Tree Labeling Research Articles

A free-air system for long-term stable carbon isotope labeling of adult forest trees

Stable carbon (C) isotopes, in particular employed in labeling experiments, are an ideal tool to broaden our understanding of C dynamics in trees and forest ecosystems. Here, we present a free-air exposure system, named isoFACE, designed for long-term stable C isotope labeling in the canopy of 25 m tall forest trees. Labeling of canopy air was achieved by continuous release of CO2 with a δ13C of −46.9‰. To this end, micro-porous tubes were suspended at c. 1 m distance vertically through the canopy, minimizing CO2 gradients from the exterior to the interior and allowing for C labeling exposure during periods of low wind speed. Target for CO2 concentration ([CO2]) increase was ambient +100 μmol mol−1. Canopy [CO2] stayed within 10% of the target during more than 57% of the time and resulted in a drop of δ13C in canopy air by 7.8‰. After 19 labeling days about 50% of C in phloem sugars and stem CO2 efflux were turned over and 20–30% in coarse root CO2 efflux and soil CO2. The isoFACE system successfully altered δ13C of canopy air for studying turn-over of C pools in forest trees and soils, highlighting their slow turn-over rates.

Separating soil respiration components with stable isotopes: natural abundance and labelling approaches

Due to the potential of forest ecosystems contributing to CO2 increase as well as to climate change mitigation, forest-atmosphere CO2 exchange has been intensively studied over last decades. However, the contribution of individual components of belowground carbon pools is still poorly known. In particular, there is no unequivocal means to separate root respiration (autotrophic) from heterotrophic respiration by soil microflora and fauna. Most studies investigating soil respiration disturbed the soil and tried to exclude autrophic respiration. Here we review alternative non invasive methods to separate the two components. Those methods share the application of the stable carbon isotope 13C, using either local changes in natural abundance of 13CO2 or artificial labelling of trees with CO2 enriched or depleted in 13C. We conclude that the applicability of natural stable isotope methods is still limited in forest ecosystems because only in a few cases there are large enough differences in 13C among soil carbon pools (usually due to the earlier presence of a C4 canopy, which is seldom in forests). On the other hand, artificial labelling with CO2 either enriched or depleted in 13C is now in a widely used for partitioning soil respiration components. However, recent findings gave clear evidence that measurements of soil CO2 efflux can be substantially influenced by the return efflux of the abiotic label. Still, especially the combination of Free Air Carbon Enrichment (FACE) with dual δ13C and δ18O stable isotope approach has the potential to provide new answers on the response sensitivity of turnover dynamics of the largest belowground soil carbon storage to elevated temperature and CO2.

Limited 15N transfer from stem-labeled leguminous trees to associated grass in an agroforestry system

Belowground nitrogen (N) transfer may be an important process for the N economy in legume-based intercropping systems. In situ estimates of N transfer based on the natural 15N abundance may be unreliable because 15N discrimination occurs during several soil and plant processes. The aim of this study was to test the use of the stem- 15N labeling method to assess in situ N transfer from a legume tree to associated grass. Grass 15N content was measured during a 203-day field experiment from 0 to 5 m from the labeled trees. The results indicated that transfer of the added 15N was limited in space (i.e., up to 1 m from the trees) and delayed in time (i.e., 15N reached the tree roots more than 3 months after labeling), which prevented estimation based on the stem- 15N labeling method. Calculations made using the observed natural 15N abundance data suggested that on average 33% of grass N was derived from N 2 fixation by the tree. New tree labeling methods have to be developed to verify these values and to obtain reliable estimates of in situ N transfer in agroforestry systems.

Odd-Graceful Labelings of Trees of Diameter 5

A difference vertex labeling of a graph G is an assignment f of labels to the vertices of G that induces for each edge xy the weight |f(x) — f(y)|. A difference vertex labeling f of a graph G of size n is odd-graceful if f is an injection from V(G) to {0, 1, …, 2n — 1} such that the induced weights are {1, 3, …, 2n — 1}. We show here that any forest whose components are caterpillars is odd-graceful. We also show that every tree of diameter up to five is odd-graceful.

