The Infinity Tree: Representing Infinities of Real Numbers with Countably Infinite Tree Structures

This paper discusses how the infinite set of real numbers between 0 and 1 could be represented by a countably infinite tree structure which would avoid Cantor’s diagonalization argument that the set of real numbers is not countably infinite. Likewise, countably infinite tree structures could represent all real numbers, and all points in any number of dimensions in multi-dimensional spaces. The objective of this paper is not to overturn previous research based on Cantor’s argument, but to suggest that this situation may be treated as a definitional or axiomatic choice. This paper proposes a “non-Cantorian” branch of cardinality theory, representing all these infinities with countably infinite tree structures. This approach would be consistent with the Continuum Hypothesis.

Analysis on Fuji Apple Tree Structures and Related Factors under Different Pruning Modes

To determine the correlations between the tree structuresof Fuji apple with different pruning modes and each factor, the data about 3 tree structures which were free spindle short shoot, free spindle long shoot and slenderspindle short shoot in Xingtang County of Hebai Province were investigated, then by SPSS anal- ysis, the correlations between the taperingness and each growth factor of inserted small branch were compared. The results showed that the taperingness of central trunk of free spindle dwarf-shoot Fuji apple treeshad negative correlations with each factor of inserted small branch, while the taperingness of central trunk of free spin- dle long-shoot Fuji apple treeshad positive correlations with each factor of inserted small branch, the taperingness of central trunk of slenderspindle short-shootFuji ap- ple treeshad negative correlation with total thickness of inserted small branch, but had positive correlations with other factors. This study can provide a scientifictheo- retical basis for the pruning technology of high-density planting trees grafting by dwarfing self-rooted rootstock.

Effects of thinning on stand structure and tree stability in an afforested oriental beech(Fagus orientalis Lipsky) stand in northeast Turkey

We studied relationships between stand structure and stand stability according to thinning intensity in an afforested oriental beech stand. Various thinning intensities were applied in sample stands. We sampled eight plots in stands that were lightly thinned, eight plots in heavily thinned stands and eight plots in unthinned stands as a control. Height and diameter distributions of the stands were measured to assess stand structure. We quantified individual tree stability and collective stability. Heavy thinning during the first thinning operation damaged the storied structure of the stand in thicket stage and affected collective structuring ability. While most control plots had multi-storied stands, after light and heavy thinning two-storied structure became more common.Large gaps occurred in the canopy after heavy thinning. On average, nine tree collectives were formed per sampling plot in the untreated stand, seven collectives after thinning in 2008 and four collectives after thinning in 2009. Stable trees accounted for 17 % of trees in control plots, 24 % in lightly thinned plots, and 15 % in heavily thinned plots. Collective stability values were 83 % in control plots, 82 % in lightly thinned plots and 36 % in heavily thinned plots. We conclude that it is necessary to retain collective structuring capacity during thinning operations for sustaining stand stability.

An Efficient Information Hiding Scheme Based on Closest Paired Tree Structure Vector Quantization

Information hiding schemes based on vector quantization （VQ） usually require lengthy VQ encoding and decoding processes. In this paper, we propose an efficient information hiding method based on closest paired tree structure vector quantization （CPTSVQ）. The simulation result shows that the execution time of the proposed scheme is much shorter than that attained by previous approaches.

The method of design for seismic data database system based on tree structure

With the massive growth of the seismic data, it is required a new method to manage them. In this paper, the design method will be reported about relational database based on tree structure. Comparing with other designs, it is not only simpler and easier to organize data, but also can simplify the design process of the database. This method has been used to design database of the earthquake monitor center station of the earthquake monitoring system for the Yangtze River Three Gorges Project and has shown good results.

Dependence Tree Structure Estimation via Copula

We propose an approach for dependence tree structure learning via copula. A nonparametric algorithm for copula estimation is presented. Then a Chow-Liu like method based on dependence measure via copula is proposed to estimate maximum spanning bivariate copula associated with bivariate dependence relations. The main advantage of the approach is that learning with empirical copula focuses on dependence relations among random variables, without the need to know the properties of individual variables as well as without the requirement to specify parametric family of entire underlying distribution for individual variables. Experiments on two real-application data sets show the effectiveness of the proposed method.

