Asymptotic results on Hoppe trees and their variations

2020 ◽  
Vol 57 (2) ◽  
pp. 441-457
Author(s):  
Ella Hiesmayr ◽  
Ümit Işlak
Keyword(s):  
Rooted Tree ◽  
Random Tree ◽  
Equal Probability ◽  
Asymptotic Results ◽  
Tree Model ◽  
Recursive Tree ◽  
Weighted Trees ◽  
Number Of Leaves ◽  
Recursive Trees ◽  
Number Of Branches

AbstractA uniform recursive tree on n vertices is a random tree where each possible $(n-1)!$ labelled recursive rooted tree is selected with equal probability. We introduce and study weighted trees, a non-uniform recursive tree model departing from the recently introduced Hoppe trees. This class generalizes both uniform recursive trees and Hoppe trees, providing diversity among the nodes and making the model more flexible for applications. We analyse the number of leaves, the height, the depth, the number of branches, and the size of the largest branch in these weighted trees.

scholarly journals Learning to Embed Sentences Using Attentive Recursive Trees

2019 ◽  
Vol 33 ◽  
pp. 6991-6998
Author(s):  
Jiaxin Shi ◽  
Lei Hou ◽  
Juanzi Li ◽  
Zhiyuan Liu ◽  
Hanwang Zhang
Keyword(s):  
Deep Learning ◽  
State Of The Art ◽  
The State ◽  
Feature Representation ◽  
Tree Structure ◽  
Tree Model ◽  
Training Strategy ◽  
Recursive Tree ◽  
Recursive Trees ◽  
Embedding Methods

Sentence embedding is an effective feature representation for most deep learning-based NLP tasks. One prevailing line of methods is using recursive latent tree-structured networks to embed sentences with task-specific structures. However, existing models have no explicit mechanism to emphasize taskinformative words in the tree structure. To this end, we propose an Attentive Recursive Tree model (AR-Tree), where the words are dynamically located according to their importance in the task. Specifically, we construct the latent tree for a sentence in a proposed important-first strategy, and place more attentive words nearer to the root; thus, AR-Tree can inherently emphasize important words during the bottomup composition of the sentence embedding. We propose an end-to-end reinforced training strategy for AR-Tree, which is demonstrated to consistently outperform, or be at least comparable to, the state-of-the-art sentence embedding methods on three sentence understanding tasks.

Unequal Probability Scheme for Fruit Count in a Guava Tree

2016 ◽  
Vol 3 (4) ◽  
Author(s):  
R. C. BHARATI
Keyword(s):  
Cross Sectional Area ◽  
Equal Probability ◽  
Sampling Scheme ◽  
Research Station ◽  
Sectional Area ◽  
Cross Sectional ◽  
Unequal Probability ◽  
Selection Probabilities ◽  
Horticultural Research ◽  
Number Of Branches

Data on fruit count corresponding to primary, secondary and tertiary branches of a randomly selected guava CV. Allahabad Safeda were recorded from the guava orchard of Horticultural Research Station, Birauli. The proposed sampling scheme in which the selection probabilities are based on length of braches between two forking points was compared with equal probability(PE), probability proportional to the number of branches(PPN), probability proportional to the cross sectional area (PPA) and probability proportional to volume (PPV) method of sampling and found to be more efficient.

Collection, characterization, conservation and utilization of Cordia sinensis Lam.: An underexploited multipurpose fruit species of hot arid regions

2020 ◽  
pp. 1-10
Author(s):  
Rahul Dev ◽  
M. Sureshkumar ◽  
Sushil Kumar ◽  
K. Venkatesan ◽  
Traloki Singh ◽  
...  
Keyword(s):  
Arid Regions ◽  
Morphological Data ◽  
Future Research ◽  
Fruit Species ◽  
Fruit Samples ◽  
Maximum Coefficient ◽  
Number Of Leaves ◽  
Collar Diameter ◽  
Scrub Forests ◽  
Number Of Branches

