Formalization of the Standard Uniform random variable

Continuous random variables are widely used to mathematically describe random phenomena in engineering and the physical sciences. In this paper, we present a higher-order logic formalization of the Standard Uniform random variable as the limit value of the sequence of its discrete approximations. We then show the correctness of this specification by proving the corresponding probability distribution properties within the HOL theorem prover, summarizing the proof steps. The formalized Standard Uniform random variable can be transformed to formalize other continuous random variables, such as Uniform, Exponential, Normal, etc., by using various non-uniform random number generation techniques. The formalization of these continuous random variables will enable us to perform an error free probabilistic analysis of systems within the framework of a higher-order-logic (HOL) theorem prover. For illustration purposes, we present the formalization of the Continuous Uniform random variable based on the formalized Standard Uniform random variable, and then utilize it to perform a simple probabilistic analysis of roundoff error in HOL.     

一种改进的多播网络编码算法

在多播网络通信中,网络编码的应用,实现了最大流最小割定理所决定的多播传输的最大理论传输容量。对这一问题,可采用线性multicast,线性broadcast,线性dispersion,以及generic等线性网络编码构造算法进行求解。但这些方法,计算复杂度较高。在研究generic线性网络编码算法的基础上,结合离散路由的使用,对其进行了改进,提出了一种改进的多播网络编码算法,并给出了算法的合理性证明。复杂度分析表明,该算法较generic线性网络编码算法,复杂度有显著的下降。     

Expected model for portfolio selection with random fuzzy returns

This paper researches portfolio selection problem in combined uncertain environment of randomness and fuzziness. Due to the complexity of the security market, expected values of the security returns may not be predicted accurately. In the paper, expected returns of securities are assumed to be given by fuzzy variables. Security returns are regarded as random fuzzy variables, i.e. random returns with fuzzy expected values. Following Markowitz's idea of quantifying investment return by the expected value of the portfolio and risk by the variance, a new type of mean–variance model is proposed. In addition, a hybrid intelligent algorithm is provided to solve the new model problem. A numeral example is also presented to illustrate the optimization idea and the effectiveness of the proposed algorithm.     

Performance Analysis and Functional Verification of the Stop-and-Wait Protocol in HOL

Real-time systems usually involve a subtle interaction of a number of distributed components and have a high degree of parallelism, which makes their performance analysis quite complex. Thus, traditional techniques, such as simulation, or the state-based formal methods usually fail to produce reasonable results. In this paper, we propose to use higher-order-logic (HOL) theorem proving for the performance analysis of real-time systems. The idea is to formalize the real-time system as a logical conjunction of HOL predicates, whereas each one of these predicates define an autonomous component or process of the given real-time system. The random or unpredictable behavior found in these components is modeled as random variables. This formal specification can then be used in a HOL theorem prover to reason about both functional and performance related properties of the given real-time system. In order to illustrate the practical effectiveness of our approach, we present the analysis of the Stop-and-Wait protocol, which is a classical example of real-time systems. The functional correctness of the protocol is verified by proving that the protocol ensures reliable data transfers. Whereas, the average message delay relation is verified in HOL for the sake of performance analysis. The paper includes the protocol’s formalization details along with the HOL proof sketches for the major theorems.     

基于Word2vec和粒子群的链路预测算法

链路预测中普遍存在两大问题:特征提取困难和类别数据不平衡.本文借鉴文本处理中的深度学习特征提取算法和优化问题中的粒子群算法, 提出一种基于词向量的粒子群优化算法(Word2vec-PSO).该方法首先通过随机游走产生网络序列后, 利用Word2vec算法对节点序列特征提取.然后在有监督的条件下, 利用粒子群算法对提取好的特征进行筛选, 并确定重采样的参数来解决类别数据不平衡问题, 并分析了不同链路预测算法的计算复杂性.最后将本文的算法与基于相似性、基于深度学习、基于不平衡数据的3类链路预测算法, 在4个不同的时序网络中进行实证对比研究.结果表明, 本文提出的链路预测算法预测精度较高, 算法更加稳定且具有普适性.     

