估计单指标模型的单调联系函数

本文我们研究了联系函数单调时单指标模型的模型估计问题. 基于投影方向的相合估计, 本文提出用I-样条的办法来估计联系函数, 并建立带惩罚函数的最小二乘准则的相合性. 通过模拟与现有的方法进行了对比, 表明我们的估计方法是非常有效的.     

混合缺失机制下两总体差异的半经验似然置信区间

假定两个总体x与y均有数据缺失,它们的分布函数分别为F(·)与G_θ(·),其中F(·)未知,G_θ(·)的概率密度函数g_θ(·)形式已知,仅依赖于一些未知的参数,利用Fractional填补法填补缺失值,在一定的条件下证明了缺失数据下两总体差异指标的半经验似然比统计量的渐近分布为x_1~2,由此可构造两总体差异指标的经验似然置信区间.     

A problem identification taxonomy for classification and automated formulation of multiple objective linear programming models

This paper considers a network supply problem in which flows between any pair of nodes are possible. It is assumed that users place a value on connection to other users in the network, and (possibly) on access to an external source. Cost on each link is an arbitrary concave function of link capacity. The objective is to study coalitional stability in this situation, when collections of flows can be served by competing suppliers. In contrast to other network games, this approach focuses on the cost of serving flows rather than the cost of attaching nodes to the network. The network is said to be stable if the derived cost function is supportable. Supportable cost functions, defined by Sharkey and Telser [9], are cost functions for which there exists a price vector which covers total cost, and simultaneously deters entry at any lower output by a rival firm with the same cost function. If the minimal cost network includes a link between every pair of nodes, then the cost function is shown to be supportable. In the special case in which link cost is independent of capacity, the cost function is also supportable. The paper also considers Steiner networks in which new nodes may be created in order to minimize total cost, or in which access may be obtained at more than one source location. When link costs are independent of capacity in such a network, it is argued that the cost function is approximately supportable in a well defined sense.     

A reflection on the implicitly restarted Arnoldi method for computing eigenvalues near a vertical line

In this article, we will study the link between a method for computing eigenvalues closest to the imaginary axis and the implicitly restarted Arnoldi method. The extension to computing eigenvalues closest to a vertical line is straightforward, by incorporating a shift. Without loss of generality we will restrict ourselves here to computing eigenvalues closest to the imaginary axis.In a recent publication, Meerbergen and Spence discussed a new approach for detecting purely imaginary eigenvalues corresponding to Hopf bifurcations, which is of interest for the stability of dynamical systems. The novel method is based on inverse iteration (inverse power method) applied on a Lyapunov-like eigenvalue problem. To reduce the computational overhead significantly a projection was added.This method can also be used for computing eigenvalues of a matrix pencil near a vertical line in the complex plane. We will prove in this paper that the combination of inverse iteration with the projection step is equivalent to Sorensen’s implicitly restarted Arnoldi method utilizing well-chosen shifts.     

Symmetry and regularity of solutions to a system with three-component integral equations

Consider the system with three-component integral equations u(x) = Rn |x y|α nw(y)rv(y)q dy,v(x) = Rn |x y|α nu(y)pw(y)rdy,w(x) = Rn |x y|α nv(y)q u(y)pdy,where 0 < α < n,n is a positive constant,p,q and r satisfy some suitable conditions.It is shown that every positive regular solution(u(x),v(x),w(x)) is radially symmetric and monotonic about some point by developing the moving plane method in an integral form.In addition,the regularity of the solutions is also proved by the contraction mapping principle.The conformal invariant property of the system is also investigated.     

A filtered polynomial approach to density estimation

In this paper, a little known computational approach to density estimation based on filtered polynomial approximation is investigated. It is accompanied by the first online available density estimation computer program based on a filtered polynomial approach. The approximation yields the unknown distribution and density as the product of a monotonic increasing polynomial and a filter. The filter may be considered as a target distribution which gets fixed prior to the estimation. The filtered polynomial approach then provides coefficient estimates for (close) algebraic approximations to (a) the unknown density function and (b) the unknown cumulative distribution function as well as (c) a transformation (e.g., normalization) from the unknown data distribution to the filter. This approach provides a high degree of smoothness in its estimates for univariate as well as for multivariate settings. The nice properties as the high degree of smoothness and the ability to select from different target distributions are suited especially in MCMC simulations. Two applications in Sects. 1 and 7 will show the advantages of the filtered polynomial approach over the commonly used kernel estimation method.      

多用户类多准则交通分配的势博弈与拥挤定价

交通管理者在解决路网拥挤问题时,并不知道出行者的出行效用,同时管理者难以对出行者的路径选择行为做出准确的观测.运用势博弈理论分析多用户类多准则交通行为的演化过程,得到了固定需求和弹性需求情形下的可容许动态(一种刻画出行者通过转换路径增加当前效用的近似调整行为的演化动态),证明当路段时间函数和逆需求函数为严格单调、连续、可微时,所对应的交通分配是势博弈问题的惟一Nash均衡点.进一步研究了固定需求下的可变拥挤道路收费问题,得到了在当前系统状态下实现系统最优交通分配的拥挤收费水平.     

