From G2 geometry to quaternionic Kähler metrics

We review a construction of quaternionic Kähler metrics starting from a rank 2 distribution in 5 dimensions. We relate it to a more general theory about Einstein deformations of symmetric metrics. Finally we ask some questions on complete metrics and relate them to a Zoll phenomenon.     

Extremal Kähler metrics and Bach–Merkulov equations

In this paper, we study a coupled system of equations on oriented compact 4-manifolds which we call the Bach–Merkulov equations. These equations can be thought of as the conformally invariant version of the classical Einstein–Maxwell equations. Inspired by the work of C. LeBrun on Einstein–Maxwell equations on compact Kähler surfaces, we give a variational characterization of solutions to Bach–Merkulov equations as critical points of the Weyl functional. We also show that extremal Kähler metrics are solutions to these equations, although, contrary to the Einstein–Maxwell analogue, they are not necessarily minimizers of the Weyl functional. We illustrate this phenomenon by studying the Calabi action on Hirzebruch surfaces.     

Quaternionic Kähler metrics associated with special Kähler manifolds

We give an explicit formula for the quaternionic Kähler metrics obtained by the HK/QK correspondence. As an application, we give a new proof of the fact that the Ferrara–Sabharwal metric as well as its one-loop deformation is quaternionic Kähler. A similar explicit formula is given for the analogous (K/K) correspondence between Kähler manifolds endowed with a Hamiltonian Killing vector field. As an example, we apply this formula in the case of an arbitrary conical Kähler manifold.     

Homogeneous Einstein–Randers metrics on Aloff–Wallach spaces

Aloff–Wallach spaces are important in the study of positively curved homogeneous Riemannian manifolds. In this paper, we find some homogeneous Einstein–Randers metrics on such spaces.     

A note on static spaces and related problems

In this paper we study static spaces introduced in Hawking and Ellis (1975)  [1], Fischer and Marsden (1975) [3] and Riemannian manifolds possessing solutions to the critical point equation introduced in Besse (1987)  [11], Hwang (2000)  [12]. In both cases, on the manifolds there is a function satisfying a particular Ricci–Hessian type equation (1.6). With an idea similar to that used in Cao et al. (2012)  [15], [16], we have made progress in solving the problem raised in Fischer and Marsden (1975)  [3] of classifying vacuum static spaces and in proving the conjecture proposed in Besse (1987)  [11] concerning manifolds admitting solutions to the critical point equation in general dimensions. We obtain even stronger results in dimension 3.     

一种基于最大流的网络结构熵

熵是可用来反映网络结构异质性的指标.针对传统熵指标不能很好反映网络全局异构性的不足,本文引入网络流的概念,综合考虑径向测度和中间测度,提出一种新的网络结构熵.特殊网络(如公用数据集Dolphins网络)的分析结果表明,本文提出的熵指标在一定程度上克服了其他网络熵指标的不足,更能够反映网络的真实拓扑结构;对随机网络、最近邻耦合网络、星型网络、无标度网络、Benchmark网络和小世界网络等典型网络的理论分析和仿真实验,进一步证明本文提出的熵指标在刻画一般复杂网络结构特征上的有效性和适用性.     

基于近似熵的突变检测新方法

近似熵是一个有效的非线性动力学指数,能够用于表征时间序列的复杂性,通过滑动窗口技术,近似熵对于一维时间序列的动力学结构突变具有一定的识别能力,但其突变检测结果依赖于子序列长度的选择,且不能准确定位突变点.鉴于此,本文提出了一种新的突变检测方法——滑动移除近似熵.测试结果表明,滑动移除近似熵具有检测结果稳定性好、准确性高等特点,明显优于滑动近似熵和Mann-Kendall方法,其在实际观测资料中的应用进一步证实了新方法的可靠性. 关键词： 近似熵 滑动移除近似熵 突变检测     

A class of asymmetric pathway distributions and an entropy interpretation

Asymmetric distributions are widely used in probability modeling and statistical analysis. Recently, various asymmetric distributions are being developed by many researchers for modeling various data sets in real life contexts. In the present paper, we introduce a new class of q-type asymmetric distributions which include q-analogues of asymmetric Laplace, exponential power, Weibull etc. and corresponding standard distributions as special cases. Also we show that this pathway model can be obtained by optimizing Mathai’s generalized entropy with more general setup, which is a generalization of various entropy measures due to Shannon and others.     

