scholarly journals Community modulated recursive trees and population dependent branching processes

2021 ◽  
Author(s):  
Shankar Bhamidi ◽  
Ruituo Fan ◽  
Nicolas Fraiman ◽  
Andrew Nobel
Keyword(s):  
Branching Processes ◽  
Recursive Trees

scholarly journals Weak convergence of the number of vertices at intermediate levels of random recursive trees

2018 ◽  
Vol 55 (4) ◽  
pp. 1131-1142 ◽  
Author(s):  
Alexander Iksanov ◽  
Zakhar Kabluchko
Keyword(s):  
Asymptotic Behavior ◽  
Weak Convergence ◽  
Gaussian Process ◽  
Branching Processes ◽  
One Dimensional ◽  
Recursive Tree ◽  
Finite Dimensional ◽  
Recursive Trees

Abstract Let Xn(k) be the number of vertices at level k in a random recursive tree with n+1 vertices. We are interested in the asymptotic behavior of Xn(k) for intermediate levels k=kn satisfying kn→∞ and kn=o(logn) as n→∞. In particular, we prove weak convergence of finite-dimensional distributions for the process (Xn ([knu]))u>0, properly normalized and centered, as n→∞. The limit is a centered Gaussian process with covariance (u,v)↦(u+v)−1. One-dimensional distributional convergence of Xn(kn), properly normalized and centered, was obtained with the help of analytic tools by Fuchs et al. (2006). In contrast, our proofs, which are probabilistic in nature, exploit a connection of our model with certain Crump–Mode–Jagers branching processes.

Some Contributions to the Theory of Near-Critical Bisexual Branching Processes

2007 ◽  
Vol 44 (02) ◽  
pp. 492-505
Author(s):  
M. Molina ◽  
M. Mota ◽  
A. Ramos
Keyword(s):  
Branching Process ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Positive Probability ◽  
Limit Laws ◽  
Bisexual Branching Processes ◽  
Probabilistic Evolution

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.

Ultrastructure of myoepithelial cell in parotid gland

1988 ◽  
Vol 46 ◽  
pp. 342-343
Author(s):  
C. N. Sun
Keyword(s):  
Parotid Gland ◽  
Osmium Tetroxide ◽  
Individual Cell ◽  
Branching Processes ◽  
Muscle Cells ◽  
Myoepithelial Cells ◽  
Uranyl Acetate ◽  
Thin Sections ◽  
Gland Carcinoma ◽  
Parotid Gland Carcinoma

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.

Regenerative Sampling and Monotonic Branching Processes.

1986 ◽  
Author(s):  
Stephen D. Durham ◽  
Kai F. Yu
Keyword(s):  
Branching Processes

On calculating extinction probabilities for branching processes in random environments

1969 ◽  
Vol 6 (03) ◽  
pp. 478-492 ◽  
Author(s):  
William E. Wilkinson
Keyword(s):  
Generating Functions ◽  
Infinite Sequence ◽  
Branching Processes ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Random Environments ◽  
Real Numbers ◽  
Discrete Time Markov Chain ◽  
Extinction Probabilities ◽  
Image Position

Consider a discrete time Markov chain {Zn } whose state space is the non-negative integers and whose transition probability matrix ║Pij ║ possesses the representation where {Pr }, r = 1,2,…, is a finite or denumerably infinite sequence of non-negative real numbers satisfying , and , is a corresponding sequence of probability generating functions. It is assumed that Z 0 = k, a finite positive integer.

scholarly journals Limit theorems for multi-type general branching processes with population dependence

2020 ◽  
Vol 52 (4) ◽  
pp. 1127-1163
Author(s):  
Jie Yen Fan ◽  
Kais Hamza ◽  
Peter Jagers ◽  
Fima C. Klebaner
Keyword(s):  
Carrying Capacity ◽  
Population Model ◽  
General Framework ◽  
Limit Theorems ◽  
Mating Systems ◽  
Law Of Large Numbers ◽  
Branching Processes ◽  
Special Section ◽  
Large Numbers ◽  
Type Population

AbstractA general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the population as a measure-valued process and obtain its asymptotics as the population grows with the environmental carrying capacity. Thus, a deterministic approximation is given, in the form of a law of large numbers, as well as a central limit theorem. This general framework is then adapted to model sexual reproduction, with a special section on serial monogamic mating systems.

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