The Southern Africa Millennium Ecosystem Assessment developed an index for quantifying the state of biodiversity. The Biodiversity Intactness Index (BII) operates at the species level, and is based on changes in species abundance, rather than changes in richness brought about by extinction. The BII uses spatial data on species richness and land use activities per ecosystem type to weight estima...

Differential and integral calculus on time scales allows to develop a theory of dynamic equations in order to unify and extend the usual differential equations and difference equations. For single variable differential and integral calculus on time scales, we refer the reader to the textbooks [4, 5] and the references given therein. Multivariable calculus on time scales was developed by the aut...

We have studied the FR I radio galaxy NGC 6251 and its environment at several wavelengths and scale lengths. On the large scale, we have probed the gravity field by measuring the velocity dispersion of the cluster members associated with NGC 6251 and relating this to the clus-ter's X-ray emission. On the small scale, the gravitational information is provided by cold HI near the nucleus and the ...

Small-world architectures may be implicated in a range of phenomena from networks of neurons in the cerebral cortex to social networks and propogation of viruses [1]-[2]. Small-world networks are interpolations of regular and random networks that retain the advantages of both regular and random networks by being highly clustered like regular networks and having small average path length between...

Recent arguments show that some curvaton field may generate the cosmological curvature perturbation. As the curvaton is independent of the inflaton field, there is a hope that the fine-tunings of inflation models can be cured by the curvaton scenario. More recently, however, D.H.Lyth discussed that there is a strong bound for the Hubble parameter during inflation even if one assumes the curvato...

We present a novel formulation, called the WaMPDE, for solving systems with forced autonomous components. An important feature of the WaMPDE is its ability to capture frequency modulation (FM) in a natural and compact manner. This is made possible by a key new concept: that of warped time, related to normal time through separate time scales. Using warped time, we obtain a completely general for...

Arguments regarding the appropriate form for the rate at which consumers extract biomass from resource populations hinge on relative time scales of underlying processes. Some ecologists argue that, because differential equation models imply instantaneous rates of change, time scale arguments do not hold. Here we point out that this reasoning is fallacious. We define three natural time scales fo...

Water-biomolecule interactions have been extensively studied in dilute solutions, crystals, and rehydrated powders, but none of these model systems may capture the behavior of water in the highly organized intracellular milieu. Because of the experimental difficulty of selectively probing the structure and dynamics of water in intact cells, radically different views about the properties of cell...

A multiple scales analysis is used to construct a uniformly accurate approximation to water hammer pressure wave attenuation that is initiated by a sudden valve opening. The method of analysis is well suited to the study of a water hammer that possesses several time scales and is applied to a mild generalization of the classical equations. It should prove useful for finding attenuation curves w...

The dynamic behavior of scalp potentials (EEG) is apparently due to some combination of global and local processes with important top-down and bottom-up interactions across spatial scales. In treating global mechanisms, we stress the importance of myelinated axon propagation delays and periodic boundary conditions in the cortical-white matter system, which is topologically close to a spherical ...