Separability of Mixed Quantum States: Linear Contractions and Permutation Criteria

Recently, a powerful separability criterion was introduced by O. Rudolf in [5] and by K. Chen et al. in [6] – basing on realignment of elements of density matrix. Composing the main idea behind the above criterion and the necessary and sufficient condition in terms of positive maps, we provide a characterization of separable states by means of linear contractions. The latter need not be positive maps. We extend the idea to multipartite systems, and find that, somewhat suprisingly, partial realigment (unlike partial transposition) can detect genuinely tri-parite entanglement. We generalize it by introducing a family of so called permutation separability criteria for multipartite states. Namely, any permutation of indices of density matrix written in product basis leads to a separability criterion. Partial transpose and realignment criterion are special cases of permutation criteria. An early version of the present paper has appeared in e-print archive as quant-ph/0206008. The premutation criterion has been then further developed in [23, 24, 25], where the problem of classification of inequivalent permutation criteria has been investigated.     

Limits of Using Signatures for Permutation Independent Boolean Comparison

This paper addresses problems that arise while checking the equivalence of two Boolean functions under arbitrary input permutations. The permutation problem has several applications in the synthesis and verification of combinational logic: it arises in the technology mapping stage of logic synthesis and in logic verification. A popular method to solve it is to compute a signature for each variable that helps to establish a correspondence between the variables. Several researchers have suggested a wide range of signatures that have been used for this purpose. However, for each choice of signature, there remain variables that cannot be uniquely identified. Our research has shown that, for a given example, this set of problematic variables tends to be the same–regardless of the choice of signatures. The paper investigates this problem.     

面向对比序列模式发现的独立精确置换检验算法

传统的对比序列模式挖掘算法存在一定数量的假阳性对比序列模式,其提供的错误信息会干扰后续任务的决策.设计一种IEP-DSP算法过滤假阳性对比序列模式.运用spade方法和WRAcc对比性度量找到候选对比序列模式和所有置换数据集合中的对比序列模式,通过模拟置换过程,使用独立精确置换检验方法为不同长度的模式建立独立精确零分布...     

Architecture Independent Characterization of Embedded Java Workloads

This paper presents architecture independent characterization of embedded Java workloads based on the industry standard GrinderBench benchmark which includes different classes of real world embedded Java applications. This work is based on a custom built embedded Java virtual machine (JVM) simulator specifically designed for embedded JVM modeling and embodies domain specific details such as thread scheduling, algorithms used for native CLDC APIs and runtime data structures optimized for use in embedded systems. The results presented include dynamic execution characteristics, dynamic bytecode instruction mix, application and API workload distribution, object allocation statistics, instruction-set coverage, memory usage statistics and method code and stack frame characteristics.     

Separability of unimodal polygons

A conjecture that any three unimodal polygons are sequentially separable is, by means of a counterexample, shown to be false.     

Circular Separability of Polygons

Two planar sets are circularly separable if there exists a circle enclosing one of the sets and whose open interior disk does not intersect the other set. This paper studies two problems related to circular separability. A linear-time algorithm is proposed to decide if two polygons are circularly separable. The algorithm outputs the smallest separating circle. The second problem asks for the largest circle included in a preprocessed, convex polygon, under some point and/ or line constraints. The resulting circle must contain the query points and it must lie in the halfplanes delimited by the query lines. Received October 25, 1998; revised April 21, 1999.     

Separability of scalar random multisine signals

Random multisines have successfully been used as input signals in many system identification experiments. In this paper, it is shown that scalar random multisine signals with a flat amplitude spectrum are separable of order one. The separability property means that certain conditional expectations are linear and it implies that random multisines can easily be used to obtain accurate estimates of the linear time-invariant part of a Hammerstein system. Furthermore, higher order separability is investigated.     

N维系统可分性的充要判据

本文给出了N维Roesser模型和一般二维系统模型可分的充要判据,并将所得结果应用于可分系统的稳定性问题,得到了相应的判据。     

Separability of spatiotemporal spectra of image sequences

The authors calculate the spatiotemporal power spectrum of 14 image sequences in order to determine the degree to which the spectra are separable in space and time and to assess the validity of the commonly used exponential correlation model. They expand the spectrum by a singular value decomposition into a sum of separable terms and define an index of spatiotemporal separability. as the fraction of the signal energy that can be represented by the first (largest) separable term. All spectra were found to be highly separable with an index of separability above 0.98. The power spectra of the sequences were well fit by a separable model, which corresponds to a product of exponential autocorrelation functions separable in space and time     

一类有限域上的置换多项式

有限域上的置换多项式在科学工程中的多个领域有着广泛的应用,尤其应用于现代通讯、密码学等领域中。基于Zha等人在文献[23]中提出,当t为偶数时,有限域Fpⁿ上形如(xp^k－x+δ)^t+γx+βTr(x)的多项式是置换的,通过进一步研究,运用证明置换多项式的一般方法,将其改进为无论t为奇数或偶数,(xp^k+1－x^p+δ)^t+γx+βTr(x)形式的多项式在Fpⁿ上均是置换的。     

On System Functions with the Property of Separability†

This paper considers linear differential (time-varying) systems which may be described by either of two system functions based on a specified integral transform. In particular, those systems are discussed for which at least one of the aforementioned system functions is separable in its two arguments. Physical interpretations of separable system functions are given and two theorems are proved which yield sufficient conditions for the presence of this property. It is also proved that the so-called ‘bi-frequency’ function of Zadeh must be Separable for linear differential systems. Finally, the problem of approximately representing a given system by a separable system function based on the Laplace transform is discussed.     

