Rebalance Research Articles

On the distance spectrum of generalized balanced trees

For positive integers m 1 , m 2 , … , m h , a generalized balanced tree T ( m 1 , m 2 , … , m h ) is a rooted tree of height h such that every vertex of depth i has m i + 1 children, 0 ≤ i ≤ h − 1 . The distance matrix D ( G ) of a simple connected graph G of order n is an n × n matrix whose ( i , j ) th entry is the distance between i th and j th vertices. A connected graph G is called a k-partitioned transmission regular graph if there exists a vertex partition { V 1 , V 2 , … , V k } of G so that for 1 ≤ i , j ≤ k , and x ∈ V i , ∑ y ∈ V j d ( x , y ) is a constant. Here we show that T ( m 1 , m 2 , … , m h ) is an ( h + 1 ) -partitioned transmission regular graph. We find an ( h + 1 ) × ( h + 1 ) matrix whose largest eigenvalue is the distance spectral radius of T ( m 1 , m 2 , … , m h ) . We obtain the characteristic polynomial of D ( T ( m 1 , m 2 , … , m h ) ) in terms of that of the smaller matrices and give an idea to find the full spectrum. Moreover, we get that D ( T ( m 1 , m 2 , … , m h ) ) has − 2 an eigenvalue with multiplicity at least m 1 ⋯ m h − 1 ( m h − 1 ) and − ( m h + 2 ) ± m h ( m h + 4 ) as eigenvalues with multiplicity at least m 1 ⋯ m h − 2 ( m h − 1 − 1 ) .

Carbon stress causes earlier budbreak in shade-tolerant species and delays it in shade-intolerant species.

Climate change may lead to C stress (negative C balance) in trees. Because nonstructural carbohydrates (NSC) are required during metabolic reactivation in the spring, C stress might delay budbreak timing. This effect is expected to be greater in shade-intolerant than in shade-tolerant species, owing to the faster C economy in the shade-intolerant. We experimentally induced C stress in saplings of six temperate tree species that differed in their light requirements by exposing them to either full light or shade from summer to spring, then recorded the date of first budbreak for the individuals. Because the levels of C reserves that represent effective C stress may differ among species, we estimated the degree of C stress by recording survival during the experiment and measuring whole-sapling NSC concentrations after budbreak. Shade reduced NSC concentrations and increased the sugar fraction in the NSC in all species. In the shade, shade-intolerant species had higher mortality and generally lower NSC concentrations than the shade-tolerant species, indicating a trend for more severe C stress in species with faster C economy. In shade-intolerant species, budbreak started earlier and proceeded faster in full lightthan in shade, but in shade-tolerant species budbreak was delayed in full light. The effects of the light environments on budbreak were not greater in shade-intolerant than in shade-tolerant species. Our study reveals a correspondence between budbreak responses to light and the light requirements of the species. This finding confirms that C metabolism has a significant role in triggering budbreak and demonstrates that whether C stress accelerates or delays budbreak depends on the species' light requirements.

Nutritional standards through Integrated Differential Diagnosis (IDD) in pomegranate (Punica granatum L.)

The foliar analysis is a useful tool to detect the nutritional status of plants, predict future problems in the reproductive cycles of fruit production and implement preventive and corrective measures to achieve a mineral balance in fruit trees, obtaining higher productivity. There is little information available on nutrient sufficiency ranges in pomegranate leaf and the literature reported differs due to diverse cultivation practices, cultivars, and agroecological conditions. Therefore, the objective of this work was to determine the mineral content of ‘Wonderful’ pomegranate leaves for each the nutritional elements and the cation balance, and to establish the nutritional standards using Integrated Differential Diagnosis (IDD). The mineral content of the pomegranate leaves was determined and based on the results, nutritional standards for macro elements, cation balance and microelements were generated through the IDD, which evaluate whether there are mineral and/or physiological imbalances. The macro elements in the cultivation of the pomegranate were the following: NO3 3747.5 µg g-1, Total Nitrogen 1.35%, P 0.14%, K 0.88%, Ca 1.65%, Mg 0.19%, Na 0.006%. For the cation balance, the optimal values ​​were: (Ca+Mg)/K 4.48 mEq 100 g-1, Ca/(K+Mg) 2.13 mEq 100 g-1, Mg/(K+Ca) 0.16 mEq 100 g-1, Ca/Mg 5.06 mEq 100 g-1, K/Mg 1.36 mEq 100 g-1. Finally, the optimal values ​​for the microelements were: Fe 59.5 µg g-1, Mn 31.4 µg g-1, Zn 6.3 µg g-1, Cu 6.1 µg g-1. The values ​​obtained for the micro and macro elements were like those reported. In the case of cation balance and foliar nitrate content, they have not been previously reported. The IDD is a promising and effective auxiliary tool to characterize the nutritional status of pomegranate trees and, in turn, an alternative to conventional methods of nutritional diagnosis with the advantage of establishing a nutritional deficiency (soil-plant relationship) or a physiological imbalance (relation plant - climate) for this crop.

