Dobinski-type relations and the Log-normal distribution

We consider sequences of generalized Bell numbers B(n), n=0,1,... for which there exist Dobinski-type summation formulas; that is, where B(n) is represented as an infinite sum over k of terms P(k)^n/D(k). These include the standard Bell numbers and their generalizations appearing in the normal ordering of powers of boson monomials, as well as variants of the "ordered" Bell numbers. For any such B we demonstrate that every positive integral power of B(m(n)), where m(n) is a quadratic function of n with positive integral coefficients, is the n-th moment of a positive function on the positive real axis, given by a weighted infinite sum of log-normal distributions.Comment: 7 pages, 2 Figure

Boundary driven zero-range processes in random media

The stationary states of boundary driven zero-range processes in random media with quenched disorder are examined, and the motion of a tagged particle is analyzed. For symmetric transition rates, also known as the random barrier model, the stationary state is found to be trivial in absence of boundary drive. Out of equilibrium, two further cases are distinguished according to the tail of the disorder distribution. For strong disorder, the fugacity profiles are found to be governed by the paths of normalized $\alpha$-stable subordinators. The expectations of integrated functions of the tagged particle position are calculated for three types of routes.Comment: 23 page

A comparison of Northeast Atlantic killer whale (Orcinus orca) stereotyped call repertoires

Funding for data collection was provided by the BBC Natural History Unit, Fundação para a Ciência e a Tecnologia (grant number SFRH/BD/30303/2006), the Icelandic Research Fund (i. Rannsóknasjóður) through a START Postdoctoral Fellowship (grant number 120248042) and a Project Grant (grant number 163060‐051), the National Geographic Global Exploration Fund (grant number GEFNE65‐12), a Marie Curie International Incoming Fellowship (project number 297116), the Office of Naval Research (grant number N00014‐08‐1‐0984), and a Russell Trust Award from the University of St. Andrews.Killer whale call repertoires can provide information on social connections among groups and populations. Killer whales in Iceland and Norway exhibit similar ecology and behavior, are genetically related, and are presumed to have been in contact before the collapse of the Atlanto-Scandian herring stock in the 1960s. However, photo-identification suggests no recent movements between Iceland and Norway but regular movement between Iceland and Shetland. Acoustic recordings collected between 2005 and 2016 in Iceland, Norway, and Shetland were used to undertake a comprehensive comparison of call repertoires of Northeast Atlantic killer whales. Measurements of time and frequency parameters of calls from Iceland (n = 4,037) and Norway (n = 1,715) largely overlapped in distribution, and a discriminant function analysis had low correct classification rate. No call type matches were confirmed between Iceland and Norway or Shetland and Norway. Three call types matched between Iceland and Shetland. Therefore, this study suggests overall similarities in time and frequency parameters but some divergence in call type repertoires. This argues against presumed past contact between Icelandic and Norwegian killer whales and suggests that they may not have been one completely mixed population.PostprintPeer reviewe

Elementary derivation of Spitzer's asymptotic law for Brownian windings and some of its physical applications

A simple derivation of Spitzer'z asymptotic law for Brownian windings [Trans.Am.Math.Soc.87,187 (1958)]is presented along with its generalizations >.These include the cases of planar Brownian walks interacting with a single puncture and Brownian walks on a single truncated cone with variable conical angle interacting with the truncated conical tip.Such situations are typical in the theories of quantum Hall effect and 2+1 quantum gravity, respectively .They also have some applications in polymer physic

High potential for weathering and climate effects of non-vascular vegetation in the Late Ordovician

It has been hypothesized that predecessors of today’s bryophytes significantly increased global chemical weathering in the Late Ordovician, thus reducing atmospheric CO2 concentration and contributing to climate cooling and an interval of glaciations. Studies that try to quantify the enhancement of weathering by non-vascular vegetation, however, are usually limited to small areas and low numbers of species, which hampers extrapolating to the global scale and to past climatic conditions. Here we present a spatially explicit modelling approach to simulate global weathering by non-vascular vegetation in the Late Ordovician. We estimate a potential global weathering flux of 2.8 (km3 rock) yr−1, defined here as volume of primary minerals affected by chemical transformation. This is around three times larger than today’s global chemical weathering flux. Moreover, we find that simulated weathering is highly sensitive to atmospheric CO2 concentration. This implies a strong negative feedback between weathering by non-vascular vegetation and Ordovician climate

