相关论文: Scaling Methods for Stochastic Chemical Reaction N…

Exact results for product-form stationary distributions of Markov chains are of interest in different fields. In stochastic reaction networks (CRNs), stationary distributions are mostly known in special cases where they are of product-form.…

Chemical reaction networks (CRNs) model the behavior of molecules in a well-mixed system. The emerging field of molecular programming uses CRNs not only as a descriptive tool, but as a programming language for chemical computation.…

We propose a novel measure valued process which models the behaviour of chemical reaction networks in spatially heterogeneous systems. It models reaction dynamics between different molecular species and continuous movement of molecules in…

We analyze asymptotic scaling properties of a model class of anomalous reaction-diffusion (ARD) equations. Numerical experiments show that solutions to these have, for large $t$, well defined scaling properties. We suggest a general…

We identify the thermodynamic conditions necessary to observe indefinite growth in homogeneous open chemical reaction networks (CRNs) satisfying mass action kinetics. We also characterize the thermodynamic efficiency of growth by…

This work provides a comprehensive scaling law and performance analysis for multi-user massive MIMO relay networks, where the relay is equipped with massive antennas and uses MRC/MRT for low-complexity processing. CSI error is considered.…

Embedding computation in biochemical environments incompatible with traditional electronics is expected to have wide-ranging impact in synthetic biology, medicine, nanofabrication and other fields. Natural biochemical systems are typically…

Certain chemical reaction networks (CRNs) when modeled as a deterministic dynamical system taken with mass-action kinetics have the property of reaction network detailed balance (RNDB) which is achieved by imposing network-related…

Disordered elastic networks provide a framework for describing a wide variety of physical systems, ranging from amorphous solids, through polymeric fibrous materials to confluent cell tissues. In many cases, such networks feature two widely…

Some results are presented on how oscillation is inherited by chemical reaction networks (CRNs) when they are built in natural ways from smaller oscillatory networks. The main results describe four important ways in which a CRN can be…

Chemical reaction networks (CRNs) exhibit complex dynamics governed by their underlying network structure. In this paper, we propose a novel approach to study the dynamics of CRNs by representing them on species graphs (S-graphs). By…

We study asymptotic behaviour of stochastic approximation procedures with three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function.…

In chemical reaction networks (CRNs) with stochastic semantics based on continuous-time Markov chains (CTMCs), the typically large populations of species cause combinatorially large state spaces. This makes the analysis very difficult in…

Reaction networks are commonly used to model the evolution of populations of species subject to transformations following an imposed stoichiometry. This paper focuses on the efficient characterisation of dynamical properties of Discrete…

We study scaling limits of non-increasing Markov chains with values in the set of non-negative integers, under the assumption that the large jump events are rare and happen at rates that behave like a negative power of the current state. We…

It is useful to have complete lists of nonisomorphic chemical reaction networks (CRNs) of a given size, with or without various restrictions. One may, for example, be interested in exploring how often certain dynamical behaviours occur in…

How does the shape of a network change as its size increases? Although random graph models provide some expectations for such "scaling behaviors" in the structure of networks, relatively little is known about how empirical network structure…

Growth and decay are system-level properties of chemical reaction networks (CRNs) relevant from prebiotic chemistry to cellular metabolism. Their properties are typically analyzed through the kinetics of particular models, which requires…

We study the model of continuous chemical reaction networks (CRNs), consisting of reactions such as $A+B \to C+D$ that can transform some continuous, nonnegative real-valued quantity (called a *concentration*) of chemical species $A$ and…

Continuous-time Markov chains are used to model stochastic systems where transitions can occur at irregular times, e.g., birth-death processes, chemical reaction networks, population dynamics, and gene regulatory networks. We develop a…