基于列表译码方法在查询访问模型下含错学习问题的分析

Regev在2005年提出了含错学习问题(LWE)，这个问题与随机线性码的译码问题密切相关，并且在密码学特别是后量子密码学中应用广泛。原始的含错学习问题是在随机访问模型下提出的，有证据证明该问题的困难性。许多研究者注意到的一个事实是当攻击者可以选择样本时，该问题是容易的。但是目前据作者所知并没有一个完整的求解算法。该文分析了查询访问模型下的带有错误学习问题，给出了完整的求解算法。分析采用的工具是将该问题联系到隐藏数问题，然后应用傅里叶学习算法进行列表译码。     

基于本体的决策问题语义理解及精炼方法

理解复杂决策问题的关键在于使决策问题所包含的领域、目标、状态、结构等信息被系统所“读懂”.本文利用本体表达语义,实现了问题语义关系表示和语义计算.在保持理解结果不变的原则上,本文提出利用语义迭代方法将计算机无法理解的问题语义转化为可完全理解的语义.本文给出了语义精炼方法并形成最优闭合问题空间,在结构复杂度和内容复杂度两方面具有最低复杂度.实验分析表明,本文提出的复杂决策问题语义理解方法是有效的.     

引入D2D通信的蜂窝网上行资源分配算法

该文研究了引入Device-to-Device (D2D)通信的蜂窝网系统中的上行资源分配问题。首先将该问题建模为一个简洁的二值整数规划问题。然而整数规划仍是NP难问题。该文利用Canonical对偶理论,得到其对偶形式。该对偶问题是一个连续域内的凸问题。证明了在特定的条件下,可以通过求解对偶问题得到原问题的最优解,且对偶间隙为零。提出了一个基于Barrier方法的算法来求解对偶问题。仿真结果表明,该文的算法优于现有算法,且性能接近最优。     

Analog Computation Using Single-Electron Circuits

Analog computation is a processing method that solves a given problem by utilizing an analogy of a physical system to the problem. An idea is presented here for relating the behavior of single-electron circuits to analog computation. As an instance, a method is proposed for solving a combinatorial problem, the three-colorability problem, by using the properties of single-electron circuits. In problem solving, a single-electron circuit is constructed that is analogous to a given problem; then, through an annealing procedure, the circuit is made to settle down to its minimun energy state. The correct solution to the problem can be obtained by checking the final arrangement of electrons in the circuit. Analog computation is a promising architecture for single-electron computing systems.     

Closed form approximations to the inverse black body radiation problem

The inverse black body radiation problem is the problem of determining the unknown area-temperature distribution of a black body from its radiated electromagnetic power spectrum. An exact iterative solution to this problem (the inverse Planck problem) was derived by this author in 1982. Recently Hamid and Ragheb derived a closed form approximation to this problem claimed to be valid for the Rayleigh-Jeans regime (the inverse Rayleigh-Jeans problems). It is shown that this Hamid-Ragheb solution is actually far superior to an inverse Rayleigh-Jeans approximation. A closed form approximation to the inverse black body radiation problem valid for the Wien regime (the inverse Wien problem) is presented, and shown to be equivalent to the leading term of the exact iterative solution of this author.     

浅谈基于问题的创新性研究与教学

分析了基于问题的创新性研究和研究性教学的内涵,特别强调了如何提出科学问题的重要性以及应遵循的需求牵引、问题驱动和问题求解的科学研究特征。并且以信息化和网络化环境下多飞行器协同作战为实例,分析了多飞行器网络化协同控制的需求和特点,进而详细论述了如何分析问题和提出问题的详细过程,并说明了不同学科知识交叉和融合应用的重要性,便于领会如何在实际中提出问题并开展基于问题的创新性研究和研究性教学。     

用动态规划方法求解最短运输路线问题

在日常生活中,很多领域都要涉及到最短路径问题,如何求解最短路径的问题是非常重要的。阐述了动态规划方法的基本思想、求解最短路径问题的步骤,并使用C语言编程解决了最短运输路线问题,说明了动态规划求解最短路径的可行性。     

三划分问题可多项式归约为唯一可达向量Petri网可达性问题

为了对基于唯一可达向量Petri网(URV-PN)的密码体制进行密码分析工作,有必要对唯一可达向量网系统的数学本质和各种性质进行深入的研究.定义了扩展的三划分问题,三划分问题是扩展的三划分问题的一种特殊情况;给出了一个一般的多项式时间复杂度算法构造扩展的三划分问题的Petri网模型;证明扩展的三划分问题有解当且仅当所构造的Petri网模型中某个标识可达;从而说明三划分问题可多项式归约为唯一可达向量Petri网系统的可达性问题,从而给出了求解唯一可达向量网系统可达性问题的一个复杂度下界.     

