Rewriting theory for the life sciences: A unifying theory of CTMC semantics

Behr, Nicolas; Krivine, Jean; Andersen, Jakob L.; Merkle, Daniel

doi:10.1016/j.tcs.2021.07.026

Cited by 9 publications

(46 citation statements)

References 34 publications

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“…In this paper, we consider the two major classes consisting of discrete-time Markov chains (DTMCs) and continuous-time Markov Chains (CTMCs) (leaving for future work the class of Markov decision processes). We will utilize the rule algebra formalism [8,2,6,7] as our central technical tool, with CTMCs in so-called mass-action semantics implemented via the stochastic mechanics framework [4,5,8,7].…”

Section: Theory: Ctmcs and Dtmcs Via Rule-algebraic Methodsmentioning

confidence: 99%

“…We will focus throughout this paper on the case 3 of Sesqui-Pushout (SqPO) semantics [10], which under certain conditions on the underlying base categories furnishes a "compositional" rewriting semantics [2], i.e., supports the requisite construction of rule algebras. Since the main theme of this paper is to advocate rewriting-based methods for implementing models, we discuss here the recent extension of the SqPOformalism to include rules with conditions and under the influence of constraints [6,7]. We refer the interested readers to [7] for the analogous formalism in the Double Pushout (DPO) setting.…”

Section: Preliminaries: "Compositional" Rewriting Theorymentioning

confidence: 99%

“…Since the main theme of this paper is to advocate rewriting-based methods for implementing models, we discuss here the recent extension of the SqPOformalism to include rules with conditions and under the influence of constraints [6,7]. We refer the interested readers to [7] for the analogous formalism in the Double Pushout (DPO) setting. Consider thus a base category C that is M -adhesive (for some class M of monomorphisms), finitary, possesses an M -initial object, M -effective unions and an epi-M -factorization, and such that all final pullback complements (FPCs) along composable pairs of M -morphisms exist (compare [7]).…”

Section: Preliminaries: "Compositional" Rewriting Theorymentioning

confidence: 99%

“…Intuitively, this is a graph transformation system of four rules over undirected graphs whose nodes are attributed by 0 or 1, shown below using • and •, respectively. Referring to [8,2,6,7] for further details, we utilise a "right-to-left" convention for rewriting rules in order to accommodate a natural order of composition of the rule algebra representations.…”

Section: Introductionmentioning

confidence: 99%

“…In the second pair of rules, an agent connected to one with a different opinion adopts the opinion of the other. We could now associate rates with these rules, resulting in a stochastic graph transformation system that allows simulation using the SimSG tool [12] and the derivation of differential equations using the rule algebra approach [8,2,6,7].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Stochastic Graph Transformation For Social Network Modeling

Behr

Bello

Ehmes

et al. 2021

Electron. Proc. Theor. Comput. Sci.

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Adaptive networks model social, physical, technical, or biological systems as attributed graphs evolving at the level of both their topology and data. They are naturally described by graph transformation, but the majority of authors take an approach inspired by the physical sciences, combining an informal description of the operations with programmed simulations, and systems of ODEs as the only abstract mathematical description. We show that we can capture a range of social network models, the so-called voter models, as stochastic attributed graph transformation systems, demonstrate the benefits of this representation and establish its relation to the non-standard probabilistic view adopted in the literature. We use the theory and tools of graph transformation to analyze and simulate the models and propose a new variant of a standard stochastic simulation algorithm to recreate the results observed.

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Section: Theory: Ctmcs and Dtmcs Via Rule-algebraic Methodsmentioning

confidence: 99%

Section: Preliminaries: "Compositional" Rewriting Theorymentioning

confidence: 99%

Section: Preliminaries: "Compositional" Rewriting Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Stochastic Graph Transformation For Social Network Modeling

Behr

Bello

Ehmes

et al. 2021

Electron. Proc. Theor. Comput. Sci.

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View full text Add to dashboard Cite

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Rewriting Theory for the Life Sciences: A Unifying Theory of CTMC Semantics

Behr

Krivine

2020

Lecture Notes in Computer Science

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The Kappa biochemistry and the MØD organo-chemistry frameworks are amongst the most intensely developed applications of rewriting theoretical methods in the life sciences to date. A typical feature of these types of rewriting theories is the necessity to implement certain structural constraints on the objects to be rewritten (a protein is empirically found to have a certain signature of sites, a carbon atom can form at most four bonds,. . .). In this paper, we contribute to the theoretical foundations of these types of rewriting theory a number of conceptual and technical developments that permit to implement a universal theory of continuous-time Markov chains (CTMCs) for stochastic rewriting systems. Our core mathematical concepts are a novel rule algebra construction for the relevant setting of rewriting rules with conditions, both in Double-and in Sesqui-Pushout semantics, augmented by a suitable stochastic mechanics formalism extension that permits to derive dynamical evolution equations for pattern-counting statistics.

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A Categorical Approach to Synthetic Chemistry

Gale,

Lobski,

Zanasi

2023

Lecture Notes in Computer Science

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We introduce a mathematical framework for retrosynthetic analysis, an important research method in synthetic chemistry. Our approach represents molecules and their interaction using string diagrams in layered props -a recently introduced categorical model for partial explanations in scientific reasoning. Such principled approach allows one to model features currently not available in automated retrosynthesis tools, such as chirality, reaction environment and protection-deprotection steps.

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Rewriting theory for the life sciences: A unifying theory of CTMC semantics

Cited by 9 publications

References 34 publications

Stochastic Graph Transformation For Social Network Modeling

Stochastic Graph Transformation For Social Network Modeling

Rewriting Theory for the Life Sciences: A Unifying Theory of CTMC Semantics

A Categorical Approach to Synthetic Chemistry

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