On two classes of interacting stochastic processes arising in cancer modeling

1983 ◽  
Vol 15 (4) ◽  
pp. 695-712 ◽  
Author(s):  
Robert Bartoszyński ◽  
Prem S. Puri
Keyword(s):  
Markov Processes ◽  
Branching Processes ◽  
The Other ◽  
Time Interval ◽  
Positive Probability ◽  
Martingale Convergence Theorem ◽  
Limiting Behavior ◽  
State Dependent ◽  
Cancer Modeling ◽  
Martingale Convergence

The processes X and Y are said to interact if the laws governing the changes of either of them at time t depend on the values of the other process at times up to t. For bivariate interacting Markov processes, their limiting behavior is analysed by means of an approximation suggested by Fuhrmann, consisting of discretizing time, and assuming that in each time interval the processes develop independently, according to the laws obtained by fixing the value of the other process at its level attained at the beginning of the interval.In this way the conditions for almost sure extinction, escape to ∞ with positive probability, etc., are obtained (by using the martingale convergence theorem) for state-dependent branching processes studied by Roi, and for bivariate processes with one component piecewise determined.

On two classes of interacting stochastic processes arising in cancer modeling

1983 ◽  
Vol 15 (04) ◽  
pp. 695-712 ◽  
Author(s):  
Robert Bartoszyński ◽  
Prem S. Puri
Keyword(s):  
Markov Processes ◽  
Branching Processes ◽  
The Other ◽  
Time Interval ◽  
Positive Probability ◽  
Martingale Convergence Theorem ◽  
Limiting Behavior ◽  
State Dependent ◽  
Cancer Modeling ◽  
Martingale Convergence

The processes X and Y are said to interact if the laws governing the changes of either of them at time t depend on the values of the other process at times up to t. For bivariate interacting Markov processes, their limiting behavior is analysed by means of an approximation suggested by Fuhrmann, consisting of discretizing time, and assuming that in each time interval the processes develop independently, according to the laws obtained by fixing the value of the other process at its level attained at the beginning of the interval. In this way the conditions for almost sure extinction, escape to ∞ with positive probability, etc., are obtained (by using the martingale convergence theorem) for state-dependent branching processes studied by Roi, and for bivariate processes with one component piecewise determined.

On supercritical Galton-Watson processes allowing immigration

1974 ◽  
Vol 11 (04) ◽  
pp. 814-817 ◽  
Author(s):  
A. G. Pakes
Keyword(s):  
Absolute Continuity ◽  
Branching Processes ◽  
Random Variables ◽  
The Other ◽  
State Dependent ◽  
The Absolute

We establish the absolute continuity of the limit random variables of two supercritical Galton-Watson branching processes, one allowing unrestricted immigration and the other having a state dependent immigration component.

scholarly journals On the Hurst exponents, Markov processes, and fractional Brownian motion

2021 ◽  
Author(s):  
Ginno Millán
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Markov Processes ◽  
The Other ◽  
Time Interval ◽  
Infinite Time Interval ◽  
Point Density ◽  
The Difference ◽  
The One ◽  
Hurst Exponents

There is much confusion in the literature over Hurst exponent (H). The purpose of this paper is to illustrate the difference between fractional Brownian motion (fBm) on the one hand and Gaussian Markov processes where H is different to 1/2 on the other. The difference lies in the increments, which are stationary and correlated in one case and nonstationary and uncorrelated in the other. The two- and one-point densities of fBm are constructed explicitly. The two-point density does not scale. The one-point density for a semi-infinite time interval is identical to that for a scaling Gaussian Markov process with H different to 1/2 over a finite time interval. We conclude that both Hurst exponents and one-point densities are inadequate for deducing the underlying dynamics from empirical data. We apply these conclusions in the end to make a focused statement about nonlinear diffusion.

On supercritical Galton-Watson processes allowing immigration

1974 ◽  
Vol 11 (4) ◽  
pp. 814-817 ◽  
Author(s):  
A. G. Pakes
Keyword(s):  
Absolute Continuity ◽  
Branching Processes ◽  
Random Variables ◽  
The Other ◽  
State Dependent ◽  
The Absolute

We establish the absolute continuity of the limit random variables of two supercritical Galton-Watson branching processes, one allowing unrestricted immigration and the other having a state dependent immigration component.