A novel ACO–GA hybrid algorithm for feature selection in protein function prediction

Protein function prediction is an important problem in functional genomics. Typically, protein sequences are represented by feature vectors. A major problem of protein datasets that increase the complexity of classification models is their large number of features. Feature selection (FS) techniques are used to deal with this high dimensional space of features. In this paper, we propose a novel feature selection algorithm that combines genetic algorithms (GA) and ant colony optimization (ACO) for faster and better search capability. The hybrid algorithm makes use of advantages of both ACO and GA methods. Proposed algorithm is easily implemented and because of use of a simple classifier in that, its computational complexity is very low. The performance of proposed algorithm is compared to the performance of two prominent population-based algorithms, ACO and genetic algorithms. Experimentation is carried out using two challenging biological datasets, involving the hierarchical functional classification of GPCRs and enzymes. The criteria used for comparison are maximizing predictive accuracy, and finding the smallest subset of features. The results of experiments indicate the superiority of proposed algorithm.     

关于漂移分析的注记

进化算法成功应用于求解各种复杂优化问题,其理论研究尚处于初级阶段。时间复杂性分析可以估计算法的平均运行时间,是进化算法理论研究中的重要方向和有力工具。讨论了漂移分析和进化算法时间复杂性的关系,利用吸收马尔科夫链给出漂移定理的一个新的证明;用一步平均漂移估计算法计算时间,得到了线性函数进化算法时间复杂度的一个一般性的结果。这些结果有助于更好地理解进化算法的工作原理和性能。     

A Deterministic Algorithm for Reconstructing Images with Interacting Discontinuities

The most common approach for incorporating discontinuities in visual reconstruction problems makes use of Bayesian techniques, based on Markov random field models, coupled with stochastic relaxation and simulated annealing. Despite their convergence properties and flexibility in exploiting a priori knowledge on physical and geometric features of discontinuities, stochastic relaxation algorithms often present insurmountable computational complexity. Recently, considerable attention has been given to suboptimal deterministic algorithms, which can provide solutions with much lower computational costs. These algorithms consider the discontinuities implicitly rather than explicitly and have been mostly derived when there are no interactions between two or more discontinuities in the image model. In this paper we propose an algorithm that allows for interacting discontinuities, in order to exploit the constraint that discontinuities must be connected and thin. The algorithm, called E-GNC, can be considered an extension of the graduated nonconvexity (GNC), first proposed by Blake and Zisserman for noninteracting discontinuities. When applied to the problem of image reconstruction from sparse and noisy data, the method is shown to give satisfactory results with a low number of iterations.     

Single-machine scheduling to minimize total convex resource consumption with a constraint on total weighted flow time

In this paper, we consider single-machine scheduling problem in which processing time of a job is described by a convex decreasing resource consumption function. The objective is to minimize the total amount of resource consumed subject to a constraint on total weighted flow time. The optimal resource allocation is obtained for any arbitrary job sequence. The computational complexity of the general problem remains an open question, but we present and analyze some special cases that are solvable by using polynomial time algorithms. For the general problem, several dominance properties and some lower bounds are derived, which are used to speed up the elimination process of a branch-and-bound algorithm proposed to solve the problem. A heuristic algorithm is also proposed, which is shown by computational experiments to perform effectively and efficiently in obtaining near-optimal solutions. The results show that the average percentage error of the proposed heuristic algorithm from optimal solutions is less than 3%.     

