Related papers: Reachability in Restricted Chemical Reaction Netwo…
Our paper reviews some key concepts in chemical reaction network theory and mathematical epidemiology, and examines their intersection, with three goals. The first is to make the case that mathematical epidemiology (ME), and also related…
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…
Reaction networks (RNs) comprise a set $X$ of species and a set $\mathscr{R}$ of reactions $Y\to Y'$, each converting a multiset of educts $Y\subseteq X$ into a multiset $Y'\subseteq X$ of products. RNs are equivalent to directed…
The stochastic kinetics of BRN are described by a chemical master equation (CME) and the underlying laws of mass action. The CME must be usually solved numerically by generating enough traces of random reaction events. The resulting…
Information geometry is based on classical Legendre duality but allows to incorporate additional structure such as algebraic constraints and Bregman divergence functions. It is naturally suited, and has been successfully used, to describe…
Many important phenomena in biochemistry and biology exploit dynamical features such as multi-stability, oscillations, and chaos. Construction of novel chemical systems with such rich dynamics is a challenging problem central to the fields…
We introduce the first cut-free nested sequent systems for first-order modal logics that admit increasing, decreasing, constant, and empty domains along with so-called general path conditions and seriality. We obtain such systems by means…
The thermodynamic and dynamical conditions necessary to observe indefinite growth in homogeneous open chemical reaction networks (CRNs) satisfying mass action kinetics were presented in Srinivas et al. (2023): Unimolecular CRNs can only…
We study linear-time temporal logics interpreted over data words with multiple attributes. We restrict the atomic formulas to equalities of attribute values in successive positions and to repetitions of attribute values in the future or…
In this paper, it is presented a methodology for implementing arbitrarily constructed time-homogenous Markov chains with biochemical systems. Not only discrete but also continuous-time Markov chains are allowed to be computed. By employing…
Bistability plays a central role in the gene regulatory networks (GRNs) controlling many essential biological functions, including cellular differentiation and cell cycle control. However, establishing the network topologies that can…
Multi-pushdown systems are a standard model for concurrent recursive programs, but they have an undecidable reachability problem. Therefore, there have been several proposals to underapproximate their sets of runs so that reachability in…
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…
Multi-stack pushdown systems are a well-studied model of concurrent computation using threads with first-order procedure calls. While, in general, reachability is undecidable, there are numerous restrictions on stack behaviour that lead to…
In this paper we propose augmented interval Markov chains (AIMCs): a generalisation of the familiar interval Markov chains (IMCs) where uncertain transition probabilities are in addition allowed to depend on one another. This new model…
Applying neural networks as controllers in dynamical systems has shown great promises. However, it is critical yet challenging to verify the safety of such control systems with neural-network controllers in the loop. Previous methods for…
The asymptotic properties of some Markov processes associated to stochastic chemical reaction networks (CRNs) driven by the kinetics of the law of mass action are analyzed. The scaling regime introduced in the paper assumes that the norm of…
Proposals for molecular communication networks as part of a future internet of bio-nano-things have become more intricate and the question of practical implementation is gaining more importance. One option is to apply detailed chemical…
Reachability queries checking the existence of a path from a source node to a target node are fundamental operators for querying and processing graph data. Current approaches for index-based evaluation of reachability queries either focus…
Information processing relying on biochemical interactions in the cellular environment is essential for biological organisms. The implementation of molecular computational systems holds significant interest and potential in the fields of…