Related papers: A Compositional Framework for Reaction Networks
We address a fundamental question: under which conditions do the dynamics and thermodynamics of open chemical reaction networks (CRNs), grounded on the notion of idealized chemostats that exchange selected species, emerge from underlying…
These lecture notes concern the basics of the theory of process behaviour. First the concept of a (labelled) transition system receives ample treatment and then the following issues concerning process behaviour are elaborated in the setting…
In this paper we develop a theory to describe innovation processes in a network of interacting units. We introduce a stochastic picture that allows for the clarification of the role of fluctuations for the survival of innovations in such a…
Robustness of biochemical systems has become one of the central questions in systems biology although it is notoriously difficult to formally capture its multifaceted nature. Maintenance of normal system function depends not only on the…
Diffusion processes are instrumental to describe the movement of a continuous quantity in a generic network of interacting agents. Here, we present a probabilistic framework for diffusion in networks and propose to classify agent…
Chemical reaction networks (CRNs) are foundational models for describing complex biochemical processes. We study noncompetitive CRNs, a class of networks whose static states are rate-independent, and that can implement ReLU neural networks.…
We present a systematic procedure for testing whether reaction networks exhibit non-expansivity or monotonicity. This procedure identifies explicit norms under which a network is non-expansive or cones for which the system is monotone-or…
Complex dynamical networks consisting of many components that interact and produce each other are difficult to understand, especially, when new components may appear. In this paper we outline a theory to deal with such systems. The theory…
Real-world complex systems such as ecological communities and neuron networks are essential parts of our everyday lives. These systems are composed of units which interact through intricate networks. The ability to predict sudden changes in…
An abstract network approach is proposed for the description of the dynamics in reactive processes. The phase space of the variables (concentrations in reactive systems) is partitioned into a finite number of segments, which constitute the…
We investigate a simple generative model for network formation. The model is designed to describe the growth of networks of kinship, trading, corporate alliances, or autocatalytic chemical reactions, where feedback is an essential element…
We present an approach for flux analysis in process algebra models of biological systems. We perceive flux as the flow of resources in stochastic simulations. We resort to an established correspondence between event structures, a broadly…
In living cells, chemical reactions form a complex network. Complicated dynamics arising from such networks are the origins of biological functions. We propose a novel mathematical method to analyze bifurcation behaviors of a reaction…
This paper is concerned with the utilization of deterministically modeled chemical reaction networks for the implementation of (feed-forward) neural networks. We develop a general mathematical framework and prove that the ordinary…
This paper presents a unified framework for analyzing the input-output behavior of discrete time complex networks viewed as open systems. Importantly, we focus on systems that are inherently modeled in discrete time-such as opinion…
Complex systems often have features that can be modeled by advanced mathematical tools [1]. Of special interests are the features of complex systems that have a network structure as such systems are important for modeling technological and…
Graph-based reaction systems were recently introduced as a generalization of the intensely studied set-based reaction systems. They deal with simple edge-labeled directed graphs, and dynamic semantics of graph-based reaction systems is…
We provide a category theoretical framework capturing two approaches to graph-based models of chemistry: formal reactions and disconnection rules. We model a translation from the latter to the former as a functor, which is faithful, and…
Inspired by Anderson et al. [J. R. Soc. Interface, 2014] we study the long-term behavior of discrete chemical reaction networks (CRNs). In particular, using techniques from both Petri net theory and CRN theory, we provide a powerful…
Petri Nets (PN) are a central, theoretically sound model for concurrent or distributed systems but, at least in their classical definition, not expressive enough to represent dynamic reconfiguration capabilities. On the other side,…