On optimal parameter selection for parabolic differential systems

In ordinary differential systems, it has been shown [4] recently that Boltyanskii's necessary conditions for optimal parameter selection [3, p. 263] can be easily derived from Gamkrelidze's general maximum principle [2]. In this note, necessary conditions on optimal parameter selection problem of parabolic differential systems are reported by using a recent result of Zolezzi [1]. The result is illustrated by an example.     

On Optimal Detectors in Multiuser Detection Problems

The paper is a supplement to [1]. Conditions under which asymptotically optimal detectors are linear are found. It is shown also that if, in contrast to [1], we consider not the Bayesian but minimax statement of the problem with unknown coefficients, then optimal detectors are linear (moreover, nonasymptotically). A geometrical meaning of Theorem 1 from [1] is explained, and it is shown that the theorem follows from some general results [2, 3] on hypotheses testing. It is also shown that some results of [4] follow from [1, Theorem 1].     

Algorithmic mapping of feedforward neural networks onto multiplebus systems

This paper addresses the problem of mapping a feedforward ANN onto a multiple bus system, MBS, with p processors and b buses so as to minimize the total execution time. We present an algorithm which assigns the nodes of a given computational layer (c-layer) to processors such that the computation lower bound [N^l/p]t_p^l and the communication lower bound [N^l/b]t_c are achieved simultaneously, where N^l is the number of nodes in the mapped c-layer l and t_p^l and t_c are the computation and communication times, respectively, associated with a node in the layer. When computation and communication are not overlapped, we show that the optimal number of processors needed is either 1 or p, depending on the ratio t_p^l/t_c . When computation and communication are overlapped, we show that the optimal number of processors needed is either 1 or ([t_p ^l/t_c])b. We show that there is a unique arrangement of interfaces such that the total number of interfaces is minimum and the optimal time is reached. Finally, we compare the relative merits of the MBS simulating ANNs over the recently introduced checkerboarding scheme     

Real-time optimization of a hydroelectric power plant

An optimal control problem modelling a hydroelectric power plant was developed and discussed by Hj. Wacker and his co-workers in [1]. In the present paper, this problem is treated within a more general framework of “non-differentiable” optimal control problems. Necessary conditions of optimality are derived and it is proven that the restricted class of controls considered in [1] indeed contains the optimal control. Furthermore, a decoupling technique is established that allows the full problem to be split into several small subproblems. Based on the new results, an efficient algorithm is developed. This algorithm allows the optimal control to be computed for more general problems with greater accuracy and for a longer time period. Numerical results are given both for the model described in [1] and for the more refined model presented in this paper.     

两类完美的门限可变多秘密共享方案

[t→t,n]门限可变方案研究如何将门限[t]改变为[t>t]以增加攻击者攻击方案的难度。基于拉格朗日插值多项式提出两类完美的门限可变多秘密共享方案：[t→t+1,n]门限可变方案[Π,Π]、[t→t+v-1,n]门限可变方案[Π,Π],并证明[Π]是[t-1,t+1,n]ramp秘密共享方案,[Π]是最优[t-1,t+v-1,n]ramp秘密共享方案,[Π,Π]是最优[t→t+v-1,n]门限可变方案。     

一种新的L1度量Fisher线性判别分析研究

Fisher线性判别分析（Fisher Linear Discriminant Analysis,FLDA）是一种典型的监督型特征提取方法,旨在最大化Fisher准则,寻求最优投影矩阵。在标准Fisher准则中,涉及到的度量为[L2]范数度量,此度量通常缺乏鲁棒性,对异常值点较敏感。为提高鲁棒性,引入了一种基于[L1]范数度量的FLDA及其优化求解算法。实验结果表明：在很多情形下,相比于传统的[L2]范数FLDA,[L1]范数FLDA具有更好的分类精度和鲁棒性。     

广义离散随机线性系统的最优递推滤波方法(Ⅱ)

本文对文献[1]给出的广义离散随机线性系统最优估计误差协方差阵进行了分析,在一定 条件下得到了误差协方差阵的上界和下界,继而讨论了由文献[1]给出的滤波器的稳定性.     

基于深度强化学习的移动机器人路径规划

为解决传统的深度[Q]网络模型下机器人探索复杂未知环境时收敛速度慢的问题,提出了基于竞争网络结构的改进深度双[Q]网络方法（Improved Dueling Deep Double [Q]-Network,IDDDQN）。移动机器人通过改进的DDQN网络结构对其三个动作的值函数进行估计,并更新网络参数,通过训练网络得到相应的[Q]值。移动机器人采用玻尔兹曼分布与[ε]-greedy相结合的探索策略,选择一个最优动作,到达下一个观察。机器人将通过学习收集到的数据采用改进的重采样优选机制存储到缓存记忆单元中,并利用小批量数据训练网络。实验结果显示,与基本DDQN算法比,IDDDQN训练的机器人能够更快地适应未知环境,网络的收敛速度也得到提高,到达目标点的成功率增加了3倍多,在未知的复杂环境中可以更好地获取最优路径。     

