Compact Tree Research Articles

Different covering numbers of compact tree ideals

Different covering numbers of compact tree ideals

Characterising trees and hyperbolic spaces by their boundaries

We use the language of proper CAT(-1) spaces to study thick, locally compact trees, the real, complex and quaternionic hyperbolic spaces and the hyperbolic plane over the octonions. These are rank 1 Euclidean buildings, respectively rank 1 symmetric spaces of non-compact type. We give a uniform proof that these spaces may be reconstructed using the cross ratio on their visual boundary, bringing together the work of Tits and Bourdon.

Label ranking oblique trees

Label ranking studies the problem of learning a preference model that maps instances to rankings over a finite set of predefined class labels. The training data used to solve this problem consists of instances labeled with rankings. Since these rankings are often incomplete, models need to be able to deal with missing information in the class labels to be more useful in practice. Several decision tree models have been proposed to learn from incomplete rankings, mainly using axis-parallel decision nodes, which is the standard approach for decision tree induction. In contrast to this strategy, this present work introduces a method for learning oblique decision trees for the label ranking problem, as they have been shown to improve performance in the standard classification scenario. Our experimentation shows that this method offers several advantages over the current decision tree model. Not only does it generate more compact tree structures, but it is also shown to achieve outstandingly better results for complete rankings and in cases with a low percentage of missing labels. Moreover, the proposed method is faster in the largest datasets than the current decision tree model.

Production and verification of novel Osmanthus hybrids

Osmanthus fragrans Lour. is prized for its fragrant, cool-season blooms, smooth leaves, and compact tree form; however, the species is limited in production and use to USDA Hardiness Zones 7 and higher. Increasing the total amount of genetic variability available for evaluation, selection, and breeding is foundational to the development of novel Osmanthus cultivars with increased cold-hardiness and improved ornamental characteristics such as high rooting rates, faster growth, fragrant flowers, and an evergreen or semi-evergreen habit. Hybridization among Osmanthus species should generate novel phenotypes and allow trait introgression among populations and breeding lines. The objectives of this study were to produce, verify, and evaluate Osmanthus hybrids by making controlled and open-pollinated crosses among Osmanthus species, using SSR markers to determine parentage of cross progeny, and comparing flowering, leaf shape, and form of hybrids offspring with parents. Fifty-eight of 66 progenies (88%) were assigned paternity at the 95% confidence level or above and 47 progenies (71%) were assigned paternity at the 99% confidence level. Novel Osmanthus hybrids were produced including O. armatus × O. fortunei, O. armatus × O. heterophyllus, and O. armatus × O. fragrans. Open-pollinated families increased in height an average of 204% and 159% per year in the first and second growing seasons, respectively. Male flower type was significantly associated with progeny flower type (χ2 = 17.5, p < 0.0001) while leaf margin was not associated with cross family (χ2 = 0.83, p = 0.84). Evaluation of more Osmanthus accessions and subsequent hybridizations will be necessary to introgress favorable genes and generate the variation necessary to expand the genus into new markets.

Banach spaces of continuous functions without norming Markushevich bases

AbstractWe investigate the question whether a scattered compact topological space K such that has a norming Markushevich basis (M‐basis, for short) must be Eberlein. This question originates from the recent solution, due to Hájek, Todorčević and the authors, to an open problem from the 1990s, due to Godefroy. Our prime tool consists in proving that does not embed in a Banach space with a norming M‐basis, thereby generalising a result due to Alexandrov and Plichko. Subsequently, we give sufficient conditions on a compact K for not to embed in a Banach space with a norming M‐basis. Examples of such conditions are that K is a zero‐dimensional compact space with a P‐point, or a compact tree of height at least . In particular, this allows us to answer the said question in the case when K is a tree and to obtain a rather general result for Valdivia compacta. Finally, we give some structural results for scattered compact trees; in particular, we prove that scattered trees of height less than ω2 are Valdivia.

