Scaling limits of a model for selection at two scales

The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. For example, a fast-replicating virus strain outcompetes slower-replicating strains at the within-host scale. However, if the fast-replicating strain causes host morbidity and is less frequently transmitted, it can be outcompeted by slower-replicating strains at the between-host scale. Here we consider a stochastic ball-and-urn process which models this type of phenomenon. We prove the weak convergence of this process under two natural scalings. The first scaling leads to a deterministic nonlinear integro-partial differential equation on the interval $[0,1]$ with dependence on a single parameter, $\lambda$. We show that the fixed points of this differential equation are Beta distributions and that their stability depends on $\lambda$ and the behavior of the initial data around $1$. The second scaling leads to a measure-valued Fleming-Viot process, an infinite dimensional stochastic process that is frequently associated with a population genetics

Inter-shell casts of entactiniid radiolarians from the Devonian of SW China

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Boundaries of Disk-like Self-affine Tiles

Let $T:= T(A, {\mathcal D})$ be a disk-like self-affine tile generated by an integral expanding matrix $A$ and a consecutive collinear digit set ${\mathcal D}$, and let $f(x)=x^{2}+px+q$ be the characteristic polynomial of $A$. In the paper, we identify the boundary $\partial T$ with a sofic system by constructing a neighbor graph and derive equivalent conditions for the pair $(A,{\mathcal D})$ to be a number system. Moreover, by using the graph-directed construction and a device of pseudo-norm $\omega$, we find the generalized Hausdorff dimension $\dim_H^{\omega} (\partial T)=2\log \rho(M)/\log |q|$ where $\rho(M)$ is the spectral radius of certain contact matrix $M$. Especially, when $A$ is a similarity, we obtain the standard Hausdorff dimension $\dim_H (\partial T)=2\log \rho/\log |q|$ where $\rho$ is the largest positive zero of the cubic polynomial $x^{3}-(|p|-1)x^{2}-(|q|-|p|)x-|q|$, which is simpler than the known result.Comment: 26 pages, 11 figure

Klebsiella pneumoniae bacteraemia complicating rotavirus gastroenteritis in two infants with glucocorticoid deficiency

Rotavirus gastroenteritis was complicated by Klebsiella Pneumoniae bacteraemia in two infants with glucocorticoid deficient conditions who were treated with 'stress dose' hydrocortisone during their illness. Delayed healing in the context of glucocorticoid administration combined with damage from rotavirus infection may result in increased risk of mucosal invasion by gastrointestinal bacteria and subsequent enteric gram-negative bacteraemia

Ion-beam-induced bending of freestanding amorphous nanowires: The importance of the substrate material and charging

Ion-beam irradiation offers great flexibility and controllability in the construction of freestanding nanostructures with multiple advanced functionalities. Here, we present and discuss the bending of free-standing nanowires, against, towards, and ultimately parallel to a flux of directional ion irradiation. Bending components both along and perpendicular to the incident ion beam were observed, and the bending behavior was found to depend both on the ion beam scanning strategy and on the conductivity of the supporting substrate. This behavior is explained by an ion-irradiation-related electrostatic interaction. Our findings suggest the prospect of exploiting this technique to engineer 3D nanostructures for advanced applications

Effects of ferroelectric-poling-induced strain on the quantum correction to low-temperature resistivity of manganite thin films

Author name used in this publication: H. L. W. ChanAuthor name used in this publication: H. S. Luo2010-2011 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Towards self-verification in finite difference code generation

Code generation from domain-specific languages is becoming increasingly popular as a method to obtain optimised low-level code that performs well on a given platform and for a given problem instance. Ensuring the correctness of generated codes is crucial. At the same time, testing or manual inspection of the code is problematic, as the generated code can be complex and hard to read. Moreover, the generated code may change depending on the problem type, domain size, or target platform, making conventional code review or testing methods impractical. As a solution, we propose the integration of formal verification tools into the code generation process. We present a case study in which the CIVL verification tool is combined with the Devito finite difference framework that generates optimised stencil code for PDE solvers from symbolic equations. We show a selection of properties of the generated code that can be automatically specified and verified during the code generation process. Our approach allowed us to detect a previously unknown bug in the Devito code generation tool

Characterizing the universal rigidity of generic frameworks

A framework is a graph and a map from its vertices to E^d (for some d). A framework is universally rigid if any framework in any dimension with the same graph and edge lengths is a Euclidean image of it. We show that a generic universally rigid framework has a positive semi-definite stress matrix of maximal rank. Connelly showed that the existence of such a positive semi-definite stress matrix is sufficient for universal rigidity, so this provides a characterization of universal rigidity for generic frameworks. We also extend our argument to give a new result on the genericity of strict complementarity in semidefinite programming.Comment: 18 pages, v2: updates throughout; v3: published versio

Bainang Terrane, Yarlung-Tsangpo suture, southern Tibet (Xizang, China): A record of intra-Neotethyan subduction-accretion processes preserved on the roof of the world

The Bainang terrane, an intra-oceanic island are subduction complex into which Tethyan oceanic rocks were accreted during the Cretaceous, is preserved within the Yarlung-Tsangpo suture zone of Tibet. The lithostratigraphic succession established from field mapping records a long history of sedimentation in different portions of the central Tethyan domain from Late Triassic to mid-Cretaceous time. These rocks are preserved within a south-verging imbricate thrust stack of thin (≪ 1 km thick) northward younging tectonic slices. Five lithotectonic units were mapped in the terrane and these units are assigned to two distinct tracts. The northern tract, which accumulated on the north side of Neotethys, was probably separated from its southern counterpart by a mid-ocean ridge. Detailed radiolarian biostratigraphy is used to constrain the timing of depositional events within each tract. Oceanic plate stratigraphy of the northern tract records its northward travel and mid-Cretaceous (late Aptian) approach towards a south-facing intra-oceanic subduction zone. Rocks in the southern tract developed closer to the Indian subcontinent and experienced thermotectonic subsidence and Mid-Jurassic basic alkaline intraplate magmatism. They were probably accreted late in the Cretaceous. Variations in structural style across the terrane indicate deformation at different depths and vertical growth of the wedge rather than lateral accretion. The overall tectonostratigraphy of the terrane reflects its development in a remote intra-oceanic setting.published_or_final_versio