This article presents two caveats for the analysis of large-scale structure. Within distances for which the fractal structure of the distribution of galaxies obtains, fluctuations may be on the scale of the measurements themselves, as is typical of fractals. Second, within this region it is...

Minkowski functionals constitute a family of order parameters which discriminate spatial patterns according to size, shape, and connectivity. Here we point out that these scalar descriptors can be complemented by vector-valued curvature measures also known as Quermaß vectors. Using examples of...

The power spectrum is traditionally parameterized by a truncated Taylor series: ln P(k) = ln P{sub *} + (n{sub *} - 1) ln(k/k{sub *}) + 1/2 n'{sub *} ln{sup 2} (k/k{sub *}). It is reasonable to truncate the Taylor series if |n'{sub *} ln(k/k{sub *})| << |n{sub *} - 1|, but it is not if |n'{sub *} ln(k/k{sub *})| {approx}> |n{sub *} - 1|. We argue that there is no...</<>

Machine learning has emerged as a important tool for separating signal events from associated background in high energy particle physics experiments. This paper describes a new machine learning method based on ensembles of rules. Each rule consists of a conjuction of a small number of simple...

We consider a toy metric in four-dimensional space–time defined in terms of a recursive hierarchical prescription. The matter distribution turns out to be extremely inhomogeneous. Surprisingly, for very large samples the average mass density tends (very slowly) to a constant. There is no trace...

In order to determine the concept of space interpretation in several multiverse hypotheses, this article analyzes a number of them, which arises from some theories of modern physics. The interpretation of space in the history of philosophy and science and their interrelation with modern physical...

A one-dimensional (1D) system obeying the Hubble expansion is studied numerically using an N-body code. The rescaling of both space and time changes the dynamics which, in the rescaled frame, is analogous to the dynamics of a 1D one-component plasma with the addition of a friction term. We start...