Laplace transforms of probability distributions and their inversions are easy on logarithmic scales

It is shown that, when expressing arguments in terms of their logarithms, the Laplace transform of a function is related to the antiderivative of this function by a simple convolution. This allows efficient numerical computations of moment generating functions of positive random variables and their inversion. The application of the method is straightforward, apart from the necessity to implement it using high-precision arithmetics. In numerical examples the approach is demonstrated to be particularly useful for distributions with heavy tails, Such as lognormal, Weibull, or Pareto distributions, which are otherwise difficult to handle. The computational efficiency compared to other methods is demonstrated for an M/G/1 queueing problem.

Some properties of the speciation model for food-web structure - Mechanisms for degree distributions and intervality

We present a mathematical analysis of the speciation model for food-web structure, which had in previous work been shown to yield a good description of empirical data of food-web topology. The degree distributions of the network are derived. Properties of the speciation model are compared to those of other models that successfully describe empirical data. It is argued that the speciation model unities the underlying ideas of previous theories. In particular, it offers a mechanistic explanation for the success of the niche model of Williams and Martinez and the frequent observation of intervality in empirical food webs. (c) 2005 Elsevier Ltd. All rights reserved.

Soil resource supply influences faunal size-specific distributions in natural food webs

The large range of body-mass values of soil organisms provides a tool to assess the ecological organization of soil communities. The goal of this paper is to identify graphical and quantitative indicators of soil community composition and ecosystem functioning, and to illustrate their application to real soil food webs. The relationships between log-transformed mass and abundance of soil organisms in 20 Dutch meadows and heathlands were investigated. Using principles of allometry, maximal use can be made of ecological theory to build and explain food webs. The aggregate contribution of small invertebrates such as nematodes to the entire community is high under low soil phosphorus content and causes shifts in the mass-abundance relationships and in the trophic structures. We show for the first time that the average of the trophic link lengths is a reliable predictor for assessing soil fertility responses. Ordered trophic link pairs suggest a self-organizing structure of food webs according to resource availability and can predict environmental shifts in ecologically meaningful ways.

“Superluminal” transmission via entanglement, superoscillations, and quasi-Dirac distributions

We analyze a system inwhich, due to entanglement between the spin and spatial degrees of freedom, the reduced transmitted state has the shape of the freely propagating pulse translated in the complex coordinate plane. In the case an apparently “superluminal” advancement of the pulse, the delay amplitude distribution is found to be a peculiar approximation to the Dirac d function, and the transmission coefficient exhibits a well-defined superoscillatory window. Analogies with potential tunneling and Wheeler’s delayed choice experiment are highlighted.

Clustering and synchrony in laying hens: The effect of environmental resources on social dynamics

Laying hens generally choose to aggregate, but the extent to which the environments in which we house them impact on social group dynamics is not known. In this paper the effect of pen environment on spatial clustering is considered. Twelve groups of four laying hens were studied under three environmental conditions: wire floor (W), shavings (Sh) and perches, peat, nestbox and shavings (PPN). Groups experienced each environment twice, for five weeks each time, in a systematic order that varied from group to group. Video recordings were made one day per week for 30 weeks. To determine level of clustering, we recorded positional data from a randomly selected 20-min excerpt per video (a total of 20 min x 360 videos analysed). On screen, pens were divided into six equal areas. In addition, PPN pens were divided into an additional four (sub) areas, to account for the use of perches (one area per half perch). Every 5 s, we recorded the location of each bird and calculated location use over time, feeding synchrony and cluster scores for each environment. Feeding synchrony and cluster scores were compared against unweighted and weighted (according to observed proportional location use) Poisson distributions to distinguish between resource and social attraction.