对称位相型滤波器及其在边缘检测中的应用

该文从概率的角度提出了两类新的滤波器：对称位相型滤波器和对称梯阶滤波器;证明了对任意给定的非负对称滤波器可用这两类滤波器的序列在（－∞,＋∞）内一致逼近;这种序列有着统一的结构形式：L（x）＝^s∑i＝1e^λi│x－μ│^Ni∑k＝0ak^（i）│x－μ│^ k。对于L（x）,文中给出了选择L（x）一些最优准则的解析表达。从而表明L（x）既具有一般性,又易进行解析处理和数值计算。对于已有文献中相关于对称指数滤波器的两类不同形式,例如Li等和Ma等,该文从理论上进一步刻画了它们的内在一致性。     

Finite horizon optimal control of non-linear discrete-time switched systems using adaptive dynamic programming with ε-error bound

In this paper, we aim to solve the finite-horizon optimal control problem for a class of non-linear discrete-time switched systems using adaptive dynamic programming(ADP) algorithm. A new ε-optimal control scheme based on the iterative ADP algorithm is presented which makes the value function converge iteratively to the greatest lower bound of all value function indices within an error according to ε within finite time. Two neural networks are used as parametric structures to implement the iterative ADP algorithm with ε-error bound, which aim at approximating the value function and the control policy, respectively. And then, the optimal control policy is obtained. Finally, a simulation example is included to illustrate the applicability of the proposed method.     

Approximate algorithms for some generalized knapsack problems

In this paper we construct approximate algorithms for the following problems: integer multiple-choice knapsack problem, binary multiple-choice knapsack problem and multi-dimensional knapsack problem. The main result can be described as follows: for every ε 0 one can construct a polynomial-time algorithm for each of the above problems such that the ratio of the value of the objective function by this algorithm and the optimal value is bounded below by 1 - ε.     

Optimal control of ε-coupled and singularly perturbed distributed-parameter systems

Many distributed-parameter systems consist of interconnected subsystems involving fast and slow physical phenomena or reducing to a number of independent subsystems when a scalar parameter ε is zero. The purpose of this paper is to treat the control of such systems by invoking the ε-coupling and singular perturbation approaches developed by Kokotovic and his co-workers for lumped-parameter large-scale systems. In the case of ε- coupled distributed-parameter systems it is shown that the optimal state feedback matrix can be approximated by a Volterra-MacLaurin series with coefficients determined by solving two lower-order decoupled Riccati and linear equations. By using an mth-order approximation of the optimal feedback matrix, one obtains a (2m+1)th order approximation of the optimal performance function. In the singular perturbation approach the result is that for an O(ε²) suboptimal control one must solve two decoupled Riccati equations, one for the fast and one for the slow subsystem, and then construct appropriately the composite control law. By using only the Riccati equation for the slow subsystem, one obtains an O(ε) suboptimal control. The singular perturbation technique is then used to treat interconnected distributed-parameter systems involving may strongly coupled slow subsystems and weakly coupled fast subsystems.     

基于动态ε支配的多目标遗传算法

基于Pareto支配的MOEA存在着一些缺陷,如容易出现退化现象等。而基于ε支配的MOEA可以比较好地解决这些问题,并具有比较理想的收敛性和分布性。但是采用传统的ε-MOEA时,最大的困难就是ε的值的设定,并且传统的MOEA得出的解在边界部分个体的丢失现象也比较严重。针对这种情况提出了一种新的基于动态ε支配的多目标遗传算法（DEMOEA）,它不需要手动设定ε的值,并且引入了动态网格概念来改善边界解丢失的现象。通过与其他两个经典的多目标进化算法的NSAGA-II和SPEA-2的对比实验,表明提出的DEMOEA能在收敛性、分布性有较好的改进。     

形式语言与自动机中关于ε的一些问题

讨论了形式语言与自动机理论中关于空串ε的一些问题。分析了ε产生式对文法和语言分类的影响;从文法和有限状态自动机的角度讨论了开始符号S和开始状态q0的作用;提出了语言增加或减少ε句子的简单方法;研究了ε-NFA的ε状态转换函数的本质;提出了ε-NFA转换为NFA的新方法,即先将ε-NFA转换为文法形式,消除ε产生式和单产生式后得到正则文法,再将正则文法转换为NFA。并用实际例子进行了验证。     

The Solution of Linear Probabilistic Recurrence Relations

Linear probabilistic divide-and-conquer recurrence relations arise when analyzing the running time of divide-and-conquer randomized algorithms. We consider first the problem of finding the expected value of the random process T(x) , described as the output of a randomized recursive algorithm T . On input x , T generates a sample (h1,···,hk) from a given probability distribution on [0,1]k and recurses by returning g(x) + Σi=1kciT(hi x) until a constant is returned when x becomes less than a given number. Under some minor assumptions on the problem parameters, we present a closed-form asymptotic solution of the expected value of T(x) . We show that E[T(x)] = Θ( xp + xp∈t1x(g(u)/ up+1 ) du) , where p is the nonnegative unique solution of the equation Σi=1kciE[hip] = 1 . This generalizes the result in [1] where we considered the deterministic version of the recurrence. Then, following [2], we argue that the solution holds under a broad class of perturbations including floors and ceilings that usually accompany the recurrences that arise when analyzing randomized divide-and-conquer algorithms.     

