Inverse Center Location Problem on a Tree

This paper discusses the inverse center location problem restricted on a tree with different costs and bound constraints. The authors first show that the problem can be formulated as a series of combinatorial linear programs, then an O（｜V｜^2 log ｜V｜） time algorithm to solve the problem is presented. For the equal cost case, the authors further give an O（｜V｜） time algorithm.     

Limited Memory BFGS Method for Least Squares Semidefinite Programming with Banded Structure

This work is intended to solve the least squares semidefinite program with a banded structure. A limited memory BFGS method is presented to solve this structured program of high dimension. In the algorithm, the inverse power iteration and orthogonal iteration are employed to calculate partial eigenvectors instead of full decomposition of n × n matrices. One key feature of the algorithm is that it is proved to be globally convergent under inexact gradient information. Preliminary numerical results indicate that the proposed algorithm is comparable with the inexact smoothing Newton method on some large instances of the structured problem.

     

Differentially Private Distributed Parameter Estimation

Data privacy is an important issue in control systems, especially when datasets contain sensitive information about individuals. In this paper, the authors are concerned with the differentially private distributed parameter estimation problem, that is, we estimate an unknown parameter while protecting the sensitive information of each agent. First, the authors propose a distributed stochastic approximation estimation algorithm in the form of the differentially private consensus+innovations(DP-CI...     

Straightforward Guess and Determine Analysis Based on Genetic Algorithm

With the development of artificial intelligence, the genetic algorithm has been widely used in many fields. In cryptography, the authors find it is natural to code an individual and design its fitness in a genetic algorithm for a straightforward guess and determine analysis(SGDA, in short).Based on this observation, the authors propose an SGDA based on genetic algorithm. Comparing it with the other three SGDAs based on exhaustive search, MILP method and CPP method respectively,the authors illust...     

New Results on H∞ Control for Nonlinear Conformable Fractional Order Systems

This paper deals with H_∞ control problem for nonlinear conformable fractional order systems. The authors first derive new sufficient condition for exponential stability of nonlinear conformable fractional order systems based on Lyapunov-like function method for conformable fractional order systems and linear matrix inequalities(LMIs) approach. Then, by introducing a new concepts of H_∞ control problem for nonlinear conformable fractional order systems, the authors study H_∞ performance analysis and H_∞ state feedback controller design problems for the considered systems. In terms of LMIs, a sufficient condition is proposed to ensure the nonlinear conformable fractional order systems are not only exponentially stable, but also satisfy H_∞ performance γ. An explicit expression for state feedback controllers is also designed to make the closed-loop system is exponentially stable with H_∞performance γ. Finally, numerical examples are given to illustrate the validity and effectiveness of the proposed results.     

Multi-facility ordered median problems in directed networks

This paper uses a finite dominating set (FDS) to investigate the multi-facility ordered median problem (OMP) in a strongly connected directed network. The authors first prove that the multi-facility OMP has an FDS in the node set, which not only generalizes the FDS result provided by Kalcsics, et al. (2002), but also extends the FDS result from the single-facility case to the multiple case, filling an important gap. Then, based on this FDS result, the authors develop an exact algorithm to solve the problem. However, if the number of facilities is large, it is not practical to find the optimal solution, because the multi-facility OMP in directed networks is NP-hard. Hence, we present a constant-approximation algorithm for the p-median problem in directed networks. Finally, we pose an open problem for future research.     

Sensor selection for random field estimation in wireless sensor networks

This paper studies the sensor selection problem for random field estimation in wireless sensor networks.The authors first prove that selecting a set of l sensors that minimize the estimation error under the D-optimal criterion is NP-complete.The authors propose an iterative algorithm to pursue a suboptimal solution.Furthermore,in order to improve the bandwidth and energy efficiency of the wireless sensor networks,the authors propose a best linear unbiased estimator for a Gaussian random field with quantized measurements and study the corresponding sensor selection problem.In the case of unknown covariance matrix,the authors propose an estimator for the covariance matrix using measurements and also analyze the sensitivity of this estimator.Simulation results show the good performance of the proposed algorithms.     