Abstract Cordia sinensis, locally known as ‘Goondi’ in India, is an underexploited multipurpose fruit species found in hot arid regions that is well adapted to drought, salt and hot conditions. The present study was undertaken to collect fruit samples from different locations in the Kachchh region of Gujarat, India, and to determine their field establishment for characterization, conservation and utilization. The maximum distribution of the species was observed in Bhuj (45%) and Mandvi (25%). Field boundaries (35%) and scrub forests (30%) had greater frequencies, whereas backyards had rarer frequencies (10%). The species most commonly occurred on levelled topography (60%) with a soil pH in the range of 8–8.5 (63%). Morphological data of three-year-old plants in the field gene bank showed a maximum coefficient of variation in the number of leaves per plant (66.6), followed by the number of branches per plant (45.62) and collar diameter (27.69). Wide variations were recorded in plant height (121.67–212 cm), spread (118–223 cm2) and the number of branches per plant (6–24.33). Specific accessions were identified for fodder (CBCG-12, CBCG-13 and CBCG-16), early flowering and fruiting (CBCG-12, CBCG-13 and CBCG-14), easier propagation by seeds (CBCG-12 and CBCG-13) and salt tolerance (CBCG-15 and CBCG-16). Preliminary findings and information provided about this species' utilization and other aspects might be useful for future research on its domestication, sole plantation and conservation aspects, improving the exploitation of this species by present and future generations.

scholarly journals Adaçayı ve Dağ Çayında Tuz Stresi Üzerine Selenyum Uygulamalarının Etkileri

2019 ◽  
Vol 7 (sp2) ◽  
pp. 29
Author(s):  
Mahmut Çamlıca ◽  
Gülsüm Yaldız ◽  
Ferit Özen ◽  
Abdurrahman Başol ◽  
Halit Aşkın
Keyword(s):  
Plant Height ◽  
Root Length ◽  
Root Weight ◽  
Fresh Leaf ◽  
Leaf Weight ◽  
Number Of Leaves ◽  
Shoot Weight ◽  
Different Doses ◽  
Number Of Branches ◽  
Fresh Root

Sage and mountain sage belong to Lamiaceae family which have commercial importance from medicinal and aromatic plants in Turkey. The aim of this study was to evaluate the effects of different doses of selenium in salinity conditions on the morphological characteristics of sage (Salvia officinalis L.) and mountain tea (Sideritis sp.). Four different doses of selenium (5, 10, 20, 40 mg/l) were applied in without salinity (0) and salinity (250 mM NaCl/l) medium. The experiment was carried out in the split plot design with three replications in the climate chamber room of the department of field crops. When the examined properties were evaluated; plant height changed between 15.56-23.85 cm, number of branches 10.50-12.78 number/plant, number of leaves 52.78-92.00 number/plant, fresh leaf weight 2.48-7.51 g/plant, dry leaf weight 0.48-3.32 g/plant, fresh root weight 1.52-7.16 g/plant, dry root weight 0.19-1.24 g/plant, root length 26.18-36.07 cm, fresh shoot weight of 1.13-7.15 g/plant and dry shoot weight 0.13-0.38 g/plant. In mountain tea, the properties were determined for plant height as 3.26-5.93 cm, for number of branches as 2.50-6.33 number/plant, for number of leaves as 28.22-91.14 number/plant, for fresh and dry leaf weights as 2.42-11,03 and 0.45-1.91 g/plant, for fresh and dry root weights as 0.71-3.97 and 0.18-0.74 g/plant, for root length as 14.78-33.26 cm, for fresh and dry shoot weights as 0.29-2.28 and 0.12-0.41 g/plant were determined. As a result of this study, 5 mg/l selenium application in salinity conditions in both plants has reached high values in terms of fresh leaf weights. In addition to this, it was found that selenium applications in salinity conditions had positive effects on dry leaf weight in sage and fresh root and fresh shoot weights in mountain tea. As a result of correlation analysis, positive correlations were found between dry leaf weight and other characteristics especially in mountain tea in terms of traits examined in both plants.

scholarly journals Pertumbuhan dan Hasil Kedelai di Lahan Rawa Lebak dengan Aplikasi Pupuk Hayati dan Kimia

2018 ◽  
Vol 45 (3) ◽  
pp. 263
Author(s):  
Endriani , ◽  
Munif Ghulamahdi ◽  
Dan Eko Sulistyono
Keyword(s):  
Glycine Max ◽  
Soil Fertility ◽  
Block Design ◽  
Randomized Block Design ◽  
National Production ◽  
Glycine Max L ◽  
Number Of Leaves ◽  
Four Levels ◽  
P Fertilizers ◽  
Number Of Branches

