Cell contamination and branching process in random environment with immigration

Vincent Bansaye (PMA)

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Cell contamination and branching process in random environment with immigration

Vincent Bansaye (PMA)

Probability · Submitted 13 May 2008

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We determine the asymptotic behavior of the number of parasites in a cell line, which follows a branching process in random environment with state dependent immigration.

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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,407 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.06 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.02 · states quantitative result 0.30 · compares with prior results 0.04 · mentions code or data availability 0.02.

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arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We consider a branching model for a population of dividing cells infected by parasites. Each cell receives parasites by inheritance from its mother cell and independent contamination from outside the population. Parasites multiply randomly inside the cell and are shared randomly between the two daughter cells when the cell divides. The law of the number of parasites which contaminate a given cell depends only on whether the cell is already infected or not. We determine the asymptotic behavior of the number of parasites in a cell line, which follows a branching process in random environment with state dependent immigration. We then derive a law of large numbers for the asymptotic proportions of cells with a given number of parasites. The main tools are branching processes in random environment and laws of large numbers for Markov tree.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We consider a branching model for a population of dividing cells infected by parasites.	contribution 0.60	0.48	0.03	asserted 0.88
s1	Each cell receives parasites by inheritance from its mother cell and independent contamination from outside the population.	method 0.93	0.13	0.02	asserted 1.00
s2	Parasites multiply randomly inside the cell and are shared randomly between the two daughter cells when the cell divides.	method 0.94	0.16	0.03	asserted 1.00
s3	The law of the number of parasites which contaminate a given cell depends only on whether the cell is already infected or not.	method 0.93	0.23	0.04	asserted 1.00
s4	We determine the asymptotic behavior of the number of parasites in a cell line, which follows a branching process in random environment with state dependent immigration.	result 0.66	0.95	0.47	asserted 1.00
s5	We then derive a law of large numbers for the asymptotic proportions of cells with a given number of parasites.	result 0.82	0.95	0.28	asserted 1.00
s6	The main tools are branching processes in random environment and laws of large numbers for Markov tree.	method 1.00	0.34	0.03	asserted 0.98

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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arXiv listing abstract v2

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C citations
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

We consider a branching model for a population of dividing cells infected by parasites. Each cell receives parasites by inheritance from its mother cell and independent contamination from outside the population. Parasites multiply randomly inside the cell and are shared randomly between the two daughter cells when the cell divides. The law of the number of parasites which contaminate a given cell depends only on whether the cell is already infected or not. We determine the asymptotic behavior of the number of parasites in a cell line, which follows a branching process in random environment with state dependent immigration. We then derive a law of large numbers for the asymptotic proportions of cells with a given number of parasites. The main tools are branching processes in random environment and laws of large numbers for Markov tree.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it

Cites it as background 1 paper

Other models on cell lineage with differentiation have been investigated, see for example Bansaye [ref] on parasite infection and Evans and Steinsaltz [ref] on asymptotic models relying on super-Brownian motion.

Detection of cellular aging in a Galton-Watson process · Introduction · 0.99

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