Continuous-time Markov chains are commonly used in practice for modeling biochemical reaction networks in which the inherent randomness of the molecular interactions cannot be ignored. This has motivated recent research effort into methods for parameter inference and experiment design for such models. The major difficulty is that such methods usually require one to iteratively solve the chemical master equation that governs the time evolution of the probability distribution of the system. This, however, is rarely possible, and even approximation techniques remain limited to relatively small and simple systems. An alternative explored in this article is to base methods on only some low-order moments of the entire probability distribution. We summarize the theory behind such moment-based... (more)

The computation of transient probabilities for continuous-time Markov chains often employs uniformization, also known as the Jensen method. The fast adaptive uniformization method introduced by Mateescu et al. approximates the probability by neglecting insignificant states and has proven to be effective for quantitative analysis of stochastic models arising in chemical and biological applications. However, this method has only been formulated for the analysis of properties at a given point of time t. In this article, we extend fast adaptive uniformization to handle expected reward properties that reason about the model behavior until time t, for example, the expected number of chemical reactions that have occurred until t. To show the feasibility of the approach, we... (more)

Recent advances in imaging technology now provide us with 3D images of developing organs. These can be used to extract 3D geometries for simulations of organ development. To solve models on growing domains, the displacement fields between consecutive image frames need to be determined. Here we develop and evaluate different landmark-free algorithms for the determination of such displacement fields from image data. In particular, we examine minimal distance, normal distance, diffusion-based, and uniform mapping algorithms and test these algorithms with both synthetic and real data in 2D and 3D. We conclude that in most cases, the normal distance algorithm is the method of choice and wherever it fails, diffusion-based mapping provides a good alternative.

The problem of gene regulatory network inference is a major concern of systems biology. In recent years, a novel methodology has gained momentum, called community network approach. Community networks integrate predictions from individual methods in a “metapredictor,” in order to compose the advantages of different methods and soften individual limitations. This article proposes a novel methodology to integrate prediction ensembles using constraint programming, a declarative modeling and problem solving paradigm. Constraint programming naturally allows the modeling of dependencies among components of the problem as constraints, facilitating the integration and use of different forms of knowledge. The new paradigm, referred to as constrained community... (more)