Filling the“vertical gap”between canopy tree species and understory shrub species:biomass allometric equations for subcanopy tree species

Subcanopy tree species are an important component of temperate secondary forests.However,their biomass equations are rarely reported,which forms a“vertical gap”between canopy tree species and understory shrub species.In this study,we destructively sampled six common subcanopy species(Syringa reticulate var.amurensis(Rupr.)Pringle,Padus racemosa(Lam.)Gilib.,Acer ginnala Maxim.,Malus baccata(Linn.)Borkh.,Rhamnus davurica Pall.,and Maackia amurensis Rupr.et Maxim.)to establish biomass equations in a temperate forest of Northeast China.The mixed-species and species-specifi c biomass allometric equations were well fi tted against diameter at breast height(DBH).Adding tree height(H)as the second predictor increased the R^(2)of the models compared with the DBH-only models by–1%to+3%.The R^(2)of DBH-only and DBH-H equations for the total biomass of mixed-species were 0.985 and 0.986,respectively.On average,the biomass allocation proportions for the six species were in the order of stem(45.5%)>branch(30.1%)>belowground(19.5%)>foliage(4.9%),with a mean root:shoot ratio of 0.24.Biomass allocation to each specifi c component diff ered among species,which aff ected the performance of the mixed-species model for particular biomass component.When estimating the biomass of subcanopy species using the equations for canopy species(e.g.,Betula platyphylla Suk.,Ulmus davidiana var.japonica(Rehd.)Nakai,and Acer mono Maxim.),the errors in individual biomass estimation increased with tree size(up to 68.8%at 30 cm DBH),and the errors in stand biomass estimation(up to 19.2%)increased with increasing percentage of basal area shared by subcanopy species.The errors caused by selecting such inappropriate models could be removed by multiplying adjustment factors,which were usually power functions of DBH for biomass components.These results provide methodological support for accurate biomass estimation in temperate China and useful guidelines for biomass estimation for subcanopy species in other regions,which can help to improve estimates of forest biomass and carbon stocks.

The Maximum and Minimum Value of Exponential RandićIndices of Quasi-Tree Graph

The exponential Randić index has important applications in the fields of biology and chemistry. The exponential Randić index of a graph G is defined as the sum of the weights e 1 d( u )d( v ) of all edges uv of G, where d( u ) denotes the degree of a vertex u in G. The paper mainly provides the upper and lower bounds of the exponential Randić index in quasi-tree graphs, and characterizes the extremal graphs when the bounds are achieved.

Developing allometric equations to estimate forest biomass for tree species categories based on phylogenetic relationships

The development of allometric biomass models is important process in biomass estimation because the reliability of forest biomass and carbon estimations largely depends on the accuracy and precision of such models.National Forest Inventories(NFI)are detailed assessments of forest resources at national and regional levels that provide valuable data for forest biomass estimation.However,the lack of biomass allometric equations for each tree species in the NFI currently hampers the estimation of national-scale forest biomass.The main objective of this study was to develop allometric biomass regression equations for each tree species in the NFI of China based on limited biomass observations.These equations optimally grouped NFI and biomass observation species according to their phylogenetic relationships.Significant phylogenetic signals demonstrated phylogenetic conservation of the crown-to-stem biomass ratio.Based on phylogenetic relationships,we grouped and matched NFI and biomass observation species into 22 categories.Allometric biomass regression models were developed for each of these 22 species categories,and the models performed successfully(R^(2)=0.97,root mean square error(RMSE)=12.9​t·ha^(–1),relative RMSE=11.5%).Furthermore,we found that phylogeny-based models performed more effectively than wood density-based models.The results suggest that grouping species based on their phylogenetic relationships is a reliable approach for the development and selection of accurate allometric equations.