Some problems and solutions in density estimation from bearing tree data: a review and synthesis

AbstractAim I detail several problems and solutions related to estimating pre‐settlement forest density from land surveyors’ bearing tree data. The data have a high value, so clarification of existing problems is needed in the development of a better theoretical framework in which to treat them. I focus on absolute density because it is the foundation for several other variables, e.g. basal area, timber volume and carbon content.Location The issues raised are relevant to the vast area encompassed by rectangular land surveys, including the General Land Office survey area of the United States (roughly, Ohio and Florida to the Pacific coast and Alaska), as well as significant areas in the eastern United States, and possibly elsewhere.Methods A literature review details the history and nature of density estimation from bearing tree data, and spatial simulations quantify the effects of certain identified problems on density estimates. The review focuses on methodological issues appearing in the ecological and biometrical literature.Results Problems encountered in the literature and addressed here include: (1) aggregated tree spatial patterns and their effect on density using traditional estimators; (2) the mis‐designation of bearing tree labels in relation to definitions given in the estimators; (3) biases due to small sample size; and (4) surveyor‐induced biases. Simulations of aggregated tree populations having a 44‐fold density variation show that estimates ranging from 5 to 127 per cent of actual can result, depending on the estimator used, the scale at which it is calculated, and the error in tree distance rank assignments. The traditionally used estimator is accurate only when trees are spatially random throughout, and sample size is not small. More robust estimators exist that can accommodate a wider range of variation in spatial pattern, sampling design and sample size. One of these is discussed in detail.Main conclusions Data users should pay much closer attention to critical aspects of bearing tree data and analytical methods, provide basic but necessary descriptive data, and more accurately represent the inherent range of possible errors of estimate. They can narrow this range of uncertainty by using the methods and considerations discussed here and in other recent work.

Formula omitted]-Total labelling of trees with sparse vertices of maximum degree

The ( 2 , 1 ) -total labelling number λ 2 t ( G ) of a graph G is the width of the smallest range of integers that suffices to label the vertices and the edges of G such that no two adjacent vertices, or two adjacent edges, have the same label and the difference between the labels of a vertex and its incident edges is at least 2. Let T be a tree with maximum degree Δ ⩾ 4 . Let D Δ ( T ) denote the set of integers k for which there exist two distinct vertices of maximum degree of distance at k in T. It was known that Δ + 1 ⩽ λ 2 t ( T ) ⩽ Δ + 2 . In this paper, we prove that if 1 ∉ D Δ ( T ) or 2 ∉ D Δ ( T ) , then λ 2 t ( T ) = Δ + 1 . The result is best possible in the sense that, for any fixed integer k ⩾ 3 , there exist infinitely many trees T with Δ ⩾ 4 and k ∉ D Δ ( T ) such that λ 2 t ( T ) = Δ + 2 .

Gene Tree Labeling Using Nonnegative Matrix Factorization on Biomedical Literature

Identifying functional groups of genes is a challenging problem for biological applications. Text mining approaches can be used to build hierarchical clusters or trees from the information in the biological literature. In particular, the nonnegative matrix factorization (NMF) is examined as one approach to label hierarchical trees. A generic labeling algorithm as well as an evaluation technique is proposed, and the effects of different NMF parameters with regard to convergence and labeling accuracy are discussed. The primary goals of this study are to provide a qualitative assessment of the NMF and its various parameters and initialization, to provide an automated way to classify biomedical data, and to provide a method for evaluating labeled data assuming a static input tree. As a byproduct, a method for generating gold standard trees is proposed.

