近似最近邻归约问题在泊松点过程上的再研究

在已发表文献中, 研究了基于图灵归约求解$ \varepsilon $-NN的问题, 即给定查询点q、点集P及近似参数$ \varepsilon $, 找到q在P中近似比不超过$ 1 + \varepsilon $的近似最近邻, 并提出了一个具有${\rm{O}}(\log n)$查询时间复杂度的图灵归约算法, 这里的查询时间是调用神谕的次数. 经过对比, 此时间优于所有现存的归约算法. 但是已发表文献中提出的归约算法的缺点在于, 其预处理时间和空间复杂度中有${\rm{O}}({(d/\varepsilon )^d})$的因子, 当维度数d较大或者近似参数$ \varepsilon $较小时, 此因子将变得不可接受. 因此, 重新研究了该归约算法, 在输入点集服从泊松点过程的情况下, 分析算法的期望时间和空间复杂度, 将算法的期望预处理时间复杂度降到${\rm{O}}(n\log n)$, 期望空间复杂度降到${\rm{O}}(n\log n)$, 而期望查询时间复杂度保持${\rm{O}}(\log n)$不变, 从而完成了在已发表文献中所提出的未来工作.     

量子线性卷积及其在图像处理中的应用

线性卷积在图像处理中发挥着重要作用, 但是在处理海量高分辨率图像时, 求解线性卷积会消耗许多计算资源. 为此, 本文就量子线性卷积及其在图像处理问题中的应用开展相关研究, 首先提出单通道, 单位步长, 零补充情况下的量子一维和二维线性卷积, 然后实现多通道, 非单位步长, 非零补充的情况, 最后将量子二维线性卷积应用于量子图像平滑, 量子图像锐化和量子图像边缘检测. 通过理论分析证明了量子线性卷积的空间复杂度${\rm{O}}(\mathrm{log}M)$和时间复杂度${\rm{O}}({\mathrm{log}}^{2}M)$较经典线性卷积有指数级下降, 且基于Qiskit的仿真实验成功验证了量子线性卷积和量子图像处理算法的正确性和可行性.     

基于数据库的属性约简模型的快速求核算法

对于基于数据库系统的属性约简模型,给出相应的简化差别矩阵和相应核的定义,并证明该核与基于数据库系统的属性约简模型的核是等价的。在此基础上设计了一个新的求核算法,其时间复杂度和空间复杂度分别为max{O（|C||U/C|²）,O（|C||U|）}和O（|U|）。     

基于信息熵的二进制差别矩阵属性约简算法

给出一个简化的二进制差别矩阵的属性约简定义,并证明该属性约简的定义与基于信息熵的属性约简的定义是等价的。为求出简化的二进制差别矩阵,设计了一个快速求简化决策表的算法,其时间复杂度为O（|C||U|）。在此基础上,设计了基于信息熵的简化二进制差别矩阵的快速属性约简算法,其时间复杂度和空间复杂度分别为max{O（|C||U|）,O（|C|²|U/C|²）}和max{O（|C||U/C|²）,O（|U|）},最后用一个实例说明了新算法的高效性。     

信息系统中正区域快速求解算法研究

正区域是粗糙集理论中最重要的概念之一,求解正区域一般算法的时间复杂度为O(|C||U|2).为了提高正区域求解效率,提出一种快速等价类划分算法,并应用于正区域求解过程中,使求正区域算法的时间复杂度降低为0(ICllUl).然后,提出负区域的概念,证明了在负区域中求解正区域的性质,并给出改进后的算法,使求解正区域的时间复杂度进一步降低为max{O(|C||U-POS{al}(D)|),O(|U|)}.理论分析和实验结果表明,该算法是正确的、高效的.     