适于GlobalAllomeTree国际数据平台的标准化中国主要树种树高-胸径方程研建

GlobalAllomeTree作为共享异速方程的国际网络平台,逐渐受到全球高度关注。当前,为促进该项国际合作,针对当前该平台缺乏中国主要树种生长异速方程的现状,系统性更新标准化中国主要树种树高-胸径方程。由于树冠和下部灌木及草丛遮挡,树高相对于胸径测量具有一定的难度,因此需要使用数学工具进行计算。选取了36个树种为材料构建树高-胸径关系方程,以全国主要树种的二元材积模型、各地区一元材积表为基础材料,以取样径阶为1 cm间隔所生成1692组树高-胸径数据作为建立方程样本,1238组外业调查数据为验证样本。建模结果表明:36个主要树种的1692组树高-胸径数据建立的全国通用性树高-胸径方程拟合相关系数(R2)为0.801,方程拟合结果较好,说明可以通过测定胸径,带入树高(H,m)-胸径(D,cm)方程(H=aDb)预估树高;对36个主要树种的树高-胸径方程进行拟合,决定系数R2值均大于0.916,平均误差(ME)、平均绝对误差(MAE)和均方根误差(RMSE)相对较小,方程整体精度较高,可广泛推广;将外业采集的1238组树高-胸径数据,根据36个主要树种树高-胸径方程拟合公式及参数估计值a、b进行方程精度验证,方程预测的平均相对误差为16.86%,在误差允许范围内,并且模型形式规范,可为GlobalAllomeTree平台用户提供科学参考。

The Dynamic-to-Static Conversion of Dynamic Fault Trees Using Stochastic Dependency Graphs and Stochastic Activity Networks

In this paper a new modeling framework for the dependability analysis of complex systems is presented and related to dynamic fault trees (DFTs). The methodology is based on a modular approach: two separate models are used to handle, the fault logic and the stochastic dependencies of the system. Thus, the fault schema, free of any dependency logic, can be easily evaluated, while the dependency schema allows the modeler to design new kind of non-trivial dependencies not easily caught by the traditional holistic methodologies. Moreover, the use of a dependency schema allows building a pure behavioral model that can be used for various kinds of dependability studies. In the paper is shown how to build and integrate the two modular models and convert them in a Stochastic Activity Network. Furthermore, based on the construction of the schema that embeds the stochastic dependencies, the procedure to convert DFTs into static fault trees is shown, allowing the resolution of DFTs in a very efficient way.

P_3-factor in Line Graphs of Trees

In this paper,we give a necessary and sufficient condition for the existence of P3-factors in the line graph of a tree.Then we present an algorithm to determine whether the line graph of a tree has a P3-factor.

Effects of landscape fragmentation of plantation forests on carbon storage in the Loess Plateau,China

Tree plantation and forest restoration are the major strategies for enhancing terrestrial carbon sequestration and mitigating climate change.The Grain for Green Project in China has positively impacted global carbon sequestration and the trend towards fragmentation of plantation forests.Limited studies have been conducted on changes in plantation biomass and stand structure caused by fragmentation,and the effect of fragmentation on the carbon storage of plantation forests remains unclear.This study evaluated the differences between carbon storage and stand structure in black locust forests in fragmented and continuous landscape in the Ansai District,China and discussed the effects of ecological significance of four landscape indices on carbon storage and tree density.We used structural equation modelling to explore the direct and indirect effects of fragmentation,edge,abiotic factors,and stand structure on above-ground carbon storage.Diameter at breast height(DBH)in fragmented forests was 53.3%thicker,tree density was 40.9%lower,and carbon storage was 49.8%higher than those in continuous forests;for all given DBH>10 cm,the trees in fragmented forests were shorter than those in continuous forests.The patch area had a negative impact on carbon storage,i.e.,the higher the degree of fragmentation,the lower the density of the tree;and fragmentation and distance to edge(DTE)directly increased canopy coverage.However,canopy coverage directly decreased carbon storage,and fragmentation directly increased carbon storage and tree density.In non-commercial forests,fragmentation reduces the carbon storage potential of plantation,and the influence of patch area,edge,and patchy connection on plantation should be considered when follow-up trees are planted and for the plantation management.Thus,expanding the area of plantation patches,repairing the edges of complex-shaped patches,enhancing the connectivity of similar patches,and applying nutrients to plantation forests at regular intervals are recommended in fragmented areas of the Loess Plateau.