人工神经网络在航迹关联中的应用研究

在分布式多传感器系统中的多节点情况下,航迹关联问题可以转化为多维分配问题。而多维分配问题是典型的组合优化问题,很难找到问题的最优解,而且其计算量随着问题规模的增加易出现指数爆炸现象。该文提出了一种三维神经网络模型,用以解决三节点情况下航迹关联的三维分配问题,并进行了实验仿真。仿真结果表明,三维人工神经劂络模型能够有效地求解此三维分配问题,并且具有较高的航迹关联正确率。另外三维神经网络模型同样可以推广到多维,用以解决航迹关联的多维分配问题。     

安全向量优势协议及其应用

百万富翁问题是安全多方计算研究的热点问题之一,也是其他安全多方计算协议的基本构成模块.安全向量优势统计问题是百万富翁问题的推广,用于两方在不泄漏自己保密向量信息的前提下统计出满足大于关系的分量的数目.本文基于同态加密算法,通过对保密的数据进行编码,设计了一个计算百万富翁问题的协议,并利用模拟范例对协议进行安全性证明.然后利用这个新的协议作为基本模块,设计了一个向量优势统计协议,通过效率分析显示我们的方案是简单、高效的.最后将向量优势统计协议应用到整除判定问题和点与若干直线关系判定问题.     

Logically rearrangeable multihop lightwave networks

The optimization problem of rearrangeable multihop lightwave networks is considered. The authors formulate the flow and wavelength assignment problem, when minimizing the maximum flow in the network, as a mixed integer optimization problem subject to linear constraints. The problem is decomposed into two independent subproblems, the wavelength assignment (or connectivity problem) and the flow assignment (or routing problem). A simple heuristic provides a meaningful formulation to the connectivity problem, in a form similar to a transportation problem. An algorithm is then proposed which finds a heuristic initial logical connectivity diagram and the corresponding routing, and then iterates from that solution by applying branch-exchange operations to the connectivity diagram. The algorithm was tested on illustrative traffic matrices for an 8 node network with two transmitters and two receivers per node, and an improvement in achievable throughput over the Perfect Shuffle interconnection pattern was shown in all cases     

Continuous-time envelope constrained filter design via orthonormalfilters

The envelope constrained (EC) filtering problem is concerned with designing a filter which minimises the gain to input noise while its response to a given signal fits into a prescribed envelope. This problem had been formulated as a constrained optimisation problem in Hilbert space. By restricting these filters to the span of a finite orthonormal set, the EC filtering problem can be posed as a finite dimensional optimisation problem with a continuum of constraints. The constrained problem is approximated by an unconstrained problem which is then solved by descent direction based algorithms. It is shown that these algorithms converge globally, and one in particular has a quadratic rate of convergence. Numerical examples using the orthonormal Laguerre series approximation are studied     

基于多离散对数问题的公钥密码

该文首先定义了多离散对数问题,给出了现有隐含子群问题量子计算算法不适用于求解该问题的必要条件,且该问题在经典计算模式下,其困难性比离散对数问题难,用于求解有限域上离散对数问题的数域筛法不适用于求解多离散对数问题。然后设计了基于多离散对数问题的公钥密码,其安全性依赖于多离散对数问题,且公私钥的数据量小,分析了算法参数的选取原则,证明了算法脱密原理的正确性,算法在每次加密时需要随机选取一个数,使得算法对同一个明文加密所得的密文不一定相同。     

Lagrangean Based Methods for Solving Large-Scale Cellular Network Design Problems

The cellular network design (CND) problem is formulated as a comprehensive linear mixed integer programming model integrating the base station location (BSL) problem, the frequency channel assignment (FCA) problem and the topological network design (TND) problem. A solution algorithm based on Lagrangean relaxation is proposed for solving this complex cellular network design problem. Pursuing the optimum solution through exact algorithms to this problem appears to be unrealistic considering the large scale nature and NP-hardness of the problem. Therefore, the solution algorithm strategy consists in computing effective lower and upper bounds for the problem. Lower bounds are evaluated through a Lagrangean relaxation technique and subgradient method. A Lagrangean heuristic is developed to compute upper bounds based on the Lagrangean solution. The bounds are improved through a customized branch and bound algorithm which takes in account specific knowledge of the problem to improve its efficiency. Thirty two random test instances are solved using the proposed algorithm and the CPLEX optimization package. The results show that the duality gap is excessive, so it cannot guarantee the quality of the solution. However, the proposed algorithm provides optimal or near optimal solutions for the problem instances for which CPLEX also provides the optimal solution. It further suggests that the proposed algorithm provides optimal or near optimal solutions for the other instances too. Finally, the results demonstrate that the proposed algorithm is superior to CPLEX as a solution approach for the CND problem.     

