently, in order to strengthen...