Evidence map›Paper›PMID 41528409›Full record

ArticleBulletin of mathematical biology2026

Mathematical Analysis for a Class of Stochastic Copolymerization Processes.

David F Anderson, Jingyi Ma, Praful Gagrani

Abstract read
In one paragraph

Article in Bulletin of mathematical biology, 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.

0numbers the graph read from it
0cells of the map it votes in
0citing papers in PubMed
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1 · What the graph read from it

What it found

Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.

The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.

2 · The registry

The trial behind it

Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.

Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.

3 · Its place in the literature

Who cites it

0 citing papers in PubMed.

No citing paper in PubMed yet.

4 · The record

Corrections and comments

PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.

5 · Who and what money

Authors and funding

3 authors.

David F AndersonDepartment of Mathematics, University of Wisconsin-Madison, Madison, USA.
Jingyi MaDepartment of Mathematics, University of Wisconsin-Madison, Madison, USA. jma276@wisc.edu.ORCID http://orcid.org/0000-0002-8401-210X
Praful GagraniInstitute of Industrial Science, The University of Tokyo, Tokyo, Japan.

Funding

Directorate for Biological Sciences 2218817Directorate for Mathematical and Physical Sciences 2051498
6 · The paper itself

Abstract

We study a stochastic model of a copolymerization process that has been extensively investigated in the physics literature. The main questions of interest include: (i) what are the criteria for transience, null recurrence, and positive recurrence in terms of the system parameters; (ii) in the transient regime, what are the limiting fractions of the different monomer types; and (iii) in the transient regime, what is the speed of growth of the polymer? Previous studies in the physics literature have addressed these questions using heuristic methods. Here, we utilize rigorous mathematical arguments to derive the results from the physics literature. Moreover, the techniques developed allow us to generalize to the copolymerization process with finitely many monomer types. We expect that the mathematical methods used and developed in this work will also enable the study of even more complex models in the future.

Indexed as

Models, ChemicalPolymerizationComputer SimulationMarkov ChainsMathematical ConceptsModels, BiologicalOrigin of LifePolymersStochastic ProcessesPolymersboundary processContinuous-time Markov chaincopolymerizationorigin of lifepolymer growthrecurrence and transiencestochastic modelingtree-like state space

Identifiers

PMID41528409
PMCPMC12799708

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Registered trials

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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.