k元船方体网络的可靠性

[k]元[n]方体[Qkn]是设计大规模多处理机系统时最常用的互连网络拓扑结构之一。对于[1≤m≤n-1],设[F]是[Qkn]中的一个由非空点集[VF]和非空边集[EF]构成的故障集,满足[Qkn-F]中不存在[Qkn-m]且[VF]破坏的[Qkn-m]的集合与[EF]破坏的[Qkn-m]的集合互不包含。设[f＊（n,m）]是破坏[Qkn]中的所有子立方[Qkn-m]所需要的故障集[F]的最小基数。证明了对于奇数[k≥3],[fk（n,1）]为[k＋1],[fk（n,n-1）]为[kn-1-1＋n],[f＊（n,m）]的上下界分别为[Cm-1n-1km＋Cm-1n-2km-1]和[km]。举例说明了上界[Cm-1n-1km＋Cm-1n-2km-1]是最优的。     

自调优自适应遗传算法的WKNN特征选择方法

针对大多已有基于[K]近邻和遗传算法的特征选择方法中没有考虑各个特征的重要度不同,并且容易出现过早收敛,特别是局部最优解问题,提出了一种基于自调优自适应遗传算法的WKNN特征选择方法。该方法使用WKNN算法预测样本的类别,为每个特征分配一个权重来衡量特征的分类能力,然后采用自调优自适应遗传算法,对变异率、种群规模和收敛阈值进行参数调整,在迭代进化过程中搜索最优特征权重向量。为了评价该方法的有效性,与已有7种特征选择方法在5个标准数据集上进行了比较。实验结果表明,该方法是有效的,且具有较高的分类性能。     

改进的自适应参数DBSCAN聚类算法

针对传统DBSCAN算法需要人工输入[Eps]和[MinPts]参数，且参数选择不合理导致聚类准确率低的问题，提出了一种改进的自适应参数密度聚类算法。采用核密度估计确定[Eps]和[MinPts]参数的合理区间，通过分析数据局部密度特点确定簇数，根据合理区间内的参数值进行聚类，计算满足簇数条件时的轮廓系数，最大轮廓系数对应的参数即为最优参数。在4种经典数据集上进行对比实验，结果表明，该算法能够自动选择最优的[Eps]和[MinPts]参数，准确率平均提高6.1%。     

The optimal projection equations for model reduction and the relationships among the methods of Wilson, Skelton, and Moore

First-order necessary conditions for quadratically optimal reduced-order modeling of linear time-invariant systems are derived in the form of a pair of modified Lyapunov equations coupled by an oblique projection which determines the optimal reduced-order model. This form of the necessary conditions considerably simplifies previous results of Wilson [1] and clearly demonstrates the quadratic extremality and nonoptimality of the balancing method of Moore [2]. The possible existence of multiple solutions of the optimal projection equations is demonstrated and a relaxation-type algorithm is proposed for computing these local extrema. A component-cost analysis of the model-error criterion similar to the approach of Skelton [3] is utilized at each iteration to direct the algorithm to the global minimum.     

The stability of long action chains in XCS

 XCS [1, 2] represents a new form of learning classifier system [3] that uses accuracy as a means of guiding fitness for selection within a Genetic Algorithm. The combination of accuracy-based selection and a dynamic niche-based deletion mechanism achieve a long sought-after goal–the reliable production, maintenance, and proliferation of the sub-population of optimally general accurate classifiers that map the problem domain [4]. Wilson [2] and Lanzi [5, 6] have demonstrated the applicability of XCS to the identification of the optimal action-chain leading to the optimum trade-off between reward distance and magnitude. However, Lanzi [6] also demonstrated that XCS has difficulty in finding an optimal solution to the long action-chain environment Woods-14 [7]. Whilst these findings have shed some light on the ability of XCS to form long action-chains, they have not provided a systematic and, above all, controlled investigation of the limits of XCS learning within multiple-step environments. In this investigation a set of confounding variables in such problems are identified. These are controlled using carefully constructed FSW environments [8, 9] of increasing length. Whilst investigations demonstrate that XCS is able to establish the optimal sub-population [O] [4] when generalisation is not used, it is shown that the introduction of generalisation introduces low bounds on the length of action-chains that can be identified and chosen between to find the optimal pathway. Where these bounds are reached a form of over-generalisation caused by the formation of dominant classifiers can occur. This form is further investigated and the Domination Hypothesis introduced to explain its formation and preservation.     

