Global stability in a diffusive Holling-Tanner predator-prey model

A diffusive Holling-Tanner predator-prey model with no-flux boundary condition is considered, and it is proved that the unique constant equilibrium is globally asymptotically stable under a new simpler parameter condition. (C) 2011 Elsevier Ltd. All rights reserved

EFFECT OF ROTATIONAL GRAZING ON PLANT AND ANIMAL PRODUCTION

It is a common understanding that rotational cattle grazing provides better yields than continuous grazing, but a quantitative analysis is lacking in agricultural literature. In rotational grazing, cattle periodically move among paddocks in contrast to continuous grazing, in which the cattle graze on a single plot for the entire grazing season. We construct a differential equation model of vegetation grazing on a fixed area to show that production yields and stockpiled forage are greater for rotational grazing than continuous grazing. Our results show that both the number of cattle per acre and stockpiled forage increase for many rotational configurations

Stability and Hopf bifurcation in a diffusive logistic population model with nonlocal delay effect

A reaction-diffusion model with logistic type growth, nonlocal delay effect and Dirichlet boundary condition is considered, and combined effect of the time delay and nonlocal spatial dispersal provides a more realistic way of modeling the complex spatiotemporal behavior. The stability of the positive spatially nonhomogeneous positive equilibrium and associated Hopf bifurcation are investigated for the case of near equilibrium bifurcation point and the case of spatially homogeneous dispersal kernel. (C) 2012 Elsevier Inc. All rights reserved

Transgene silencing and transgene-derived siRNA production in tobacco plants homozygous for an introduced AtMYB90 construct

Transgenic tobacco (Nicotiana tabacum) lines were engineered to ectopically over-express AtMYB90 (PAP2), an R2-R3 Myb gene associated with regulation of anthocyanin production in Arabidopsis thaliana. Independently transformed transgenic lines, Myb27 and Myb237, accumulated large quantities of anthocyanin, generating a dark purple phenotype in nearly all tissues. After self-fertilization, some progeny of the Myb27 line displayed an unexpected pigmentation pattern, with most leaves displaying large sectors of dramatically reduced anthocyanin production. The green-sectored 27Hmo plants were all found to be homozygous for the transgene and, despite a doubled transgene dosage, to have reduced levels of AtMYB90 mRNA. The observed reduction in anthocyanin pigmentation and AtMYB90 mRNA was phenotypically identical to the patterns seen in leaves systemically silenced for the AtMYB90 transgene, and was associated with the presence of AtMYB90-derived siRNA homologous to both strands of a portion of the AtMYB90 transcribed region. Activation of transgene silencing in the Myb27 line was triggered when the 35S::AtMYB90 transgene dosage was doubled, in both Myb27 homozygotes, and in plants containing one copy of each of the independently segregating Myb27 and Myb237 transgene loci. Mapping of sequenced siRNA molecules to the Myb27 TDNA (including flanking tobacco sequences) indicated that the 3' half of the AtMYB90 transcript is the primary target for siRNA associated silencing in both homozygous Myb27 plants and in systemically silenced tissues. The transgene within the Myb27 line was found to consist of a single, fully intact, copy of the AtMYB90 construct. Silencing appears to initiate in response to elevated levels of transgene mRNA (or an aberrant product thereof) present within a subset of leaf cells, followed by spread of the resulting small RNA to adjacent leaf tissues and subsequent amplification of siRNA production.Funding for this research is provided by the United States Department of Agriculture

The Effect of Delay on a Diffusive Predator-Prey System with Holling Type-Ii Predator Functional Response

A delayed diffusive predator-prey system with Holling type-II predator functional response subject to Neumann boundary conditions is considered here. The stability/instability of nonnegative equilibria and associated Hopf bifurcation are investigated by analyzing the characteristic equations. By the theory of normal form and center manifold, an explicit formula for determining the stability and direction of periodic solution bifurcating from Hopf bifurcation is derived

Learning Representation for Clustering via Prototype Scattering and Positive Sampling

Existing deep clustering methods rely on either contrastive or non-contrastive representation learning for downstream clustering task. Contrastive-based methods thanks to negative pairs learn uniform representations for clustering, in which negative pairs, however, may inevitably lead to the class collision issue and consequently compromise the clustering performance. Non-contrastive-based methods, on the other hand, avoid class collision issue, but the resulting non-uniform representations may cause the collapse of clustering. To enjoy the strengths of both worlds, this paper presents a novel end-to-end deep clustering method with prototype scattering and positive sampling, termed ProPos. Specifically, we first maximize the distance between prototypical representations, named prototype scattering loss, which improves the uniformity of representations. Second, we align one augmented view of instance with the sampled neighbors of another view -- assumed to be truly positive pair in the embedding space -- to improve the within-cluster compactness, termed positive sampling alignment. The strengths of ProPos are avoidable class collision issue, uniform representations, well-separated clusters, and within-cluster compactness. By optimizing ProPos in an end-to-end expectation-maximization framework, extensive experimental results demonstrate that ProPos achieves competing performance on moderate-scale clustering benchmark datasets and establishes new state-of-the-art performance on large-scale datasets. Source code is available at \url{https://github.com/Hzzone/ProPos}.Comment: Accepted by TPAMI 202