Random Tree Growth with Branching Processes — A Survey

Author(s):  
Anna Rudas ◽  
Bálint Tóth

1993 ◽  
Vol 3 (4) ◽  
Author(s):  
G.D. Makarov

AbstractThe paper is devoted to the relation between random trees and branching processes for which the number of descendants of one particle has the Poisson distribution. The main result of the paper consists in finding the leading term of the asymptotics of the probabilities of large deviations for the height of a random tree. Similar problems were considered in [1-6].



2009 ◽  
Vol 2009 (04) ◽  
pp. P04009 ◽  
Author(s):  
F David ◽  
W M B Dukes ◽  
T Jonsson ◽  
S Ö Stefánsson


2007 ◽  
Vol 44 (02) ◽  
pp. 492-505
Author(s):  
M. Molina ◽  
M. Mota ◽  
A. Ramos

We investigate the probabilistic evolution of a near-critical bisexual branching process with mating depending on the number of couples in the population. We determine sufficient conditions which guarantee either the almost sure extinction of such a process or its survival with positive probability. We also establish some limiting results concerning the sequences of couples, females, and males, suitably normalized. In particular, gamma, normal, and degenerate distributions are proved to be limit laws. The results also hold for bisexual Bienaymé–Galton–Watson processes, and can be adapted to other classes of near-critical bisexual branching processes.



Author(s):  
C. N. Sun

Myoepithelial cells have been observed in the prostate, harderian, apocrine, exocrine sweat and mammary glands. Such cells and their numerous branching processes form basket-like structures around the glandular acini. Their shapes are quite different from structures seen either in spindleshaped smooth muscle cells or skeletal muscle cells. These myoepithelial cells lie on the epithelial side of the basement membrane in the glands. This presentation describes the ultrastructure of such myoepithelial cells which have been found also in the parotid gland carcinoma from a 45-year old patient.Specimens were cut into small pieces about 1 mm3 and immediately fixed in 4 percent glutaraldehyde in phosphate buffer for two hours, then post-fixed in 1 percent buffered osmium tetroxide for 1 hour. After dehydration, tissues were embedded in Epon 812. Thin sections were stained with uranyl acetate and lead citrate. Ultrastructurally, the pattern of each individual cell showed wide variations.



1901 ◽  
Vol 22 (1) ◽  
pp. 71-88
Author(s):  
C. E. Hall
Keyword(s):  


AccessScience ◽  
2015 ◽  
Keyword(s):  


1893 ◽  
Vol 36 (918supp) ◽  
pp. 14674-14674
Keyword(s):  


2018 ◽  
Vol 76 (2) ◽  
pp. 115-130 ◽  
Author(s):  
G Guo ◽  
K Fang ◽  
J Li ◽  
HW Linderholm ◽  
D Li ◽  
...  


2020 ◽  
Vol 81 ◽  
pp. 1-14
Author(s):  
M Keyimu ◽  
Z Li ◽  
Y Zhao ◽  
Y Dong ◽  
B Fu ◽  
...  

Historical temperature reconstructions at high altitudes are still insufficient in southwestern China, which is considered one of the most sensitive areas to climate change in the world. Here we developed a tree ring-width chronology of Faxon fir Abies fargesii var. faxoniana at the upper timber line on Zhegu Mountain, Miyaluo Scenic Area, western Sichuan, China. The climate-tree growth relationship analysis indicated temperature as the dominant regulator on radial tree growth in this region. The reconstruction of aggregated maximum temperature (TMX) of autumn and winter for the period 1856-2016 was achieved with a linear regression model that accounted for 43.6% of the actual variability in the common time series (1954-2016). The reconstruction identified 4 warm periods and 3 cold periods. Similarities of warm and cold periods with previously published reconstructions from nearby sites indicated the reliability of our reconstruction. The significant positive correlation between TMX reconstruction and the Asian-Pacific Oscillation index and the Atlantic Multi-decadal Oscillation index suggested a linkage between large-scale climate circulations and the thermal variability at a multi-decadal scale on the western Sichuan Plateau. We also found that solar activity exerted a strong influence on decadal temperature variability in this region. The cold periods were matched well with historical large volcanic eruptions. Our results strengthen the historical climatic information in southwestern China and contribute to further understanding the regional thermal variability as well as its driving mechanism.



Author(s):  
G.G. Cossens ◽  
M.F. Hawke

During the first 20 years of a Pinus radiata tree rotation, tree growth and pasture yield were assessed under a range of tree spacings at Invermay and Akatore, two coastal sites in Eastern Otago. Pasture yield in association with trees thinned to 100 stems per hectare (sph) was comparable to that from open pasture up to a tree age of 12 years. By the 19th year, however, pasture production declined to 63% of open pasture yield at Invermay and to 42% at Akatore. At 200 and 400 sph at Akatore, pasture yield was similar to that from open pasture at tree age 12 years but declined to 27% and 0% of open pasture yield respectively by year 20. At both Invermay and Akatore, the ryegrass and clover content of open pasture was relatively constant throughout the term of the trial. However, both the ryegrass and clover content of pasture beneath trees began to decline by tree age 12 years with a very rapid decline at Akatore in the number of pasture species at 200 sph by the 19th year. No pasture remained at 400 sph, after 19 years. Livestock carrying capacity with sheep on tree treatments at Invermay decreased from 100% of open pasture at year 6 to 60% by year 10. At Akatore, livestock carrying capacity averaged over the 20-year life of the trial was 4.1 stock units per hectare with a maximum of 8.1 stock units at a tree age of 8 years. Tree growth at both sites was similar, averaging between 1 and 1.1 m/year in height over 20 years, with trees at Invermay at 100 sph averaging 9% greater height and diameter growth than at Akatore. Increasing tree stocking from 100 to 200 to 400 sph at Akatore, resulted in increased tree height, but decreased diameter at breast height. A comparison of the East Otago trees with those in a similar trial at Tikitere (Rotorua) 900 km further north indicated that the southern trees were about 6 years later in their growth pattern by tree age 20 years. On both sites, soil pH tended to be lower in the presence of trees and was significantly lower than in open pasture by year 20. The results and comparisons with the Tikitere data suggest that, in an integrated agroforestry regime, there will be livestock grazing under the trees further into the tree rotation in Otago than in North Island sites. However, slower tree growth would result in a longer rotation time to harvest. Current recommendations to farmers are to plant trees on the less productive areas of the farm and adopt a tree stocking rate which fully utilises the site. Keywords: agroforestry, livestock, pasture, Pinus radiata, soil pH, tree stocking



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