Abstract:
A genome-wide transcriptional profile of Bradyrhizobium japonicum, the nitrogen-fixing endosymbiont of the soybean plant, revealed differential expression of approximately 15% of the genome after a 1 mM treatment with the phytohormone indole-3-acetic acid (IAA). A total of 1,323 genes were differentially expressed (619 up-regulated and 704 down-regulated) at a two-fold cut off with q value ≤ 0.05. General stress response genes were induced, such as those involved in response to heat, cold, oxidative, osmotic, and desiccation stresses and in exopolysaccharide (EPS) biosynthesis. This suggests that IAA is effective in activating a generalized stress response in B. japonicum. The transcriptional data were corroborated by the finding that stress tolerance of B. japonicum in cell viability assays was enhanced when pre-treated with 1 mM IAA compared to controls. The IAA treatment also stimulated biofilm formation and EPS production by B. japonicum, especially acidic sugar components in the total EPS. The IAA pre-treatment did not influence the nodulation ability of B. japonicum. The data provide a comprehensive overview of the potential transcriptional responses of the symbiotic bacterium when exposed to the ubiquitous hormone of its plant host.

Abstract:
In phyllosphere microbiology, the distribution of resources available to bacterial colonizers of leaf surfaces is generally understood to be very heterogeneous. However, there is little quantitative understanding of the mechanisms that underlie this heterogeneity. Here, we tested the hypothesis that different parts of the cuticle vary in the degree to which they allow diffusion of the leaf sugar fructose to the surface. To this end, individual, isolated cuticles of poplar leaves were each analyzed for two properties: (1) the permeability for fructose, which involved measurement of diffused fructose by gas chromatography and flame ionization detection (GC–FID), and (2) the number and size of fructose-permeable sites on the cuticle, which was achieved using a green-fluorescent protein (GFP)-based bacterial bioreporter for fructose. Bulk flux measurements revealed an average permeance P of 3.39 × 10？9 ms？1, while the bioreporter showed that most of the leaching fructose was clustered to sites around the base of shed trichomes, which accounted for only 0.37% of the surface of the cuticles under study. Combined, the GC–FID and GFP measurements allowed us to calculate an apparent rate of fructose diffusion at these preferential leaching sites of 9.15 × 10？7 ms？1. To the best of our knowledge, this study represents the first successful attempt to quantify cuticle permeability at a resolution that is most relevant to bacterial colonizers of plant leaves. The estimates for P at different spatial scales will be useful for future models that aim to explain and predict temporal and spatial patterns of bacterial colonization of plant foliage based on lateral heterogeneity in sugar permeability of the leaf cuticle.

Abstract:
We developed the individual-based model PHYLLOSIM to explain observed variation in the size of bacterial clusters on plant leaf surfaces (the phyllosphere). Specifically, we tested how different ‘waterscapes’ impacted the diffusion of nutrients from the leaf interior to the surface and the growth of individual bacteria on these nutrients. In the ‘null’ model or more complex ‘patchy’ models, the surface was covered with a continuous water film or with water drops of equal or different volumes, respectively. While these models predicted the growth of individual bacterial immigrants into clusters of variable sizes, they were unable to reproduce experimentally derived, previously published patterns of dispersion which were characterized by a much larger variation in cluster sizes and a disproportionate occurrence of clusters consisting of only one or two bacteria. The fit of model predictions to experimental data was about equally poor (<5%) regardless of whether the water films were continuous or patchy. Only by allowing individual bacteria to detach from developing clusters and re-attach elsewhere to start a new cluster, did PHYLLOSIM come much closer to reproducing experimental observations. The goodness of fit including detachment increased to about 70–80% for all waterscapes. Predictions of this ‘detachment’ model were further supported by the visualization and quantification of bacterial detachment and attachment events at an agarose-water interface. Thus, both model and experiment suggest that detachment of bacterial cells from clusters is an important mechanism underlying bacterial exploration of the phyllosphere.

