We introduce a new method for the enumeration of self-avoiding walks based on the lace expansion. We also introduce an algorithmic improvement, called the two-step method, for self-avoiding walk enumeration problems. We obtain significant extensions of existing series on the cubic and hypercubic lattices in all dimensions d 3: we enumerate 32-step… (More)
We evaluate the virial coefficients B k for k ≤ 10 for hard spheres in dimensions D = 2, · · · , 8. Virial coefficients with k even are found to be negative when D ≥ 5. This provides strong evidence that the leading singularity for the virial series lies away from the positive real axis when D ≥ 5. Further analysis provides evidence that negative virial… (More)
We exactly calculate the fourth virial coefficient for hard spheres in even dimensions for D = 4, 6, 8, 10, and 12.
Forecasts of range dynamics now incorporate many of the mechanisms and interactions that drive species distributions. However, connectivity continues to be simulated using overly simple distance-based dispersal models with little consideration of how the individual behaviour of dispersing organisms interacts with landscape structure (functional… (More)
Deviance information criterion (DIC) calculation and selection of the negative binomial distribution Giant cuttlefish counts were overdispersed (i.e. Poisson variance exceeded the mean) with an excess of zeros, so we tested the ability of four distributions (Poisson, zero-inflated Poisson, negative binomial and zero-inflated negative binomial) to account… (More)
We present new results for the virial coefficients B k with k ≤ 10 for hard spheres in dimensions D = 2, · · · , 8.