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Topic: Branching process

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In the News (Thu 18 Apr 19)

  Branching process - Wikipedia, the free encyclopedia
In probability theory, a branching process is a Markov process that models a population in which each individual in generation n produces some random number of individuals in generation n + 1, according to a fixed probability distribution that does not vary from individual to individual.
Branching processes are used to model reproduction; for example, the individuals might correspond to bacteria, each of which generates 0, 1, or 2 offspring with some probability in a single time unit.
Branching processes can also be used to model other systems with similar dynamics, e.g., the spread of surnames in genealogy or the propagation of neutrons in a nuclear reactor.
en.wikipedia.org /wiki/Branching_process   (340 words)

 Estimation Of The Parameters Of A Branching Process From Migrating Binomial Observations (ResearchIndex)   (Site not responding. Last check: 2007-10-22)
Estimation Of The Parameters Of A Branching Process From Migrating Binomial Observations (1998)
5 A branching process with a state-dependent immigration compo..
2 Sequential estimation for branching processes with immigrati..
citeseer.ist.psu.edu /jacob98estimation.html   (581 words)

On the statistics of branching processes with immigration.
On the critical branching migration processes with predominated emigration.
Age-dependent branching processes with emigration and population dynamics.
www.math.bas.bg /~statlab/Yanevpub.html   (993 words)

 [No title]
Branching morphogenesis is a particular form of tissue morphogenesis; it is a process whereby ducts are formed in a developing tissue.
This process has received a significant amount of attention because a number of the genes that have been shown to be important in branching morphogenesis in mammary tissue have also been shown to be important in tumor growth.
For example, the process of branching morphogenesis in-vivo is initiated by the release of ovarian hormones, which in turn results in the release of matrix metalloproteinases, and they then degrade a particular component of the ECM called the basement membrane (BM).
socrates.berkeley.edu /~mgrant/summary.html   (1511 words)

Branching processes are stochastic models of an asexually reproducing population.
In a branching random walk that has a strong drift downwards a natural object for study is the all-time maximum of the process.
Under weaker assumptions about the behaviour of the environment process than have hitherto been made, there are many questions to be asked about the behaviour of the branching process.
www.shef.ac.uk /sheffield/jsp/polopoly.jsp?a=24349&d=3389   (673 words)

 [No title]   (Site not responding. Last check: 2007-10-22)
In this paper, we investigate subclasses of flow event structures which are both suited for the process algebraic composition operators, and for action refinement as a means of regarding processes on different levels of abstraction.
Restricted to the class of finitely branching, concrete, sequential processes, only fifteen of them turn out to be different, and most semantics found in the literature that can be defined uniformly in terms of action relations coincide with one of these fifteen.
It is also argued that the use of the completeness result for branching congruence in obtaining the completeness result for weak congruence leads to a considerable simplification with respect to the only direct proof presented in the literature.
boole.stanford.edu /pub/ABSTRACTS   (6385 words)

 Branching process -- Facts, Info, and Encyclopedia article   (Site not responding. Last check: 2007-10-22)
It is not hard to show that, starting with one individual in generation zero, the (Click link for more info and facts about expected) expected size of generation n equals μ
If μ is less than 1, then the expected number of individuals goes rapidly to zero, which implies ultimate extinction with probability 1 by (Click link for more info and facts about Markov's inequality) Markov's inequality.
In (Click link for more info and facts about theoretical ecology) theoretical ecology, the parameter μ of a branching process is called the (Click link for more info and facts about basic reproductive rate) basic reproductive rate.
www.absoluteastronomy.com /encyclopedia/b/br/branching_process.htm   (302 words)

A simple version of this process arises when each child receives an independent displacement from their parent, so that any line of descent is simply a random walk.
Quite a lot is already known about this process, for it has been studied by various people over the last thirty years.
For discrete-time branching random walk and continuous time branching diffusion there are satisfactory theories concerning stable clustering.
www.shef.ac.uk /sheffield/jsp/polopoly.jsp?a=24349&d=3389   (673 words)

 J. D. Biggins -- Publications   (Site not responding. Last check: 2007-10-22)
Uniform convergence of martingales in the branching random walk Ann.
Near-constancy phenomena in branching processes, (with N.H. Bingham) Math.
Large deviations in the supercritical branching process, (with N.H. Bingham).
www.shef.ac.uk /~st1jdb/Bibliog.html   (542 words)

 Measure change in multitype branching, J. D. Biggins, A. E. Kyprianou
The Kesten-Stigum theorem for the one-type Galton-Watson process gives necessary and sufficient conditions for mean convergence of the martingale formed by the population size normed by its expectation.
The application of the approach to various branching processes is indicated.
MacPhee, I. and Schuh, H. A Galton--Watson branching process in varying environments with essentially constant means and two rates of growth.
projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.aap/1086957585   (811 words)

 Amaury Lambert
Lambert A. (1999) The branching process conditioned to be never extinct (unpublished).
Lambert A. (2002) The genealogy of continuous-state branching processes with immigration.
Lambert A. The branching process with logistic growth.
www.biologie.ens.fr /ecologie/ecoevolution/lambert/index.en.html   (259 words)