杂波环境下共享频谱恒模波形设计

针对射频频谱环境愈发拥挤问题,深入研究了通过波形设计的手段实现频谱共享的问题。为紧密贴近工程实践,提出了一种新的方法设计恒定幅度信号的问题。该算法首先针对雷达发射端,提出雷达波形满足特定的时域与频谱要求,施加约束,然后考虑雷达接收滤波器接收杂波,以优化最大信干噪比建立优化问题模型,得到了一个非凸的分式规划问题模型。最后,利用分步优化方法分解为两个优化问题,并且将非凸问题松弛为可解的凸问题再利用高斯随机化方法得到优化信号,多次循环优化。仿真结果验证了该算法的有效性,该方法设计得到的探测信号能够实现频谱共存,而且信干噪比性能能够得到保证。      

改进遗传算法下的车辆路径问题研究

车辆路径问题是一种典型的组合优化类问题,随着客户对物流要求的不断提升,基本的遗传算法已经很难满足客户的需求。基本的遗传算法在求解这类问题的时候,经常会出现早熟收敛,以及对车辆的运送时间存在限制等方面的缺陷,不能够对这类问题进行最优化求解,所以本文采用改进的遗传算法就车辆路径问题进行研究,并探究改进下的遗传算法在求解车辆路径问题时的有效性。     

Subhierarchical method for solving problems of diffraction of electromagnetic waves by a dielectric body in a rectangular waveguide

The problem of diffraction of an external electromagnetic field by a locally inhomogeneous body placed in a rectangular waveguide with perfectly conducting walls is considered. The formulated problem is reduced to a volume singular integral equation. The problem is solved with the use of the numerical collocation method. A subhierarchical method is applied to analyze the problem for structures of a complex geometric shape. Because of a large amount of computation, the problem is solved with the use of parallel algorithms realized on a supercomputer complex.     

一种分布式的OFDMA系统资源分配算法

本文研究OFDMA系统的资源分配问题,把该问题建模为一个在基站的总发射功率一定的条件下,使系统中各个用户的权重速率之和最大化的数学模型。并提出一种基于对偶分解的分布式资源分配算法,将该问题分解为一个关于基站的主问题以及若干个关于用户的子问题。各个用户可以通过对子问题的求解获得各自的子载波以及功率的分配方案;而基站通过对主问题的求解使得满足子载波与功率的分配能够满足约束条件的要求,实现各用户权重速率和最大化的优化目标。所提算法能够把一个复杂的优化问题分解为若干个独立的子问题进行并行求解,因此可以有效地降低计算的复杂度以及基站的运算量。仿真结果表明,该算法能够在较少的迭代步数内得到一个近似最优解。      

基于0-1背包问题的两种算法

0-1背包问题是组合优化领域里的一个典型问题,是属于易于描述却难于解决的NP难题,有效解决0-1背包问题具有重要意义。首先给出了0-1背包问题的描述,然后详细介绍了回溯法和分支限界法的算法思想和搜索策略,并对两种算法进行了比较和分析。     

Numerical aspects of a dissipative inverse problem

Two numerical aspects of the solution of a one-dimensional electromagnetic inverse problem are considered: the numerical solution of delay integral equations and the sensitivity of the solution of the inverse problem to small changes in the data. In addition a numerical technique is developed for the solution of the direct problem in the time domain. The problem considered is one in which the conductivity and permittivity of the scatterer are continuous functions of depth. The incident field is a transverse electric (TE) plane wave of arbitrary shape, and the inverse problem uses the resulting reflected and transmitted transients to reconstruct the scatterer. For the sake of simplicity, a known scatterer is used to numerically generate the data required for the inverse problem. This is done by using the scattering operators for the problem. The scattering data thus obtained is used to formulate a generalized Gelfand-Levitan integral equation whose solution yields the conductivity and permittivity profiles of the scatterer. The sensitivity of this inversion process is investigated by altering the scattering data.