Soybean (Glycine max L. Merrill) demand is high in Indonesia, however national production is low, therefore improving productivity is important. The research was aimed to determine the effect of application of biofertilizer containing N- fixing and P- solubilizing bacteria on the growth and production of soybean in lowland swamp. The experiment was conducted  at  Labuhan Ratu VI Village, District of Labuhan Ratu, East Lampung Regency from September to December 2014. The experiment was arranged in factorial randomized block design with three replications. N and P fertilizers were applied in four levels. Doses of N were 0, 11.25, 22.50, 33.75 kg ha-1, doses of P were 0, 36, 72, 108 P2O5 kg ha-1, in combination with and without biofertilizer application. The results showed that interaction between biofertilizer and N significantly affected number of branches and number of leaves at maximum vegetative phase. The influence of three types of fertilizer had no significant effect on the productivity of soybean in lowland swamp with soil pH of 7.0 and medium soil fertility. It is recommended to apply Biofertilizer + 11,25 kg N ha-1 + 36 kg P2O5 ha-1 to obtain high soybean production in lowland swamp area.<br /><br />Keywords: nitrogen, phosphate, productivity, soil fertility<br /><br />

scholarly journals Labels distance in bucket recursive trees with variable capacities of buckets

2021 ◽  
Vol 13 (2) ◽  
pp. 413-426
Author(s):  
S. Naderi ◽  
R. Kazemi ◽  
M. H. Behzadi
Keyword(s):  
Partial Differential Equations ◽  
Probability Distribution ◽  
Differential Equations ◽  
Generating Function ◽  
Generating Functions ◽  
Function Approach ◽  
Closed Formula ◽  
Tree Model ◽  
Partial Differential ◽  
Recursive Trees

Abstract The bucket recursive tree is a natural multivariate structure. In this paper, we apply a trivariate generating function approach for studying of the depth and distance quantities in this tree model with variable bucket capacities and give a closed formula for the probability distribution, the expectation and the variance. We show as j → ∞, lim-iting distributions are Gaussian. The results are obtained by presenting partial differential equations for moment generating functions and solving them.

scholarly journals EFFECT OF DIPPING IN GIBBERLLIC ACID AND SPRAYING NUTRIENT SOLUTION AGRO LEAF ON SOME VEGETATIVE GROWTH AND YIELD OF JERUSALUM ARTICHOKE.

2016 ◽  
Vol 47 (4) ◽  
Author(s):  
Sadik & et al.
Keyword(s):  
Leaf Area ◽  
Nutrient Solution ◽  
Vegetative Growth ◽  
Dry Weight ◽  
Factorial Experiment ◽  
Growth And Yield ◽  
Control Treatment ◽  
Highest Weight ◽  
Number Of Leaves ◽  
Number Of Branches

This study was conducted in experimental fields, Department of Horticulture, University of Bagdad, in Abu-Graib  during season 2011-2012 for jerusalum artichoke. This study was included the effect of dipping tubers in three concentrations of GA3(2.5,5,10g/l) (G1,G2,G3),as well as to control treatment (G0), and spraying nutrient solution Agro leaf A1 (8g/l), as well as to control treatment (A0). This study was made by using Factorial experiment (4*2) within the design RCBD with three replicates. Results could be summarized as follows: G3A0 increased field emergence (12.00 day), G2A0 increased percentage of germination (99.33%) and G2A1 increased number of branches (4.60 stem.plant-1) but the treatment G1A1gave highest rate for number of leaves, leaf area, guide of leaf area, dry weight of the vegetative parts and dry weight of 100gm tubers as(4495.10 leaf.plant-1, 2246.20 dsm2, 99.84, 922.40g, 24.00g.) respectively. The treatments gave significant differences quantity yield, so treatment G3A0 gave highest weight of the tubers as(45.55g.) but the treatment G3A1 gave highest number of the tubers as(68.00 tuber.plant-1 ) and highest yield of plant as (2890g/plant).