 23Chess   (Site not responding. Last check: 2007-10-22)
Klee schematically describes the branching process: starting from the trunk, for each new ramification level the branches are reduced in both the length and the thickness, according to a progression of odd numbers, explicitly written beside the corresponding branching levels: 9, 7, 5, 3, 1.
In qualitative terms, the numerical series fits to the to the behaviour of the logistic model: at first the growth rate increases ever more (exponential growth), but once its maximum is reached, it gradually decreases (asymptotic behaviour), according to the typical sigmoid growth curve.
In the late 20’s Klee further deepened the module, and solved the problem with an interesting circular scheme displayed in Animation 14: the rectangles were substituted with a single right-angled polygonal line, which closed the pathway by returning to its starting point, generating patterns quite similar to those of the overlapped rectangles.
www.mi.sanu.ac.yu /vismath/giunti/23Chess.htm   (602 words)

 [No title]   (Site not responding. Last check: 2007-10-22)
In 1997 Le Jan and Sznitman introduced a new (and surprising) model for the analysis of the Navier-Stokes equations, by representing the the solution of the Fourier transformed equations as the expected value of a multiplicative functional defined on a multi-type branching process.
The associated processes are are constructed in such a way that the nonlinearity of the equation is expressed through the bifurcations of the branching process.
Known and new results on the branching process representations of solutions in physical space (branching Brownian motion) will be presented, along with a new "dual" representation of solutions to the KPP equation in Fourier space (A Le Jan - Sznitman type branching process).
www.math.ubc.ca /~limic/orum_seminar.html   (186 words)

 Probability Abstract Service   (Site not responding. Last check: 2007-10-22)
The branching Brownian motions that, in the infinite density limit, provide a particle picture for the super Brownian motion have a local time in only one dimension, an intersection local time up to three dimensions, and a renormalised self-intersection local time only in dimensions one and two.
Neil O'Connell We obtain an stickbreaking branching process approximation for the reduced family tree in a near-critical Markov branching process when the time interval considered is long, and apply it to the problem of estimating the age of our most recent common female ancestor.
www.economia.unimi.it /PAS/Letters/letter_12.shtml   (1895 words)

 Asymptotic Genealogy of a Critical Branching Process (ResearchIndex)   (Site not responding. Last check: 2007-10-22)
Abstract: t,n be a continuous-time critical branching process conditioned to have population n at time t.
We also consider a Bernoulli(p) sampling process on the leaves of t,n, and define the p-sampled history p (T t,n) to be the smallest subtree of containing all the sampled...
9 The Branching process in a Brownian excursion (context) - Neveu, Pitman - 1989
citeseer.ist.psu.edu /popovic02asymptotic.html   (360 words)

 Modelling the PCR amplification process by a size-dependent branching process and estimation of the efficiency, N. ...
Jacob, C. and Peccoud, J. Estimation of the parameters of a branching process from migrating binomial observations.
Lalam, N. and Jacob, C. Estimation of the offspring mean in a supercritical or near-critical size-dependent branching process.
Lalam, N. and Jacob, C. Modelling the PCR amplification process with size-dependent branching processes and estimation of the efficiency.
projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.aap/1086957587   (518 words)

 Branching and Spatial Structure   (Site not responding. Last check: 2007-10-22)
Therefore, the branching process can give rise to an increase in the radiated power density at certain position.
Of course this increase is due to the increase in the path length.
(a) The brunching process with the branching length increasing as
macul.ciencias.uchile.cl /alejo/fractal_antenna/node5.html   (545 words)

 Longtime Behavior of a Branching Process Controlled By Branching Catalysts - Dawson, Fleischmann (ResearchIndex)   (Site not responding. Last check: 2007-10-22)
Abstract: The model under consideration is a catalytic branching model constructed in [DF96], where the catalysts themselves suffer a spatial branching mechanism.
Main attention is paid to dimension d = 3: The key result is a convergence theorem towards a limit with full intensity (persistence), which in a sense is comparable with the situation for the "classical" continuous super-Brownian motion.
Longtime behavior of a branching process controlled by branching catalysts.
citeseer.ist.psu.edu /dawson96longtime.html   (553 words)

 Branching morphogenesis and kidney disease -- Shah et al. 131 (7): 1449 -- Development
(D) At the tips of the branches, the epithelium induces the mesenchyme to form pre-tubular aggregates, which are stimulated to undergo mesenchymal to epithelial transformation (E,F) through the formation of comma-shaped (E) and S-shaped (F) bodies to form components of the nephron (G): renal tubules (proximal and distal) and the epithelial component of the glomerulus.
The interactions between soluble morphogens, metanephric mesenchyme and matrix molecules during the branching process of the ureteric tree.
These stimulatory and inhibitory branching morphogens may govern the process of vectorial branching by altering expression of distal effector molecules at tips, branches and stalks, which are known to be important in branching morphogenesis, such as (C) proteinases [e.g.
dev.biologists.org /cgi/content/full/131/7/1449   (8377 words)

