On the Structure of Spatial Branching Processes

The paper is a contribution to the theory of branching processes with discrete time and a general phase space in the sense of [2]. We characterize the class of regular, i.e. in a sense sufficiently random, branching processes (Φk) k∈Z by almost sure properties of their realizations without making any assumptions about stationarity or existence of moments. This enables us to classify the clans of (Φk) into the regular part and the completely non-regular part. It turns out that the completely non-regular branching processes are built up from single-line processes, whereas the regular ones are mixtures of left-tail trivial processes with a Poisson family structure.

Strategic adoption in a two-sided market : a study of college applications in Brazil

This paper measures the importance of indirect network effects in the adoption by colleges and students of ENEM, a standardized exam for high-school students in Brazil that can be used in college application processes. We estimate network effects and find that they are economically significant. Students are more likely to take ENEM the larger the number of colleges adopting it. Similarly, colleges are more likely to adopt it the larger the number of students taking the exam. Moreover, we find evidence that colleges play strategically and that heterogeneity determines their decisions. A college is less likely to adopt ENEM the larger the number of competitors adopting it. Colleges’ characteristics such as ownership and organization affect adoption decisions. In a counterfactual exercise we compare colleges’ adoption decisions under competition and under joint colleges’ payoffs maximization. Adoption rates are significantly reduced when colleges internalize the competitive effect, i.e., the effect of their decisions on other colleges’ payoffs. On the other hand, they increase when indirect network effects - the effect of students’ response to their decisions on other colleges’ payoffs - are also internalized. Competitive adoption rates are found to exceed joint optimum rates by a small difference. These results suggest that, without considering students’ welfare, adoption rates are excessive, but close to the joint optimum.

The Role of Online Platforms for Media Markets – Two‐Dimensional Spatial Competition in a Two‐Sided Market

We analyze the market for online and offline media in a model of two-dimensional spatial competition where media outlets sell content and advertising space. Consumer preferences are distributed along the style and type of news coverage where the distance costs may vary across dimensions. For integrated provision of online and offline platforms we show that entering the online market reduces average profits and may even constitute a prisoner's dilemma. Specialized provision may yield polarization in the style and type dimensions. This is in contrast to the maximum–minimum differentiation result previously established in the literature on multidimensional horizontal competition. We show that maximal differentiation in both dimensions occurs due to the discrete nature of the type dimension and asymmetric advertising markets.

An inverse problem for the Helmholtz equation involving two semi-infinite fluids

An analytical method is developed for solving an inverse problem for Helmholtz's equation associated with two semi-infinite incompressible fluids of different variable refractive indices, separated by a plane interface. The unknowns of the inverse problem are: (i) the refractive indices of the two fluids, (ii) the ratio of the densities of the two fluids, and (iii) the strength of an acoustic source assumed to be situated at the interface of the two fluids. These are determined from the pressure on the interface produced by the acoustic source. The effect of the surface tension force at the interface is taken into account in this paper. The application of the proposed analytical method to solve the inverse problem is also illustrated with several examples. In particular, exact solutions of two direct problems are first derived using standard classical methods which are then used in our proposed inverse method to recover the unknowns of the corresponding inverse problems. The results are found to be in excellent agreement.

Limit theorems for sequences of random trees

We consider a random tree and introduce a metric in the space of trees to define the ""mean tree"" as the tree minimizing the average distance to the random tree. When the resulting metric space is compact we have laws of large numbers and central limit theorems for sequence of independent identically distributed random trees. As application we propose tests to check if two samples of random trees have the same law.

