Related papers: Statistical Model Checking for Biological Applicat…
In biochemical systems some of the chemical species are present with only small numbers of molecules. In this situation discrete and stochastic simulation approaches are more relevant than continuous and deterministic ones. The fundamental…
The use of mathematical methods for the analysis of chemical reaction systems has a very long history, and involves many types of models: deterministic versus stochastic, continuous versus discrete, and homogeneous versus spatially…
Statistical system models provide the basis for the examination of various sorts of distributions. Classification distributions are a very common and versatile form of statistics in e.g. real economic, social, and IT systems. The…
We present an improvement of the Gillespie Exact Stochastic Simulation Algorithm, which leverages a bitwise representation of variables to perform independent simulations in parallel. We show that the subsequent gain in computational yield…
This limited review is intended as an introduction to the fast growing subject of mathematical modelling of cell metabolism and its biochemical pathways, and more precisely on pathways linked to apoptosis of cancerous cells. Some basic…
We deal with a small enough tumor section to consider it homogeneous, such that populations of lymphocytes and cancer cells are independent of spatial coordinates. A stochastic model based in one step processes is developed to take into…
Much of our mechanistic understanding of the functions of biological macromolecules is based on static structural experiments, which can be modelled either as single structures or conformational ensembles. While these provide us with…
Complex biological processes are usually experimented along time among a collection of individuals. Longitudinal data are then available and the statistical challenge is to better understand the underlying biological mechanisms. The…
Systems biology seeks to create math models of biological systems to reduce inherent biological complexity and provide predictions for applications such as therapeutic development. However, it remains a challenge to determine which math…
The concepts of probability, statistics and stochastic theory are being successfully used in structural engineering. Markov Chain modelling is a simple stochastic process model that has found its application in both describing stochastic…
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
In statistics, it is important to have realistic data sets available for a particular context to allow an appropriate and objective method comparison. For many use cases, benchmark data sets for method comparison are already available…
The biomolecules in and around a living cell -- proteins, nucleic acids, lipids, carbohydrates -- continuously sample myriad conformational states that are thermally accessible at physiological temperatures. Simultaneously, a given…
We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized…
Statistical boosting algorithms have triggered a lot of research during the last decade. They combine a powerful machine-learning approach with classical statistical modelling, offering various practical advantages like automated variable…
Stochastic models for chemical reaction networks have become very popular in recent years. For such models, the estimation of parameter sensitivities is an important and challenging problem. Sensitivity values help in analyzing the network,…
Molecular interactions are wired in a fascinating way resulting in complex behavior of biological systems. Theoretical modeling provides a useful framework for understanding the dynamics and the function of such networks. The complexity of…
Many embedded and real-time systems have a inherent probabilistic behaviour (sensors data, unreliable hardware,...). In that context, it is crucial to evaluate system properties such as "the probability that a particular hardware fails".…
We address the problem of parameter estimation in models of systems biology from noisy observations. The models we consider are characterized by simultaneous deterministic nonlinear differential equations whose parameters are either taken…
Statistical methods are based on model assumptions, and it is statistical folklore that a method's model assumptions should be checked before applying it. This can be formally done by running one or more misspecification tests of model…