OFFSS: optimal fuzzy-valued feature subset selection

Feature subset selection is a well-known pattern recognition problem, which aims to reduce the number of features used in classification or recognition. This reduction is expected to improve the performance of classification algorithms in terms of speed, accuracy and simplicity. Most existing feature selection investigations focus on the case that the feature values are real or nominal, very little research is found to address the fuzzy-valued feature subset selection and its computational complexity. This paper focuses on a problem called optimal fuzzy-valued feature subset selection (OFFSS), in which the quality-measure of a subset of features is defined by both the overall overlapping degree between two classes of examples and the size of feature subset. The main contributions of this paper are that: 1) the concept of fuzzy extension matrix is introduced; 2) the computational complexity of OFFSS is proved to be NP-hard; 3) a simple but powerful heuristic algorithm for OFFSS is given; and 4) the feasibility and simplicity of the proposed algorithm are demonstrated by applications of OFFSS to fuzzy decision tree induction and by comparisons with three different feature selection techniques developed recently.     

基于限定PSO初始化空间的随机最大似然算法

针对随机最大似然算法（SML）在波达方位（DOA）估计中由于多维非线性优化导致计算复杂度大的问题，提出一种限定粒子群（PSO）算法搜索空间的SML算法。该算法克服了一个缺陷，即在采用ESPRIT算法限定PSO初始化空间时，在阵列结构是非均匀线性阵列而且信号是相干信号时ESPRIT算法不能直接处理信号，且需要采用一组预处理技术，这增加了算法计算的复杂度。提出的算法的关键之处在于采用假设技术确定初始化点来代替ESPRIT算法的解，结合克拉美罗界（CRB）确定PSO算法的初始化解空间。这一方法不必再采用预处理技术，且利用限定PSO初始化空间的算法大大降低了SML算法的计算复杂度。实验结果表明，提出的算法为相干情况和非相干情况都提供了相当好的初始值。最后，将该算法与许多现有算法进行比较，验证提出算法的有效性和准确性。     

基于图像分割的实时空间错误隐藏算法

基于模板的空间错误隐藏算法计算复杂度较高。为此,提出一种基于图像分割的实时空间错误隐藏算法。将分割后错误块边界的同类纹理作为参考模板,在对应的纹理区域中寻找最佳匹配块,以实现错误隐藏。实验结果表明,与传统算法相比,该算法能获得较好的隐藏效果,且计算量较低。     

Scheduling Multi-Mode Projects under Uncertainty to Optimize Cash Flows: A Monte Carlo Ant Colony System Approach

Project scheduling under uncertainty is a challenging field of research that has attracted increasing attention. While most existing studies only consider the single-mode project scheduling problem under uncertainty, this paper aims to deal with a more realistic model called the stochastic multi-mode resource constrained project scheduling problem with discounted cash flows (S-MRCPSPDCF). In the model, activity durations and costs are given by random variables. The objective is to find an optimal baseline schedule so that the expected net present value (NPV) of cash flows is maximized. To solve the problem, an ant colony system (ACS) based approach is designed. The algorithm dispatches a group of ants to build baseline schedules iteratively using pheromones and an expected discounted cost (EDC) heuristic. Since it is impossible to evaluate the expected NPV directly due to the presence of random variables, the algorithm adopts the Monte Carlo (MC) simulation technique. As the ACS algorithm only uses the best-so-far solution to update pheromone values, it is found that a rough simulation with a small number of random scenarios is enough for evaluation. Thus the computational cost is reduced. Experimental results on 33 instances demonstrate the effectiveness of the proposed model and the ACS approach.     

批量无等待调度问题的微粒群蛙跳混合优化算法*

将离散微粒群与蛙跳算法相结合解决以最大完工时间为指标的批量无等待流水线调度问题.结合微粒群算法较强的全局收敛能力和蛙跳算法较强的深度搜索能力,设计了三种混合算法,平衡了算法的全局开发能力和局部探索能力.对随机生成不同规模的实例进行了广泛的实验,仿真实验结果的比较表明了所得混合算法的有效性和高效性.     