Tree-dependent extreme values: the exponential case

1990 ◽  
Vol 27 (01) ◽  
pp. 124-133 ◽  
Author(s):  
Vijay K. Gupta ◽  
Oscar J. Mesa ◽  
E. Waymire
Keyword(s):  
Branching Process ◽  
Extreme Values ◽  
Rooted Tree ◽  
Domain Of Attraction ◽  
Extreme Value Distribution ◽  
Value Theory ◽  
Extreme Value ◽  
Extinction Time ◽  
Brownian Excursion ◽  
Weighted Trees

The length of the main channel in a river network is viewed as an extreme value statistic L on a randomly weighted binary rooted tree having M sources. Questions of concern for hydrologic applications are formulated as the construction of an extreme value theory for a dependence which poses an interesting contrast to the classical independent theory. Equivalently, the distribution of the extinction time for a binary branching process given a large number of progeny is sought. Our main result is that in the case of exponentially weighted trees, the conditional distribution of n–1/2 L given M = n is asymptotically distributed as the maximum of a Brownian excursion. When taken with an earlier result of Kolchin (1978), this makes the maximum of the Brownian excursion a tree-dependent extreme value distribution whose domain of attraction includes both the exponentially distributed and almost surely constant weights. Moment computations are given for the Brownian excursion which are of independent interest.

scholarly journals On the Zagreb Index of Random Recursive Trees

2011 ◽  
Vol 48 (04) ◽  
pp. 1189-1196 ◽  
Author(s):  
Qunqiang Feng ◽  
Zhishui Hu
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Asymptotic Normality ◽  
Random Process ◽  
Central Limit ◽  
Topological Indices ◽  
Zagreb Index ◽  
Martingale Central Limit Theorem ◽  
Recursive Tree ◽  
Recursive Trees

We investigate the Zagreb index, one of the topological indices, of random recursive trees in this paper. Through a recurrence equation, the first two moments ofZn, the Zagreb index of a random recursive tree of sizen, are obtained. We also show that the random process {Zn− E[Zn],n≥ 1} is a martingale. Then the asymptotic normality of the Zagreb index of a random recursive tree is given by an application of the martingale central limit theorem. Finally, two other topological indices are also discussed in passing.

scholarly journals Studies on the Variability and Combining Ability for Improved Growth and Yield of Local Eggplant Genotypes (Solanum melongena L.)

2016 ◽  
Vol 8 (2) ◽  
pp. 226-231 ◽  
Author(s):  
Ndueso Michael AKPAN ◽  
Peter OGBONNA ◽  
Vincent ONYIA ◽  
Emeka OKECHUKWU ◽  
Agatha ATUGWU ◽  
...  
Keyword(s):  
Combining Ability ◽  
Solanum Melongena ◽  
Principal Component ◽  
Fruit Yield ◽  
Growth And Yield ◽  
Days To Flowering ◽  
Genetic Components ◽  
Filial Generation ◽  
Number Of Leaves ◽  
Number Of Branches

Ten genotypes of eggplant (Solanum melongena L.) comprising of four genitors and six hybrids generated using diallel crosses were evaluated to estimate the magnitude of genetic variability,  their general combing ability (GCA) and specific combining ability (SCA) for improved growth and yield of eggplant. The results obtained showed a significant (p ≤ 0.05) difference among the genotypes in all the traits studied.  The highest fruit yield per plant and fruit yield per hectare was obtained in ‘Yalo’ × ‘K3’ combination, with 1.77 kg per plant and 50.50 tonnes per hectare, respectively. The cluster analysis grouped the studied genotypes into three and six clusters for genitors alone and genitors with first filial generation (F1s), respectively. Principal component analysis showed that number of leaves, number of fruits and number of branches per plant contributed more to the total variations observed in the eggplant populations. Significant GCA and SCA effect were obtained for most characters analyzed, indicating the importance of both additive and non-additive genetic components. The genotype ‘Iyoyo’ was the best general combiner in regard to days to flowering and number of fruits per plant. ‘Yalo’ was the best general combiner in fruits’ circumference and diameter, fruit yield per plant and per hectare. The cross ‘Uyo’ × ‘Iyoyo’ was the best specific combiner in days to flowering, whereas ‘K3’ × ‘Iyoyo’ and ‘Yalo’ × ‘K3’ were the best specific combinations in number of fruits, fruit yield per plant and per hectare.

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