 The interplay of matrix metalloproteinases, morphogens and growth factors is necessary for branching of mammary ...
The interplay of matrix metalloproteinases, morphogens and growth factors is necessary for branching of mammary epithelial cells -- Simian et al.
mammary epithelium of transgenic mice increases branching morphogenesis,
Shown are the percentage of branching organoids in the presence of growth factors alone (white bars) and growth factors+Pg (hatched bars).
dev.biologists.org /cgi/content/full/128/16/3117   (7715 words)

 Papers by S.Sagitov
Sagitov, S. Critical branching processes with several types of particles and with immigration.
Sagitov, S. Multidimentional limit theorems for a branching process with one type of particles.
Sagitov, S. A multidimentional critical branching process generated by a large number of particles of a single type.
www.math.chalmers.se /~serik/branching.html   (324 words)

 [No title]   (Site not responding. Last check: 2007-10-22)
In this talk I will outline links between branching process theory and the theory of non-linear partial differential equations, concentrating on the semilinear hyperbolic system I am currently studying.
The gist of the idea is simple: set up a branching process that corresponds to the PDE. Then, study of the branching process should yield insight (and indeed concrete information) into the PDE, and vice versa.
The simplest link between branching processes and differential equations is well-known - conditioning on the first jump of the process and some simple manipulation yields a differential equation.
www.kent.ac.uk /IMS/personal/odl/abstract.txt   (200 words)

 Bisexual Galton-Watson branching process with population-size-dependent mating, M. Molina, M. Mota, A. Ramos
In this paper, we introduce a bisexual Galton-Watson branching process with mating function dependent on the population size in each generation.
Necessary and sufficient conditions for the process to become extinct with probability 1 are investigated for two possible conditions on the sequence of mating functions.
Some results for the probability generating functions associated with the process are also given.
projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.jap/1034082121   (166 words)

 BPML 0.4
A conditional process branching is based on the information contained in the business process instance context..
A conditional participant branching is a decision taken by a participant and communicated to the process instance as a message.
This is actually the essence of a business process definition: a business process is a collection of collaborations between a role represented by the BPMS and any number of participants, which can be users, systems, or business partners.
www.ebpml.org /bpml_0_4.htm   (712 words)

 Concurrency Abstracts   (Site not responding. Last check: 2007-10-22)
We represent concurrent processes as Boolean propositions or gates, cast in the role of acceptors of concurrent behavior.
Furthermore it is argued that in abstract interleaving semantics (at least for finite processes) branching bisimulation congruence is the finest reasonable congruence possible.
In models of concurrent processes constraints on the order of events are often represented by partial orders, and schedules of events are then defined using an algebra of standard operations such as sequential and parallel composition.
boole.stanford.edu /abstracts.html   (9620 words)

 On the Extinction Probability of a Branching Process with Two Kinds of Interaction of Particles   (Site not responding. Last check: 2007-10-22)
On the Extinction Probability of a Branching Process with Two Kinds of Interaction of Particles: Theory of Probability & Its Applications Vol.
A continuous-time Markov branching process with a single type T of particles is considered in which any pair of particles T+T produces offspring independently of all other particles.
Representations for the extinction probabilities of this process are obtained under certain assumptions on the offspring distribution.
epubs.siam.org /sam-bin/dbq/article/97898   (178 words)

Therefore the notion of branching bisimulation equivalence is introduced which strongly preserves the branching structure of processes, in the sense that it preserves computations together with the potentials in all intermediate states that are passed through, even if silent moves are involved.
Restricted to the domain of finitely branching, concrete, sequential processes, only twelve of them turn out to be different, and most semantics found in the literature that can be defined uniformly in terms of action relations coincide with one of these twelve.
These include the history preserving bisimulation, which is the coarsest equivalence that fully respects branching time, causality and their interplay, as well as the ST-bisimulation, a branching time respecting equivalence that takes causality into account to the extent that it is expressible by actions overlapping in time.
theory.stanford.edu /~rvg/abstracts.html   (11237 words)

Neveu's continuous state branching process, superprocess, branching process with infinite mean, non-Lipschitz non-linearity, immortal process, instantaneous mass propagation, locally countably infinite biodiversity
Impressed by Neveu's (1992) continuous-state branching process we learned about from Bertoin and Le Gall (2000), a class of finite measure-valued cadlag superprocesses X with Neveu's branching mechanism is constructed.
The log-Laplace equation related to X has the locally non-Lipschitz function u log u as non-linear term (instead of u to the power (1+b) in the case of the approximating processes) and is thus interesting in its own.
www.wias-berlin.de /publications/preprints/821   (133 words)

 Prestige and probability and the process of ``branching''
For a description of the process of gaining prestige, losing prestige, becoming standardized and being ``extinct'', an appropriate mathematical model can be found in the probability theory.
This model is called the Galton-Watson-Process,   or the process of Branching .
By the model of Galton-Waston Processes it becomes possible to anticipate a possible development of one specific accent in its social context.
coral.lili.uni-bielefeld.de /~ttrippel/labov/node16.html   (530 words)

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