Asymptotic analysis for an extended discrete Lotka–Volterra system related to matrix eigenvalues

The integrable discrete hungry Lotka–Volterra (dhLV) system is easily transformed to the qd-type dhLV system, which resembles the recursion formula of the qd algorithm for computing matrix eigenvalues. Some of the qd-type dhLV variables play a role for assisting the time evolution of the others. This property does not appear in the original dhLV system. In this article, we first show the existence of a centre manifold for the qd-type dhLV system. With the help of the centre manifold theory, we next investigate the local convergence of the qd-type dhLV system, and then clarify the monotonicity related to the qd-type dhLV variables at the final phase of the convergence.     

Fourier type analysis and the marcenko equation

For certain Fourior type operators P a transform calculus is developed and used to derive a general canonical Marcenko equation connecting P and more general Q via scattering data from Q.     

Beyond statistical methods: teaching critical thinking to first-year university students

We discuss a major change in the way we teach our first-year statistics course. We have redesigned this course with emphasis on teaching critical thinking. We recognized that most of the students take the course for general knowledge and support of other majors, and very few are planning to major in statistics. We identified the essential aspects of a first-year statistics course, given this student mix, focusing on a simple question, ‘Given this is the last chance you have to teach statistics, what are the essential skills students need?’ We have moved from thinking about statistics skills needed for a statistician to skills needed to participate in today's society. We have changed the way we deliver the course with less emphasis on lectures and more on alternative resources including on-line tutorials, Excel, computer-based skills testing, web-based learning materials and smaller group activities such as study groups and example classes. Feedback from students shows that they are very receptive and enthusiastic.     

A continuous model for the theory of organizational structure

We investigate a general class of linear models of dyadic interactions with a constant discrete time delay. We prove that the changes in stability of the stationary states occur for various intervals of the parameters that determine the strength and nature of emotional interactions between the partners. The dynamics of interactions depend on both reactivity of partners to their own emotional states as well as to the partner's states. The results suggest that reactivity to the partner's states has greater impact on the dynamics of the relationship than the reactivity to one's own states. Moreover, the results underscore the importance of deliberation in maintaining the stability of the relationship. Moreover, we have found that multiple stability switches are only possible when one of the partners reacts with delay to their own emotional states. We also propose a generalization to triadic interactions.     

数据缺损矩阵低秩分解的正则化方法

数据缺损下矩阵低秩逼近问题出现在许多数据处理分析与应用领域. 由于极高的元素缺损率,数据缺损下的矩阵低秩逼近呈现很大的不适定性, 因而寻求有效的数值算法是一个具有挑战性的课题. 本文系统完整地综述了作者近期在这方面的一些研究进展, 给出了基本模型问题的不适定性理论分析, 提出了两种新颖的正则化方法: 元素约束正则化和引导正则化, 分别适用于中等程度的数据缺损和高度元素缺损的矩阵低秩逼近. 本文同时也介绍了相应快速有效的数值算法. 在一些实际的大规模数值例子中, 这些新的正则化算法均表现出比现有其他方法都好的数值特性.     

偶数阶自共轭微分算子谱的离散性条件

In this paper, we consider differential operators of 2nd-order
a[u]=(-1)^k(a_k(x)u^(k)(x))(k), x∈(0, ∞)
whose coefficients a_k(x) are restricted by powers of e^x, and give conditions on the coefficients sufficient to ensure that the spectrum is discrete; next we formulate necessary and sufficient conditions for the discreteness of the spectrum of differential operators whose coefficients a_k(x) may increase as e^αkx as x→∞.     

Risk minimizing hedging for a partially observed high frequency data model

Risk-minimizing hedging strategies for contingent claims are studied in a general model for intraday stock price movements in the case of partial information. The dynamics of the risky asset price is described throught a marked point process Y, whose local characteristics depend on some unobservable hidden state variable X. In the model presented the processes Y and X may have common jump times, which means that the trading activity may affect the law of X and could be also related to the presence of catastrophic events. The hedger is restricted to observing past asset prices. Thus, we are in presence not only of an incomplete market situation but also of partial information. Considering the case where the price of the risky asset is modeled directly under a martingale measure, the computation of the risk-minimizing hedging strategy under this partial information is obtained by using a projection result (M. Schweizer, Risk minimizing hedging strategies under restricted information, Mathematical Finance 4 (1994) 327–342). This approach leads to a filtering problem with marked point process observations whose solution, obtained via the Kushner-Stratonovich equation, allows us to provide a complete solution to the heding problem.     

船摇数据实时滤波与预报的时序法

作为船摇数据建立一个时序时域模型-长自回归模型,在此模型基础上给出了船摇数据的实时滤波和预报的方法,并从均方误差、预报误差、残差序列的相关性、拟合方差、仿真计算等多方面考察了滤波及预报效果。AR（p)模型的系数估计采用最小二乘递推方法,用较少的运算量和存贮量,得到了较高的估值精度。该方法是一种非常值得推荐的船摇数据实时处理方法。     

Compression of Multivariate Discrete Measures and Applications

In this article, we discuss two methods for the compression of multivariate discrete measures, with applications to node reduction in numerical cubature and least-squares approximation. The methods are implemented in the Matlab computing environment, in dimension two.