An Interval Polynomial Interpolation Problem and Its Lagrange Solution

In many practical problems, we need to use interpolation: we know that the value of a quantity is uniquely determined by some other quantity x (i.e., y = f(x)), we have measured several pairs of values (xi, yi), and we want to predict y for a given x. We can only guarantee estimates for y if we have some a priori information about the function f(x). In particular, in some problems, we know that f(x) is a polynomial of known degree d (e.g., that it is linear, or that it is quadratic). For this polynomial interpolation, with interval uncertainty of the input data (xi, yi), we present several reasonable algorithms that compute, for a given x0, guaranteed bounds for f(x0).     

On the Applicability of the Interval Gaussian Algorithm

We consider a linear interval system with a regular n × n interval matrix [A] which has the form [A] = I + [-R,R]. For such a system we prove necessary and sufficient conditions for the applicability of the interval Gaussian algorithm where applicability means that the algorithm does not break down by dividing by an interval which contains zero. If this applicability is guaranteed we compare the output vector [x]G with the interval hull of the solution set . In particular, we show that in each entry of [x]G at least one of the two bounds is optimal. Linear interval systems of the above-mentioned form arise when a given general system is preconditioned with the midpoint inverse of the underlying coefficient matrix.     

Properties of interval operators

In this paper we give some properties of interval operatorsF which guarantee the convergence of the interval sequence {X _k} defined byX _k+1:=F(X_k)∩X_k to a unique fixed interval \(\hat X\) . This interval \(\hat X\) encloses the “zero-set”X ^* of a function strip \(G(x): = [g(x),\bar g(x)]\) . for some known interval operators we investigate under which assumptions these properties are valid.     

一类NFA 到DFA 的直接转化方法

NFA的确定化具有重要的理论和实际意义.迄今为止,普遍采用子集构造法将一个NFA(非确定性自动机)转化为DFA(确定性自动机),但这种方法需要引入空输入ε及状态子集I的ε-闭包,其计算过程相对繁琐.而且在确定化过程中对于NFA状态集存在ε-closure重复计算和由于对非ε转换的判断而引起的重复计算等问题.本文描述了一种将一类NFA直接转化为DFA的方法.在本方法中,不需要引入空输入ε,可根据原始的NFA状态图或状态转移表直接得出等价的DFA状态图或状态转移表,而且所有状态都是单一的状态而非集合状态,便于软硬件实现与测试.     

Numerical analysis of continuous time Markov decision processes over finite horizons

Continuous time Markov decision processes (CTMDPs) with a finite state and action space have been considered for a long time. It is known that under fairly general conditions the reward gained over a finite horizon can be maximized by a so-called piecewise constant policy which changes only finitely often in a finite interval. Although this result is available for more than 30 years, numerical analysis approaches to compute the optimal policy and reward are restricted to discretization methods which are known to converge to the true solution if the discretization step goes to zero. In this paper, we present a new method that is based on uniformization of the CTMDP and allows one to compute an ε-optimal$\epsilon \text{-optimal}$ policy up to a predefined precision in a numerically stable way using adaptive time steps.     

ε-支持向量回归机算法及其应用

针对现有传统的一些图像去噪方法难以获得清晰图像边缘的问题,提出了利用ε-SVR技术构建图像去噪滤波器的新方法。ε-支持向量回归机通过引入ε不敏感损失函数,可以实现具有较强鲁棒性的回归,而且回归估计是稀疏的,保留了SVM的所有优点。分析了ε-支持向量回归机理论算法及其在图像去噪中的应用,使用ε-支持向量回归机对图像进行滤波并且与最小值滤波、均值滤波和维纳滤波等常用的滤波方法相比较,还比较了SVM各种核函数对不同噪声的滤波效果和分析了不同阶数的Multinomial核的滤波效果。实验结果表明了ε-支持向量回归机能够有效地去除噪声,不但信噪比较高而且比较清晰,同时具有良好的稀疏性。     

New slope methods for sharper interval functions and a note on Fischer's acceleration method

This paper presents algorithms evaluating sharper bounds for interval functionsF(X) :IR ⁿ →IR. We revisit two methods that use partial derivatives of the function, and develop four other inclusion methods using the set of slopesS _f (x, z) off atx εX with respect to somez εIR ⁿ . All methods can be implemented using tools that automatically evaluate gradient and slope vectors by using a forward strategy, so the complex management of reverse accumulation methods is avoided. The sharpest methods compute each component of gradients and slopes separately, by substituting each interval variable at a time. Backward methods bring no great advantage in the sharpest algorithms, since object-oriented forward implementations are easy and immediate. Fischer's acceleration scheme [2] was also tested with interval variables. This method allows the direct evaluation of the productf′(x) * (x?z) as a single real number (instead of working with two vectors) and we used it to computeF′(X) * (X?z) for an interval vectorX. We are led to decide against such acceleration when interval variables are involved.     