Graph Convolutional Networks Embedding Textual Structure Information for Relation Extraction

Deep neural network-based relational extraction research has made significant progress in recent years,andit provides data support for many natural language processing downstream tasks such as building knowledgegraph,sentiment analysis and question-answering systems.However,previous studies ignored much unusedstructural information in sentences that could enhance the performance of the relation extraction task.Moreover,most existing dependency-based models utilize self-attention to distinguish the importance of context,whichhardly deals withmultiple-structure information.To efficiently leverage multiple structure information,this paperproposes a dynamic structure attention mechanism model based on textual structure information,which deeplyintegrates word embedding,named entity recognition labels,part of speech,dependency tree and dependency typeinto a graph convolutional network.Specifically,our model extracts text features of different structures from theinput sentence.Textual Structure information Graph Convolutional Networks employs the dynamic structureattention mechanism to learn multi-structure attention,effectively distinguishing important contextual features invarious structural information.In addition,multi-structure weights are carefully designed as amergingmechanismin the different structure attention to dynamically adjust the final attention.This paper combines these featuresand trains a graph convolutional network for relation extraction.We experiment on supervised relation extractiondatasets including SemEval 2010 Task 8,TACRED,TACREV,and Re-TACED,the result significantly outperformsthe previous.

About the Conjecture of Felicitous Trees

A tree T is felicitous if there is a labelling l of its vertices with distinct integers from the set {0,1,2,…,｜E(T)｜}, so that the induced edge labelling l′ defined by l′(e)=l(u)+l(v) mod ｜E(T)｜ for each e=uv∈E(T), assigns each edge e a different label. In this paper, we constructively proved that more classes of trees are felicitous. In the end, we gave a conjecture that every lobster tree is felicitous.

Circular L(j,k)-labeling numbers of trees and products of graphs

Let j, k and m be three positive integers, a circular m-L（j, k）-labeling of a graph G is a mapping f： V（G）→{0, 1, …, m-1}such that f（u）-f（v）m≥j if u and v are adjacent, and f（u）-f（v）m≥k if u and v are at distance two,where a-bm=min{a-b,m-a-b}. The minimum m such that there exists a circular m-L（j, k）-labeling of G is called the circular L（j, k）-labeling number of G and is denoted by σj, k（G）. For any two positive integers j and k with j≤k,the circular L（j, k）-labeling numbers of trees, the Cartesian product and the direct product of two complete graphs are determined.

Packing 4-Partite Tree into Complete 4-Partite Graph

For graphs G and H,an embedding of G into H is an injection ϕ:V(G)→V(H)such that ϕ(a)ϕ(b)∈E(H)whenever ab∈E(G).A packing of p graphs G_(1),G_(2),…,G_(p) into H is a p-tupleΦ=(ϕ_(1),ϕ_(2),…,ϕ_(p))such that,for i=1,2,…,p,ϕ_(i) is an embedding of Gi into H and the p sets ϕ_(i)(E(G_(i)))are mutually disjoint.Motivated by the"Tree Packing Conjecture"made by Gyar fas and Lehel,Wang Hong conjectured that for each k-partite tree,there is a packing of two copies of T(X)into a complete k-partite graph B_(n+m)(Y),where m=■k/2」..In this paper,we confirm this conjecture for k=4.

Construction of tree volume equations for Chinese fir plantations in Guizhou Province, southwestern China

Forest volume, the major component of forest biomass, is an important issue in forest resource monitoring.It is estimated from tree volume tables or equations. Based on tree volume data of 1840 sample trees from Chinese fir （Cunninghamia lanceolata） plantations in Guizhou Province in southwestern China, parallel one- and two-variable tree volume tables and tree height curves for central and other areas were constructed using an error-in-variable modeling method. The results show that, although the one-variable tree volume equations and height curves between the central and other areas were significantly different, the two-variable volume equations were sufficiently close, so that a generalized two-variable tree volume equation could be established for the entire province.

BLOW-UP PROBLEMS FOR NONLINEAR PARABOLIC EQUATIONS ON LOCALLY FINITE GRAPHS

Let G =（V, E） be a locally finite connected weighted graph, and ？ be the usual graph Laplacian. In this article, we study blow-up problems for the nonlinear parabolic equation ut = ？u ＋ f（u） on G. The blow-up phenomenons for ut = ？u ＋ f（u） are discussed in terms of two cases：（i） an initial condition is given;（ii） a Dirichlet boundary condition is given. We prove that if f satisfies appropriate conditions, then the corresponding solutions will blow up in a finite time.

