English
Related papers

Related papers: A Compositional Framework for Reaction Networks

200 papers

The analysis of complex reaction networks is of great importance in several chemical and biochemical fields (interstellar chemistry, prebiotic chemistry, reaction mechanism, etc). In this article, we propose to simultaneously refine and…

Molecular Networks · Quantitative Biology 2008-03-11 Raphaël Plasson , Hugues Bersini , Axel Brandenburg

A reaction network is a chemical system involving multiple reactions and chemical species. Stochastic models of such networks treat the system as a continuous time Markov chain on the number of molecules of each species with reactions as…

Probability · Mathematics 2007-05-23 Karen Ball , Thomas G. Kurtz , Lea Popovic , Greg Rempala

The premise of this paper is the following value proposition: Models are good when they describe a system of phenomena, and they are better when they can predict the effect of interventions upon the system. We introduce a formalism by which…

Quantitative Methods · Quantitative Biology 2020-05-13 Vincent Wang

Many physical systems--from mechanical lattices and electrical circuits to biological tissues and architected metamaterials--can be understood as networks transmitting physical quantities. We present a unified mathematical framework for…

Soft Condensed Matter · Physics 2025-08-07 José M. Ortiz-Tavárez , William Stephenson , Xiaoming Mao

This work proposes action networks as a semantically well-founded framework for reasoning about actions and change under uncertainty. Action networks add two primitives to probabilistic causal networks: controllable variables and persistent…

Artificial Intelligence · Computer Science 2013-02-28 Adnan Darwiche , Moises Goldszmidt

Chemical reaction network theory provides powerful tools for rigorously understanding chemical reactions and the dynamical systems and differential equations that represent them. A frequent issue with mathematical analyses of these networks…

Quantitative Methods · Quantitative Biology 2025-12-23 Joseph M. Sauder , Bruce P. Ayati , Ryan Kinser

We use categorical methods to define a new flavor of Petri nets where transitions can only fire a limited number of times, specified by a quantity that we call mana. We do so with chemistry in mind, looking at ways of modelling the behavior…

Category Theory · Mathematics 2021-12-30 Fabrizio Romano Genovese , Fosco Loregian , Daniele Palombi

We consider approaches for causal semantics of Petri nets, explicitly representing dependencies between transition occurrences. For one-safe nets or condition/event-systems, the notion of process as defined by Carl Adam Petri provides a…

Logic in Computer Science · Computer Science 2021-03-02 Rob van Glabbeek , Ursula Goltz , Jens-Wolfhard Schicke

We present a systematic mathematical analysis of the qualitative steady-state response to rate perturbations in large classes of reaction networks. This includes multimolecular reactions and allows for catalysis, enzymatic reactions,…

Dynamical Systems · Mathematics 2017-11-22 Bernhard Brehm , Bernold Fiedler

Chemical reaction network theory is a field of applied mathematics concerned with modeling chemical systems, and can be used in other contexts such as in systems biology to study cellular signaling pathways or epidemiology to study the…

Algebraic Geometry · Mathematics 2024-06-17 Maize Curiel , Elise Farr , Galileo Fries , Luis David García Puente , Julian Hutchins , Vuong Nguyen Hoang

Reaction systems are discrete dynamical systems inspired by bio-chemical processes, whose dynamical behaviour is expressed by set-theoretic operations on finite sets. Reaction systems thus provide a description of bio-chemical phenomena…

Formal Languages and Automata Theory · Computer Science 2020-08-05 Alberto Dennunzio , Enrico Formenti , Luca Manzoni , Antonio E. Porreca

We consider the chemical reaction networks and study currents in these systems. Reviewing recent decomposition of rate functionals from large deviation theory for Markov processes, we adapt these results for reaction networks. In…

Mathematical Physics · Physics 2019-12-16 Johannes Zimmer , D. R. Michiel Renger

We propose a framework for the specification of behaviour-preserving reconfigurations of systems modelled as Petri nets. The framework is based on open nets, a mild generalisation of ordinary Place/Transition nets suited to model open…

Logic in Computer Science · Computer Science 2015-07-01 Paolo Baldan , Andrea Corradini , Hartmut Ehrig , Reiko Heckel , Barbara König

To what extent do the characteristic features of a chemical reaction network reflect its purpose and function? In general, one argues that correlations between specific features and specific functions are key to understanding a complex…

Statistical Mechanics · Physics 2012-03-22 Sang Hoon Lee , Sebastian Bernhardsson , Petter Holme , Beom Jun Kim , Petter Minnhagen

In living cells, biochemical reactions are catalyzed by specific enzymes and connect to one another by sharing substrates and products, forming complex networks. In our previous studies, we established a framework determining the responses…

Molecular Networks · Quantitative Biology 2017-09-06 Takashi Okada , Atsushi Mochizuki

For a large Markovian model, a "product form" is an explicit description of the steady-state behaviour which is otherwise generally untractable. Being first introduced in queueing networks, it has been adapted to Markovian Petri nets. Here…

Discrete Mathematics · Computer Science 2012-04-17 Serge Haddad , Jean Mairesse , Hoang-Thach Nguyen

Chemical reaction networks (CRNs) are prototypical complex systems because reactions are nonlinear and connected in intricate ways, and they are also essential to understand living systems. Here, I discuss how recent developments in…

Statistical Mechanics · Physics 2020-12-23 Massimiliano Esposito

Many biological, technological, and social systems can be effectively described as networks of interacting subsystems. Typically, these networks are not isolated objects, but interact with their environment through both signals and…

Systems and Control · Electrical Eng. & Systems 2026-01-06 Amirhossein Nazerian , Malbor Asllani , Melvyn Tyloo , Wai Lim Ku , Francesco Sorrentino

The reachability semantics for Petri nets can be studied using open Petri nets. For us an "open" Petri net is one with certain places designated as inputs and outputs via a cospan of sets. We can compose open Petri nets by gluing the…

Category Theory · Mathematics 2022-07-26 John C. Baez , Jade Master

This paper initiates the dialectical approach to net theory. This approach views nets as special, but very important and natural, dialectical systems. By following this approach, a suitably generalized version of nets, called dialectical…

Logic in Computer Science · Computer Science 2018-10-16 Robert E. Kent