Effects of Environmental Factors on the Nonstructural Carbohydrates in Larix principis-rupprechtii

Nonstructural carbohydrates (NSCs) reflect the carbon balance in trees and play a central role in their responses to environmental stresses. However, our understanding of tree NSC storage dynamics under environmental stress is unclear. Here, we quantified the deciduous conifer Larix principis-rupprechtii at five altitudes on Luya Mountain, North-Central China. We measured NSCs in different organs and simultaneously monitored environmental variables during the growing seasons in 2018 and 2019. The results showed that temperature was the main environmental factor affecting tree NSCs. Furthermore, as the soil–atmosphere temperature gradient decreased, the concentrations of soluble sugars in the needles increased while their starch decreased, as well as the concentrations of starch in the shoots, stems, and roots increased. These results may indicate that temperature gradients may assist carbohydrate allocation within individual trees. The NSCs, especially starch, in the needles increased with lower soil moisture, and the soluble sugars and starch in the needles and shoots increased with a higher vapor pressure deficit. The soluble sugars in the stems were significantly affected by soil moisture, and the NSCs in the roots were mainly affected by temperature. These results provide new insights to improve our understanding of the environmental stress effects on future forest C balances.

Intelligent microscopic 3D shape reconstruction method based on 3D time-frequency transformation

Three-dimensional (3D) shape reconstruction methods based on image focus information generally use a unified focus evaluation metric for the depth-of-field image sequences of microscopic objects. With the absence of the correlation among these sequences, this kind of reconstruction method fails to correct the depth errors of consecutive frame images that result from textural sparsity or low contrast in images. In this paper, different image sequences of microscopic objects are interpreted as 3D image data, such that the correlation among all the sequences can be introduced to the reconstruction. Then, a reconstruction framework encompassing multiview analysis, locally stable clustering, and selective fusion as its key components is established from the perspective of 3D time-frequency transformation. To be specific, we analyze the advantage of 3D image data in shape reconstruction over general 2D image data and construct a 3D time-frequency transform that maps a 3D image to depth images, which contain information of varying scales, regions, and directions. Next, to enhance depth image features, a locally stable clustering algorithm is constructed based on multimodal textural features, which improves the adaptive selection ability of depth images with good homogeneity. Finally, we propose the selective fusion of depth images, which outputs accurate 3D morphology results by fitting multiple layers of noise-free depth images through a layer-by-layer sifting balance tree designed in this study. The effectiveness of the proposed method is verified on simulation data and real scenes. The reconstruction method of this perspective may bring fresh air to the field of submicron industrial measurement and sophisticated manufacturing.

Decoupling of tree height and root depth across the globe and the implications for tree mortality during drought events

Tree height (Htree) and root depth (Droot) are the two most critical functional traits for plant ecological strategies. However, the global varying patterns of Htree and Droot and the ecological significance for tree survival under changed climate conditions are less understood. Here, we compiled Htree, Droot, and six root traits related to soil resource absorption for 301 field-grown tree species distributed 776 sites worldwide. The relationships between Htree and Droot across different climate conditions and the implications for tree mortality during drought events were investigated. We found Htree and Droot were often decoupled in angiosperms and gymnosperms among different climate conditions. Greater Htree was prone to occur in warm and moist climates, while greater Droot tended to occur in warm and dry climates with low soil water availability. Phylogenetic analysis revealed that trees have evolved towards smaller Htree but deeper Droot from the deep time. Although dense root structures to some extent contributed to sustaining the resource supply–demand balance of large trees with shallow roots (great Htree/ Droot), the large trees with greater Htree/ Droot were more vulnerable to drought-induced mortality. The findings suggest that the linkage of below- and above-ground reaches has a pivotal role in understanding tree mortality during drought events. The insight will allow more accurate vegetation model prediction for tree sorting processes under climate change scenarios.