An on-line scheduling problem of parallel machines with common maintenance time

In this paper, the authors consider an on-line scheduling problem of m (m ≥ 3) identical machines with common maintenance time interval and nonresumable availability. For the case that the length of maintenance time interval is larger than the largest processing time of jobs, the authors prove that any on-line algorithm has not a constant competitive ratio. For the case that the length of maintenance time interval is less than or equal to the largest processing time of jobs, the authors prove a lower bound of 3 on the competitive ratio. The authors give an on-line algorithm with competitive ratio $4 - \tfrac{1} {m} $ . In particular, for the case of m = 3, the authors prove the competitive ratio of the on-line algorithm is $\tfrac{{10}} {3} $ .     

On-Line Scheduling on Parallel Machines to Minimize the Makespan

This paper considers two parallel machine scheduling problems,where the objectives of both problems are to minimize the makespan,and the jobs arrive over time,on two uniform machines with speeds 1 and s(s≥1),and on m identical machines,respectively.For the first problem,the authors show that the on-line LPT algorithm has a competitive ratio of(1 +5~(1/2))/2≈1.6180 and the bound is tight.Furthermore,the authors prove that the on-line LPT algorithm has the best possible competitive ratio if s≥1.8020.For the second problem,the authors present a lower bound of(15-(17)~(1/2))/8≈1.3596 on the competitive ratio of any deterministic on-line algorithm.This improves a previous result of 1.3473.     

Scheduling problems with rejection to minimize the maximum flow time

This paper considers the scheduling problem with rejection on m identical parallel machines to minimize the maximum flow time. The authors show that this problem is NP-hard even when there is a single machine and all jobs have two distinct release dates. Furthermore, the authors present a dynamic programming algorithm and two approximation algorithms to solve them.     

Curvature-Based r-Adaptive Isogeometric Analysis with Injectivity-Preserving Multi-Sided Domain Parameterization

Inspired by the r-refinement method in isogeometric analysis, in this paper, the authors propose a curvature-based r-adaptive isogeometric method for planar multi-sided computational domains parameterized by toric surface patches. The authors construct three absolute curvature metrics of isogeometric solution surface to characterize its gradient information, which is more straightforward and effective. The proposed method takes the internal weights as optimization variables and the resulting par...     

Test on Stochastic Block Model: Local Smoothing and Extreme Value Theory

In this paper, to obtain a consistent estimator of the number of communities, the authors present a new sequential testing procedure, based on the locally smoothed adjacency matrix and the extreme value theory. Under the null hypothesis, the test statistic converges to the type I extreme value distribution, and otherwise, it explodes fast and the divergence rate could even reach n in the strong signal case where n is the size of the network, guaranteeing high detection power. This method is simple to use and serves as an alternative approach to the novel one in Lei (2016) using random matrix theory. To detect the change of the community structure, the authors also propose a two-sample test for the stochastic block model with two observed adjacency matrices. Simulation studies justify the theory. The authors apply the proposed method to the political blog data set and find reasonable group structures.

     

大规模应急救援物资运输模型的构建与求解

分析大规模突发性公共事件或自然灾害情况下救援物资运输与商业运输的不同特点，指出救援物资运输问题综合了多货物多起止点网络流问题与多种运输方式满载车辆调度问题，在此基础上为描述该问题设计一种多模式分层网络，并利用延期费用和划分时段的方法构建问题的多目标数学规划模型。提出一个基于拉格朗日松弛法的解决方法，将原问题分解为货物流与车辆流问题两个子问题，通过多货物流与最小费用循环流算法分别求解，最后通过实例计算验证谊解法具有良好的收敛性与计算效率。     

Improve Robustness and Accuracy of Deep Neural Network with L2,∞ Normalization

In this paper, the L_2,∞ normalization of the weight matrices is used to enhance the robustness and accuracy of the deep neural network(DNN) with Relu as activation functions. It is shown that the L_2,∞ normalization leads to large dihedral angles between two adjacent faces of the DNN function graph and hence smoother DNN functions, which reduces over-fitting of the DNN. A global measure is proposed for the robustness of a classification DNN, which is the average radius of th...     

