This talk consider the effect of media coverage and the carry capacity of local hospital on the spreading of infectious disease. The number of patients need to be treated may exceed the carry capacity of the local hospitals during the spreading of a severe infectious disease. We propose models with general and saturation recovery from infective individuals to understand their effect on the emergency disease control. It is shown that saturation recovery from infective individuals leads to vital dynamics, such as bistability and periodicity, when the basic reproduction number is less than unity.

As we know, there are many systems undergoing different kinds of snaking bifurcations, such as slanted snaking, collapsed snaking etc., and isola bifurcations including a stack of isolas and a nested of isolas. In this talk, we will focus on the existence of snakes and isolas of a non-symmetric system. Conditions are derived that guarantee snaking or result in diagrams that either consist entirely of isolas.

In real-life application, multiple graphs clustering have been shown a great clustering performance by exploiting heterogeneous information from various correlated graphs. Leveraging inter-relations information among different graphs has also been demonstrated an effective way to achieved better clustering result. In this talk, we discuss some recent results for multiple graphs clustering. Experimental results on both synthetic data sets and real data sets are also presented to illustrate the discussion.

学 术 报 告报告人：刘权兴研究员(华东师范大学)题目：以潮间带贻贝空间自组织生态系统阐述复杂性对生态恢复力的影响时间： 3月8日（星期二），下午3:00-4:00地点：致远楼102欢迎各位参加！刘权兴，华东师大大学河口海岸学国家重点实验室研究员，2015年入选华东师范大学紫江青年学者。2002-2009年从中北大学（原华北工学院）分别获得应用化学学士学位、应用数学硕士学位，师从我国著名生物数学家靳祯教授。2013年从荷兰格罗宁根...

In this talk, we study critical points to the generalized Ginzburg-Landau equations in high dimensions (n ≥ 3) which satisfy a suitable energy bound, but are not necessarily energy minimizers. We are interested in the limits of such solutions as the parameter in the equations tend to zero.

I will talk about recent progress on super-rigidity of J-holomorphic curves via Hormander’s L^2 method. By perturbing the Dolbeault-Dirac operator to real Cauchy-Riemann operators, we establish the transversality of index 0 immersed J-holomorphic curves and their unbranched multi-coverings for generic J, this answers affirmatively a question raised by C. Wendl.

In this talk, we will show the existence and stability of the spatially inhomogeneous periodic solutions for some diffusive population models subject to Dirichlet or Neumann boundary conditions. For the Dirichlet boundary condition problem, we demonstrate that the spatially inhomogeneous periodic solutions can be bifurcated from the positive steady state for both Logistic and weak Allee type population models. For a special Logistic type model, such bifurcated periodic solutions are shown to be persistent when the parameter is far away from the bifurcation values. For the Neumann boundary condition problem, we establish the existence of various spatially inhomogeneous periodic solutions for the diffusive Nicholson’s blowflies population model. Such periodic solutions are numerically observable in a relatively long time period although they are not stable. This talk is mainly based on some joint works with Junping Shi, Junjie Wei and Xingfu Zou

Center manifold method has been a very powerful approach in studying stability of nonlinear ordinary differential equation (ODE) systems and it has also proved to be useful in studying the stability of partial differential equation (PDE) systems. Through the center manifold method, we conduct stability analysis on an initial-boundary-value problem of a nonlinear Korteweg-de Vries equation posed on a finite interval (0, $2/pi /sqrt{7/3}$).

The main contribution of this paper is to propose a new convex optimization model for multiplicative noise and blur removal. The main idea is to rewrite a blur and multiplicative noise equation such that both image variable and noise variable are decoupled. The resulting objective function involves the total variation regularization term, the term of variance of the inverse of noise, the ℓ1-norm of the data fitting term among the observed image

In this talk, I will present some necessary and sufficient conditions are established for a two-agent flock model with processing delay to admit a time-asymptotic flocking. The results provide a relation based on which proper initial positions and velocities can be selected to form a flocking with predetermined position displacement distance. It is shown that the processing delay can terminate a flocking, can induce a flocking and can lead to a flocking bifurcation resulting a periodic flocking. It is also shown that the processing delay can induce flocking switches in the sense that as the processing delay varies, the flocking may follow a switching pattern as no flocking-flocking-periodic flocking-flocking-divergence. The talk is based on an ongoing project with Xiao Wang and Jianhong Wu (York University)