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.

Study of ground-state titanium ion velocity distributions in laser-produced plasma plumes

The velocity distribution of ground-state titanium ions within a low-temperature plasma resulting from the laser ablation of a titanium target has been investigated. A KrF excimer laser was focused onto the target at moderate fluences (

DNA double-strand break distributions in X-ray and alpha-particle irradiated V79 cells: Evidence for non-random breakage

Many studies have shown that with increasing LET of ionizing radiation the RBE (relative biological effectiveness) for dsb (double strand breaks) induction remains around 1.0 despite the increase in the RBE for cell killing. This has been attributed to an increase in the complexity of lesions, classified as dsb with current techniques, at multiply damaged sites. This study determines the molecular weight distributions of DNA from Chinese hamster V79 cells irradiated with X-rays or 110 keV/mu m alpha-particles. Two running conditions for pulsed-field gel-electrophoresis were chosen to give optimal separation of fragments either in the 225 kbp-5.7 Mbp range or the 0.3 kbp to 225 kbp range. Taking the total fraction of DNA migrating into the gel as a measure of fragmentation, the RBE for dsb induction was less than 1.0 for both molecular weight regions studied. The total yields of dsb were 8.2 x 10(-9) dsb/Gy/bp for X-rays and 7.8 x 10(-9) dsb/Gy/bp for a-particles, measured using a random breakage model. Analysis of the RBE of alpha-particles versus molecular weight gave a different response. In the 0.4 Mbp-57 Mbp region the RBE was less than 1.0; however, below 0.4 Mbp the RBE increased above 1.0. The frequency distributions of fragment sizes were found to differ from those predicted by a model assuming random breakage along the length of the DNA and the differences were greater for alpha-particles than for X-rays. An excess of fragments induced by a single-hit mechanism was found in the 8-300 kbp region and for X-rays and alpha-particles these corresponded to an extra 0.8 x 10(-9) and 3.4 x 10(-9) dsb/bp/Gy, respectively. Thus for every alpha-particle track that induces a dsb there is a 44% probability of inducing a second break within 300 kbp and for electron tracks the probability is 10%. This study shows that the distribution of damage from a high LET alpha-particle track is significantly different from that observed with low LET X-rays. In particular, it suggests that the fragmentation patterns of irradiated DNA may be related to the higher-order chromatin repealing structures found in intact cells.

A study of DNA fragmentation patterns in cells irradiated with charged particles: evidence for non-random distributions

Many studies have shown that the effectiveness of radiations of varying LET is similar when yields of dsb have been measured, despite large differences in biological response. Recent evidence has suggested however, that current techniques underestimate the yields of dsb. By monitoring the fragmentation of DNA over a wide range of fragment sizes ( 6 Mbp) by pulsed field electrophoresis, RBE values greater than 1.0 for radiations of around 100 keV/mm have been determined. The data provide evidence for the production of correlated breaks produced within cells as particle tracks traverse the nucleus. The highly ordered structure of DNA within mammalian cells may lead to clustering of breaks over distances related to the repeating unit structures of the chromatin. As well as these regionally damaged sites, a major contributor to radiation effectiveness will be the localised clustering of damage in the 1 - 20 bp region. A major effort is required to elucidate the relative importance of these levels of clustering and their importance in biological response.

Energy distributions of copper ions and atoms sputtered by atomic and molecular ions

Non-resonant multiphoton ionization combined with quadrupole and time-of-flight analysis has been used to study sputtering by both atomic and molecular ion beams. The mass spectra and energy distributions of both sputtered atoms and secondary ions produced by 3.6 keV Ar+, N+, N-2(+), CF2+ and CF3+ ion bombardment at 45 degrees to a polycrystalline copper target have been measured. The energy distributions of the copper ions and atoms are found to be different and quite complex. The ion distributions can generally be described by a linear collision cascade model, with possible evidence for a knock-on contribution. The sputtered atom distributions are partially described by a combination of linear collision cascade and dense cascade (thermal spike) models. This is interpreted as support for a time-evolving sputtering mechanism.