Branching processes and random mappings of finite sets

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.

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Ultrastructure of myoepithelial cell in parotid gland

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100103772 ◽

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.

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Regenerative Sampling and Monotonic Branching Processes.

10.21236/ada170145 ◽

1986 ◽

Author(s):

Stephen D. Durham ◽

Kai F. Yu

Keyword(s):

Branching Processes

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Some results on the structure of irregular branching processes by infinite mean

Advances in Applied Probability ◽

10.1017/s0001867800032328 ◽

1979 ◽

Vol 11 (02) ◽

pp. 292-293

Author(s):

H.-J. Schuh

Keyword(s):

Branching Processes

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On calculating extinction probabilities for branching processes in random environments

Journal of Applied Probability ◽

10.1017/s0021900200026553 ◽

1969 ◽

Vol 6 (03) ◽

pp. 478-492 ◽

Cited By ~ 5

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.

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