MINIMUM CONGESTION SPANNING TREES IN BIPARTITE AND RANDOM GRAPHS

The first problem considered in this article reads： is it possible to find upper estimates for the spanning tree congestion in bipartite graphs, which are better than those for general graphs？ It is proved that there exists a bipartite version of the known graph with spanning tree congestion of order n3/2, where n is the number of vertices. The second problem is to estimate spanning tree congestion of random graphs. It is proved that the standard model of random graphs cannot be used to find graphs whose spanning tree congestion has order greater than n3/2.

Minimum Dominating Tree Problem for Graphs

A dominating tree T of a graph G is a subtree of G which contains at least one neighbor of each vertex of G.The minimum dominating tree problem is to find a dominating tree of G with minimum number of vertices,which is an NP-hard problem.This paper studies some polynomially solvable cases,including interval graphs,Halin graphs,special outer-planar graphs and others.

On the ordering of the Kirchhoff indices of the complements of trees and unicyclic graphs

The Kirchhoff index Kf(G) of a graph G is defined to be the sum of the resistance distances between all pairs of vertices of G. In this paper, we develop a novel method for ordering the Kirchhoff indices of the complements of trees and unicyclic graphs. With this method, we determine the first five maximum values of Kf■ and the first four maximum values of Kf(ū),where ■ and ū are the complements of a tree T and unicyclic graph U, respectively.

Applications of Graph Theory to Gross Error Detection for GPS Geodetic Control Networks

This paper describes a broad perspective of the application of graph theory to establishment of GPS control networks whereby the GPS network is considered as a connected and directed graph with three components.In this algorithm the gross error detection is undertaken through loops of different spanning trees using the "Loop Law" in which the individual components Δ X, Δ Y and Δ Z sum up to zero.If the sum of the respective vector components ∑X,∑Y and ∑Z in a loop is not zero and if the error is beyond the tolerable limit (ε>w),it indicates the existence of gross errors in one of the baselines in the loop and therefore the baseline must be removed or re_observed.After successful screening of errors by graph theory,network adjustment can be carried out.In this paper,the GPS data from the control network established as reference system for the HP Dam at Baishan county in Liaoning province is presented to illustrate the algorithm.

Uniquely Tree Colorable Graphs

In this paper, the concepts of tree chromatic numbers and uniquely tree colorable graphs are introduced. After discussion some fundamental properties, three necessary conditions for a simple graph to be uniquely tree colorable are given. Moreover, a series of uniquely tree colorable graphs are constructed.

Individual tree extraction from terrestrial laser scanning data via graph pathing

Background:Individual tree extraction from terrestrial laser scanning(TLS)data is a prerequisite for tree-scale estimations of forest biophysical properties.This task currently is undertaken through laborious and time-consuming manual assistance and quality control.This study presents a new fully automatic approach to extract single trees from large-area TLS data.This data-driven method operates exclusively on a point cloud graph by path finding,which makes our method computationally efficient and universally applicable to data from various forest types.Results:We demonstrated the proposed method on two openly available datasets.First,we achieved state-of-the-art performance on locating single trees on a benchmark dataset by significantly improving the mean accuracy by over 10% especially for difficult forest plots.Second,we successfully extracted 270 trees from one hectare temperate forest.Quantitative validation resulted in a mean Intersection over Union(mIoU)of 0.82 for single crown segmentation,which further led to a relative root mean square error(RMSE%)of 21.2% and 23.5% for crown area and tree volume estimations,respectively.Conclusions:Our method allows automated access to individual tree level information from TLS point clouds.The proposed method is free from restricted assumptions of forest types.It is also computationally efficient with an average processing time of several seconds for one million points.It is expected and hoped that our method would contribute to TLS-enabled wide-area forest qualifications,ranging from stand volume and carbon stocks modelling to derivation of tree functional traits as part of the global ecosystem understanding.

An Optimal Parallel Algorithm for Constructing a Spanning Tree on Proper Circle Trapezoid Graphs

Given a simple graph G with n vertices and m edges, the spanning tree problem is to find a spanning tree for a given graph G. This problem has many applications, such as electric power systems, computer network design and circuit analysis. For a simple graph, the spanning tree problem can be solved in O(log n) time with O(m+n) processors on the CRCW PRAM. In general, it is known that more efficient parallel algorithms can be developed by restricting classes of graphs. In this paper, we shall propose a parallel algorithm which runs O(log n) time with O(n/log n) processors on the EREW PRAM for constructing on proper circle trapezoid graphs.