On the continued Erlang loss function

We prove two fundamental results in teletraffic theory. The first is the frequently conjectured convexity of the analytic continuation B(x, a) of the classical Erlang loss function as a function of x, x 0. The second is the uniqueness of the solution of the basic set of equations associated with the ‘equivalent random method’

Dissimilar response of plant and soil biota communities to long-term nutrient adition in grasslands

The long-term effect of fertilizers on plant diversity and productivity is well known, but long-term effects on soil biota communities have received relatively little attention. Here, we used an exceptional long-lasting (>40 years) grassland fertilization experiment to investigate the long-term effect of Ca, N, PK, and NPK addition on the productivity and diversity of both vegetation and soil biota. Whereas plant diversity increased by liming and decreased by N and NPK, the diversity of nematodes, collembolans, mites, and enchytraeids increased by N, PK, or NPK. Fertilization with NPK and PK increased plant biomass and biomass of enchytraeids and collembolans. Biomass of nematodes and earthworms increased by liming. Our results suggest that soil diversity might be driven by plant productivity rather than by plant diversity. This may imply that the selection of measures for restoring or conserving plant diversity may decrease soil biota diversity. This needs to be tested in future experiment

Entropy and Hausdorff Dimension in Random Growing Trees

We investigate the limiting behavior of random tree growth in preferential attachment models. The tree stems from a root, and we add vertices to the system one-by-one at random, according to a rule which depends on the degree distribution of the already existing tree. The so-called weight function, in terms of which the rule of attachment is formulated, is such that each vertex in the tree can have at most K children. We define the concept of a certain random measure mu on the leaves of the limiting tree, which captures a global property of the tree growth in a natural way. We prove that the Hausdorff and the packing dimension of this limiting measure is equal and constant with probability one. Moreover, the local dimension of mu equals the Hausdorff dimension at mu-almost every point. We give an explicit formula for the dimension, given the rule of attachment

Stochasticity in the adaptive dynamics of evolution: The bare bones

First a population model with one single type of individuals is considered. Individuals reproduce asexually by splitting into two, with a population-size-dependent probability. Population extinction, growth and persistence are studied. Subsequently the results are extended to such a population with two competing morphs and are applied to a simple model, where morphs arise through mutation. The movement in the trait space of a monomorphic population and its possible branching into polymorphism are discussed. This is a first report. It purports to display the basic conceptual structure of a simple exact probabilistic formulation of adaptive dynamics

Mutation, selection, and ancestry in branching models: a variational approach

We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated genealogical tree is viewed both in the forward and the backward direction of time. The stationary type distribution of the reversed process, the so-called ancestral distribution, turns out as a key for the study of mutation-selection balance. This balance can be expressed in the form of a variational principle that quantifies the respective roles of reproduction and mutation for any possible type distribution. It shows that the mean growth rate of the population results from a competition for a maximal long-term growth rate, as given by the difference between the current mean reproduction rate, and an asymptotic decay rate related to the mutation process; this tradeoff is won by the ancestral distribution. Our main application is the quasispecies model of sequence evolution with mutation coupled to reproduction but independent across sites, and a fitness function that is invariant under permutation of sites. Here, the variational principle is worked out in detail and yields a simple, explicit result.Comment: 45 pages,8 figure

National Commission on Social, Emotional, and Academic Development: A Research Agenda for the Next Generation

We know more now than we ever have about how learning happens. But there are still many questions to be answered and, too often, important insights from research aren't communicated to the very people who could use it most - the educators who work with our children on a daily basis. This research agenda for the next generation makes recommendations for a new research paradigm that bridges the divide between scholarly research and what's actionable in our classrooms, schools, and communities

Discrete Feynman-Kac formulas for branching random walks

Branching random walks are key to the description of several physical and biological systems, such as neutron multiplication, genetics and population dynamics. For a broad class of such processes, in this Letter we derive the discrete Feynman-Kac equations for the probability and the moments of the number of visits $n_V$ of the walker to a given region $V$ in the phase space. Feynman-Kac formulas for the residence times of Markovian processes are recovered in the diffusion limit.Comment: 4 pages, 3 figure

Preservation of information in a prebiotic package model

The coexistence between different informational molecules has been the preferred mode to circumvent the limitation posed by imperfect replication on the amount of information stored by each of these molecules. Here we reexamine a classic package model in which distinct information carriers or templates are forced to coexist within vesicles, which in turn can proliferate freely through binary division. The combined dynamics of vesicles and templates is described by a multitype branching process which allows us to write equations for the average number of the different types of vesicles as well as for their extinction probabilities. The threshold phenomenon associated to the extinction of the vesicle population is studied quantitatively using finite-size scaling techniques. We conclude that the resultant coexistence is too frail in the presence of parasites and so confinement of templates in vesicles without an explicit mechanism of cooperation does not resolve the information crisis of prebiotic evolution.Comment: 9 pages, 8 figures, accepted version, to be published in PR

A Parsec Scale Accelerating Radio Jet in the Giant Radio Galaxy NGC315

Observations of the core of the giant radio galaxy NGC315 made with VLBI interferometers are discussed in the context of a relativistic jet. The sidedness asymmetry suggests Doppler favoritism from a relativistic jet. The presence of moving features in the jet as well as jet counter--jet brightness ratios hint at an accelerating, relativistic jet. An increasing jet velocity is also supported by a comparison of the jet's observed properties with the predictions of an adiabatic expansion model. On the parsec scale, the jet is unpolarized at a wavelength of 6 cm to a very high degree in clear distinction to the high polarization seen on the kiloparsec scale.Comment: 24 pages with 8 figures. ApJ in pres