Insights on the stem elongation of spur-type bud sport mutant of ‘Red Delicious’ apple

The decreased capacity of auxin-, CTK-, and BR-mediated cell division and cell enlargement pathways, combined with the enhanced capacity of GA and ETH-, JA-, ABA-, SA-mediated stress-resistant pathways were presumed to be the crucial reasons for the formation of spur-type 'Red Delicious' mutants. Vallee Spur', which exhibit short internodes and compact tree shape, is the fourth generation of the spur-type bud sport mutant of 'Red Delicious'. However, the underlying molecular mechanism of these properties remains unclear. Here, comparative phenotypic, full-length transcriptome and phytohormone analyses were performed between 'Red Delicious' (NSP) and 'Vallee Spur' (SP). The new shoot internode length of NSP was ˃ 1.53-fold higher than that of the SP mutant. Cytological analysis showed that the stem cells of the SP mutant were smaller and more tightly arranged relative to the NSP. By Iso-Seq, a total of 1426 differentially expressed genes (DEGs) were detected, including 808 upregulated and 618 downregulated genes in new shoot apex with 2 leaves of the SP mutant. Gene expressions involved in auxin, cytokinin (CTK), and brassinosteroid (BR) signal transduction were mostly downregulated in the SP mutant, whereas those involved in gibberellin (GA), ethylene (ETH), jasmonate (JA), ABA, and salicylic acid (SA) signal transduction were mostly upregulated. The overall thermogram analysis of hormone levels in the shoot apex carrying two leaves detected by LC-MS/MS absolute quantification showed that the levels of IAA-Asp, IAA, iP7G, OPDA, and 6-deoxyCS were significantly upregulated in the SP mutant, while the remaining 28 hormones were significantly downregulated. It is speculated that the decreased capacity of auxin, CTK, and BR-mediated cell division and cell enlargement pathways is crucial for the formation of the SP mutant. GA and stress-resistant pathways of ETH, JA, ABA, and SA also play vital roles in stem elongation. These results highlight the involvement of phytohormones in the formation of stem elongation occurring in 'Red Delicious' spur-type bud sport mutants and provide information for exploring its biological mechanism.

LCTree-Based Approach for Mining Frequent Items in Real-Time.

With the increase of real-time stream data, knowledge discovery from stream data becomes more and more important, which requires an efficient data structure to store transactions and scan sliding windows once to discover frequent itemsets. We present a new method named Linking Compact Tree (LCTree). We designed an algorithm by using an improved data structure to create objective tree, which can find frequent itemsets with linear complexity. Secondly, we can merge items in sliding windows by one scan with Head Linking List data structure. Third, by implementing data structure of Tail Linking List, we can locate the obsolete nodes and remove them easily. Finally, LCTree is able to find all exact frequent items in data stream with reduced time and space complexity by using such a linear data structure. Experiments on datasets with different sizes and types were conducted to compare the proposed LCTree technique with well-known frequent item mining methods including Cantree, FP-tree, DSTree, CPSTree, and Gtree. The results of experiments show presented algorithm has better performance than other methods, and also confirm that it is a promising solution for detecting frequent item sets in real time applications.

ASSESSMENT AND MONITORING OF VILLAGE FOREST RESOURCES

The area of village forest (0.27 million hectare) is very limited in comparison with government forest land (2.14 million hectare). But the village woodlot area contributes 85% of the total consumption and the remaining 15% is contributed by government forest land. Need for correct assessment and monitoring is discussed. The main objective of this paper is to recommend appropriate sampling design for correct assessment of village forest resources. A case study was undertaken in the district of Chittagong located at the south-east corner of Bangladesh. A study population of 900 households was formed consisting of 14 rural thanas in the district. The seven parameters defined under five variables were calculated for complete enumeration. The parameters were estimated through Cluster Sampling, Two Stage Sampling and Stratified Two Stage Sampling (Self-Weight) taking 250 sample households in each method. The estimates were compared with the enumerated values on the basis of percentage standard error, percentage accuracy, percentage bias and 95% confidence interval. Stratified Two Stage Sampling (Self-Weighted) provided the best estimates for true total homestead area (78.4 ha for 97 ha), for true total compact tree garden area (49.6 ha for 49 ha), for true total volume of trees (9432.2 m3 for 9490 m3 ), for true total number of bamboos (53546 for 53229), for volume of compact trees per hectare (164.9m3 for 172 m3) and true number of households with bamboo plantation (413 for 407). Stratified Two Stage Sampling (Self-Weighted) was found to be a suitable technique and was recommended to apply as field sampling design for correct assessment of village forest resources. A continuous monitoring system was also suggested.