Random Mating Between Two Widely Divergent Mitochondrial Lineages of Cryptolestes ferrugineus (Coleoptera: Laemophloeidae): A Test of Species Limits in a Phosphine-Resistant Stored Product Pest

Effective pest management relies on accurate delimitation of species and, beyond this, on accurate species identification. Mitochondrial COI sequences are useful for providing initial indications in delimiting species but, despite acknowledged limitations in the method, many studies involving COI sequences and species problems remain unresolved. Here we illustrate how such impasses can be resolved with microsatellite and nuclear sequence data, to assess more directly the amount of gene flow between divergent lineages. We use a population genetics approach to test for random mating between two 8 ± 2% divergent COI lineages of the rusty grain beetle, Cryptolestes ferrugineus (Stephens). This species has become strongly resistant to phosphine, a fumigant used worldwide for disinfesting grain. The possibility of cryptic species would have significant consequences for resistance management, especially if resistance was confined to one mitochondrial lineage. We find no evidence of restricted gene flow or nonrandom mating across the two COI lineages of these beetles, rather we hypothesize that historic population structure associated with early Pleistocene climate changes likely contributed to divergent lineages within this species.

Efficient preconditioning of the method of lines for solving nonlinear two-sided space-fractional diffusion equations

A standard method for the numerical solution of partial differential equations (PDEs) is the method of lines. In this approach the PDE is discretised in space using �finite di�fferences or similar techniques, and the resulting semidiscrete problem in time is integrated using an initial value problem solver. A significant challenge when applying the method of lines to fractional PDEs is that the non-local nature of the fractional derivatives results in a discretised system where each equation involves contributions from many (possibly every) spatial node(s). This has important consequences for the effi�ciency of the numerical solver. First, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. Second, since the Jacobian matrix of the system is dense (partially or fully), methods that avoid the need to form and factorise this matrix are preferred. In this paper, we consider a nonlinear two-sided space-fractional di�ffusion equation in one spatial dimension. A key contribution of this paper is to demonstrate how an eff�ective preconditioner is crucial for improving the effi�ciency of the method of lines for solving this equation. In particular, we show how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.

Efficient solution of two-sided nonlinear space-fractional diffusion equations using fast Poisson preconditioners

We develop a fast Poisson preconditioner for the efficient numerical solution of a class of two-sided nonlinear space fractional diffusion equations in one and two dimensions using the method of lines. Using the shifted Gr¨unwald finite difference formulas to approximate the two-sided(i.e. the left and right Riemann-Liouville) fractional derivatives, the resulting semi-discrete nonlinear systems have dense Jacobian matrices owing to the non-local property of fractional derivatives. We employ a modern initial value problem solver utilising backward differentiation formulas and Jacobian-free Newton-Krylov methods to solve these systems. For efficient performance of the Jacobianfree Newton-Krylov method it is essential to apply an effective preconditioner to accelerate the convergence of the linear iterative solver. The key contribution of our work is to generalise the fast Poisson preconditioner, widely used for integer-order diffusion equations, so that it applies to the two-sided space fractional diffusion equation. A number of numerical experiments are presented to demonstrate the effectiveness of the preconditioner and the overall solution strategy.

Nucleotide sequences of an Australian and a Canadian isolate of potato leafroll luteovirus and their relationships with two European isolates

The genomes of an Australian and a Canadian isolate of potato leafroll virus have been cloned and sequenced. The sequences of both isolates are similar (about 93%), but the Canadian isolate (PLRV-C) is more closely related (about 98% identity) to a Scottish (PLRV-S) and a Dutch isolate (PLRV-N) than to the Australian isolate (PLRV-A). The 5'-terminal 18 nucleotide residues of PLRV-C, PLRV-A, PLRV-N and beet western yellows virus have 17 residues in common. In contrast, PLRV-S shows no obvious similarity in this region. PLRV-A and PLRV-C genomic sequences have localized regions of marked diversity, in particular a 600 nucleotide residue sequence in the polymerase gene. These data provide a world-wide perspective on the molecular biology of PLRV strains and their comparison with other luteoviruses and related RNA plant viruses suggests that there are two major subgroups in the plant luteoviruses.