一种基于二进制表示的快速求核算法

在基于粗糙集的知识发现过程中,计算条件属性对论域的划分U/C和求解属性核是尤为关键的步骤。一般需要逐个比较对象的所有条件属性值才能得出结果。提出一种基于二进制表示的方法,只需比较对象的属性值的“和”。该方法先求得所有条件属性值的“和”,仅对该“和”进行一次比较,再通过判断该“和”是否重复,就能得出U/C,理论分析得到该算法的复杂度为O(|C||U|);然后把计算U/C的思想应用于求解属性核,提出了一种新的快速计算属性核的高效算法。理论分析表明,无论信息系统是否一致,该算法的复杂度均可达到O(|C||U|)。随后通过一个实例阐明了算法的具体步骤,最后通过实验验证了算法的正确性和高效性。     

相似度三支决策模糊粗糙集模型的决策代价研究

在三支决策模糊粗糙集模型中,一些学者基于相似度三支决策模糊粗糙集模型建立了目标函数来得到最优阈值对 $\left( {\alpha ,\;\beta } \right)$ 的计算方法,但在该过程的研究中,学者并没有在相似度三支决策模糊粗糙集模型中讨论关于决策代价的描述问题。基于模糊信息系统用新的函数来描述决策代价成为计算阈值对 $\left( {\alpha ,\;\beta } \right)$ 的一种方法,首先,在模糊信息系统中,通过建立一个描述决策代价的函数,将模糊信息系统中的模糊数与三支决策的决策代价联系在一起;然后对隶属频率进行拟合,得到了三支决策中决策代价的数值描述;最后,通过两个实例说明了该方法的可行性和适用性。     

一种快速属性核求解算法

在Rough Set理论中,计算属性核是最重要的计算之一。以桶排序的思想设计了一个新的求解U/C的算法,其时间复杂度被降为O（|C||U|）。基于此,提出了一个新的求核算法,其时间复杂度被降为[O(|C|2|U|)]。通过实验证明了求核算法的高效性。     

基于改进的差别矩阵的快速属性约简算法

为了解决基于差别矩阵属性约简的计算效率问题,首先以计数排序的思想设计了一个新的计算U/C的高效算法,其时间复杂度降为O(|C||U|)。其次分析了基于差别矩阵的属性约简算法的不足,提出了改进的差别矩阵的定义,利用快速计算核属性算法生成的核属性和出现频率最多的属性来降低差别矩阵的大小,并设计了基于改进的差别矩阵的快速属性约简算法,证明了该新算法的时间复杂度和空间复杂度分别被降为max(O|C|2Σ0≤i相似文献   

基于可分辨矩阵的快速求核算法

目前求核算法存在以下不足:求得的核与基于正区域的核不一致,算法的时间和空间复杂度不理想.针对上述问题,提出一种简化的可分辨矩阵的定义和求核方法,并证明了由该方法获得的核与基于正区域的核是等价的.为了提高算法效率,采用分布计数的基数排序思想设计等价类U/C划分算法,其时间复杂度为O(|C||U|).在此基础上,给出快速求核算法,其时间和空间复杂度分别降为max{O(|C||U/C|2),O(|C||U|)}和O(|C||U/C|2).最后,实例说明了算法的有效性.     

Quantum search algorithm for set operation

The operations of data set, such as intersection, union and complement, are the fundamental calculation in mathematics. It’s very significant that designing fast algorithm for set operation. In this paper, the quantum algorithm for calculating intersection set ${\text{C}=\text{A}\cap \text{B}}$ is presented. Its runtime is ${O\left( {\sqrt{\left| A \right|\times \left| B \right|\times \left|C \right|}}\right)}$ for case ${\left| C \right|\neq \phi}$ and ${O\left( {\sqrt{\left| A \right|\times \left| B \right|}}\right)}$ for case ${\left| C \right|=\phi}$ (i.e. C is empty set), while classical computation needs O (|A| × |B|) steps of computation in general, where |.| denotes the size of set. The presented algorithm is the combination of Grover’s algorithm, classical memory and classical iterative computation, and the combination method decrease the complexity of designing quantum algorithm. The method can be used to design other set operations as well.     

Quantum Error Correction of Time-correlated Errors

The complexity of the error correction circuitry forces us to design quantum error correction codes capable of correcting a single error per error correction cycle. Yet, time-correlated error are common for physical implementations of quantum systems; an error corrected during the previous cycle may reoccur later due to physical processes specific for each physical implementation of the qubits. In this paper, we study quantum error correction for a restricted class of time-correlated errors in a spin-boson model. The algorithm we propose allows the correction of two errors per error correction cycle, provided that one of them is time-correlated. The algorithm can be applied to any stabilizer code when the two logical qubits and are entangled states of 2 ⁿ basis states in .      

