Abstract The seemingly universal phenomenon of scale-dependent effective dimensions in non-perturbative theories quantum gravity has been shown to be a potential source phenomenology. dimension from only considered for scalar fields. It is, however, possible that the non-manifold like structures, are expected appear near Planck scale, have an depends on type field under consideration. To invest...

Dynamical Localization theory has drawn attention to general spectral conditions which make quantum wave packet diffusion possible, and it was found that dimensional properties of the Local Density of States play a crucial role in that connection. In this paper an abstract result in this vein is presented. Time averaging over the trajectory of a wavepacket up to time T defines a statistical ope...

In this paper, we consider spectral properties of Riesz product measures supported on homogeneous Cantor sets and we show the existence of spectral measures with arbitrary Hausdorff dimensions, including non-atomic zero-dimensional spectral measures and one-dimensional singular spectral measures.

Abstracts — The spectral test provides a reliable measure for lattice assessment and can be computed very efficiently. It has extensively been applied to find good lattices for several MC and QMC applications. In order to enable comparisons across dimensions, a normalized spectral test is widely used. We empirically demonstrate significant shortcomings of this normalization in high dimensions, ...

n many applications of color technology such as spectral color reproduction, it is of interest to represent the spectral data with lower dimensions than spectral space dimensions. It is more than half of a century that Principal Component Analysis (PCA) method has been applied to find the number of independent basis vectors of spectral dataset and representing spectral reflectance with lower di...