基于谱密度评价随机性

为了评价一个平稳过程的随机性, 我们基于谱密度提出了一个图方法. 当图中的散点呈现线性关系的时候, 我们可以判定这个序列是随机的. 为了说明这个思想, 我们用模拟的办法来检验伪随机数的随机性. 另外, 我们也用了一个实际数据来考察数据的相关性. 这两个例子都说明了我们的图方法是非常有效的.     

定义在复数上的复模糊值函数

把所有的关于y轴对称的模糊数都定义为零模糊数,则两个相同的模糊数的差为零,利用~ar-+~ar+这样一个数值来描述模糊数的序关系,就可以得到关于纵向对称的模糊数都是等同的.在此基础之上对实模糊数的模糊距离及极限进行了研究.并研究了复模糊数的距离与复模糊数列的极限以及复模糊值函数的极限.将研究的复模糊值函数是定义在复数集C上取值于F(C)(所有的复模糊数的集合)中的复模糊数的函数.在新的序关系意义下讨论复模糊值函数的极限,并讨论复模糊值函数的收敛性质及Cauchy收敛判别法等.     

Piecewise parametric polynomial fuzzy sets

We present a scheme for tractable parametric representation of fuzzy set membership functions based on the use of a recursive monotonic hierarchy that yields different polynomial functions with different orders. Polynomials of the first order were found to be simple bivalent sets, while the second order polynomials represent the typical saw shape triangles. Higher order polynomials present more diverse membership shapes. The approach demonstrates an enhanced method to manage and fit the profile of membership functions through the access to the polynomials order, the number and the multiplicity of anchor points as wells as the uniformity and periodicity features used in the approach. These parameters provide an interesting means to assist in fitting a fuzzy controller according to system requirements. Besides, the polynomial fuzzy sets have tractable characteristics concerning the continuity and differentiability that depend on the order of the polynomials. Higher order polynomials can be differentiated as many times as the order of the polynomial less the multiplicity of the anchor points. An algorithmic optimization approach using the steepest descent method is introduced for fuzzy controller tuning. It was shown that the controller can be optimized to model a certain output within small number of iterations and very small error margins. The mathematics generated by the approach is consistent and can be simply generalized to standard applications. The recursive propagation was noticed for its clarity and ease of calculations. Further, the degree of association between the sets is not limited to the neighbors as in traditional applications; instead, it may extend beyond.Such approach can be useful in dynamic fuzzy sets for adaptive modeling in view of the fact that the shape parameters can be easily altered to get different profiles while keeping the math unchanged. Hypothetically, any shape of membership functions under the partition of unity constraint can be produced. The significance of the mentioned characteristics of such modeling can be observed in the field of combinatorial and continuous parameter optimization, automated tuning, optimal fuzzy control, fuzzy-neural control, membership function fitting, adaptive modeling, and many other fields that require customized as well as standard fuzzy membership functions. Experimental work of different scenarios with diverse fuzzy rules and polynomial sets has been conducted to verify and validate our results.     

Some characterizations of orthant monotonic norms

In real n-space the orthant monotonic norms of Gries [5] can be given a new characterization similar to one for monotonic norms: a norm is orthant monotonic if and only if for every D=diag(δ₁,δ₂,…,δ_n)?0, the operator norm of D equals max δ_i. This gives an alternative proof to Gries's: a norm is orthant monotonic if and only if its dual norm is orthant monotonic. Also, it follows that the principal axis vectors are self-dual for orthant monotonic norms.     

Optimality of monotonic policies for two-action Markovian decision processes,with applications to control of queues with delayed information

We consider a discrete-time Markov decision process with a partially ordered state space and two feasible control actions in each state. Our goal is to find general conditions, which are satisfied in a broad class of applications to control of queues, under which an optimal control policy is monotonic. An advantage of our approach is that it easily extends to problems with both information and action delays, which are common in applications to high-speed communication networks, among others. The transition probabilities are stochastically monotone and the one-stage reward submodular. We further assume that transitions from different states are coupled, in the sense that the state after a transition is distributed as a deterministic function of the current state and two random variables, one of which is controllable and the other uncontrollable. Finally, we make a monotonicity assumption about the sample-path effect of a pairwise switch of the actions in consecutive stages. Using induction on the horizon length, we demonstrate that optimal policies for the finite- and infinite-horizon discounted problems are monotonic. We apply these results to a single queueing facility with control of arrivals and/or services, under very general conditions. In this case, our results imply that an optimal control policy has threshold form. Finally, we show how monotonicity of an optimal policy extends in a natural way to problems with information and/or action delay, including delays of more than one time unit. Specifically, we show that, if a problem without delay satisfies our sufficient conditions for monotonicity of an optimal policy, then the same problem with information and/or action delay also has monotonic (e.g., threshold) optimal policies.     

一类倒向随机微分方程L~p解对终值的单调连续性

在生成元g满足关于y单调且关于z Lipschitz连续的条件下,范(2007)得到了倒向随机微分方程L~p解对终值的单调连续结果.在g关于y单调且关于z一致连续的条件下证明了倒向随机微分方程L~p解的单调连续性,推广了范(2007)的工作,并且方法是新的.     