Distributed Consensus-Based <Emphasis Type="Italic">K</Emphasis>-Means Algorithm in Switching Multi-Agent Networks

This paper discusses a distributed design for clustering based on the K-means algorithm in a switching multi-agent network, for the case when data are decentralized stored and unavailable to all agents. The authors propose a consensus-based algorithm in distributed case, that is, the double-clock consensus-based K-means algorithm (DCKA). With mild connectivity conditions, the authors show convergence of DCKA to guarantee a distributed solution to the clustering problem, even though the network topology is time-varying. Moreover, the authors provide experimental results on various clustering datasets to illustrate the effectiveness of the fully distributed algorithm DCKA, whose performance may be better than that of the centralized K-means algorithm.     

<Emphasis Type="Italic">L</Emphasis><Subscript>2</Subscript> disturbance attenuation for a class of time-delay Hamiltonian systems

This paper considers the problem of L ₂-disturbance attenuation for a class of time-delay port-controlled Hamiltonian systems. A γ-dissipative inequality is established by using a proper control law and a storage function. Then based on the Razumikhin stability theorem, a sufficient condition is proposed for the asymptotically stability of the closed-loop system. Finally, the authors investigate the case that there are time-invariant uncertainties belonging to some convex bounded polytypic domain and an L ₂ disturbance attenuation control law is proposed. Study of illustrative example with simulation shows that the presented method in this paper works very well in the disturbance attenuation of time-delay Hamiltonian systems.     

Distance-Based Regression Analysis for Measuring Associations

Distance-based regression model, as a nonparametric multivariate method, has been widely used to detect the association between variations in a distance or dissimilarity matrix for outcomes and predictor variables of interest in genetic association studies, genomic analyses, and many other research areas. Based on it, a pseudo-F statistic which partitions the variation in distance matrices is often constructed to achieve the aim. To the best of our knowledge, the statistical properties of the pseudo-F statistic has not yet been well established in the literature. To fill this gap, the authors study the asymptotic null distribution of the pseudo-F statistic and show that it is asymptotically equivalent to a mixture of chi-squared random variables. Given that the pseudo-F test statistic has unsatisfactory power when the correlations of the response variables are large, the authors propose a square-root F-type test statistic which replaces the similarity matrix with its square root. The asymptotic null distribution of the new test statistic and power of both tests are also investigated. Simulation studies are conducted to validate the asymptotic distributions of the tests and demonstrate that the proposed test has more robust power than the pseudo-F test. Both test statistics are exemplified with a gene expression dataset for a prostate cancer pathway.

     

Recurrences for Callan’s Generalization of Narayana Polynomials

By using Chen, Hou and Mu’s extended Zeilberger algorithm, the authors obtain two recurrence relations for Callan’s generalization of Narayana polynomials. Based on these recurrence relations, the authors further prove the real-rootedness and asymptotic normality of Callan’s Narayana polynomials.

     

Improved Algorithm for Minimum Data Aggregation Time Problem in Wireless Sensor Networks

Wireless sensor networks promise a new paradigm for gathering data via collaboration among sensors spreading over a large geometrical region. Many applications impose delay requirements for data gathering and ask for time-efficient schedules for aggregating sensed data and sending to the data sink. In this paper, the authors study the minimum data aggregation time problem under collision-free transmission model. In each time round, data sent by a sensor reaches all sensors within its transmission range, but a sensor can receive data only when it is the only data that reaches the sensor. The goal is to find the method that schedules data transmission and aggregation at sensors so that the time for all requested data to be sent to the data sink is minimal. The authors propose a 7△/log2｜s｜＋c, new approximation algorithm for this NP-hard problem with guaranteed performance ratio which significantly reduces the current best ratio of △- 1, where S is the set of sensors containing source data, A is the maximal number of sensors within the transmission range of any sensor, and e is a constant. The authors also conduct extensive simulation, the obtained results justify the improvement of proposed algorithm over the existing one.     

Long-Time Behavior and Density Function of a Stochastic Chemostat Model with Degenerate Diffusion

This paper considers a stochastic chemostat model with degenerate diffusion. Firstly, the Markov semigroup theory is used to establish sufficient criteria for the existence of a unique stable stationary distribution. The authors show that the densities of the distributions of the solutions can converge in L¹ to an invariant density. Then, conditions are obtained to guarantee the washout of the microorganism. Furthermore, through solving the corresponding Fokker-Planck equation, the authors give the exact expression of density function around the positive equilibrium of deterministic system. Finally, numerical simulations are performed to illustrate the theoretical results.