Diierential operators have been widely used for multiscale geometric descriptions of images. The eecient computation of these diierential operators is always desirable. Moreover, it has not been clear whether such representations are invertible. For certain applications, it is usually required that such representations should be invertible so that one can facilitate the processing of informatio...

Differential operators have been widely used for multiscale geometric descriptions of images. The efficient computation of these differential operators is always desirable. Moreover, it has not been clear whether such representations are invertible. For certain applications, it is usually required that such representations should be invertible so that one can facilitate the processing of inform...

Nowadays, multiscale modelling is recognized as the most suitable way to study biological processes. Indeed, almost every phenomenon in nature exhibits a multiscale behaviour, i.e., it is the outcome of interactions that occur at different spatial and temporal scales. Although several ways to provide “multilayer” models have been proposed, only Complex Automata naturally embed spatial informati...

The tensile properties of multiscale, hybrid, thermoplastic-based nanocomposites reinforced with nano-CaCO3 particles and micro–short glass fibers (SGF) were predicted by a two-step, three-dimensionalmodel using ANSYS finite element (FE) software. Cylindrical and cuboid representative volume elements were generated to obtain the effective behavior of the multiscale hybrid composites. In the fir...

It is now widely acknowledged that traditional wavelets are not very effective in dealing with multidimensional signals containing distributed discontinuities. Shearlet Transform is a new discrete multiscale directional representation, which combines the power of multiscale methods with a unique ability to capture the geometry of multidimensional data and is optimally efficient in representing ...

We present a novel approach for estimating the intrinsic dimension of certain point clouds: we assume that the points are sampled from a manifold M of dimension k, with k << D, and corrupted by D-dimensional noise. When M is linear, one may analyze this situation by PCA: with no noise one would obtain a rank k matrix, and noise may be treated as a perturbation of the covariance matrix. WhenM is...