Time and type of pruning affect tree growth and yield in high-density olive orchards

The effect of different strategies and the time of pruning on olive vegetative-reproductive behavior was studied in a 5-year-old high-density orchard (1,250 trees ha−1, cv. ‘Ascolana tenera’). The treatments were: a) winter lateral pruning and topping, b) summer lateral pruning and winter topping, c) winter lateral pruning and summer topping and d) summer lateral pruning and topping. Selective spring pruning maintaining a conical shape of the canopy was used as the Control. Topping significantly maintained tree height recorded at the end of the 3-year trial in comparison to the Control (3.84 ± 0.45 m), in particular summer treatments maintained the final tree height at 3.0 ± 0.26 m. Summer topping and lateral pruning significantly reduced canopy volume compared to winter pruning and the Control. There was less vegetative re-sprouting in the control and, on the average, less for summer than for winter pruning in the same year of pruning. There were no significant differences between the treatments regarding the seasonal vegetative growth of 1-year-old mixed shoots. Fruit yield per tree was significantly higher with time-split pruning (part in winter and part in summer) with respect to conical-shape pruning of the canopy. Results suggest that the proposed management of pruning with winter lateral pruning and summer topping contributes to good vegetative-reproductive balance of young trees with high yield and a more compact shape.

LP-BT: A location privacy protection algorithm based on ball trees

LP-BT: A location privacy protection algorithm based on ball trees

Balanced Binary Tree Schemes for Computing Zernike Radial Polynomials

Balanced Binary Tree Schemes for Computing Zernike Radial Polynomials

An Algorithm Based on Self-balancing Binary Search Tree to Generate Balanced, Intra-homogeneous and Inter-homogeneous Learning Groups

An Algorithm Based on Self-balancing Binary Search Tree to Generate Balanced, Intra-homogeneous and Inter-homogeneous Learning Groups

A symbolic-arithmetic for teaching double-black node removal in red-black trees

A red-black (RB) tree is a data structure with red and black nodes coloration. The red and black color of nodes make up the principal component for balancing a RB tree. A balanced tree has an equal number of black nodes on any simple path. But when a black leaf node is deleted, a double-black (DB) node is formed, thus, causing a reduction in black heights and the tree becomes unbalanced. Rebalancing a RB tree with a DB node is a fairly complex process. Teaching and learning the removal of DB nodes is also challenging. This paper introduces a simplified novel method which is a symbolic-algebraic arithmetic procedure for the removal of DB nodes and the rebalancing of black heights in RB trees. This simplified approach has enhanced student learning of the DB node removal in RB trees. Feedback from students showed the learnability, workability and acceptance of the symbolic-algebraic method in balancing RB trees after a delete operation.

FPGA-Based Updatable Packet Classification Using TSS-Combined Bit-Selecting Tree

OpenFlow switches are being deployed in SDN to enable a wide spectrum of non-traditional applications. As a promising alternative to brutal force TCAMs, FPGA-based packet classification is being actively investigated. However, none of the existing FPGA designs can achieve high performance on both search and update for large-scale rule sets. To address this issue, we propose TcbTree, an FPGA-based algorithmic scheme for packet classification. Specifically, at the algorithmic side, i) a two-stage framework consisting of heterogeneous algorithms is proposed, where most rules can be mapped into several balanced trees without rule replications, ii) for the remaining few rules, a centralized TSS (Tuple Space Search) architecture together with a real-time feedback scheme is designed to enhance the efficiency of TSS search on FPGA, and iii) a tree dilution method is designed to equalize rule distribution in trees, so that the latency of tree search can be reduced. At the hardware side, i) an efficient data structure set is designed to convert tree traversal to addressing process, which breaks the constraints of limited tree depth and imbalanced node distribution, and ii) distinct from fully pipelined designs, multiple levels of parallelism are efficiently explored with multi-core, multi-search-engine and coarse-grained pipelines herein. Experimental results using ClassBench show that, with the implementation of TcbTree on FPGA, the average classification throughputs for 1k, 10k, 32k and 100k rule sets achieve 788.8 MPPS, 404.3 MPPS, 237 MPPS and 41.8 MPPS, respectively, and the update throughput for all benchmark rule sets is above 1 MUPS.