Which truth values in fuzzy logics are definable?

In fuzzy logic, every word or phrase describing uncertainty is represented by a real number from the interval [0, 1]. There are only denumerable many words and phrases and continuum many real numbers; thus, not every real number corresponds to some common sense degree of uncertainty. In this article, for several fuzzy logics, we describe which numbers are describing such degrees, i.e., in mathematical terms, which real numbers are definable in the corresponding fuzzy logic. © 2003 Wiley Periodicals, Inc.     

A parameter optimization approach to robust PI-controller design for systems with interval plants

The purpose of this paper is to develop an analytic way for designing optimal PI-controllers for the interval plant family. Optimality means that the coefficient intervals of the plant stabilized by a PI-controller is maximized. It will be shown that the optimization problem can be formulated in terms of an eigenvalue minimization problem of matrix pairs of the form （H（h0, g0）, H（δ1,k, δ2,k））, where k= 1, 2, 3, 4 and both H（h0, g0） and H（δ1,k,δ2,k） are frequency independent Hurwitz-like matrices. A numerical example is provided to illustrate that optimal controller parameters can be successfully obtained by a two-dimensional search.     

The effect of monomolecular surface films on the microwave brightness temperature of the sea surface

Abstract

Airborne microwave radiometer measurements at 1·43 and 2·65 GHz over a sea surface covered with a monomolecular oleyl alcohol surface film and over adjacent slick sea surfaces are presented. The measurements show that at 2·65 GHz the brightness temperature T _B is not affected by the slick, while at 1·43 GHz it drops from 93 K to a minimum value of almost O K. This implies that at 1·43 GHz the emissivity of the slick-covered sea surface is extremely small, similar to a metallic layer, and that this resonant-type phenomenon is confined to a narrow frequency band of width δ?/ ?<0·6.

The theoretical implications of these experimental findings are discussed in the framework of the Debye relaxation theory of polar liquids. It is conjectured that a thin layer of water molecules polarized by the surface film gives rise to an anomalous dispersion, which causes the large decrease in brightness temperature at 1·43 GHz.

The modulus of the relative dielectric constant ε? is estimated to be ≥ 5·2 × 10^?4 and the thickness of the emitting layer ≤1·9 × 10^?4 m for 1·43 GHz. Furthermore, the film-induced surface activation energy is calculated to be 9·18 × 10^?21 J. These values seem reasonable in the light of the theories on the physicochemical structure of surface layers.     

Maximizing biogas production from the anaerobic digestion

This paper presents an optimal control law policy for maximizing biogas production of anaerobic digesters. In particular, using a simple model of the anaerobic digestion process, we derive a control law to maximize the biogas production over a period T using the dilution rate as the control variable. Depending on initial conditions and constraints on the actuator (the dilution rate D(·)), the search for a solution to the optimal control problem reveals very different levels of difficulty. In the present paper, we consider that there are no severe constraints on the actuator. In particular, the interval in which the input flow rate lives includes the value which allows the biogas to be maximized at equilibrium. For this case, we solve the optimal control problem using classical tools of differential equations analysis. Numerical simulations illustrate the robustness of the control law with respect to several parameters, notably with respect to initial conditions. We use these results to show that the heuristic control law proposed by Steyer et al., 1999 [20] is optimal in a certain sense. The optimal trajectories are then compared with those given by a purely numerical optimal control solver (i.e. the “BOCOP” toolkit) which is an open-source toolbox for solving optimal control problems. When the exact analytical solution to the optimal control problem cannot be found, we suggest that such numerical tool can be used to intuiter optimal solutions.     

HOW DIFFICULT IS IT TO INVENT A NONTRIVIAL GAME?

Everyone who has ever tried to invent a new game knows that it is very difficult to make it nontrivial. In this paper, we explain this empirical fact by showing that almost all games (in some reasonable sense) are trivial. We also estimate the number of nontrivial games and compare this number with the number of all possible games of a given size.     

An Algorithm for the Exact Numerical Integration of a Special Class of Functions

The classical Gaussian quadrature rules yield very inaccurate results when they are used for the integration of functions of the form f(x)=P(x,\cos(cx+d))\exp(-a^{2}x^{2}+bx) over the infinite interval (-\infty, \infty) , where a\gt 0, b, c, d are real numbers and P is a polynomial. In this paper we propose a new algorithm that computes this type of integrals without error in the machine precision. The algorithm can also be used for the multiple integrals. We give some numerical examples to compare the results obtained by the new algorithm and those obtained by some other methods including the classical Gauss-Hermite integration rules.