Many studies have examined whether communities are structured by random or deterministic processes, and both are likely to play a role, but relatively few studies have attempted to quantify the degree of randomness in species composition. We quantified, for the first time, the degree of randomness in forest bird communities based on an analysis of spatial autocorrelation in three regions of Ger...

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

We describe fully polynomial randomized approximation schemes for the problems of determining the number of Hamilton paths and cycles in an n-vertex graph with minimum degree (g + e)n, for any fixed e > 0. We show that the exact counting problems are #P-complete. We also describe fully polynomial randomized approximation schemes for counting paths and cycles of all sizes in such graphs.

There is considerable interest in cell biology in determining whether, and to what extent, the spatial arrangement of nuclear objects affects nuclear function. A common approach to address this issue involves analyzing a collection of images produced using some form of fluorescence microscopy. We assume that these images have been successfully pre-processed and a spatial point pattern represent...

Many conceptual studies of local cortical networks assume completely random wiring. For spatially extended networks, however, such random graph models are inadequate. The geometry of neuronal dendrites and axons induces distance-dependent connectivity. Here, we investigated several types of spatial embedding that are widely used in modeling. Both regarding the spatial positions of nodes and in ...

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...