Advances in Nonnegative Matrix and Tensor Factorization

Advances in Nonnegative Matrix and Tensor Factorization

Labeling Schemes for Tree Representation

This paper deals with compact label-based representations for trees. Consider an n-node undirected connected graph G with a predefined numbering on the ports of each node. The all-ports tree labeling ℒall gives each node v of G a label containing the port numbers of all the tree edges incident to v. The upward tree labeling ℒup labels each node v by the number of the port leading from v to its parent in the tree. Our measure of interest is the worst case and total length of the labels used by the scheme, denoted M up (T) and S up (T) for ℒup and M all (T) and S all (T) for ℒall . The problem studied in this paper is the following: Given a graph G and a predefined port labeling for it, with the ports of each node v numbered by 0,…,deg (v)−1, select a rooted spanning tree for G minimizing (one of) these measures. We show that the problem is polynomial for M up (T), S up (T) and S all (T) but NP-hard for M all (T) (even for 3-regular planar graphs). We show that for every graph G and port labeling there exists a spanning tree T for which S up (T)=O(nlog log n). We give a tight bound of O(n) in the cases of complete graphs with arbitrary labeling and arbitrary graphs with symmetric port labeling. We conclude by discussing some applications for our tree representation schemes.

General compact labeling schemes for dynamic trees

Let F be a function on pairs of vertices. An F-labeling scheme is composed of a marker algorithm for labeling the vertices of a graph with short labels, coupled with a decoder algorithm allowing one to compute F(u, v) for any two vertices u and v directly from their labels. As applications for labeling schemes concern mainly large and dynamically changing networks, it is of interest to study distributed dynamic labeling schemes. This paper investigates labeling schemes for dynamic trees. We consider two dynamic tree models, namely, the leaf-dynamic tree model in which at each step a leaf can be added to or removed from the tree and the leaf-increasing tree model in which the only topological event that may occur is that a leaf joins the tree. A general method for constructing labeling schemes for dynamic trees (under the above mentioned dynamic tree models) was previously developed in Korman et al. (Theory Comput Syst 37:49–75, 2004). This method is based on extending an existing static tree labeling scheme to the dynamic setting. This approach fits many natural functions on trees, such as distance, separation level, ancestry relation, routing (in both the adversary and the designer port models), nearest common ancestor etc.. Their resulting dynamic schemes incur overheads (over the static scheme) on the label size and on the communication complexity. In particular, all their schemes yield a multiplicative overhead factor of Ω(log n) on the label sizes of the static schemes. Following (Korman et al., Theory Comput Syst 37:49–75, 2004), we develop a different general method for extending static labeling schemes to the dynamic tree settings. Our method fits the same class of tree functions. In contrast to the above paper, our trade-off is designed to minimize the label size, sometimes at the expense of communication. Informally, for any function k(n) and any static F-labeling scheme on trees, we present an F-labeling scheme on dynamic trees incurring multiplicative overhead factors (over the static scheme) of $$O(\log_{k(n)} n)$$ on the label size and $$O(k(n)\log_{k(n)} n)$$ on the amortized message complexity. In particular, by setting $$k(n) = n^{\epsilon}$$ for any $$0 < \epsilon < 1$$ , we obtain dynamic labeling schemes with asymptotically optimal label sizes and sublinear amortized message complexity for the ancestry relation, the id-based and label-based nearest common ancestor relation and the routing function.

Average case analysis for tree labelling schemes

We study how to label the vertices of a tree in such a way that we can decide the distance of two vertices in the tree given only their labels. Gavoille et al. proved that for any such distance labelling scheme, the maximum label length is at least 1 8 log 2 n − O ( log n ) bits, where n is the number of vertices in the input tree T . They also gave a separator-based labelling scheme that has the optimal label length Θ ( log n ⋅ log ( H n ( T ) ) ) , where H n ( T ) is the height of T . We present two distance labelling schemes, namely, the backbone-based scheme and rake-based scheme, which also achieve the optimal label length. The two schemes always perform at least as well as the separator scheme. Furthermore, the rake-based scheme has a much smaller expected label length under certain tree distributions. With these new schemes, we also can find the least common ancestor of any two vertices based on their labels only.

