GWLS-SVR模型的红枣树叶片叶绿素含量估算

叶绿素含量是红枣树光合作用能力、生长状况、营养状况的指示剂,不同地理位置种植的红枣树受到自然、人为等因素的影响,叶绿素含量分布有所不同,该研究实地测定了若羌县枣树叶片高光谱反射率及表征叶绿素含量的枣树叶片SPAD（soil plant analysis development)值。为了高效无损地估算红枣树叶片SPAD值,计算了红枣树叶片SPAD值全局莫兰指数,以SPAD值和高光谱波段之间的相关性为基础,通过C_P统计量计算重要程度高的特征波段,运用地理加权最小二乘支持向量回归GWLS-SVR（geographically weighted least squares-support vector regression）模型对红枣树叶片SPAD值进行预测,与多元线性回归（MLR）、支持向量机回归（SVR）模型比较并探讨GWLS-SVR模型估算红枣树叶片SPAD值的能力。结果表明：（1）光谱一阶导数可以有效去除噪声并突出光谱信息尤其是492~510,542~543,642~652,657~670和682~692 nm区间内显著的提高了与SPAD值的相关性。（2）C_P统计量方法能够有效的选择敏感区间的特征波段,进而提高模型估算精度,由统计量方法计算出原始光谱重要程度最高的两个变量为595与696 nm,光谱一阶导数的特征波段为688 nm。其中对于同一个敏感波段区间的波段组合总有单个波段的统计量低于多个波段组合的统计量,这可能是相近波段间的较强共线性导致的。（3）若羌县红枣树叶片SPAD值存在显著的空间聚集性,全局莫兰指数为0.125 8（p<0.1）,适合建立考虑空间位置的GWLS-SVR模型。（4）结合Bootstrap再抽样与t检验模型检验得到结合地理位置信息的GWLS-SVR模型总体上估算能力优于SVR和MLR模型,且结果高度显著（p<0.001）,其中基于光谱一阶导数的GWLS-SVR模型为最优的红枣树叶片SPAD值估算模型（R2为0.975,MSE为1.082）,能够为高光谱定量反演红枣树SPAD值进而快速无损的监测红枣生长状况提供一定参考。     

Cardinality constrained connected balanced partitions of trees under different criteria

In this paper we study the problem of partitioning a tree with $n$ weighted vertices into $p$ connected components. For each component, we measure its gap, that is, the difference between the maximum and the minimum weight of its vertices, with the aim of minimizing the sum of such differences. We present an $O\left(n^3{p}^2\right)$ time and $O\left(n^{3}p\right)$ space algorithm for this problem. Then, we generalize it, requiring a minimum of $ϵ\ge 1$ nodes in each connected component, and provide an $O\left(n^3{p}^2{ϵ}^2\right)$ time and $O\left(n^{3}pϵ\right)$ space algorithm to solve this new problem version. We provide a refinement of our analysis involving the topology of the tree and an improvement of the algorithms for the special case in which the weights of the vertices have a heap structure. All presented algorithms can be straightforwardly extended to other similar objective functions. Actually, for the problem of minimizing the maximum gap with a minimum number of nodes in each component, we propose an algorithm which is independent of $ϵ$ and requires $O(n^{2}logn{p}^2)$ time and $O\left(n^{2}p\right)$ space.     

Random tree recursions: Which fixed points correspond to tangible sets of trees?

Let be the set of rooted trees containing an infinite binary subtree starting at the root. This set satisfies the metaproperty that a tree belongs to it if and only if its root has children u and v such that the subtrees rooted at u and v belong to it. Let p be the probability that a Galton‐Watson tree falls in . The metaproperty makes p satisfy a fixed‐point equation, which can have multiple solutions. One of these solutions is p, but what is the meaning of the others? In particular, are they probabilities of the Galton‐Watson tree falling into other sets satisfying the same metaproperty? We create a framework for posing questions of this sort, and we classify solutions to fixed‐point equations according to whether they admit probabilistic interpretations. Our proofs use spine decompositions of Galton‐Watson trees and the analysis of Boolean functions.     

