TY - JOUR A1 - Winkelmann, Stefanie A1 - Schütte, Christof T1 - The Spatiotemporal Master Equation: Approximation of Reaction-Diffusion Dynamics via Markov State Modeling JF - Journal of Chemical Physics N2 - Accurate modeling and numerical simulation of reaction kinetics is a topic of steady interest.We consider the spatiotemporal chemical master equation (ST-CME) as a model for stochastic reaction-diffusion systems that exhibit properties of metastability. The space of motion is decomposed into metastable compartments and diffusive motion is approximated by jumps between these compartments. Treating these jumps as first-order reactions, simulation of the resulting stochastic system is possible by the Gillespie method. We present the theory of Markov state models (MSM) as a theoretical foundation of this intuitive approach. By means of Markov state modeling, both the number and shape of compartments and the transition rates between them can be determined. We consider the ST-CME for two reaction-diffusion systems and compare it to more detailed models. Moreover, a rigorous formal justification of the ST-CME by Galerkin projection methods is presented. Y1 - 2016 U6 - https://doi.org/10.1063/1.4971163 VL - 145 IS - 21 ER - TY - CHAP A1 - Mukhopadhyay, Anirban T1 - Total Variation Random Forest: Fully automatic MRI segmentation in congenital heart disease T2 - RAMBO 2016, HVSMR 2016: Reconstruction, Segmentation, and Analysis of Medical Images Y1 - 2016 U6 - https://doi.org/10.1007/978-3-319-52280-7_17 VL - LNCS 10129 SP - 165 EP - 171 ER - TY - CHAP A1 - Mukhopadhyay, Anirban A1 - Morillo, Oscar A1 - Zachow, Stefan A1 - Lamecker, Hans T1 - Robust and Accurate Appearance Models Based on Joint Dictionary Learning Data from the Osteoarthritis Initiative T2 - Lecture Notes in Computer Science, Patch-Based Techniques in Medical Imaging. Patch-MI 2016 N2 - Deformable model-based approaches to 3D image segmentation have been shown to be highly successful. Such methodology requires an appearance model that drives the deformation of a geometric model to the image data. Appearance models are usually either created heuristically or through supervised learning. Heuristic methods have been shown to work effectively in many applications but are hard to transfer from one application (imaging modality/anatomical structure) to another. On the contrary, supervised learning approaches can learn patterns from a collection of annotated training data. In this work, we show that the supervised joint dictionary learning technique is capable of overcoming the traditional drawbacks of the heuristic approaches. Our evaluation based on two different applications (liver/CT and knee/MR) reveals that our approach generates appearance models, which can be used effectively and efficiently in a deformable model-based segmentation framework. Y1 - 2016 U6 - https://doi.org/10.1007/978-3-319-47118-1_4 VL - 9993 SP - 25 EP - 33 ER -