LG-Tree: An Efficient Labeled Index for Shortest Distance Search on Massive Road Networks

With the development of mobile Internet technology, the road network in the real world is becoming larger and more complex, and the real-time response to the shortest distance query has become a high requirement for many industrial applications. Many existing approaches, such as G-tree or G*-tree, have been proposed to answer such search problems, however, these approaches are not efficient enough in dealing with very large graphs. To this end, we propose a novel index called LG-tree, which partitions the large graph into sub-graphs, and then indexes these subgraphs using a balanced tree. For each leaf node of LG-tree, a Distance Inverted File (DIF) is constructed, and these DIFs preserve all the connectivity information between the border vertices on the original graph. Inspired by the state-of-the-art label methods, we propose a novel hierarchy computing approach for each border vertex of LG-tree. Based on DIF and the hierarchy of border vertices, the border vertex list for each border is established, which is convenient for us to calculate the shortest distance and path between a query vertex <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$v_{q}$ </tex-math></inline-formula> and a target vertex <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula> . Specifically, the number of levels of a vertex hierarchy increases dramatically as the graph size increases, and calculating vertex labels on a very large graph is an NP-hard problem. In order to further improve the calculation efficiency of the shortest distance between vertices, a heuristic method is proposed to limit the level of vertex hierarchy. In addition, a stage-based dynamic programming search method is proposed to divide all search situations between <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$v_{q}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula> into three cases to guarantee the efficiency of the shortest distance search. Extensive experiments are conducted to show that LG-tree and the stage-based method have better performance than the state-of-the-art approaches.

Two results about the Sackin and Colless indices for phylogenetic trees and their shapes.

The Sackin and Colless indices are two widely-used metrics for measuring the balance of trees and for testing evolutionary models in phylogenetics. This short paper contributes two results about the Sackin and Colless indices of trees. One result is the asymptotic analysis of the expected Sackin and Colless indices of tree shapes (which are full binary rooted unlabelled trees) under the uniform model where tree shapes are sampled with equal probability. Another is a short direct proof of the closed formula for the expected Sackin index of phylogenetic trees (which are full binary rooted trees with leaves being labelled with taxa) under the uniform model.

Spectral properties of balanced trees and dendrimers

We investigate the spectral properties of balanced trees and dendrimers, with a view toward unifying and improving the existing results. Here we find a semi-factorized formula for their characteristic polynomials. Afterwards, we determine their spectra via the aforementioned factors. In the end, we analyze the behavior of the energy of dendrimers and compute lower and upper bound approximations for it.

The Shape of Phylogenies Under Phase-Type Distributed Times to Speciation and Extinction

Phylogenetic trees describe relationships between extant species, but beyond that their shape and their relative branch lengths can provide information on broader evolutionary processes of speciation and extinction. However, currently many of the most widely used macro-evolutionary models make predictions about the shapes of phylogenetic trees that differ considerably from what is observed in empirical phylogenies. Here, we propose a flexible and biologically plausible macroevolutionary model for phylogenetic trees where times to speciation or extinction events are drawn from a Coxian phase-type (PH) distribution. First, we show that different choices of parameters in our model lead to a range of tree balances as measured by Aldous’ beta statistic. In particular, we demonstrate that it is possible to find parameters that correspond well to empirical tree balance. Next, we provide a natural extension of the beta statistic to sets of trees. This extension produces less biased estimates of beta compared to using the median beta values from individual trees. Furthermore, we derive a likelihood expression for the probability of observing an edge-weighted tree under a model with speciation but no extinction. Finally, we illustrate the application of our model by performing both absolute and relative goodness-of-fit tests for two large empirical phylogenies (squamates and angiosperms) that compare models with Coxian PH distributed times to speciation with models that assume exponential or Weibull distributed waiting times. In our numerical analysis, we found that, in most cases, models assuming a Coxian PH distribution provided the best fit.

