Transport Properties of Random Walks on Scale-Free/Regular-Lattice Hybrid Networks

We study numerically the mean access times for random walks on hybrid disordered structures formed by embedding scale-free networks into regular lattices, considering different transition rates for steps across lattice bonds ($F$) and across network shortcuts ($f$). For fast shortcuts ($f/F\gg 1$) and low shortcut densities, traversal time data collapse onto an universal curve, while a crossover behavior that can be related to the percolation threshold of the scale-free network component is identified at higher shortcut densities, in analogy to similar observations reported recently in Newman-Watts small-world networks. Furthermore, we observe that random walk traversal times are larger for networks with a higher degree of inhomogeneity in their shortcut distribution, and we discuss access time distributions as functions of the initial and final node degrees. These findings are relevant, in particular, when considering the optimization of existing information networks by the addition of a small number of fast shortcut connections.Comment: 8 pages, 6 figures; expanded discussions, added figures and references. To appear in J Stat Phy

Sensing small-scale human activity in the palaeoecological record: fine spatial resolution pollen analyses from Glen Affric, northern Scotland

This paper examines the importance of palynological site selection criteria, speci"cally basin size, for the detection of vegetation mosaics and small- or local-scale human activity within a spatially diverse, mosaic landscape. Using a site selection strategy which recognizes landscape patchiness, pollen analyses from three small peat basins (10-56 m diameter) in an open, exposed upland valley (greater than 250 m OD) provide records which are sensitive to local vegetation mosaics and small-scale, localized agriculture. The results indicate c. 4000 14C years (4400 cal. years) of land use, with spatial and temporal variations in the valley. Contrasts between the sequences suggest that local pollen production remains an important component of the pollen rain deposited in small peat basins, even in open environments; this is especially true of palynological‘agricultural indicators'. By comparison, sites with regional pollen source areas underestimate the spatial diversity of the upland landscape, and are insensitive to small-scale human activity in an environment where the fragmentary distribution of soils suitable for agriculture favoured a small-scale, dispersed pattern of farming. It is therefore essential to match the spatial resolution of pollen records with the grain size or scale of variations in the environment under investigation in order to sense the scale of mosaics in vegetation and agriculture within patchy landscapes