光滑lp范数压缩感知图像重构优化算法

针对已有压缩感知重构算法重构精度不高、消耗时间长的问题,在研究[lp]范数和光滑[l0]范数压缩感知重构算法的基础上提出改进算法。通过极大熵函数构造一种光滑函数来逼近最小[lp] 范数,对解序列进行离散化来近似最小[lp]范数的最优解,结合图像分块压缩感知技术（BCS）,在MATLAB中对测试图像进行仿真实验。结果表明,与传统的BOMP（Block Orthogonal Matching Pursuit）算法和IRLS（Iteratively Reweighted Least Squares）算法相比,改进后的算法不仅提高了重构精度,而且大大降低运行时间。     

An iterative procedure for solving convex optimal control problems

A doubly iterative procedure for computing optimal controls in linear systems with convex cost functionals is presented. The procedure is based on an algorithm due to Gilbert [3] for minimizing a quadratic form on a convex set. Each step of the procedure makes use of an algorithm due to Neustadt and Paiewonsky [1] to solve a strictly linear optimal control problem.     

Solving the Beck and Wieland model with optimal experimentation in DualPC

Currently, there is a renewed interest in the use of optimal experimentation (adaptive control) in economics. Example are found in [Amman and Kendrick, 1999], [Amman and Kendrick, 2003], [Cosimano, in?press], [Cosimano and Gapen, 2005b], [Cosimano and Gapen, 2005a], [Cosimano and Gapen, 2006], [Tesfaselassie et?al., 2007], [Tucci, 1997], [Wieland, 2000a] and [Wieland, 2000b]. In this paper we present the Beck & Wieland model [Beck, G., & Wieland, V. (2002). Learning and control in a changing economic environment. Journal of Economic Dynamics and Control, 26, 1359-1378] and the methodology to solve this model with time-varying parameters using the various control methods described in [Kendrick, 1981] and [Kendrick, 2002]. Furthermore, we also provide numerical results using the DualPC software [Amman, H. M., & Kendrick, D. A. (1999). The DualI/DualPC software for optimal control models: User’s guide. Working paper, Austin, TX 78712, USA: Center for Applied Research in Economics, University of Texas] and show first evidence that optimal experimentation or Dual Control may produce better results than Expected Optimal Feedback.     

多密度自适应确定DBSCAN算法参数的算法研究

DBSCAN算法的Eps和MinPts参数需要人为设定,取值不当会导致聚类结果准确度不高,且在密度分布差异大的数据集上,由于参数的全局性,错误地应用于不同密度的簇,导致不能正确地发现簇.针对以上问题,提出一种多密度自适应参数确定算法,利用经过去噪衰减后的数据集的自身分布特性生成候选Eps和MinPts参数列表,并在簇数...     

MIMO自校正控制器的全局收敛算法

本文为随机多变量线性系统建立了全局收敛的MIMO自校正控制器算法。使用这种随机适应控制算法，不论系统和算法的初始条件如何，总能保证系统参数未知条件下的适应控制渐近地达到系统参数已知条件下的最优控制效果。文献[1]、[2]的绝大部分结果和[3]中的随机结果大体上可视为本文结果的特殊情况。使用这种算法，不用在线解方程组，避免了麻烦的矩阵求逆运算。     

相空间坐标受限时的最优控制问题

对于相空间坐标受限的最优控制问题,P.B.加姆克列利德泽等得到了控制最优性的必要条件(即熟知的极大值原理)和衔接点处的“跳跃条件”.但是文献[1]中所用的数学工具不是初等的,推证过程也较繁长,不易为工程技术界所理解.本文在应用文献[1]中某些分析的基础上,采用文献[2,3]中的方法处理这一问题,作法较为简单,而且除了得到[1]中的结论外,还可得到一些新的结果,例如,文中所得到的某些充分条件以及对于线性系统“小范围”最优性的必要充分条件等.     

Randomness, Stochasticity, and Approximations

Polynomial time unsafe approximations for intractable sets were introduced by Meyer and Paterson [9] and Yesha [19], respectively. The question of which sets have optimal unsafe approximations has been investigated extensively; see, e.g., [1], [5], [15], and [17]. Recently, Wang [15], [17] showed that polynomial time random sets are neither optimally unsafe approximable nor Δ -levelable. In this paper we show that: (1) There exists a polynomial time stochastic set in the exponential time complexity class which has an optimal unsafe approximation. (2) There exists a polynomial time stochastic set in the exponential time complexity class which is Δ -levelable. The above two results answer a question asked by Ambos-Spies and Lutz [2]: What kind of natural complexity property can be characterized by p -randomness but not by p -stochasticity? Our above results also extend Ville's [13] historical result. The proof of our first result shows that, for Ville's stochastic sequence, we can find an optimal prediction function f such that we will never lose our own money betting according to f (except the money we have earned), that is to say, if at the beginning we have only $1 and we always bet $1 that the next selected bit is 1 , then we always have enough money to bet on the next bit. Our second result shows that there is a stochastic sequence for which there is a betting strategy f such that we will never lose our own money betting according to f (except the money we have earned), but there is no such optimal betting strategy. That is to say, for any such betting strategy, we can find another betting strategy which could be used to make money more quickly. Received May 1997, and in final form September 1998.