We derive generalized estimators for a number of spatial statistics that have been used in the analysis of spatially resolved omics data, such as Ripleys K, H and L functions, clustering index, and degree of clustering, which allow these statistics to be calculated on data modelled by arbitrary random measures. Our estimators generalize those typically used to calculate these statistics on poin...

The mean conditional fixation time of a mutant is an important measure of stochastic population dynamics, widely studied in ecology and evolution. Here, we investigate the effect of spatial randomness on the mean conditional fixation time of mutants in a constant population of cells, N. Specifically, we assume that fitness values of wild type cells and mutants at different locations come from g...

Attempts are made to employ persistent homology to infer topological properties of point cloud data. Two potential approaches are introducted and briefly evaluated, both relying on Monte Carlo estimation and the program PLEX [9]. First, homology signatures are compared to a null distribution that exhibits complete spatial randomness. This can be regarded as similar to hypothesis testing with th...

We define a pair-correlation function that can be used to characterize spatiotemporal patterning in experimental images and snapshots from discrete simulations. Unlike previous pair-correlation functions, the pair-correlation functions developed here depend on the location and size of objects. The pair-correlation function can be used to indicate complete spatial randomness, aggregation, or seg...