Mean passage times for tridiagonal transition matrices and a two-parameter ehrenfest urn model

Krafft, Olaf; Schaefer, Martin

doi:10.1017/s0021900200044697

Cited by 11 publications

(23 citation statements)

References 4 publications

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“…In the following, we will denote by R A the reduced transition rate matrix in which the rows and the columns corresponding to the absorbing states (j = 0, j = N ) are removed, and by R −1 A its inverse. Let us note that R A is a tridiagonal matrix, which allows for major simplifications of analytical calculations [70]. Note that in order to obtain the transition rate matrix associated to B individuals, one just needs to apply the reversal j ↔ N − j.…”

Section: The Moran Processmentioning

confidence: 99%

Quantifying the impact of a periodic presence of antimicrobial on resistance evolution in a homogeneous microbial population of fixed size

Marrec

Bitbol

2018

Preprint

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The evolution of antimicrobial resistance often occurs in a variable environment, as antimicrobial is given periodically to a patient or added and removed from a medium. This environmental variability has a huge impact on the microorganisms' fitness landscape, and thus on the evolution of resistance. Indeed, mutations conferring resistance often carry a fitness cost in the absence of antimicrobial, which may be compensated by subsequent mutations. As antimicrobial is added or removed, the relevant fitness landscape thus switches from a fitness valley to an ascending landscape or vice-versa.Here, we investigate the effect of these time-varying patterns of selection within a stochastic model. We focus on a homogeneous microbial population of fixed size subjected to a periodic alternation of phases of absence and presence of an antimicrobial that stops growth. Combining analytical approaches and stochastic simulations, we quantify how the time necessary for fit resistant bacteria to take over the microbial population depends on the period of the alternations. We demonstrate that fast alternations strongly accelerate the evolution of resistance, and that a plateau is reached once the period gets sufficiently small. Besides, the acceleration of resistance evolution is stronger for larger populations. For asymmetric alternations, featuring a different duration of the phases with and without antimicrobial, we shed light on the existence of a broad minimum of the time taken by the population to fully evolve resistance. At this minimum, if the alternations are sufficiently fast, the very first resistant mutant that appears ultimately leads to full resistance evolution within the population. This dramatic acceleration of the evolution of antimicrobial resistance likely occurs in realistic situations, and can have an important impact both in clinical and experimental situations.

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Section: The Moran Processmentioning

confidence: 99%

Quantifying the impact of a periodic presence of antimicrobial on resistance evolution in a homogeneous microbial population of fixed size

Marrec

Bitbol

2018

Preprint

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“…Several generalizations have been proposed for this urn model (Krafft and Schaefer, 1993;Klein, 1956), however, these investigations mostly focus on mathematically tractable variants. In the following we report generalizations, which focus on applications to feedback processes.…”

Section: Ehrenfest Urn Modelmentioning

confidence: 99%

Towards swarm calculus: urn models of collective decisions and universal properties of swarm performance

Hamann

2013

Swarm Intell

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Methods of general applicability are searched for in swarm intelligence with the aim of gaining new insights about natural swarms and to develop design methodologies for artificial swarms. An ideal solution could be a 'swarm calculus' that allows to calculate key features of swarms such as expected swarm performance and robustness based on only a few parameters. To work towards this ideal, one needs to find methods and models with high degrees of generality. In this paper, we report two models that might be examples of exceptional generality. First, an abstract model is presented that describes swarm performance depending on swarm density based on the dichotomy between cooperation and interference. Typical swarm experiments are given as examples to show how the model fits to several different results. Second, we give an abstract model of collective decision making that is inspired by urn models. The effects of positive feedback probability, that is increasing over time in a decision making system, are understood by the help of a parameter that controls the feedback based on the swarm's current consensus. Several applicable methods, such as the description as Markov process, calculation of splitting probabilities, mean first passage times, and measurements of positive feedback, are discussed and applications to artificial and natural swarms are reported.

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“…And stationary distribution of active member number follows binomial distribution, ( , /( + )) [19].…”

Section: Model Of Number Of Active Membersmentioning

confidence: 99%

Research on Effectiveness Modeling of the Online Chat Group

Zhang

Dong

2013

Mathematical Problems in Engineering

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The online chat group is a small-scale multiuser social networking platform, in which users participate in the discussions and send and receive information. Online chat group service providers are concerned about the number of active members because more active members means more advertising revenues. For the group owners and members, efficiency of information acquisition is the concern. So it is of great value to model these two indicators' impacting factors. This paper deduces the mathematical models of the number of active members and efficiency of information acquisition and then conducts numerical experiment. The experimental results provide evidences about how to improve the number of active members and efficiency of information acquisition.

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Mean passage times for tridiagonal transition matrices and a two-parameter ehrenfest urn model

Cited by 11 publications

References 4 publications

Quantifying the impact of a periodic presence of antimicrobial on resistance evolution in a homogeneous microbial population of fixed size

Quantifying the impact of a periodic presence of antimicrobial on resistance evolution in a homogeneous microbial population of fixed size

Towards swarm calculus: urn models of collective decisions and universal properties of swarm performance

Research on Effectiveness Modeling of the Online Chat Group

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