Dynamic Entanglement and Separability Criteria for Quantum Computing Bit States

A theoretical framework is demonstrated to evaluate the degree of entanglement of bit states in quantum computing. Separability of general superposition of Hilbert space unit vectors is discussed, and criteria in amplitude as well as in phase are derived. By these criteria the possibility of different quantum gates such as controlled not (CN), controlled controlled not (CCN), controlled rotation (CR), and controlled phase shift (CPS), to create the entanglement is examined. Furthermore, the selection of measurement mode external to the quantum system is incorporated in the formula using Kronecker delta (δ _kx ), introducing the concept of dynamic entanglement. With this the process of wavefunction collapse upon measurement is understood as the result of the activation of the dynamic entanglement. A firefly in a box model is used to show a pure state of ontological uncertainty, which is in a dynamically entangled state in Hilbert space.     

On potentially negative space time covariances obtained as sum of products of marginal ones

Most of the literature on spatio-temporal covariance models proposes structures that are positive in the whole domain. However, problems of physical, biological or medical nature need covariance models allowing for negative values or oscillations from positive to negative values. In this paper, we propose an easy-to-implement and interpretable class of models that admits this type of covariances. We show particular analytical examples that may be of interest in the biometrical context. Work partially funded by grants GV04A724 (Generalitat Valenciana) and MTM2004-06231 (Spanish Ministry of Science and Education).     

高分六号宽幅数据识别火烧迹地的光谱及指数分析

为探究利用高分六号卫星宽幅（GF-6 WFV）数据识别火烧迹地的适宜光谱波段和指数,选取2019年发生在我国内蒙古大兴安岭林区的三处雷击火形成的火烧迹地作为研究区,结合GF-6 WFV波段组成,选取归一化植被指数（normalized difference vegetation index, NDVI）、全球环境监测指数（global environment monitoring index, GEMI）、增强植被指数（enhanced vegetation index, EVI）、燃烧面积指数（burned area index, BAI）、土壤调节植被指数（soil-adjusted vegetation index, SAVI）、改进型土壤调节植被指数（modified soil-adjusted vegetation index, MSAVI）和归一化差异水体指数（normalized difference water index, NDWI）等7个光谱指数及地面叶绿素指数（MERIS terrestrial chlorophyll index, MTCI）、归一化差值红边指数（normalized difference red edge index 1, NDRE1）、改进的叶绿素吸收指数（modified chlorophyll absorption ratio index 2, MCARI2）和改进的归一化土壤指数（modified normalized difference soil index, MNDSI）等4个改进指数,基于同期影像和前后两期影像进行火烧迹地和其他典型类别的区分度计算,并利用上述11个指数及指数差值进行火烧迹地的识别,定量评价了GF-6 WFV各波段、所选光谱指数及改进指数识别火烧迹地的能力。结果表明：（1）GF-6 WFV的近红外波段和新增的两个红边波段区分度较高,反映火烧迹地特征的能力较强。（2）在区分火烧迹地和火烧前正常植被上,NDVI, GEMI, EVI, BAI, SAVI, MSAVI和NDWI 7个光谱指数等的区分能力较强,4个改进指数中,NDRE1和MCARI2的区分能力较好,MNDSI和MTCI的区分效果较差。（3）在区分同期影像火烧迹地和其余典型类别上,BAI, NDVI, MCARI2和NDWI区分效果较优,其次为NDRE1, GEMI, EVI, SAVI和MSAVI,而MNDSI, MTCI的区分能力较差。（4）在利用所选指数和指数差值识别火烧迹地中,GEMI, EVI, BAI, SAVI和MSAVI的识别精度均较优,其次是MCARI2, NDVI和NDWI,做差后提取精度显著上升,Kappa系数均提升到0.80以上,MTCI, MNDSI和NDRE1提取效果较差。综合比较,BAI和GEMI识别效果最好,NDVI, EVI, SAVI, MSAVI, NDWI和MCARI2的识别能力中等,而MNDSI, NDRE1和MTCI等3个改进指数识别火烧迹地的能力较差。     

