In 1959, Rényi proposed the information dimension and the d-dimensional entropy to measure the information content of general random variables. This paper proposes a generalization of information dimension to stationary stochastic processes by defining the information dimension rate as the entropy rate of the uniformly-quantized stochastic process divided by minus the logarithm of the quantizer...

A new data dimension-reduction method, called Internal Information Redundancy Reduction (IIRR), is proposed for application to Optical Emission Spectroscopy (OES) datasets obtained from industrial plasma processes. For example in a semiconductor manufacturing environment, real-time spectral emission data is potentially very useful for inferring information about critical process parameters such...

We present a model of (modified) gravity on spacetimes with fractal structure based on packing of spheres, which are (Euclidean) variants of the Packed Swiss Cheese Cosmology models. As the action functional for gravity we consider the spectral action of noncommutative geometry, and we compute its asymptotic expansion on a space obtained as an Apollonian packing of 3-dimensional spheres inside ...

A spectral reflectance reconstruction method based on combining PCA and regularized polynomial is proposed to optimize the spectral data and channel response. Firstly, the PCA method is used to reduce the high dimensional spectral data of the training samples. Then, the polynomial expansion for channel response of the sample is carried out to improve the accuracy of spectral reconstruction thro...

Abstract: This paper aims to present a polynomial approach to the steady-state optimal filtering for delayed systems. The design of the steady-state filter involves solving one polynomial equation and one spectral factorization. The key problem in this paper is the derivation of spectral factorization for systems with delayed measurement, which is more difficult than the standard systems withou...

In [32, 31], fast deterministic algorithms based on spectral methods were derived for the Boltzmann collision operator for a class of interactions including the hard spheres model in dimension 3. These algorithms are implemented for the solution of the Boltzmann equation in dimension 2 and 3, first for homogeneous solutions, then for general non homogeneous solutions. The results are compared t...

Light transport is often characterized within a high-dimensional space although practitioners have long known that it commonly behaves as a much lower-dimensional phenomenon. We study the effective dimension of light transport over a neighborhood on the scene manifold and show that under plausible assumptions the dimensionality is characterized by the spectrum of the spatio-spectral concentrati...

Most natural surfaces and surfaces of engineering interest, e.g., polished or sandblasted surfaces, are self-affine fractal over a wide range of length scales, with the fractal dimension Df 1⁄4 2:15 0:15. We give several examples illustrating this and a simple argument, based on surface fragility, for why the fractal dimension usually is \2.3. A kinetic model of sandblasting is presented, which...

Auditory-nerve spike trains exhibit fractal behavior, and therefore traditional renewal-point-process models fail to describe them adequately. Previous measures of the fractal exponent of these spike trains are based on the Fano factor and consequently cannot exceed unity. Two estimates of the fractal exponent are considered which do not suuer from this limit: one derived from the Allan varianc...