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.

scholarly journals Effect of Co-Inoculation of Bacillus sp. Strain with Bacterial Endophytes on Plant Growth and Colonization in Tomato Plant (Solanum lycopersicum)

2021 ◽  
Vol 12 (2) ◽  
pp. 480-490
Author(s):  
Ahsanul Salehin ◽  
Ramesh Raj Puri ◽  
Md Hafizur Rahman Hafiz ◽  
Kazuhito Itoh
Keyword(s):  
Plant Growth ◽  
Solanum Lycopersicum ◽  
Plant Growth Promotion ◽  
Tomato Plant ◽  
Growth Promotion ◽  
Growth Parameters ◽  
The Other ◽  
Time Interval ◽  
Bacillus Sp ◽  
F 33

Colonization of a biofertilizer Bacillus sp. OYK strain, which was isolated from a soil, was compared with three rhizospheric and endophytic Bacillus sp. strains to evaluate the colonization potential of the Bacillus sp. strains with a different origin. Surface-sterilized seeds of tomato (Solanum lycopersicum L. cv. Chika) were sown in the sterilized vermiculite, and four Bacillus sp. strains were each inoculated onto the seed zone. After cultivation in a phytotron, plant growth parameters and populations of the inoculants in the root, shoot, and rhizosphere were determined. In addition, effects of co-inoculation and time interval inoculation of Bacillus sp. F-33 with the other endophytes were examined. All Bacillus sp. strains promoted plant growth except for Bacillus sp. RF-37, and populations of the rhizospheric and endophytic Bacillus sp. strains were 1.4–2.8 orders higher in the tomato plant than that of Bacillus sp. OYK. The plant growth promotion by Bacillus sp. F-33 was reduced by co-inoculation with the other endophytic strains: Klebsiella sp. Sal 1, Enterobacter sp. Sal 3, and Herbaspirillum sp. Sal 6., though the population of Bacillus sp. F-33 maintained or slightly decreased. When Klebsiella sp. Sal 1 was inoculated after Bacillus sp. F-33, the plant growth-promoting effects by Bacillus sp. F-33 were reduced without a reduction of its population, while when Bacillus sp. F-33 was inoculated after Klebsiella sp. Sal 1, the effects were increased in spite of the reduction of its population. Klebsiella sp. Sal 1 colonized dominantly under both conditions. The higher population of rhizospheric and endophytic Bacillus sp. in the plant suggests the importance of the origin of the strains for their colonization. The plant growth promotion and colonization potentials were independently affected by the co-existing microorganisms.

THE EMISSION OF IONIZING RADIATION DURING A SPARK DISCHARGE

1957 ◽  
Vol 35 (3) ◽  
pp. 324-331 ◽  
Author(s):  
W. A. Prowse ◽  
G. R. Bainbridge
Keyword(s):  
Ionizing Radiation ◽  
High Voltage ◽  
Voltage Pulse ◽  
High Voltage Pulse ◽  
Spark Discharge ◽  
The Other ◽  
Time Interval ◽  
Delay Lines

A high voltage pulse lasting 0.35 microsecond is applied to a pair of delay lines, so that two pulses can be picked up from adjustable points of connection on the lines. One is applied to an irradiating gap and the other to a longer test gap, the gaps being so arranged that only mid-gap irradiation occurs. The sparking probability, P, of the test gap is used to indicate the presence of ionizing radiation. Variations of P with the time interval between the two pulses are recorded. They indicate that ionizing radiation is emitted in repeated short flashes. Photographic observations support this view.

scholarly journals State-dependent behavior and alternative behavioral strategies in brown trout (Salmo trutta L.) fry

2015 ◽  
Author(s):  
Joacim Näslund ◽  
Jörgen I Johnsson
Keyword(s):  
Brown Trout ◽  
Salmo Trutta ◽  
Population Based ◽  
Swimming Activity ◽  
The Other ◽  
Behavioral Strategies ◽  
Food Ration ◽  
State Dependent ◽  
Behavioral Trials ◽  
Bodily State

Animals generally adjust their behavior in response to bodily state (e.g. size and energy reserves) to optimize energy intake in relation to mortality risk, weighing predation probability against starvation. Here we investigated whether brown trout adjust their behavior in relation to feeding history (energetic status) and body size during a major early-life selection bottleneck, when fast growth also appear to be important. We manipulated growth using different food ration schemes over two consecutive time periods (P1 = 12 days, P2 = 23 days), excluding social effects through individual isolation. During these experimental periods the fish were fed either high or low food rations in a crossed design. In behavioral trials following the treatment, where acute hunger levels were standardized among all treatments, fish that were initially fed high rations (P1) and thereafter low rations (P2) had on average 15-21% higher swimming activity than the other groups, but large within-treatment variation rendered only weak statistical support for the effect. Furthermore, fish on low ration during P2 tended to be more aggressive than fish on high ration. Size was related to behavioral expression, with larger fish being more active and aggressive. Swimming activity and active aggression were positively correlated, forming a behavioral syndrome in the studied population. Based on these behavioral traits we could also distinguish two behavioral clusters, one consisting of more active and aggressive individuals, and the other consisting of less active and aggressive individuals. This indicates that two behavioral strategies may exist in young brown trout.

Sign in / Sign up

Export Citation Format

Share Document