STRUCTURE OF COMPUTATIVE TREE FOR COMPUTABLE FUNCTION

In this paper, we study the computative structure of computable function - a structure of computative tree, and, by analysis on it, got the most general algorithm and model for computation on computable functions.

Effects of Different Water and Fertilizer Combinations on Tree Structure,Leaf Parameters and Photosynthesis of Apple Saplings

[ Objective] This study aimed to investigate the effects of different water and fertilizer combinations on apple saplings. [ Method] ＇ Tianhong 2＇ Fuji /SH40/Malus robusta Rehd. was used as the experimental material to analyze the effects of different irrigation modes and combinations of basal fertilizer and dressing fertilizer on tree structure, leaf parameters and photosynthesis of apple saplings. [ Result] The results showed that different water and fertilizer combinations ex- hibited varying effects on tree structure, leaf parameters and photosynthesis of apple saplings. To be specific, applying 432 000 kg/hm2 basal fertilizer, 480 kg/hm2 urea and 915 kg/hmz organic fertilizer ＋ 0 ＋ 915 kg/hm2 organic fertilizer as dressing fertilizer, and 1% urea as leaf fertilizer was conducive to promoting growth of branches and leaves, increasing leaf thickness, individual leaf area and SPAD, and improving photosynthesis of apple saplings under half root irrigation and whole root irrigation conditions. In addition, the effects were more significant under whole root irrigation conditions. [ Conclusion] Selecting the appropriate water and fertilizer combination is conducive to the growth of apple saplings.

Analysis of Short-Shoot Fuji Apple Tree Structure and Correlative Factors

In order to clarify the correlation between short-shoot Fuji apple tree structure and different factors under different trimming and pruning modes,we investigate the trunk taperingness of free-spindle short-shoot Fuji and slender-spindle short-shoot Fuji,respectively,as well as the total thickness,average thickness,total length and average length of small main branches in the standard demonstration apple garden in Xingtang County of Hebei Province. By SPSS analysis,we study the correlation between trunk taperingness of trees with different shapes and the growth indices of their small main branches. The results show that the trunk taperingness of free-spindle short-shoot Fuji apple is negatively correlated with the total thickness,average thickness,total length and average length of small main branches,but the correlation is not significant; the trunk taperingness of slender-spindle short-shoot Fuji apple is negatively correlated with the total thickness but positively correlated with other factors,and the correlation with average length reaches a significant level. The results of this study can provide a scientific basis for guiding the high-density dwarf rootstock short-shoot Fuji apple tree trimming technology.

Some of the Mechanisms for Coexistence of Tree Species Diversity in Tropical Forests: A Review of Effects of Tree Density Dependence

Tree communities contribute to maintenance of species diversity in tropical forests. Coexistence of many tree species is not without competition. Therefore, coexistence of tree species and size diversities occur sequentially or simultaneously in tropical natural forests. Understanding coexistence and competition mechanisms of tree species requires knowledge of interactions within and between species. However, many conservation efforts and strategies failed due to inability to identify and maintain functional coexistence mechanisms among tree species in the forest. Also, most trees died because of pressure on their habitats and not because of limiting growth resources. Hence, species identity, minimum distance and size of the neighbouring trees which are responsible for coexistence of competing trees in most tropical forests have not been explicitly reviewed. Therefore, this review evaluated some of the density dependent mechanisms for coexistence of tree species alpha diversity in tropical forests. Many interactive mechanisms are responsible for coexistence tree species in tropical forests. Inter- and intra-specific competitions are the most significant and both facilitate positive and negative density dependence. Therefore, switching from negative to positive density dependence may occur in some situations. Positive and negative density effects regulate species abundance and coexistence through conspecific and heterospecific structures. Aggregates of conspecific and heterospecific neighbours constitute forest spatial structure. Negative density interactions are mutually exclusive and basically ranged from effect of species identity of neighbours, distance to neighbours and tree size of the neighbours to reference trees in the community structures. Some mechanisms shorten distances for heterospecific than conspecific interactions. Conspecific structures improved survival and growth of rare tree species. Interactive mechanisms in tree community and population structures facilitate species diversity and size inequality, respectively.