Harmonic maps and stability on locally conformal Kähler manifolds

We study harmonic and pluriharmonic maps on locally conformal Kähler manifolds. We prove that there are no nonconstant holomorphic pluriharmonic maps from a locally conformal Kähler manifold to a Kähler manifold and that any holomorphic harmonic map from a compact locally conformal Kähler manifold to a Kähler manifold is stable.     

A new approach for protein design based on the relative entropy

A new effective and fast minimization approach completely based on the physical theory is proposed for protein design. The sequence space is essentially searched according to the Boltzmann distribution. In this approach, the relative entropy is used as a minimization object function. The method has been tested on an off-lattice model of proteins and the results are better than those obtained from other similar work. Therefore, it can be applied as a uniform frame for both folding and inverse folding of proteins.     

一种基于点和边差异性的网络结构熵

熵是反映网络异构性的重要指标. 由于只是关注网络结构中"点"或"边"的单一作用,基于度分布和度相对值的两种传统熵在刻画网络结构特征时均存在缺陷. 文章综合考虑"点"和"边"差异性,定义一种新的网络结构熵,并对规则网络、随机网络和无标度网络等结构熵进行理论分析和仿真实验. 结果表明,这种新网络结构熵可以更有效地反映网络的结构特征,尤其是对于稀疏网络及星型网络的结构差异解释更为合理. 关键词： 均匀网络 无标度网络 熵     

Network connectivity entropy and its application on network connectivity reliability

The network structure entropy has served as one of the index measuring network heterogeneity, but it gives no considerations to the impact of isolated nodes on the network structure. In addition, the all-terminal reliability is zero and is unable to compare it between disconnected networks. Therefore, the concept of network connectivity entropy is suggested to remove the current bottleneck and helps facilitate new index in terms of network connectivity reliability. This study fully proves the rules as follows: when the edges of network are diminishing, the newly-established network connectivity reliability will remain unchanged or become weaker; conversely, when the edges of network are increasing, the network connectivity reliability will remain unchanged or become stronger. Thus, the proposed index of network connectivity reliability is proved reasonable. Furthermore, the impaired metro network of Nanjing city is exemplified to demonstrate the validity and practicability of network connectivity reliability. The result shows that this new approach is in good position to compute network connectivity reliability quickly and effectively, and also to compare it between different networks.     

A remark on papers by pixton and oliveira: Genericity of symplectic diffeomorphisms ofS 2 with positive topological entropy

We prove the existence of an open and dense subset of mapsfDiff (S²) which have positive topological entropy. It follows that these maps have infinitely many hyperbolic periodic points and an exponential growth rate of hyperbolic periodic points. The proof is an application of Pixton's theorem     

基于脉冲耦合神经网络和图像熵的各向异性扩散模型研究

在图像去噪过程中, 大部分基于偏微分方程的各向异性扩散模型均使用梯度信息检测边缘, 当边缘部分被噪声严重污染时, 这些方法不能有效检测出这些边缘, 因而无法保留边缘特征. 为了较完整的保留图像的区域信息, 用脉冲耦合神经网络(PCNN)能使具有相似输入的神经元同时产生脉冲的性质对噪声图像做处理, 得到图像熵序列, 并将图像熵序列作为边缘检测算子引入到扩散方程中, 不仅能克服仅用梯度作为边缘检测算子易受噪声影响的弊端, 而且能较完整地保留图像的区域信息. 然后, 用最小交叉熵准则搜索使去噪前后图像信息量差异最小的阈值, 设计最佳阈值控制扩散强度, 建立基于脉冲耦合神经网络与图像熵改进的各向异性扩散模型(PCNN-IEAD). 分析与仿真结果表明, 该模型与经典模型相比, 保留了更多的图像信息, 能够兼顾去除图像的噪声和保护图像的边缘纹理等细节信息, 较完整的保留了图像的区域信息, 性能指标同样也证实了新模型的优越性. 另外, 该模型的运行时间较经典模型的短, 因此, 该模型是一个理想的模型.     