Enhanced Multi-Objective A* Using Balanced Binary Search Trees

This work addresses a Multi-Objective Shortest Path Problem (MO-SPP) on a graph where the goal is to find a set of Pareto-optimal solutions from a start node to a destination in the graph. A family of approaches based on MOA* have been developed to solve MO-SPP in the literature. Typically, these approaches maintain a "frontier" set at each node during the search process to keep track of the non-dominated, partial paths to reach that node. This search process becomes computationally expensive when the number of objectives increases as the number of Pareto-optimal solutions becomes large. In this work, we introduce a new method to efficiently maintain these frontiers for multiple objectives by incrementally constructing balanced binary search trees within the MOA* search framework. We first show that our approach correctly finds the Pareto-optimal front, and then provide extensive simulation results for problems with three, four and five objectives to show that our method runs faster than existing techniques by up to an order of magnitude.

A subfunctionalisation model of gene family evolution predicts balanced tree shapes

We consider a subfunctionalisation model of gene family evolution. A family of n genes that perform z functions is represented by an n×z binary matrix Yt where a 1 in the ijth position indicates that gene i can perform function j. Yt evolves according to a continuous time Markov chain (CTMC) that represents the processes of gene duplication, coding region loss and regulatory region loss with the restriction that each function is protected by selection, meaning that each column in the matrix must contain at least one 1.We generate gene trees based on the CTMC {Yt,t⩾0}. We analyse the long-run behaviour of the model and specify the conditions where we expect gene trees to continue to grow and where we expect them to have a stable number of genes. We show that different choices of rate parameters for the processes of duplication and loss lead to different tree shapes as measured by two common tree-shape statistics: the β-statistic for measuring tree balance and the γ-statistic for assessing diversification rate. We use an extension of β that is estimated from sets of trees. This extension is less biased compared to using the average β value for individual trees.When the rate of gene duplication dominates the rate of gene loss, the process is unstable and the distribution of tree shapes is close to following the uniform ranked tree shape (URT) distribution. However, when the process is stable, gene trees are predicted to have positive values of β indicating balanced trees and negative values of γ indicating that diversification occurs more towards the root of the tree. The results of our analyses suggest that comparing the tree-shape statistics of empirical gene-trees to the predictions presented here will provide a test of the subfunctionalisation model.

Multi-criteria Optimization of a CCHP System Using Balanced Tree Growth Algorithm

Multi-criteria Optimization of a CCHP System Using Balanced Tree Growth Algorithm

Searching for Sustainable-Irrigation Issues of Clementine Orchards in the Syrian Akkar Plain: Effects of Irrigation Method and Canopy Size on Crop Coefficients, Transpiration, and Water Use with SIMDualKc Model

Citrus is one of the most valuable crops in Syria, with the largest production areas in the Tartus and Latakia provinces. Water-saving policies have been adopted to modernize the irrigation systems and increase water productivity. Following dedicated research, this study aimed to evaluate the water balance in clementine trees irrigated with diverse methods and schedules using the SIMDualKc software model. Two experiments are reported: one with 10–14 years old trees irrigated with different methods (2007−2011) and the other with the same trees but now 18−20 years old, irrigated with different schedules (2015−2019). The SIMDualKc model successfully simulated the soil water contents measured in the various field plots, with root mean square error values lower than 0.004 m3 m−3 and modeling efficiencies up to 0.83. The model-calibrated standard basal crop coefficients (Kcb) were approximately constant throughout all growing stages, assuming values of 0.54−0.55 for the mature trees having smaller height (h) and fraction of ground cover (fc), and 0.64 for older trees with larger canopies, i.e., larger h and fc. With drip irrigation, single Kc had a higher value (1.14) at the end, non-growing, and initial stages, and a lower value (0.75–0.76) during mid-season (Kc mid), because precipitation was lesser then, contributing less to soil evaporation. On the other hand, Kc values were nearly constant with micro-sprinkler and surface irrigation techniques because the ground was fully wetted. The Kcb values derived from the fraction of ground cover and height (A&amp;P approach) were similar to those obtained from the model, thus showing that the A&amp;P approach represents a practical alternative to estimate Kcb in the practice of irrigation management. The soil water balance further revealed a large weight of the terms corresponding to the non-beneficial water consumption and non-consumptive water use when the fraction wetted was large and the application efficiencies were low. These terms were reduced, namely, evaporation losses when drip irrigation was used. This study, thus, provides a valuable tool for improving the irrigation management, water saving, and water productivity of Syrian citrus production systems.