Labeling trees with a condition at distance two

An L ( h , k ) -labeling of a graph G is an integer labeling of vertices of G , such that adjacent vertices have labels which differ by at least h , and vertices at distance two have labels which differ by at least k . The span of an L ( h , k ) -labeling is the difference between the largest and the smallest label. We investigate L ( h , k ) -labelings of trees of maximum degree Δ , seeking those with small span. Given Δ , h and k , span λ is optimal for the class of trees of maximum degree Δ , if λ is the smallest integer such that every tree of maximum degree Δ has an L ( h , k ) -labeling with span at most λ . For all parameters Δ , h , k , such that h < k , we construct L ( h , k ) -labelings with optimal span. We also establish optimal span of L ( h , k ) -labelings for stars of arbitrary degree and all values of h and k .

Formula omitted]-graceful labelings of partial cubes

Partial cubes are graphs that allow isometric embeddings into hypercubes. Θ -graceful labelings of partial cubes are introduced as a natural extension of graceful labelings of trees. It is shown that several classes of partial cubes are Θ -graceful, for instance even cycles, Fibonacci cubes, and (newly introduced) lexicographic subcubes. The Cartesian product of Θ -graceful partial cubes is again such and we wonder whether in fact any partial cube is Θ -graceful. A connection between Θ -graceful labelings and representations of integers in certain number systems is established. Some directions for further investigation are also proposed.

Matching and anatomical labeling of human airway tree

Matching of corresponding branchpoints between two human airway trees, as well as assigning anatomical names to the segments and branchpoints of the human airway tree, are of significant interest for clinical applications and physiological studies. In the past, these tasks were often performed manually due to the lack of automated algorithms that can tolerate false branches and anatomical variability typical for in vivo trees. In this paper, we present algorithms that perform both matching of branchpoints and anatomical labeling of in vivo trees without any human intervention and within a short computing time. No hand-pruning of false branches is required. The results from the automated methods show a high degree of accuracy when validated against reference data provided by human experts. 92.9% of the verifiable branchpoint matches found by the computer agree with experts' results. For anatomical labeling, 97.1% of the automatically assigned segment labels were found to be correct.

Systems of distant representatives

We introduce a new notion of Systems of Distant Representatives of families of subsets of a metric space. We are in particular interested in the computational complexity of deciding the existence of such systems, for different distance parameters and for various metric spaces. The problem contains as a subproblem the well known polynomial time solvable problem of Systems of Distinct Representatives (for discrete metric and distance parameter 1). We prove several NP-hardness results, e.g., for discrete metric and distance parameter 2, or for Euclidean metric spaces. We also show a direct connection to practically motivated and previously studied problems such as scheduling, distance constrained graph labeling, map labeling, disjoint representatives of hypergraphs and independent sets in graphs. Finally, we mention our original motivation for studying distant representatives which comes from the distance constrained graph labeling and our complexity results imply a significant difference in the computational complexity of L ( p , q ) -labeling of trees for q = 1 and q > 1 .

A Study of the Major Graph Labelings of Trees

Tree is one of the most studied and practically useful classes of graphs and is the attention of a great number of studies. There is absence of generalized results for tree as a class and even for one kind of labeling as whole. Only specialized results exist limited to specific types of trees only. A number of conjectures stand being unsolved. Graham and Sloane (1980) conjectured trees to be Harmonious and Ringel-Kotzig conjectured trees to be Graceful about three decades ago. Kotzig and Rosa (1970) ask the question whether all trees are Magic or not. No generalized result for Antimagic labeling is given for trees so far. This paper presents the methodologies to obtain the major labeling schemes for trees viz., Harmonious, Sequential, Felicitous, Graceful, Antimagic and found the trees to be not Magic except T(2,1), thus solving the said conjectures. These findings could also be useful for those working in fields where graphs serve as models.

