Asymptotic profile of a mutualistic model on a periodically evolving domain

In order to investigate the impact of periodically evolving domain on the mutualism interaction of two species,we study a mutualistic model on a periodically evolving domain.To overcome the difficulty caused by the advection and dilution terms,we transform the model to a reaction-difusion problem in a fixed domain.By means of eigenvalue problems,the threshold parameters are introduced.The asymptotic profiles of the solutions on an evolving domain are studied by using the threshold parameters and the upper and lower solutions method.The impact of the domain evolution rate on the persistence or extinction of species is analyzed.Numerical simulations are performed to illustrate our analytical results.

Spontaneous Infection and Periodic Evolving of Domain in a Diffusive SIS Epidemic Model

In this paper, we consider a susceptible-infective-susceptible(SIS) reaction-diffusion epidemic model with spontaneous infection and logistic source in a periodically evolving domain. Using the iterative technique,the uniform boundedness of solution is established. In addition, the spatial-temporal risk index R0(ρ) depending on the domain evolution rate ρ(t) as well as its analytical properties are discussed. The monotonicity of R0(ρ)with respect to the diffusion coefficients of the infected dI, the spontaneous infection rate η(ρ(t)y) and interval length L is investigated under appropriate conditions. Further, the existence and asymptotic behavior of periodic endemic equilibria are explored by upper and lower solution method. Finally, some numerical simulations are presented to illustrate our analytical results. Our results provide valuable information for disease control and prevention.

Evolvable dialogue state tracking for statistical dialogue management

Statistical dialogue management is the core of cognitive spoken dialogue systems （SDS） and has attracted great research interest. In recent years, SDS with the ability of evolution is of particular interest and becomes the cuttingedge of SDS research. Dialogue state tracking （DST） is a process to estimate the distribution of the dialogue states at each dialogue turn, given the previous interaction history. It plays an important role in statistical dialogue management. To provide a common testbed for advancing the research of DST, international DST challenges （DSTC） have been organised and well-attended by major SDS groups in the world. This paper reviews recent progresses on rule-based and statistical approaches during the challenges. In particular, this paper is focused on evolvable DST approaches for dialogue domain extension. The two primary aspects for evolution, semantic parsing and tracker, are discussed. Semantic enhancement and a DST framework which bridges rule-based and statistical models are introduced in detail. By effectively incorporating prior knowledge of dialogue state transition and the ability of being data-driven, the new framework supports reliable domain extension with little data and can continuously improve with more data available. This makes it excellent candidate for DST evolution. Experiments show that the evolvable DST approaches can achieve the state-of-the-art performance and outperform all previously submitted trackers in the third DSTC.