求解一类二阶段有补偿问题的对偶梯度法

利用对偶理论，本文给出了求解一类具有简单补偿的非线性二阶段问题的新对偶梯度法．在假设目标函数为可分连续可微凸函数的条件下，在每一选代步可将原二阶段有补偿问题转化为几个一维凸规划问题，大大简化了问题的求解．所给算法简单易行，文中还证明了该算法的全局收敛性．     

Reliable computing with unreliable components: Using separable environments to stabilize long-term information storage

How, in the face of both intrinsic and extrinsic volatility, can unconventional computing fabrics store information over arbitrarily long periods? Here, we argue that the predictable structure of many realistic environments, both natural and artificial, can be used to maintain useful categorical boundaries even when the computational fabric itself is inherently volatile and the inputs and outputs are partially stochastic. As a concrete example, we consider the storage of binary classifications in connectionist networks, although the underlying principles should be applicable to other unconventional computing paradigms. Specifically, we demonstrate that an unsupervised, activity dependent plasticity rule, AHAH (Anti-Hebbian-And-Hebbian), allows binary classifications to remain stable even when the underlying synaptic weights are subject to random noise. When embedded in environments composed of separable features, the weight vector is restricted by the AHAH rule to local attractors representing stable partitions of the input space, allowing unsupervised recovery of stored binary classifications following random perturbations that leave the system in the same basin of attraction. We conclude that the stability of long-term memories may depend not so much on the reliability of the underlying substrate, but rather on the reproducible structure of the environment itself, suggesting a new paradigm for reliable computing with unreliable components.     

Entanglement of multipartite Schmidt-correlated states

We generalize the Schmidt-correlated states to multipartite systems. The related equivalence under SLOCC, the separability, entanglement witness, entanglement measures of negativity, concurrence and relative entropy are investigated in detail for the generalized Schmidt-correlated states.     

Order-convexity in order topologies

In this survey the role of order-convexity in topologies compatible with a preference (i.e a negatively transitive partial order) is considered. Two main issues are highlighted:the (topoiogical) subspaces of preference ordered topological spaces, and the orderability of a topological space     

Entanglement and phase

Entanglement is the cornerstone of all new technological implications of quantum mechanics, which meanwhile extend into the realm of theoretical chemistry. In this contribution, the relation between entanglement and phase factors is investigated in terms of statistical operators. After the introduction of a simplified definition of the separability of a statistical operator, a new way to obtain phase information from experiments is presented, and the emergence of separability from non-separability is explained by the loss of a special phase operator containing the quantum part of the system's information. Dedicated to my doctoral adviser, Prof. Dr. Karl Jug, Hannover, in honor of his 65th birthday     

A fixed-center spherical separation algorithm with kernel transformations for classification problems

We consider a special case of the optimal separation, via a sphere, of two discrete point sets in a finite dimensional Euclidean space. In fact we assume that the center of the sphere is fixed. In this case the problem reduces to the minimization of a convex and nonsmooth function of just one variable, which can be solved by means of an “ad hoc” method in O(p log p) time, where p is the dataset size. The approach is suitable for use in connection with kernel transformations of the type adopted in the support vector machine (SVM) approach. Despite of its simplicity the method has provided interesting results on several standard test problems drawn from the binary classification literature. This research has been partially supported by the Italian “Ministero dell’Istruzione, dell’Università e della Ricerca Scientifica”, under PRIN project Numerical Methods for Global Optimization and for some classes of Nonsmooth Optimization Problems (2005017083.002).     

Discrete embedded modes in the continuum in 2D lattices

We study the problem of constructing bulk and surface embedded modes (EMs) inside the quasi-continuum band of a square lattice, using a potential engineering approach à la Wigner and von Neumann. Building on previous results for the one-dimensional (1D) lattice, and making use of separability, we produce examples of two-dimensional envelope functions and the two-dimensional (2D) potentials that produce them. The 2D embedded mode decays like a stretched exponential, with a supporting potential that decays as a power law. The separability process can cause that a 1D impurity state (outside the 1D band) can give rise to a 2D embedded mode (inside the band). The embedded mode survives the addition of random perturbations of the potential; however, this process introduces other localized modes inside the band, and causes a general tendency towards localization of the perturbed modes.