基于可分离性判据的自适应加权纹理图像分割*

进行自适应加权,以提高可分离性好的特征在分类中所起的作用,使加权后的特征具有更好的分类效果。实验表明,该方法的分割结果比未加权的效果要好。     

多值逻辑量子置换门的酉矩阵表示

理论上量子可逆电路不存在能量耗散问题,因此量子计算系统对环境产生的负面影响可以达到最低.多值逻辑量子置换门是构建多值逻辑量子电路的基本单元.该文从数学的角度研究多值逻辑量子置换门的酉矩阵,提出了一种构造多值逻辑量子置换门酉矩阵的方法,并对其正确性进行了讨论.在此基础之上,又给出了构造混合多值逻辑量子置换门酉矩阵的框架,利用此框架可以方便地构造任何混合逻辑量子置换门的酉矩阵.酉矩阵是量子门的数学模型,可以清晰地反映出量子门的数学性质.研究量子门的酉矩阵对验证量子门的正确性和可靠性,分析量子状态在电路中的演化过程及发展趋势具有一定的意义.     

Computing the Subgroups of a Permutation Group

A new method for computing the conjugacy classes of subgroups of a finite group is described.     

一种基于混沌的图像置乱网络的设计

该文利用Logistic映射生成的混沌序列具有遍历性和良好的相关性等特点,提出了一种混沌图像置乱网络,并对置乱网络的遍历时间复杂度及其置乱性质进行了分析。计算机模拟结果显示,这种图像置乱网络具有良好的置乱性质,可以有效的保障加密图像的安全性。     

Separability of Polyhedra for Optimal Filtering of Spatial and Constraint Data

The filtering method considered in this paper is based on approximation of a spatial object in d-dimensional space by the minimal convex polyhedron that encloses the object and whose facets are normal to preselected axes. These axes are not necessarily the standard coordinate axes; furthermore, their number is not determined by the dimension of the space. We optimize filtering by selecting optimal such axes based on a preprocessing analysis of stored objects or a sample thereof. The number of axes selected represents a trade-off between access time and storage overhead, as more axes usually lead to better filtering but require more overhead to store the associated access structures. We address the problem of minimizing the number of axes required to achieve a predefined quality of filtering and the reverse problem of optimizing the quality of filtering when the number of axes is fixed. In both cases we also show how to find an optimal collection of axes. To solve these problems, we introduce and study the key notion of separability classification, which is a general tool potentially useful in many applications of a computational geometry flavor. The approach is best suited to applications in which the spatial data is relatively static, some directions are more dominant than others, and the dimension of the space is not high; maps are a prime example.     

The Two-Point Correlation Function: A Measure of Interclass Separability

In this paper we introduce the two-point correlation function as a measure of interclass separability. We present a theoretical study of this statistic in a general M-dimensional feature space and propose a fast algorithm for the efficient computation of it. We test the algorithm and illustrate the properties of the statistic using test data in 1D and 2D feature spaces and discuss the boundary effects of the feature space. We also present a discussion of the limitations of the proposed statistic and apply it to the assessment of inter-class separability in a texture segmentation context.     

Separability and hidden symmetries of Kerr-Taub-NUT spacetime in Kaluza-Klein theory

The Kerr-Taub-NUT spacetime in the Kaluza-Klein theory represents a localized stationary and axisymmetric object in four dimensions from the Kaluza-Klein viewpoint. That is, it harbors companion electromagnetic and dilaton fields, thereby showing up the signature of the extra fifth dimension. We explore the separability structure of this spacetime and show that the Hamilton-Jacobi equation for geodesics admits complete separation of variables only for massless geodesics. This implies the existence of hidden symmetries in the spacetime, which are generated by a conformal Killing tensor. Using a simple trick built up on a conformally related metric (an “effective” metric) with the Killing tensor, we construct an explicit expression for the conformal Killing tensor.     

比特置换运算单元的设计与实现

比特置换操作在对称密码算法中使用频率非常高,但传统处理器对比特置换操作并不直接支持.为此,美国普林斯顿大学的Ruby B. Lee提出比特置换指令,并证明了比特置换指令对提高通用处理器上实现的密码算法的性能有明显作用[10].本文重点研究比特置换指令的实现技术,提出一种比特置换运算单元的实现算法,并在FPGA上进行验证.     

Permutation equivalence of cubic rotation symmetric Boolean functions

Rotation symmetric Boolean functions have been extensively studied for about 15 years because of their applications in cryptography and coding theory. Until recently little was known about the basic question of when two such functions are affine equivalent. The simplest case of quadratic rotation symmetric functions which are generated by cyclic permutations of the variables in a single monomial was only settled in 2009. For the much more complicated case of cubic rotation symmetric functions generated by a single monomial, the affine equivalence classes under permutations which preserve rotation symmetry were determined in 2011. It was conjectured then that the cubic equivalence classes are the same if all nonsingular affine transformations, not just permutations, are allowed. This conjecture is probably difficult, but here we take a step towards it by proving that the cubic affine equivalence classes found in 2011 are the same if all permutations, not just those preserving rotation symmetry, are allowed. The needed new idea uses the theory of circulant matrices.