A Multi-Objective Optimal Evolutionary Algorithm Based on Tree-Ranking

Multi-objective optimal evolutionary algorithms (MOEAs) are a kind of new effective algorithms to solve Multi-objective optimal problem (MOP). Because ranking, a method which is used by most MOEAs to solve MOP, has some shortcoming s, in this paper, we proposed a new method using tree structure to express the relationship of solutions. Experiments prove that the method can reach the Pare-to front, retain the diversity of the population, and use less time.

Enhancing Navigability:An Algorithm for Constructing Tag Trees

Purpose： This study introduces an algorithm to construct tag trees that can be used as a userfriendly navigation tool for knowledge sharing and retrieval by solving two issues of previous studies, i.e. semantic drift and structural skew.Design/methodology/approach： Inspired by the generality based methods, this study builds tag trees from a co-occurrence tag network and uses the h-degree as a node generality metric. The proposed algorithm is characterized by the following four features：（1） the ancestors should be more representative than the descendants,（2） the semantic meaning along the ancestor-descendant paths needs to be coherent,（3） the children of one parent are collectively exhaustive and mutually exclusive in describing their parent, and（4） tags are roughly evenly distributed to their upper-level parents to avoid structural skew. Findings： The proposed algorithm has been compared with a well-established solution Heymann Tag Tree（HTT）. The experimental results using a social tag dataset showed that the proposed algorithm with its default condition outperformed HTT in precision based on Open Directory Project（ODP） classification. It has been verified that h-degree can be applied as a better node generality metric compared with degree centrality.Research limitations： A thorough investigation into the evaluation methodology is needed, including user studies and a set of metrics for evaluating semantic coherence and navigation performance.Practical implications： The algorithm will benefit the use of digital resources by generating a flexible domain knowledge structure that is easy to navigate. It could be used to manage multiple resource collections even without social annotations since tags can be keywords created by authors or experts, as well as automatically extracted from text.Originality/value： Few previous studies paid attention to the issue of whether the tagging systems are easy to navigate for users. The contributions of this study are twofold：（1） an algorithm was developed to construct tag trees with consideration given to both semanticcoherence and structural balance and（2） the effectiveness of a node generality metric, h-degree, was investigated in a tag co-occurrence network.

Document Clustering Based on Constructing Density Tree

This paper focuses on document clustering by clustering algorithm based on a DEnsityTree (CABDET) to improve the accuracy of clustering. The CABDET method constructs a density-based treestructure for every potential cluster by dynamically adjusting the radius of neighborhood according to local density. It avoids density-based spatial clustering of applications with noise (DBSCAN) ′s global density parameters and reduces input parameters to one. The results of experiment on real document show that CABDET achieves better accuracy of clustering than DBSCAN method. The CABDET algorithm obtains the max F-measure value 0.347 with the root node's radius of neighborhood 0.80, which is higher than 0.332 of DBSCAN with the radius of neighborhood 0.65 and the minimum number of objects 6.

XML-based Framework of Parametric Design for Typical Parts

Parametric design of typical parts holds a very important position during process of product designs. In order to develop a parametric design system of typical parts compatible with heterogeneous CAD systems, this paper presents a framework of a network-oriented design system of typical parts, enabled by eXtensible Markup Language (XML), capable of providing parametric design. Firstly, an overview of the framework is presented. In order to map the part feature hierarchy tree of 3D model into an XML tree, an XML-based part template is introduced. The methods of XML-based parametric design and parametric design navigation are described. Finally, an application example of prototype system under the Pro/Engineer platform is given. The application indicates that the proposed framework is valid for parametric design of typical parts/components in heterogeneous CAD systems.