Black hole entropy and the modified uncertainty principle: A heuristic analysis

Recently Ali et al. (2009) proposed a Generalized Uncertainty Principle (or GUP) with a linear term in momentum (accompanied by Plank length). Inspired by this idea here we calculate the quantum corrected value of a Schwarzschild black hole entropy and a Reissner-Nordström black hole with double horizon by utilizing the proposed generalized uncertainty principle. We find that the leading order correction goes with the square root of the horizon area contributing positively. We also find that the prefactor of the logarithmic contribution is negative and the value exactly matches with some earlier existing calculations. With the Reissner-Nordström black hole we see that this model-independent procedure is not only valid for single horizon spacetime but also valid for spacetimes with inner and outer horizons.     

基于信息熵和灰度相关的图像拼接算法

提出一种基于信息熵和灰度相关的全景重叠图拼接算法。该算法综合了基于灰度相关和信息熵的优点。通过匹配连续区域的熵的兰氏距离获得了比较精确的定位,利用灰度相关进行了匹配验证和精确调整了两幅待拼接图像。实验表明,算法原理简单、拼接速度快,对图像亮度差异具有较强的抗干扰能力,鲁棒性好。     

A novel infrared small target detection method based on BEMD and local inverse entropy

Compared to other targets, it is more difficult to detect infrared small targets due to several aspects such as the low signal to noise ratio, low contrast, small size, the lack of shape and texture information of the targets, especially under complex background. In this paper, a novel infrared small target detection method based on peer group filter (PGF), bi-dimensional empirical mode decomposition (BEMD) and local inverse entropy (LIE) is proposed to overcome these difficulties. The PGF is implemented to remove the noise and improve the signal-to-noise ratio of the initial image. Our proposed BEMD algorithm is able to estimate the background effectively and get the target image by removing the background from the original image and segmenting the Intrinsic Mode Functions (IMFs) making use of the local inverse entropy. Experimental results demonstrate that the novel method can extract the small targets validly and accurately.     

基于最大熵估计Alpha谱缩放与平移量的温度与发射率分离算法

在热红外波段, 为了使温度与发射率分离过程不依赖数据库提供的经验信息, 并且实现更高的反演精度和更快的计算速度, 研究了一种新的温度与发射率分离算法. 首先, 在维恩近似原理的基础上, 求解了Alpha谱分布, 并利用Alpha谱描述光谱发射率的形状信息. 其次, 改进了最大熵温度与发射率分离算法: 应用最大熵估计模型对Alpha谱缩放与平移量进行估计, 减少了待估计参数的数量, 大幅简化了求解过程. 最后, 进行了算法的数值仿真实验: 求解了典型地物目标的温度与光谱发射率, 并且分析了算法对系统噪声的鲁棒性. 仿真数据表明: 发射率估计的最大RMSE为0.017, 温度估计的最大绝对误差的绝对值为0.62 K; 对系统添加测量信噪比为11的高斯白噪声, 发射率估计的相对RMSE为2.67%, 温度估计的相对误差为1.26%. 结果表明: 本文所述算法求解精度高, 计算速度快, 具备良好的鲁棒性.     

基于变分模态分解与多尺度排列熵的生物组织变性识别

根据高强度聚焦超声(HIFU)治疗中超声散射回波信号的特点,本文利用变分模态分解(VMD)与多尺度排列熵(MPE)对生物组织变性识别进行了研究.首先对生物组织中的超声散射回波信号进行变分模态分解,根据各阶模态的功率谱信息熵值分离出噪声分量和有用分量;对分离出的有用信号进行重构并提取其多尺度排列熵;然后通过Gustafson-Kessel (GK)模糊聚类确定聚类中心,采用欧氏贴近度与择近原则对生物组织进行变性识别.将所提方法应用于HIFU治疗中超声散射回波信号实验数据,用遗传算法对多尺度排列熵的参数优化后,对293例未变性组织和变性组织的超声散射回波信号数据进行了多尺度排列熵分析,发现变性组织的超声散射回波信号的多尺度排列熵值要高于未变性组织;多尺度排列熵可以较好地识别生物组织是否变性.相对于EMD-MPE-GK模糊聚类以及VMD-小波熵(WE)-GK模糊聚类变性识别方法,本文所提方法中变性与未变性组织特征交叠区域数据点更少,聚类效果和分类性能更好;本实验环境下生物组织变性识别结果表明,该方法的识别率更高,高达93.81%.