Group shops scheduling with makespan criterion subject to random release dates and processing times

This paper deals with a stochastic group shop scheduling problem. The group shop scheduling problem is a general formulation that includes the other shop scheduling problems such as the flow shop, the job shop and the open shop scheduling problems. Both the release date of each job and the processing time of each job on each machine are random variables with known distributions. The objective is to find a job schedule which minimizes the expected makespan. First, the problem is formulated in a form of stochastic programming and then a lower bound on the expected makespan is proposed which may be used as a measure for evaluating the performance of a solution without simulating. To solve the stochastic problem efficiently, a simulation optimization approach is developed that is a hybrid of an ant colony optimization algorithm and a heuristic algorithm to generate good solutions and a discrete event simulation model to evaluate the expected makespan. The proposed approach is tested on instances where the random variables are normally, exponentially or uniformly distributed and gives promising results.     

改进的几何定理机器证明的概率性算法

将几何定理机器证明的研究方法概括为确定性算法与概率性算法两大类,针对已有的确定性算法和概率性算法的证明速率偏低或占用内存过大等问题,提出一种改进的概率性算法。主要是在改进对多项式中独立变元次数的上界估计的算法的基础上,结合Schwartz-Zippel定理和统计学理论,通过随机检验若干实例来证明几何定理,并能控制证明结果不真的概率在给定的小范围内。通过改进的概率性算法,成功在2秒内证明出代数法难以证明的五圆定理。最后的多组对比实验进一步表明,改进的概率性算法具有明显高效性。     

一种基于码本聚类的低复杂度用户选择算法

现有块对角化(BD)预编码系统用户选择算法较少考虑利用已选用户与剩余用户之间的关系来排除不可选用户.针对这点不足,给出了一种采用码本聚类的低复杂度用户选择算法( CodeGreedy算法).该算法采用弦距离刻画用户信道的相关性,以此为依据将用户划分到不同码本空间中,聚集在同一码本空间的用户信道具有较强的相关性,形成互斥...     

A neural-network learning theory and a polynomial time RBFalgorithm

This paper presents a new learning theory (a set of principles for brain-like learning) and a corresponding algorithm for the neural-network field. The learning theory defines computational characteristics that are much more brain-like than that of classical connectionist learning. Robust and reliable learning algorithms would result if these learning principles are followed rigorously when developing neural-network algorithms. This paper also presents a new algorithm for generating radial basis function (RBF) nets for function approximation. The design of the algorithm is based on the proposed set of learning principles. The net generated by this algorithm is not a typical RBF net, but a combination of "truncated" RBF and other types of hidden units. The algorithm uses random clustering and linear programming (LP) to design and train this "mixed" RBF net. Polynomial time complexity of the algorithm is proven and computational results are provided for the well known Mackey-Glass chaotic time series problem, the logistic map prediction problem, various neuro-control problems, and several time series forecasting problems. The algorithm can also be implemented as an online adaptive algorithm.     

Numerical study of singularly perturbed differential-difference equation arising in the modeling of neuronal variability

The objective of this paper is to present a numerical study of a class of boundary value problems of singularly perturbed differential difference equations (SPDDE) which arise in computational neuroscience in particular in the modeling of neuronal variability. The mathematical modeling of the determination of the expected time for the generation of action potential in the nerve cells by random synaptic inputs in dendrites includes a general boundary-value problem for singularly perturbed differential difference equation with shifts. The problem considered in this paper exhibit turning point behavior which add to the complexity in the construction of numerical approximation to the solution of the problem as well as in obtaining theoretical estimates on the solution. Exponentially fitted finite difference scheme based on Il’in-Allen-Southwell fitting is used on a specially designed mesh. Some numerical examples are given to validate convergence and computational efficiency of the proposed numerical scheme. Effect of the shifts on the layer structure is illuminated for the considered examples.     

基于模型诊断的分步求解

对诊断问题的分解进行研究,给出了候选诊断的分解与组合定理.在此基础上,提出了利用分步求解方法实现诊断分解的算法,并对算法的正确性、完备性和复杂性进行了证明.实验结果表明,分步求解方法明显提高了包含多个输出的系统的诊断效率.与利用变量假定例化值分解诊断问题的方法相比,该算法能提高了效率并且扩大了适用范围.