Vertex-magic labeling of trees and forests

A vertex-magic total labeling of a graph G( V, E) is a one-to-one map λ from E∪ V onto the integers {1,2,…,| E|+| V|} such that λ(x)+∑λ(xy), where the sum is over all vertices y adjacent to x, is a constant, independent of the choice of vertex x. In this paper we examine the existence of vertex-magic total labelings of trees and forests. The situation is quite different from the conjectured behavior of edge-magic total labelings of these graphs. We pay special attention to the case of so-called galaxies, forests in which every component tree is a star.

Relaxed Graceful Labellings of Trees

A graph $G$ on $m$ edges is considered graceful if there is a labelling $f$ of the vertices of $G$ with distinct integers in the set $\{0,1,\dots,m\}$ such that the induced edge labelling $g$ defined by $g(uv)=|f(u)-f(v)|$ is a bijection to $\{1,\dots,m\}$. We here consider some relaxations of these conditions as applied to tree labellings: 1. Edge-relaxed graceful labellings, in which repeated edge labels are allowed, 2. Range-relaxed graceful labellings, in which the upper bound $m'$ is allowed to go higher than the number of edges, and 3. Vertex-relaxed graceful labellings, in which repeated vertex labels are allowed. The first of these had been looked at by Rosa and Širáň (1995). Here some linear bounds in the relevant metrics are given for range-relaxed and vertex-relaxed graceful labellings.

Modeling the 3D coronary tree for labeling purposes

Coronary artery diseases are usually revealed using X-ray angiographies. Such images are complex to analyze because they provide a 2D projection of a 3D object. Medical diagnosis suffers from inter- and intra-clinician variability. Therefore, reliable software for the 3D reconstruction and labeling of the coronary tree is strongly desired. It requires the matching of the vessels in the different available angiograms, and an approach which identifies the arteries by their anatomical names is a way to solve this difficult problem. This paper focuses on the automatic labeling of the left coronary tree in X-ray angiography. Our approach is based on a 3D topological model, built from the 3D anthropomorphic phantom, Coronix. The phantom is projected under different angles of view to provide a data base of 2D topological models. On the other hand, the vessel skeleton is extracted from the patient’s angiogram. The algorithm compares the skeleton with the 2D topological model which has the most similar vascular net shape. The method performs in a hierarchical manner, first labeling the main artery, then the sub-branches. It handles inter-individual anatomical variations, segmentation errors and image ambiguities. We tested the method on standard angiograms of Coronix and on clinical examinations of nine patients. We demonstrated successful scores of 90% correct labeling for the main arteries and 60% for the sub-branches. The method appears to be particularly efficient for the arteries in focus. It is therefore a very promising tool for the automatic 3D reconstruction of the coronary tree from monoplane temporal angiographic clinical sequences.

Expression of a kinase anchoring protein 79 in the human fetal amygdala.

The expression of AKAP (a kinase anchoring protein) 79 enriched in postsynaptic densities has been investigated in the human amygdaloid nuclei of the 8th gestational month. Nuclear specific diffuse and cellular immunostaining is observed. An outstanding feature of cellular immunostaining is the labelling of somata and dendritic trees in a manner that allows neuronal classification. Bipolar, multipolar, and pyramidal AKAP79-positive neurons are found throughout the amygdala; the highest packing density of immunostained neurons is seen within the central and lateral nucleus. Dense diffuse immunolabelling is observed in the lateral and accessory basal nucleus. The results indicate that AKAP79 is expressed in various neuronal types (projection as well as local circuit neurons). Diffuse staining does not always match with cellular labelling within a nucleus, thus, AKAP79 may be particularly enriched in dendrites in some nuclei. The widespread distribution of AKAP79 indicates its possible role in various amygdaloid circuitries; thus, AKAP79 does not seem to be restricted to definite functional systems in the 8th month.