Related papers: Statistical Model Checking for Biological Applicat…
Stochastic kinetic models are often used to describe complex biological processes. Typically these models are analytically intractable and have unknown parameters which need to be estimated from observed data. Ideally we would have…
Model-based safety analysis approaches aim at finding critical failure combinations by analysis of models of the whole system (i.e. software, hardware, failure modes and environment). The advantage of these methods compared to traditional…
Modeling biological processes is a highly demanding task because not all processes are fully understood. Mathematical models allow us to test hypotheses about possible mechanisms of biological processes. The mathematical mechanisms…
Statistical mechanics is one of the most powerful and elegant tools in the quantitative sciences. One key virtue of statistical mechanics is that it is designed to examine large systems with many interacting degrees of freedom, providing a…
We consider the problem of computing the satisfaction probability of a formula for stochastic models with parametric uncertainty. We show that this satisfaction probability is a smooth function of the model parameters. This enables us to…
The problem of detecting changes in the statistical properties of a stochastic system and time series arises in various branches of science and engineering. It has a wide spectrum of important applications ranging from machine monitoring to…
The stochastic simulation of large-scale biochemical reaction networks is of great importance for systems biology since it enables the study of inherently stochastic biological mechanisms at the whole cell scale. Stochastic Simulation…
Stochastic reaction network models are widely utilized in biology and chemistry to describe the probabilistic dynamics of biochemical systems in general, and gene interaction networks in particular. Most often, statistical analysis and…
Diffusion probabilistic models have made their way into a number of high-profile applications since their inception. In particular, there has been a wave of research into using diffusion models in the prediction and design of biomolecular…
Automation is becoming ubiquitous in all laboratory activities, leading towards precisely defined and codified laboratory protocols. However, the integration between laboratory protocols and mathematical models is still lacking. Models…
Simulation models are an absolute necessity in the human and social sciences, which can only very exceptionally use experimental science methods to construct their knowledge. Models enable the simulation of social processes by replacing the…
Key processes in biological and chemical systems are described by networks of chemical reactions. From molecular biology to biotechnology applications, computational models of reaction networks are used extensively to elucidate their…
The M{\O}D computational framework implements rule-based generative chemistries as explicit transformations of graphs representing chemical structural formulae. Here, we expand M{\O}D by a stochastic simulation module that simulates the…
Comparisons of different treatments or production processes are the goals of a significant fraction of applied research. Unsurprisingly, two-sample problems play a main role in Statistics through natural questions such as `Is the the new…
Stochastic reaction networks, which are usually modeled as continuous-time Markov chains on $\mathbb Z^d_{\ge 0}$, and simulated via a version of the "Gillespie algorithm," have proven to be a useful tool for the understanding of processes,…
Comprehensive simulations of the entire biochemistry of cells have great potential to help physicians treat disease and help engineers design biological machines. But such simulations must model networks of millions of molecular species and…
The mathematical models used to capture features of complex, biological systems are typically non-linear, meaning that there are no generally valid simple relationships between their outputs and the data that might be used to validate them.…
The modelling and analysis of biological systems has deep roots in Mathematics, specifically in the field of ordinary differential equations (ODEs). Alternative approaches based on formal calculi, often derived from process algebras or term…
Auto-regulatory feedback loops are one of the most common network motifs. A wide variety of stochastic models have been constructed to understand how the fluctuations in protein numbers in these loops are influenced by the kinetic…
Bioprocess mechanistic modeling is essential for advancing intelligent digital twin representation of biomanufacturing, yet challenges persist due to complex intracellular regulation, stochastic system behavior, and limited experimental…