A Tree Structure Storage Model of BOM

Through the analysis of BOM and in comparison with other storage forms, a tree-structure storage model has been proposed. It use two tables to record parent components and child components respectively. Each table has a location point combined by three fields. And other link fields in the child component table present the relationship between levels of a product tree. Compared with Gozintograph mode, the BOM design on tree structure has many advantages.

Kernel-Based Semantic Relation Detection and Classification via Enriched Parse Tree Structure

This paper proposes a tree kernel method of semantic relation detection and classification （RDC） between named entities. It resolves two critical problems in previous tree kernel methods of RDC. First, a new tree kernel is presented to better capture the inherent structural information in a parse tree by enabling the standard convolution tree kernel with context-sensitiveness and approximate matching of sub-trees. Second, an enriched parse tree structure is proposed to well derive necessary structural information, e.g., proper latent annotations, from a parse tree. Evaluation on the ACE RDC corpora shows that both the new tree kernel and the enriched parse tree structure contribute significantly to RDC and our tree kernel method much outperforms the state-of-the-art ones.

Investigation of a Network Failure Problem with a Significant Path, from the Perspective of Crisis Management

The objective of this study is to investigate a network failure problem with a significant path, emerging from the context of crisis management, such as in the case of natural disasters. For a given tree with m failed edges, we assume that we have sufficient resources to recover k edges of the m edges. Each node has a positive weight. In this situation, we consider which k edges should be fixed in order to maximize the sum of the weights of the nodes reachable from the significant path. In this paper, we formulate such a problem as a combinatorial problem. Further, we show that a part of our problem may be solved by translating it into the terms of the so-called tree knapsack problem.

Asynchronous Nested Optimization Algorithms and Their Parallel Implementation

Large scale optimization problems can only be solved in an efficient way, if their special structure is taken as the basis of algorithm design. In this paper we consider a very broad class of large-scale problems with special structure, namely tree structured problems. We show how the exploitation of the structure leads to efficient decomposition algorithms and how it may be implemented in a parallel environment.

Peregrine Soliton and Akhmediev Breathers in a Chameleon Electrical Transmission Line

We analyze the particular behavior exhibited by a chaotic waves field containing Peregrine soliton and Akhmediev breathers. This behavior can be assimilated to a tree with “roots of propagation” which propagate randomly. Besides, this strange phenomenon can be called “tree structures”. So, we present the collapse of dark and bright solitons in order to build up the above mentioned chaotic waves field. The investigation is done in a particular nonlinear transmission line called chameleon nonlinear transmission line. Thus, we show that this line acts as a bandpass filter at low frequencies and the impact of distance, frequency and dimensionless capacitor are also presented. In addition, the chameleon’s behavior is due to the fact that without modifying the appearance structure, it can present alternatively purely right- or left-handed transmission line. This line is different to the composite one.

TLS-bridged co-prediction of tree-level multifarious stem structure variables from worldview-2 panchromatic imagery: a case study of the boreal forest

In forest ecosystem studies,tree stem structure variables(SSVs)proved to be an essential kind of parameters,and now simultaneously deriving SSVs of as many kinds as possible at large scales is preferred for enhancing the frontier studies on marcoecosystem ecology and global carbon cycle.For this newly emerging task,satellite imagery such as WorldView-2 panchromatic images(WPIs)is used as a potential solution for co-prediction of tree-level multifarious SSVs,with static terrestrial laser scanning(TLS)assumed as a‘bridge’.The specific operation is to pursue the allometric relationships between TLS-derived SSVs and WPI-derived feature parameters,and regression analyses with one or multiple explanatory variables are applied to deduce the prediction models(termed as Model1s and Model2s).In the case of Picea abies,Pinus sylvestris,Populus tremul and Quercus robur in a boreal forest,tests showed that Model1s and Model2s for different tree species can be derived(e.g.the maximum R^(2)=0.574 for Q.robur).Overall,this study basically validated the algorithm proposed for co-prediction of multifarious SSVs,and the contribution is equivalent to developing a viable solution for SSV-estimation upscaling,which is useful for large-scale investigations of forest understory,macroecosystem ecology,global vegetation dynamics and global carbon cycle.