A note on generating finer‐grain parallelism in a representation tree

The representation tree lies at the heart of the algorithm of Multiple Relatively Robust Representations for computing orthogonal eigenvectors of a symmetric tridiagonal matrix without Gram–Schmidt. A representation tree describes the incremental shift relations between relatively robust representations of eigenvalue clusters of an unreduced tridiagonal matrix, which are needed to strongly separate close eigenvalues in the relative sense. At the bottom of the representation tree, each leaf defines a relatively isolated eigenvalue to high relative accuracy. The shape of the representation tree plays a pivotal role for complexity and available parallelism: a deeper tree consisting of multiple levels of nodes involves tasks associated to more work (i.e., eigenvalue refinement to resolve eigenvalue clusters) and less parallelism (i.e., a longer critical path as well as potential data movement and synchronization). An embarrassingly parallel, ideal tree on the other hand consists of a root and leaves only. As highly parallel hybrid graphics processing unit/multicore platforms with large memory now become available as commodity platforms, exploiting parallelism in traditional algorithms becomes key to modernizing the components of standard software libraries such as LAPACK. This paper focuses on LAPACK's Multiple Relatively Robust Representations algorithm and investigates the critical case where a representation tree contains a long sequential chain of large (fat) nodes that hamper parallelism. This key problem needs to be addressed as it concerns all sorts of computing environments, distributed computing, symmetric multiprocessor, as well as hybrid graphics processing unit/multicore architectures. We present an improved representation tree that often offers a significantly shorter critical path and finer computational granularity of smaller tasks that are easier to schedule. In a study of selected synthetic and application matrices, we show that an average 75% reduction in the length of the critical path and 82% reduction in task granularity can be achieved. Copyright © 2011 John Wiley & Sons, Ltd.     

DRL-M4MR: An intelligent multicast routing approach based on DQN deep reinforcement learning in SDN

Traditional multicast routing methods have some problems in constructing a multicast tree. These problems include limited access to network state information, poor adaptability to dynamic and complex changes in the network, and inflexible data forwarding. To address these defects, the optimal multicast routing problem in software-defined networking (SDN) is tailored as a multiobjective optimization problem, and DRL-M4MR, an intelligent multicast routing algorithm based on the deep Q network (DQN) deep reinforcement learning (DRL) method is designed to construct a multicast tree in a software-defined network. First, combining the characteristics of SDN global network-aware information, the multicast tree state matrix, link bandwidth matrix, link delay matrix and link packet loss rate matrix are designed as the state space of the reinforcement learning agent to solve the problem in that the original method cannot make full use of network status information. Second, the action space of the agent is all the links in the network, and the action selection strategy is designed to add the links to the current multicast tree in four cases. Third, single-step and final reward function forms are designed to guide the agent to make decisions to construct the optimal multicast tree. The double network architectures, dueling network architectures and prioritized experience replay are adopted to improve the learning efficiency and convergence of the agent. Finally, after the DRL-M4MR agent is trained, the SDN controller installs the multicast flow entries by reversely traversing the multicast tree to the SDN switches to implement intelligent multicast routing. The experimental results show that, compared with existing algorithms, the multicast tree constructed by DRL-M4MR can obtain better bandwidth, delay, and packet loss rate performance after training, and it can make more intelligent multicast routing decisions in a dynamic network environment. Code and DRL model are available at https://github.com/GuetYe/DRL-M4MR.     

Edge Kempe equivalence of regular graph covers

Let $G$ be a finite $d$-regular graph with a proper edge coloring. An edge Kempe switch is a new proper edge coloring of $G$ obtained by switching the two colors along some bichromatic cycle. We prove that any other edge coloring can be obtained by performing finitely many edge Kempe switches, provided that $G$ is replaced with a suitable finite covering graph. The required covering degree is bounded above by a constant depending only on $d$.