Phenotype and mechanism analysis of plant dwarfing in pear regulated by abscisic acid

Close planting of dwarf varieties is currently the main cultivation direction for pear trees, and the screening of excellent dwarf varieties is an important goal for breeders. In this study, the dwarfing pear variety ‘601D’ and its vigorous mutant ‘601T’ were used to show their biological characteristics and further explore the dwarfing mechanism in ‘601D’. The biological characteristics showed that ‘601D’ had a shorter internode length, a shorter and more compact tree body, thicker and broader leaves, lower stomata density, larger stomata size (dimension), and higher photosynthetic capacity. The biological characteristics of ‘601T’ showed notable contrasts. The results of endogenous hormone tests indicated that the contents of abscisic acid (ABA), ABA-glucosyl ester, and GA4 were higher in ‘601D’, but the trans-zeatin content was lower. By transcriptomic analysis, significant differences were found in the biosynthetic and metabolic pathways of ABA. Related transcription factors such as bHLH, WRKY, and homeobox also participated in the regulation of plant dwarfing. We therefore examined three hormones with obvious differences with ‘601T’, and found that only ABA could induce ‘601T’ to return to a dwarfing plant phenotype. Therefore, we conclude that the dwarfing of ‘601D’ is caused by an excessive accumulation of ABA. This study provides a new theoretical basis for breeding dwarf varieties.

Weakly Corson compact trees

We introduce and study a new topology on trees, that we call the countably coarse wedge topology. Such a topology is strictly finer than the coarse wedge topology and it turns every chain complete, rooted tree into a Fr\'echet--Urysohn, countably compact topological space. We show the r\^{o}le of such topology in the theory of weakly Corson and weakly Valdivia compacta. In particular, we give the first example of a compact space $T$ whose every closed subspace is weakly Valdivia, yet $T$ is not weakly Corson. This answers a question due to Ond\v{r}ej Kalenda.

Homotopy Hubbard trees for post-singularly finite exponential maps

AbstractWe extend the concept of a Hubbard tree, well established and useful in the theory of polynomial dynamics, to the dynamics of transcendental entire functions. We show that Hubbard trees in the strict traditional sense, as invariant compact trees embedded in $\mathbb {C}$ , do not exist even for post-singularly finite exponential maps; the difficulty lies in the existence of asymptotic values. We therefore introduce the concept of a homotopy Hubbard tree that takes care of these difficulties. Specifically for the family of exponential maps, we show that every post-singularly finite map has a homotopy Hubbard tree that is unique up to homotopy, and that post-singularly finite exponential maps can be classified in terms of homotopy Hubbard trees, using a transcendental analogue of Thurston’s topological characterization theorem of rational maps.

Exploring the effects of the spatial arrangement and leaf area density of trees on building wall temperature

As single urban landscape elements, buildings and trees have important impacts on the urban microthermal environment. Thus, the interaction between trees and buildings requires more thorough investigation. In this study, typical residential districts in Nanjing, Jiangsu Province, China, are selected as the research area, and different evaluation indexes are established to explore the influence of trees on building surface temperature. ENVI-met simulations of the different established scenarios based on the spatial configuration analysis of buildings and trees in the study area were performed to determine the influence of the distance between individual trees, the distance between trees and walls (spatial position) and the leaf area density (LAD) value (attribute) of trees on the surface temperature of buildings. The results showed that 1) the best wall cooling times in the east, west, south and north were 12:00, 17:00, 14:00 and 16:00, respectively; 2) the best cooling effect was achieved at vertical heights of 12–14 m; 3) a compact tree arrangement reduced the shortwave radiation that reached the wall during the daytime by a large extent and thus had the best cooling effect in all scenes; and 4) trees with an LAD of 1.1 led to 20 °C greater cooling for a brick in one day than trees with an LAD of 0.3. This research attempts to reveal the influence of trees on building surface temperature and provide the corresponding decision basis for tree planning in residential areas to reduce the impact of urban heat pressure on human health and energy consumption.