Stability and convergence of a new finite volume method for a two-sided space-fractional diffusion equation

In this paper, we consider a two-sided space-fractional diffusion equation with variable coefficients on a finite domain. Firstly, based on the nodal basis functions, we present a new fractional finite volume method for the two-sided space-fractional diffusion equation and derive the implicit scheme and solve it in matrix form. Secondly, we prove the stability and convergence of the implicit fractional finite volume method and conclude that the method is unconditionally stable and convergent. Finally, some numerical examples are given to show the effectiveness of the new numerical method, and the results are in excellent agreement with theoretical analysis.

Two sided reproductions of portrait of unidentified man and unidentified woman Portraits; Groups

Digital Image

Two Complete Genome Sequences of Phasey Bean Mild Yellows Virus, a Novel Member of the Luteoviridae from Australia

We present here the complete genome sequences of a novel polerovirus from Trifolium subterraneum (subterranean clover) and Cicer arietinum (chickpea) and compare these to a partial viral genome sequence obtained from Macroptilium lathyroides (phasey bean). We propose the name phasey bean mild yellows virus for this novel polerovirus.

Performance analysis of the random early detection algorithm

In this article we consider a finite queue with its arrivals controlled by the random early detection algorithm. This is one of the most prominent congestion avoidance schemes in the Internet routers. The aggregate arrival stream from the population of transmission control protocol sources is locally considered stationary renewal or Markov modulated Poisson process with general packet length distribution. We study the exact dynamics of this queue and provide the stability and the rates of convergence to the stationary distribution and obtain the packet loss probability and the waiting time distribution. Then we extend these results to a two traffic class case with each arrival stream renewal. However, computing the performance indices for this system becomes computationally prohibitive. Thus, in the latter half of the article, we approximate the dynamics of the average queue length process asymptotically via an ordinary differential equation. We estimate the error term via a diffusion approximation. We use these results to obtain approximate transient and stationary performance of the system. Finally, we provide some computational examples to show the accuracy of these approximations.

Phylogenetic relationships within mammalian order Carnivora indicated by sequences of two nuclear DNA genes

Phylogenetic relationships among 37 living species of order Carnivora spanning a relatively broad range of divergence times and taxonomic levels were examined using nuclear sequence data from exon1 of the IRBP gene (approximate to1.3 kb) and first intron

HDAC6 and Ubp-M BUZ domains recognize specific C-terminal sequences of proteins.

The BUZ/Znf-UBP domain is a protein module found in the cytoplasmic deacetylase HDAC6, E3 ubiquitin ligase BRAP2/IMP, and a subfamily of ubiquitin-specific proteases. Although several BUZ domains have been shown to bind ubiquitin with high affinity by recognizing its C-terminal sequence (RLRGG-COOH), it is currently unknown whether the interaction is sequence-specific or whether the BUZ domains are capable of binding to proteins other than ubiquitin. In this work, the BUZ domains of HDAC6 and Ubp-M were subjected to screening against a one-bead-one-compound (OBOC) peptide library that exhibited random peptide sequences with free C-termini. Sequence analysis of the selected binding peptides as well as alanine scanning studies revealed that the BUZ domains require a C-terminal Gly-Gly motif for binding. At the more N-terminal positions, the two BUZ domains have distinct sequence specificities, allowing them to bind to different peptides and/or proteins. A database search of the human proteome on the basis of the BUZ domain specificities identified 11 and 24 potential partner proteins for Ubp-M and HDAC6 BUZ domains, respectively. Peptides corresponding to the C-terminal sequences of four of the predicted binding partners (FBXO11, histone H4, PTOV1, and FAT10) were synthesized and tested for binding to the BUZ domains by fluorescence polarization. All four peptides bound to the HDAC6 BUZ domain with low micromolar K(D) values and less tightly to the Ubp-M BUZ domain. Finally, in vitro pull-down assays showed that the Ubp-M BUZ domain was capable of binding to the histone H3-histone H4 tetramer protein complex. Our results suggest that BUZ domains are sequence-specific protein-binding modules, with each BUZ domain potentially binding to a different subset of proteins.