Abstraction-Guided Truncations for Stationary Distributions of Markov Population Models

Backenköhler, Michael; Bortolussi, Luca; Großmann, Gerrit; Wolf, Verena

doi:10.1007/978-3-030-85172-9_19

Cited by 8 publications

(5 citation statements)

References 43 publications

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“…We highlight that for the "positive row" case, [12] also provides converging bounds, however through a different route. Another topic of interest are continuous time Markov chains, where abstraction-and truncation-based algorithms are applicable [21,3] and computation of the stationary distribution can be used for time-bounded reachability [17].…”

Section: Related Workmentioning

confidence: 99%

“…In [8,15], a stopping criterion for reachability was independently discovered by additionally computing converging upper bounds. 3 The difference between upper and lower bounds then gives a straightforward stopping criterion: Once the difference between upper and lower bound in the initial state is smaller than ε, we can stop the iteration.…”

Section: A2 Value Iterationmentioning

confidence: 99%

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Correct Approximation of Stationary Distributions

Meggendorfer¹

2023

Preprint

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A classical problem for Markov chains is determining their stationary (or steady-state) distribution. This problem has an equally classical solution based on eigenvectors and linear equation systems. However, this approach does not scale to large instances, and iterative solutions are desirable. It turns out that a naive approach, as used by current model checkers, may yield completely wrong results. We present a new approach, which utilizes recent advances in partial exploration and mean payoff computation to obtain a correct, converging approximation.

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Section: Related Workmentioning

confidence: 99%

Section: A2 Value Iterationmentioning

confidence: 99%

Correct Approximation of Stationary Distributions

Meggendorfer¹

2023

Preprint

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“…Although our approach is applicable to very general types of abstractions, for simplicity and specificity we consider in this paper only the exponential partitioning for some parameter 1 < c ≤ 2 given as {[0,0]} ∪ {[ c n−1 , c n − 1] : n ∈ N} for all dimensions. For example with c=2 the intervals are [0,0], [1,1], [2,3], [4,7], [8,15], . .…”

Section: Related Conceptsmentioning

confidence: 99%

“…To build a plausible and computationally tractable abstraction of CRNs, various state-space reduction techniques have been proposed that either truncate states of the underlying CTMC with insignificant probability [31,22,30] or leverage structural properties of the CTMC to aggregate/lump selected sets of states [1,2]. The interval abstraction of the species population is a widely used approach to mitigate the state-space explosion problem [37,13,29].…”

Section: Introductionmentioning

confidence: 99%

Abstraction-Based Segmental Simulation of Chemical Reaction Networks

Helfrich¹,

Češka²,

Křetínský³

et al. 2022

Preprint

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Simulating chemical reaction networks is often computationally demanding, in particular due to stiffness. We propose a novel simulation scheme where long runs are not simulated as a whole but assembled from shorter precomputed segments of simulation runs. On the one hand, this speeds up the simulation process to obtain multiple runs since we can reuse the segments. On the other hand, questions on diversity and genuineness of our runs arise. However, we ensure that we generate runs close to their true distribution by generating an appropriate abstraction of the original system and utilizing it in the simulation process. Interestingly, as a by-product, we also obtain a yet more efficient simulation scheme, yielding runs over the system's abstraction. These provide a very faithful approximation of concrete runs on the desired level of granularity, at a low cost. Our experiments demonstrate the speedups in the simulations while preserving key dynamical as well as quantitative properties.

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“…Due to low copy number of molecules, gene expression is a stochastic process [1,21]. The typical question asked of a mathematical model is to determine the distribution of a protein level at steady state [3,45]. Traditionally, the number of cells is treated as a discrete variable which is subject to production and depletion events [4,48].…”

Section: Introductionmentioning

confidence: 99%

Joint Distribution of Protein Concentration and Cell Volume Coupled by Feedback in Dilution

Zabaikina

Bokes

Singh

2023

Preprint

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We consider a protein that negatively regulates the rate with which a cell grows. Since less growth means less protein dilution, this mechanism forms a positive feedback loop on the protein concentration. We couple the feedback model with a simple description of the cell cycle, in which a division event is triggered when the cell volume reaches a critical threshold. Following the division we either track only one of the daughter cells (single cell framework) or both cells (population framework). For both frameworks, we find an exact time-independent distribution of protein concentration and cell volume. We explore the consequences of dilution feedback on ergodicity, population growth rate, and the bias of the population distribution towards faster growing cells with less protein.

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Abstraction-Guided Truncations for Stationary Distributions of Markov Population Models

Cited by 8 publications

References 43 publications

Correct Approximation of Stationary Distributions

Correct Approximation of Stationary Distributions

Abstraction-Based Segmental Simulation of Chemical Reaction Networks

Joint Distribution of Protein Concentration and Cell Volume Coupled by Feedback in Dilution

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