There are several methods to test the hypothesis of complete spatial randomness of point patterns. In this paper, we compare the performance of distance-based tests, such as the T 2 methods, and angle-based tests. The comparison takes into account the sampling effort needed to carry out the tests. Among the angle-based tests, we introduce modifications to the originally proposed test by Assunçã...

The analysis of point patterns often begins with a test of complete spatial randomness using summaries such as the emptyspace function F or the nearest neighbour distance distribution function G. These functions constitute basic summaries upon which many studies are based, depending on their shape. As the map of points is usually considered accurate, Monte Carlo tests are performed on the obser...

Do completely unpredictable events exist? Classical physics excludes fundamental randomness. Although quantum theory makes probabilistic predictions, this does not imply that nature is random, as randomness should be certified without relying on the complete structure of the theory being used. Bell tests approach the question from this perspective. However, they require prior perfect randomness...

A central object of study in the field of algorithmic randomness are notions of randomness for sequences, i.e., infinite sequences of zeros and ones. These notions are usually defined with respect to the uniform measure on the set of all sequences, but extend canonically to other computable probability measures. This way each notion of randomness induces an equivalence relation on the computabl...

Abstract Activated carbon can be manufactured from waste coffee grounds via physical and/or chemical activation processes. However, challenges remain to quantify the differences in surface morphology between activated granules and grounds. This paper presents a novel quantitative method determine quality of processes performed presence intensity inhomogeneity identify characteristics The spatia...

Multivariate interaction between two or more classes (or species) has important consequences in many fields and causes multivariate clustering patterns such as segregation or association. The spatial segregation occurs when members of a class tend to be found near members of the same class (i.e., near conspecifics) while spatial association occurs when members of a class tend to be found near m...

The motion of assemblies of point vortices in a periodic parallelogram can be described by the complex position zj(t) whose time derivative is given by the sum of the complex velocities induced by other vortices and the solid rotation centered at zj . A numerical simulation up to 100 vortices in a square periodic box is performed with various initial conditions, including single and double rows...