Obligation rules for minimum cost spanning tree situations and their monotonicity properties

We consider the class of Obligation rules for minimum cost spanning tree situations. The main result of this paper is that such rules are cost monotonic and induce also population monotonic allocation schemes. Another characteristic of Obligation rules is that they assign to a minimum cost spanning tree situation a vector of cost contributions which can be obtained as product of a double stochastic matrix with the cost vector of edges in the optimal tree provided by the Kruskal algorithm. It turns out that the Potters value (P-value) is an element of this class.     

轴对称弹性体的有限元分析

轴对称弹性力学问题的有限元分析长期以来都是采用三角圆环有限元和线性形状函数.由于积分困难,常用近似积分求得刚度矩阵,这种近似积分对于靠近旋转对称轴的元素,误差很大,所以,长期以来,被认为不满意的办法.也有用精确积分计算刚度矩阵的.但本文指出,这种积分只适用于有中孔的轴对称体.对于实心的轴对称体而言,这种刚度矩阵都不收敛,计算是无效的.本文提出了一种新的形状函数,当径向座标r接近于零时,这种形状函数的径向位移u自然地接近于零.如果用这种新的形状函数,则由此计算求得的刚度矩阵,不论三角圆环有限元的位置是否靠近轴线.都是存在的.这种有限元,就能用于计算实心的轴对称体的问题.     

Benefit sharing in holding situations

A situation is studied where one agent has available an amount of storage facility and the other agents have some goods, part of which can be stored generating benefits. The problem of sharing the benefits produced by full cooperation between agents is tackled in this paper, by introducing a related cooperative game. This game turns out to be a big boss game with interesting theoretical properties. A solution concept, relying on optimal storage plans and associated holding prices, is also introduced, and its relationship with the core of the above holding game is explored in detail. The family of monotonic decreasing bijective mappings, defined on the set of non-negative real numbers, plays an important role in our approach.     

Bankruptcy prediction of small and medium enterprises using a flexible binary generalized extreme value model

We introduce a binary regression accounting-based model for bankruptcy prediction of small and medium enterprises (SMEs). The main advantage of the model lies in its predictive performance in identifying defaulted SMEs. Another advantage, which is especially relevant for banks, is that the relationship between the accounting characteristics of SMEs and response is not assumed a priori (eg, linear, quadratic or cubic) and can be determined from the data. The proposed approach uses the quantile function of the generalized extreme value distribution as link function as well as smooth functions of accounting characteristics to flexibly model covariate effects. Therefore, the usual assumptions in scoring models of symmetric link function and linear or pre-specified covariate-response relationships are relaxed. Out-of-sample and out-of-time validation on Italian data shows that our proposal outperforms the commonly used (logistic) scoring model for different default horizons.     

Algorithmic aspects of the substitution decomposition in optimization over relations,set systems and Boolean functions

In the last years, decomposition techniques have seen an increasing application to the solution of problems from operations research and combinatorial optimization, in particular in network theory and graph theory. This paper gives a broad treatment of a particular aspect of this approach, viz. the design of algorithms to compute the decomposition possibilities for a large class of discrete structures. The decomposition considered is thesubstitution decomposition (also known as modular decomposition, disjunctive decomposition, X-join or ordinal sum). Under rather general assumptions on the type of structure considered, these (possibly exponentially many) decomposition possibilities can be appropriately represented in acomposition tree of polynomial size. The task of determining this tree is shown to be polynomially equivalent to the seemingly weaker task of determining the closed hull of a given set w.r.t. a closure operation associated with the substitution decomposition. Based on this reduction, we show that for arbitrary relations the composition tree can be constructed in polynomial time. For clutters and monotonic Boolean functions, this task of constructing the closed hull is shown to be Turing-reducible to the problem of determining the circuits of the independence system associated with the clutter or the prime implicants of the Boolean function. This leads to polynomial algorithms for special clutters or monotonic Boolean functions. However, these results seem not to be extendable to the general case, as we derive exponential lower bounds for oracle decomposition algorithms for arbitrary set systems and Boolean functions.     

A novel approach to Bilevel nonlinear programming

Recently developed methods of monotonic optimization have been applied successfully for studying a wide class of nonconvex optimization problems, that includes, among others, generalized polynomial programming, generalized multiplicative and fractional programming, discrete programming, optimization over the efficient set, complementarity problems. In the present paper the monotonic approach is extended to the General Bilevel Programming GBP Problem. It is shown that (GBP) can be transformed into a monotonic optimization problem which can then be solved by “polyblock” approximation or, more efficiently, by a branch-reduce-and-bound method using monotonicity cuts. The method is particularly suitable for Bilevel Convex Programming and Bilevel Linear Programming.      

On the Bernoulli two-armed bandit problem

The paper is initially concerned with monotonic properties of the posterior success probabilities when the prior success probabilities are distributed according to an arbitrary joint distribution function (Bayesian approach). Next a dynamic programming model is proposed and monotonic properties of the optimal expected cumulative discounted reward are proved. Finally, optimality properties are given for the case when one prior success probability is known.