Related papers: Comparison Theorems for Stochastic Chemical Reacti…
We propose a new approach for estimating the finite dimensional transition matrix of a Markov chain using a large number of independent sample paths observed at random times. The sample paths may be observed as few as two times, and the…
Stochastic reaction network models are often used to explain and predict the dynamics of gene regulation in single cells. These models usually involve several parameters, such as the kinetic rates of chemical reactions, that are not…
In this paper the qualitative dynamical properties of so-called generalized ribosome flow models are studied. Ribosome flow models known from the literature are generalized by allowing an arbitrary directed network structure between the…
Random walks find applications in many areas of science and are the heart of essential network analytic tools. When defined on temporal networks, even basic random walk models may exhibit a rich spectrum of behaviours, due to the…
We consider the problem of inferring the unknown parameters of a stochastic biochemical network model from a single measured time-course of the concentration of some of the involved species. Such measurements are available, e.g., from…
Continuous-time Markov chains on non-negative integers can be used for modeling biological systems, population dynamics, and queueing models. Qualitative behaviors of birth-and-death models, typical examples of such one-dimensional…
More than ever, today we are left with the abundance of molecular data outpaced by the advancements of the phylogenomic methods. Especially in the case of presence of many genes over a set of species under the phylogeny question, more…
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…
Recurrent neural networks (RNNs) are commonly applied to clinical time-series data with the goal of learning patient risk stratification models. Their effectiveness is due, in part, to their use of parameter sharing over time (i.e., cells…
Switching ARMA models greatly enhance the standard linear models to the extent that different ARMA model is allowed in a different regime, and the regime switching is typically assumed a Markov chain on the finite states of potential…
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,…
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…
This paper studies the stability of sampled and networked control systems with sampling and communication times governed by probabilistic clocks. The clock models have few restrictions, and can be used to model numerous phenomena such as…
Atom tracing is essential for understanding the fate of labeled atoms in biochemical reaction networks, yet existing computational methods either simplify label correlations or suffer from combinatorial explosion. We introduce a…
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…
A central task in many applications is reasoning about processes that change in a continuous time. The mathematical framework of Continuous Time Markov Processes provides the basic foundations for modeling such systems. Recently, Nodelman…
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…
We introduce a new model of \emph{step} Chemical Reaction Networks (step CRNs), motivated by the step-wise addition of materials in standard lab procedures. Step CRNs have ordered reactants that transform into products via reaction rules…
Estimation of parameter sensitivities for stochastic chemical reaction networks is an important and challenging problem. Sensitivity values are important in the analysis, modeling and design of chemical networks. They help in understanding…
Rule-based modelling allows to represent molecular interactions in a compact and natural way. The underlying molecular dynamics, by the laws of stochastic chemical kinetics, behaves as a continuous-time Markov chain. However, this Markov…