报告题目：Centre-augmented L2-type regularization for subgroup l…

报 告 人：林华珍

时 间：2022年5月10日（周二）上午10：30-11:30

地 点：腾讯会议 ：719460972

简 介：The existing methods for subgroup analysis can be roughly divided into two categories: finite mixture models (FMM) and regularization methods with an L1 -type penalty. In this paper, by introducing the group centres and L2 -type penalty in the loss function, we propose a novel centre-augmented regularization (CAR) method; this method can be regarded as a unification of the regularization method and FMM and hence exhibits higher efficiency and robustness and simpler computations than the existing methods. Particularly, its computational complexity is reduced from the $O(n^2)$ of the conventional pairwise-penalty method to only $O(nK)$, where n is the sample size and K is the number of subgroups. The asymptotic normality of CAR is established, and the convergence of the algorithm is proven. CAR is applied to a dataset from a multicenter clinical trial: Buprenorphine in the Treatment of Opiate Dependence; a larger $R^2$ is produced and three additional significant variables are identif...

报告题目：On the dynamics of the diffusive Field-Noyes model for…

报 告 人：衣凤岐

时 间：2022年5月6日（周五）

地 点：腾讯会议：499651593

简 介：In this talk, I will report our recent works on the dynamics of a diffusive Field-Noyes model for the Belousov-Zhabotinskii reaction. We are mainly concerned with the global existence, boundedness and the asymptotic behaviors of the solutions. Of our particular interests, we focus on the existence of attraction region which attracts all the solutions of the system (regardless of the initial values), the global asymptotic stability of the constant positive equilibrium solution, the lumped parameter phenomenon, as well as Turing instability of the spatially homogeneous periodic solutions. In particular, a general formula in terms of the diffusion rates for the general 3 × 3 reaction-diffusion system is derived to determine Turing instability of the Hopf bifurcating periodic solutions, which extends our earlier results on general 2 × 2 reaction-diffusion system. This is a joint work with Mi Wang.

报告题目：Mixed-mode oscillations (MMOs) in a three-timescale th…

报 告 人：沈建和

时 间：2022年5月6日（周五）下午2:00-3:00

地 点：腾讯会议：402570480

简 介：In this paper, we will study the bifurcations of mixed-mode oscillations in a singularly perturbed tritrophic food chain model with three distinct timescales. Based on geometric singular perturbation theory (GSPT) and bifurcation theory, a variety of rich and interesting dynamics, including the birth of mixed-mode oscillations (MMOs), relaxation oscillations, canard explosion and bistability are observed in this three-timescale three-dimensional slow-fast model.