Stochastic Gravity

Gravity is treated as a stochastic phenomenon based on fluctuations of the metric tensor of general relativity. By using a (3+1) slicing of spacetime, a Langevin equation for the dynamical conjugate momentum and a Fokker-Planck equation for its probability distribution are derived. The Raychaudhuri equation for a congruence of timelike or null geodesics leads to a stochastic differential equation for the expansion parameter $\theta$ in terms of the proper time $s$. For sufficiently strong metric fluctuations, it is shown that caustic singularities in spacetime can be avoided for converging geodesics. The formalism is applied to the gravitational collapse of a star and the Friedmann-Robertson-Walker cosmological model. It is found that owing to the stochastic behavior of the geometry, the singularity in gravitational collapse and the big-bang have a zero probability of occurring. Moreover, as a star collapses the probability of a distant observer seeing an infinite red shift at the Schwarzschild radius of the star is zero. Therefore, there is a vanishing probability of a Schwarzschild black hole event horizon forming during gravitational collapse.Comment: Revised version. Eq. (108) has been modified. Additional comments have been added to text. Revtex 39 page

Pattern and process in Amazon tree turnover, 1976-2001

Previous work has shown that tree turnover, tree biomass and large liana densities have increased in mature tropical forest plots in the late twentieth century. These results point to a concerted shift in forest ecological processes that may already be having significant impacts on terrestrial carbon stocks, fluxes and biodiversity. However, the findings have proved controversial, partly because a rather limited number of permanent plots have been monitored for rather short periods. The aim of this paper is to characterize regional-scale patterns of 'tree turnover' (the rate with which trees die and recruit into a population) by using improved datasets now available for Amazonia that span the past 25 years. Specifically, we assess whether concerted changes in turnover are occurring, and if so whether they are general throughout the Amazon or restricted to one region or environmental zone. In addition, we ask whether they are driven by changes in recruitment, mortality or both. We find that: (i) trees 10 cm or more in diameter recruit and die twice as fast on the richer soils of southern and western Amazonia than on the poorer soils of eastern and central Amazonia; (ii) turnover rates have increased throughout Amazonia over the past two decades; (iii) mortality and recruitment rates have both increased significantly in every region and environmental zone, with the exception of mortality in eastern Amazonia; (iv) recruitment rates have consistently exceeded mortality rates; (v) absolute increases in recruitment and mortality rates are greatest in western Amazonian sites; and (vi) mortality appears to be lagging recruitment at regional scales. These spatial patterns and temporal trends are not caused by obvious artefacts in the data or the analyses. The trends cannot be directly driven by a mortality driver (such as increased drought or fragmentation-related death) because the biomass in these forests has simultaneously increased. Our findings therefore indicate that long-acting and widespread environmental changes are stimulating the growth and productivity of Amazon forests

An international network to monitor the structure, composition and dynamics of Amazonian forests (RAINFOR)

The Amazon basin is likely to be increasingly affected by environmental changes: higher temperatures, changes in precipitation, CO2 fertilization and habitat fragmentation. To examine the important ecological and biogeochemical consequences of these changes, we are developing an international network, RAINFOR, which aims to monitor forest biomass and dynamics across Amazonia in a co-ordinated fashion in order to understand their relationship to soil and climate. The network will focus on sample plots established by independent researchers, some providing data extending back several decades. We will also conduct rapid transect studies of poorly monitored regions. Field expeditions analysed local soil and plant properties in the first phase (2001–2002). Initial results suggest that the network has the potential to reveal much information on the continental-scale relations between forest and environment. The network will also serve as a forum for discussion between researchers, with the aim of standardising sampling techniques and methodologies that will enable Amazonian forests to be monitored in a coherent manner in the coming decades

A multi-layer extension of the stochastic heat equation

Motivated by recent developments on solvable directed polymer models, we define a 'multi-layer' extension of the stochastic heat equation involving non-intersecting Brownian motions.Comment: v4: substantially extended and revised versio