A System of Relational Syllogistic Incorporating Full Boolean Reasoning

We present a system of relational syllogistic, based on classical propositional logic, having primitives of the following form: $$\begin{array}{ll}\mathbf{Some}\, a \,{\rm are} \,R-{\rm related}\, {\rm to}\, \mathbf{some} \,b;\\ \mathbf{Some}\, a \,{\rm are}\,R-{\rm related}\, {\rm to}\, \mathbf{all}\, b;\\ \mathbf{All}\, a\, {\rm are}\,R-{\rm related}\, {\rm to}\, \mathbf{some}\, b;\\ \mathbf{All}\, a\, {\rm are}\,R-{\rm related}\, {\rm to}\, \mathbf{all} \,b.\end{array}$$ Such primitives formalize sentences from natural language like ‘All students read some textbooks’. Here a, b denote arbitrary sets (of objects), and R denotes an arbitrary binary relation between objects. The language of the logic contains only variables denoting sets, determining the class of set terms, and variables denoting binary relations between objects, determining the class of relational terms. Both classes of terms are closed under the standard Boolean operations. The set of relational terms is also closed under taking the converse of a relation. The results of the paper are the completeness theorem with respect to the intended semantics and the computational complexity of the satisfiability problem.     

Population Variance under Interval Uncertainty: A New Algorithm

In statistical analysis of measurement results, it is often beneficial to compute the range V of the population variance when we only know the intervals of possible values of the x_i. In general, this problem is NP-hard; a polynomialtime algorithm is known for the case when the measurements are sufficiently accurate, i.e., when for all In this paper, we show that we can efficiently compute V under a weaker (and more general) condition .     

An efficient simulation algorithm on Kripke structures

A number of algorithms for computing the simulation preorder (and equivalence) on Kripke structures are available. Let $\varSigma $ denote the state space, ${\rightarrow }$ the transition relation and $P_{\mathrm {sim}}$ the partition of $\varSigma $ induced by simulation equivalence. While some algorithms are designed to reach the best space bounds, whose dominating additive term is $|P_{\mathrm {sim}}|^2$ , other algorithms are devised to attain the best time complexity $O(|P_{\mathrm {sim}}||{\rightarrow }|)$ . We present a novel simulation algorithm which is both space and time efficient: it runs in $O(|P_ {\mathrm {sim}}|^2 \log |P_{\mathrm {sim}}| + |\varSigma |\log |\varSigma |)$ space and $O(|P_{\mathrm {sim}}||{\rightarrow }|\log |\varSigma |)$ time. Our simulation algorithm thus reaches the best space bounds while closely approaching the best time complexity.     

聚焦式模糊变结构控制及其在主汽温控制中的应用

针对具有纯滞后、大惯性、参数漂移大的非线性复杂系统,本文提出一种聚焦式模糊变结构控制算法,使系统在多种干扰下具有较强鲁棒性的同时,具有较快的响应速度．控制器采用偏差e、偏差变化速率de/dt和偏差累积∫edt作为输入信号,利用聚焦式量化算法对这3个输入论域进行离散化,模糊化后采用模糊变结构算法对三维输入进行二维的模糊推理,大大简化了模糊推理的过程．仿真结果表明:新算法具有很好的动态品质,可以有效地消除系统的稳态误差．该算法在广东某电厂2#机组锅炉的汽温控制系统中得到成功的应用,其控制效果良好．     

基于区分对象对的不完备决策表求核

在差别矩阵的基础上,针对不完备决策表提出了基于差别矩阵的区分对象对集定义,并证明求不完备决策表的核可以转化到求基于差别矩阵的区分对象对集上。在此基础上,提出了一种基于区分对象对的不完备决策表求核算法,该算法的时间复杂度为：[max{O(|C||U||Upos|),O(K|C||U|)}],优于同类算法的时间复杂度;用实例说明了新算法的有效性。     

Behavior of confined fluids in nanoslit pores: the normal pressure tensor

The aim of our research is to develop a theory, which can predict the behavior of confined fluids in nanoslit pores. The nanoslit pores studied in this work consist of two structureless and parallel walls in the xy plane located at z = 0 and z = H, in equilibrium with a bulk homogeneous fluid at the same temperature and at a given uniform bulk density. We have derived the following general equation for prediction of the normal pressure tensor P _zz of confined inhomogeneous fluids in nanoslit pores: