Ripley’s K(t) function is a tool to analyze completely mapped spatial point process data. Spatial point process data consists of the locations of events. These are usually recorded in 2 dimensions, but they may be locations along a line or in space. Here I will only describe K(t) for 2 dimensional spatial data. Completely mapped data includes the locations of all events in a predefined study ar...

The analysis of point event patterns in geography, ecology and epidemiology have a long tradition (e.g. Snow, 1855; Clark & Evans, 1954; Harvey, 1966; Mantel, 1967; Cliff & Ord, 1981). The patterns detected are usually broadly classified as random, uniform or clustered. Whilst spatial randomness has traditionally been assumed to have no underlying process of interest, Phillips (1999) has pointe...

The characterization, identification, and understanding of spatial patterns are central concerns of geography. Deeply rooted in the notion that geographic location matters, one testable assumption is that near things are more related than distant things—a concept often referred to as Tobler’s first law of geography. One means of quantifying this assumption is using measures of spatial autocorre...

MOTIVATION Microscopy advances have enabled the acquisition of large-scale biological images that capture whole tissues in situ. This in turn has fostered the study of spatial relationships between cells and various biological structures, which has proved enormously beneficial toward understanding organ and organism function. However, the unique nature of biological images and tissues precludes...

In this paper, we investigate the emergence of a predator-prey system with Ivlevtype functional response and reaction-diffusion. We study how diffusion affects the stability of predator-prey coexistence equilibrium and derive the conditions for Hopf and Turing bifurcation in the spatial domain. Based on the bifurcation analysis, we give the spatial pattern formation, the evolution process of th...

Background: Malnutrition is a great challenge for the public health system. Therefore, this study aimed to study the spatial pattern malnutrition using GIS in the world's countries. Materials and Methods: In this cross-sectional study, secondar...

Five contrasting deciduous forest stands were studied to characterise the spatial structural 23 variability in human-influenced forests. These stands are representative of cultural forest types 24 widely represented in western Europe: one plantation, two coppices, one wood-pasture, and one 25 high forest stand. All stems with DBH > 5 cm were measured and mapped, and stem DBH 26 distributions, s...

We propose a novel method for the description of spatial patterns formed by a coverage of point sets representing galaxy samples. This method is based on a complete family of morphological measures known as Minkowski functionals, which includes the topological Euler characteristic and geometric descriptors to specify the content, shape and connectivity of spatial sets.