Initial performance of ‘Gem’ avocado trees in the Central-Western region of São Paulo State

The introduction of new avocado cultivars into producing countries of the Southern Hemisphere may extend the offer period of fresh fruit for export. The ‘Gem’ (‘3-29-5’) avocado is known for extending the marketing period of ‘Hass’-like avocados. This study aimed to evaluate the horticultural performance of ‘Gem’ avocado trees between the 4th and 6th years after planting (2016-2018), in a commercial orchard in the Central-Western region of the State of São Paulo, Brazil. ‘Gem’ avocado trees grafted onto seedling rootstocks were evaluated regarding tree size, shoot growth, flowering, and fruit yield, quality and maturation. In the evaluated biennium, the trees showed a strong upright growth habit and compact tree size. Flowering occurred mainly in indeterminate inflorescences. Fruit yield varied between 106.89 to 116.89 kg tree-1, and 75-91% of the fruit classified within size counts 12 (306 to 365 g/fruit) to 18 (211 to 235 g/fruit), and reached physiological maturity in late June, but could be picked until October, i.e, four to eight months later than ‘Hass’. ‘Gem’ is a new alternative for extending fruit offer of late-maturity avocado cultivars and allowing higher profit to the farmers.

Faster repetition-aware compressed suffix trees based on Block Trees

The suffix tree is a fundamental data structure in stringology, but its space usage, though linear, is an important problem in applications like Bioinformatics. We design and implement a new compressed suffix tree (CST) targeted to highly repetitive texts, such as large genomic collections of the same species. Our first contribution is to enhance the Block Tree, a data structure that captures the repetitiveness of its input sequence, to represent the topology of trees with large repeated subtrees. Our so-called Block-Tree Compressed Topology (BT-CT) data structure augments the Block Tree nodes with data that speeds up tree navigation. Our Block-Tree CST (BT-CST), in turn, uses the BT-CT to compress the topology of the suffix tree, and also replaces the sampling of the suffix array and its inverse with grammar- and/or Block-Tree-based representations of those arrays.Our experimental results show that BT-CTs reach navigation speeds comparable to compact tree representations that are insensitive to repetitiveness, while using 2–10 times less space on the topologies of the suffix trees of repetitive collections. Our BT-CST is slightly larger than previous repetition-aware suffix trees based on grammar-compressed topologies, but outperforms them in time, often by orders of magnitude.

MapTree

In this paper we propose an approach for computing multiple high-quality near-isometric dense correspondences between a pair of 3D shapes. Our method is fully automatic and does not rely on user-provided landmarks or descriptors. This allows us to analyze the full space of maps and extract multiple diverse and accurate solutions, rather than optimizing for a single optimal correspondence as done in most previous approaches. To achieve this, we propose a compact tree structure based on the spectral map representation for encoding and enumerating possible rough initializations, and a novel efficient approach for refining them to dense pointwise maps. This leads to a new method capable of both producing multiple high-quality correspondences across shapes and revealing the symmetry structure of a shape without a priori information. In addition, we demonstrate through extensive experiments that our method is robust and results in more accurate correspondences than state-of-the-art for shape matching and symmetry detection.

Metabolic Profiling of Hybrids Generated from Pummelo and Citrus latipes in Relation to Their Attraction to Diaphorina citri, the Vector of Huanglongbing.

The citrus industry at present is severely affected by huanglongbing disease (HLB). HLB is caused by the supposed bacterial pathogen “Candidatus Liberibacter asiaticus” and is transmitted by the insect vector, the Asian citrus psyllid, Diaphorina citri Kuwayama. Developing new citrus hybrids to improve HLB management is much needed. In this study, we investigated the metabolomic profiles of three new hybrids produced from the cross of C2-5-12 Pummelo (Citrus maxima (L.) Osbeck) × pollen from Citrus latipes. The hybrids were selected based on leaf morphology and seedling vigor. The selected hybrids exhibited compact and upright tree architecture as seen in C. latipes. Hybrids were verified by simple sequence repeat markers, and were subjected to metabolomic analysis using gas chromatography-mass spectrometry. The volatile organic compounds (VOCs) and polar metabolites profiling also showed that the new hybrids were different from their parents. Interestingly, the levels of stored VOCs in hybrid II were higher than those observed in its parents and other hybrids. The level of most VOCs released by hybrid II was also higher than that released from its parents. Additionally, the preference assay showed that hybrid II was more attractive to D. citri than its parents and other hybrids. The leaf morphology, compact and upright architecture of hybrid II, and its attraction to D. citri suggest that it could be used as a windbreak and trap tree for D. citri (double duty), once its tolerance to HLB disease is confirmed. Our results showed that metabolomic analysis could be successfully used to understand the biochemical mechanisms controlling the interaction of D. citri with its host plants.