Abstract:
Consider a random sample from a bivariate distribution function $F$ in the max-domain of attraction of an extreme-value distribution function $G$. This $G$ is characterized by two extreme-value indices and a spectral measure, the latter determining the tail dependence structure of $F$. A major issue in multivariate extreme-value theory is the estimation of the spectral measure $\Phi_p$ with respect to the $L_p$ norm. For every $p\in[1,\infty]$, a nonparametric maximum empirical likelihood estimator is proposed for $\Phi_p$. The main novelty is that these estimators are guaranteed to satisfy the moment constraints by which spectral measures are characterized. Asymptotic normality of the estimators is proved under conditions that allow for tail independence. Moreover, the conditions are easily verifiable as we demonstrate through a number of theoretical examples. A simulation study shows a substantially improved performance of the new estimators. Two case studies illustrate how to implement the methods in practice.

Abstract:
In the world of multivariate extremes, estimation of the dependence structure still presents a challenge and an interesting problem. A procedure for the bivariate case is presented that opens the road to a similar way of handling the problem in a truly multivariate setting. We consider a semi-parametric model in which the stable tail dependence function is parametrically modeled. Given a random sample from a bivariate distribution function, the problem is to estimate the unknown parameter. A method of moments estimator is proposed where a certain integral of a nonparametric, rank-based estimator of the stable tail dependence function is matched with the corresponding parametric version. Under very weak conditions, the estimator is shown to be consistent and asymptotically normal. Moreover, a comparison between the parametric and nonparametric estimators leads to a goodness-of-fit test for the semiparametric model. The performance of the estimator is illustrated for a discrete spectral measure that arises in a factor-type model and for which likelihood-based methods break down. A second example is that of a family of stable tail dependence functions of certain meta-elliptical distributions.

Abstract:
In many-server systems it is crucial to staff the right number of servers so that targeted service levels are met. These staffing problems typically lead to constraint satisfaction problems that are hard to solve. During the last decade, a powerful many-server asymptotic theory has been developed to solve such problems and optimal staffing rules are known to obey the square-root staffing principle. This paper develops many-server asymptotics in the so-called QED regime, and presents refinements to many-server asymptotics and square-root staffing for a Markovian queueing model with admission control and retrials.

Abstract:
The dominant pole approximation (DPA) is a classical analytic method to obtain from a generating function asymptotic estimates for its underlying coefficients. We apply DPA to a discrete queue in a critical many-sources regime, in order to obtain tail asymptotics for the stationary queue length. As it turns out, this regime leads to a clustering of the poles of the generating function, which renders the classical DPA useless, since the dominant pole is not sufficiently dominant. To resolve this, we design a new DPA method, which might also find application in other areas of mathematics, like combinatorics, particularly when Gaussian scalings related to the central limit theorem are involved.

Abstract:
This paper demonstrates the occurrence of the feature called BRAVO (Balancing Reduces Asymptotic Variance of Output) for the departure process of a finite-buffer Markovian many-server system in the QED (Quality and Efficiency-Driven) heavy-traffic regime. The results are based on evaluating the limit of a formula for the asymptotic variance of death counts in finite birth--death processes.

Abstract:
Scale-free networks arise from power-law degree distributions. Due to the finite size of real-world networks, the power law inevitably has a cutoff at some maximum degree $\Delta$. We investigate the relative size of the giant component $S$ in the large-network limit. We show that $S$ as a function of $\Delta$ increases fast when $\Delta$ is just large enough for the giant component to exist, but increases ever more slowly when $\Delta$ increases further. This makes that while the degree distribution converges to a pure power law when $\Delta\to\infty$, $S$ approaches its limiting value at a slow pace. The convergence rate also depends on the power-law exponent $\tau$ of the degree distribution. The worst rate of convergence is found to be for the case $\tau\approx2$, which concerns many of the real-world networks reported in the literature.

Abstract:
Consider a random sample in the max-domain of attraction of a multivariate extreme value distribution such that the dependence structure of the attractor belongs to a parametric model. A new estimator for the unknown parameter is defined as the value that minimizes the distance between a vector of weighted integrals of the tail dependence function and their empirical counterparts. The minimization problem has, with probability tending to one, a unique, global solution. The estimator is consistent and asymptotically normal. The spectral measures of the tail dependence models to which the method applies can be discrete or continuous. Examples demonstrate the applicability and the performance of the method.