SOME RAMSEY THEORY IN BOOLEAN ALGEBRA FOR COMPLEXITY CLASSES

It is known that for two given countable sets of unary relations A and B on ω there exists an infinite set H ? ω on which A and B are the same. This result can be used to generate counterexamples in expressibility theory. We examine the sharpness of this result.     

一类非单调线性互补问题的高阶Dikin型仿射尺度算法

对于一类非单调线性互补问题提出了一个新算法：高阶Dikin型仿射尺度算法，算法的每步迭代．基于线性规划Dikin原始-对偶算法思想来求解一个线性方程组得到迭代方向，再适当选取步长，得到了算法的多项式复杂性。     

谱绝对值均匀的前馈流密码的线性复杂度的稳定性研究

本文提出了一种前馈流密码纵向信息泄漏的收集方法，并在此基础上深入地研究了上人有谱绝对值均匀质非线性滤波函数的前馈密码的线性得和杂度稳定性问题。     

Model selection and prediction: Normal regression

This paper discusses the topic of model selection for finite-dimensional normal regression models. We compare model selection criteria according to prediction errors based upon prediction with refitting, and prediction without refitting. We provide a new lower bound for prediction without refitting, while a lower bound for prediction with refitting was given by Rissanen. Moreover, we specify a set of sufficient conditions for a model selection criterion to achieve these bounds. Then the achievability of the two bounds by the following selection rules are addressed: Rissanen's accumulated prediction error criterion (APE), his stochastic complexity criterion, AIC, BIC and the FPE criteria. In particular, we provide upper bounds on overfitting and underfitting probabilities needed for the achievability. Finally, we offer a brief discussion on the issue of finite-dimensional vs. infinite-dimensional model assumptions.Support from the National Science Foundation, grant DMS 8802378 and support from ARO, grant DAAL03-91-G-007 to B. Yu during the revision are gratefully acknowledged.     

控制犯两类错误后验概率的统计试验方案设计

本文用ＢＡＹＥＳ理论提出了通过控制犯两类错误后验概率来设计试验方案的一种新方法，与以往的方法比较，该方法利用先验分布的信息减少了样本的容量。     

住院病人构成动态分析与预测

本文对某一综合性教学医院１９８２～１９９１年住院病人进行疾病顺位动态分析与预测．结果表明：①肿瘤、消化、呼吸系统疾病顺位居高不下；②传染病、神经系统和感觉器官疾病顺位逐年下降；③循环、泌尿生殖系统疾病顺位有上升趋势　对疾病变化因素和统计预测进行了讨论．     

Towards Pure Adaptive Search

The algorithm known as Pure Adaptive Search is a global optimisation ideal with desirable complexity. In this paper we temper it to a framework we term Somewhat Adaptive Search. This retains the desirable complexity, but allows scope for a practical realisation. We introduce a new algorithm termed Pure Localisation Search which attempts to reach the practical ideal. For a certain class of one variable functions the gap is bridged.     

Complexity of the pipeline computation of a family of inner products

We are interested in the minimum time T(S) necessary for computing a family S = { < S_i, S_j >: ? S_i, S_j?R^p, (i, j) ?E } of inner products of order p, on a systolic array of order p × 2. We first prove that the determination of T(S) is equivalent to the partition problem and is thus NP-complete. Then we show that the designing of an algorithm which runs in time T(S) + 1 is equivalent to the problem of finding an undirected bipartite eulerian multigraph with the smallest number of edges, which contains a given undirected bipartite graph, and can therefore be solved in polynomial time.     

Parametric simplex algorithms for a class of NP-Complete problems whose average number of steps is polynomial

We will show that the average number of steps of parametric simplex algorithms for obtaining global minima of rank-one and rank-two bilinear-programming problems are lower-order polynomial functions of the problem size under the standard assumptions on the distribution of the data imposed in the probabilistic analysis of the simplex method. This means that there exist algorithms for some special class of NP-complete problems, whose average number of arithmetics are polynomial order of the problem size.     

On the scattering properties of a weakly charged polymer gel

A phenomenological model is presented to describe weakly charged polymer gels based on the classical elasticity theory. The structure factor of the gel is calculated considering both thermal and frozen concentration fluctuations as well as the screened Coulomb interaction. In agreement with the recent experimental finding the result shows anomalous crosslink-density dependence of the scattering profiles. Received: 28 March 1997 / Revised: 4 September 1997 / Accepted: 23 October 1997