Optimal skeleton and reduced Huffman trees

A skeleton Huffman tree is a Huffman tree from which all full subtrees of depth h≥1 have been pruned. Skeleton Huffman trees are used to save storage and enhance processing time in several applications such as decoding, compressed pattern matching and wavelet trees for random access. A reduced skeleton tree prunes the skeleton Huffman tree further to an even smaller tree. The resulting more compact trees can be used to further enhance the time and space complexities of the corresponding algorithms. However, it is shown that the straightforward ways of basing the constructions of a skeleton tree as well as that of a reduced skeleton tree on a canonical Huffman tree do not necessarily yield the least number of nodes. New algorithms for achieving such trees are given.

A Novel High Gain Wideband MIMO Antenna for 5G Millimeter Wave Applications

A compact tree shape planar quad element Multiple Input Multiple Output (MIMO) antenna bearing a wide bandwidth for 5G communication operating in the millimeter-wave spectrum is proposed. The radiating element of the proposed design contains four different arcs to achieve the wide bandwidth response. Each radiating element is backed by a 1.57 mm thicker Rogers-5880 substrate material, having a loss tangent and relative dielectric constant of 0.0009 and 2.2, respectively. The measured impedance bandwidth of the proposed quad element MIMO antenna system based on 10 dB criterion is from 23 GHz to 40 GHz with a port isolation of greater than 20 dB. The measured radiation patterns are presented at 28 GHz, 33 GHz and 38 GHz with a maximum total gain of 10.58, 8.87 and 11.45 dB, respectively. The high gain of the proposed antenna further helps to overcome the atmospheric attenuations faced by the higher frequencies. In addition, the measured total efficiency of the proposed MIMO antenna is observed above 70% for the millimeter wave frequencies. Furthermore, the MIMO key performance metrics such as Mean Effective Gain (MEG) and Envelope Correlation Coefficient (ECC) are analyzed and found to conform to the required standard of MEG < 3 dB and ECC < 0.5. A prototype of the proposed quad element MIMO antenna system is fabricated and measured. The experimental results validate the simulation design process conducted with Computer Simulation Technology (CST) software.

Frechet distance on the set of compact trees

We introduce a counterpart of the Frechet distance for the rooted trees in a metric space. Some properties and possible generalizations of this distance are discussed.

Muscarinic Modulation of Morphologically Identified Glycinergic Neurons in the Mouse PreBötzinger Complex.

The cholinergic system plays an essential role in central respiratory control, but the underlying mechanisms remain elusive. We used whole-cell recordings in brainstem slices from juvenile mice expressing enhanced green fluorescent protein (EGFP) under the control of the glycine transporter type 2 (GlyT2) promoter, to examine muscarinic modulation of morphologically identified glycinergic neurons in the preBötzinger complex (preBötC), an area critical for central inspiratory rhythm generation. Biocytin-filled reconstruction of glycinergic neurons revealed that the majority of them had few primary dendrites and had axons arborized within their own dendritic field. Few glycinergic neurons had axon collaterals extended towards the premotor/motor areas or ran towards the contralateral preBötC, and had more primary dendrites and more compact dendritic trees. Spontaneously active glycinergic neurons fired regular spikes, or less frequently in a “burst-like” pattern at physiological potassium concentration. Muscarine suppressed firing in the majority of regular spiking neurons via M2 receptor activation while enhancing the remaining neurons through M1 receptors. Interestingly, rhythmic bursting was augmented by muscarine in a small group of glycinergic neurons. In contrast to its heterogeneous modulation of glycinergic neuronal excitability, muscarine generally depressed inhibitory and excitatory synaptic inputs onto both glycinergic and non-glycinergic preBötC neurons, with a stronger effect on inhibitory input. Notably, presynaptic muscarinic attenuation of excitatory synaptic input was dependent on M1 receptors in glycinergic neurons and on M2 receptors in non-glycinergic neurons. Additional field potential recordings of excitatory synaptic potentials in the M2 receptor knockout mice indicate that glycinergic and non-glycinergic neurons contribute equally to the general suppression by muscarine of excitatory activity in preBötC circuits. In conclusion, our data show that preBötC glycinergic neurons are morphologically heterogeneous, and differ in the properties of synaptic transmission and muscarinic modulation in comparison to non-glycinergic neurons. The dominant and cell-type-specific muscarinic inhibition of synaptic neurotransmission and spiking may contribute to central respiratory disturbances in high cholinergic states.