@misc{BanischDjurdjevacConradSchuette2015, author = {Banisch, Ralf and Djurdjevac Conrad, Natasa and Sch{\"u}tte, Christof}, title = {Reactive flows and unproductive cycles for random walks on complex networks}, issn = {1438-0064}, doi = {10.1140/epjst/e2015-02417-8}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-54239}, year = {2015}, abstract = {We present a comprehensive theory for analysis and understanding of transition events between an initial set A and a target set B for general ergodic finite-state space Markov chains or jump processes, including random walks on networks as they occur, e.g., in Markov State Modelling in molecular dynamics. The theory allows us to decompose the probability flow generated by transition events between the sets A and B into the productive part that directly flows from A to B through reaction pathways and the unproductive part that runs in loops and is supported on cycles of the underlying network. It applies to random walks on directed networks and nonreversible Markov processes and can be seen as an extension of Transition Path Theory. Information on reaction pathways and unproductive cycles results from the stochastic cycle decomposition of the underlying network which also allows to compute their corresponding weight, thus characterizing completely which structure is used how often in transition events. The new theory is illustrated by an application to a Markov State Model resulting from weakly damped Langevin dynamics where the unproductive cycles are associated with periodic orbits of the underlying Hamiltonian dynamics.}, language = {en} } @article{WinkelmannSchuettevonKleist2014, author = {Winkelmann, Stefanie and Sch{\"u}tte, Christof and von Kleist, Max}, title = {Markov Control Processes with Rare State Observation: Theory and Application to Treatment Scheduling in HIV-1}, volume = {12}, journal = {Communications in Mathematical Sciences}, number = {5}, doi = {10.4310/CMS.2014.v12.n5.a4}, pages = {859 -- 877}, year = {2014}, abstract = {Markov Decision Processes (MDP) or Partially Observable MDPs (POMDP) are used for modelling situations in which the evolution of a process is partly random and partly controllable. These MDP theories allow for computing the optimal control policy for processes that can continuously or frequently be observed, even if only partially. However, they cannot be applied if state observation is very costly and therefore rare (in time). We present a novel MDP theory for rare, costly observations and derive the corresponding Bellman equation. In the new theory, state information can be derived for a particular cost after certain, rather long time intervals. The resulting information costs enter into the total cost and thus into the optimization criterion. This approach applies to many real world problems, particularly in the medical context, where the medical condition is examined rather rarely because examination costs are high. At the same time, the approach allows for efficient numerical realization. We demonstrate the usefulness of the novel theory by determining, from the national economic perspective, optimal therapeutic policies for the treatment of the human immunodeficiency virus (HIV) in resource-rich and resource-poor settings. Based on the developed theory and models, we discover that available drugs may not be utilized efficiently in resource-poor settings due to exorbitant diagnostic costs.}, language = {en} } @article{DjurdjevacConradBanischSchuette2015, author = {Djurdjevac Conrad, Natasa and Banisch, Ralf and Sch{\"u}tte, Christof}, title = {Modularity of Directed Networks: Cycle Decomposition Approach}, journal = {Journal of Computational Dynamics 2 (2015) pp. 1-24}, doi = {10.3934/jcd.2015.2.1}, year = {2015}, abstract = {The problem of decomposing networks into modules (or clusters) has gained much attention in recent years, as it can account for a coarsegrained description of complex systems, often revealing functional subunits of these systems. A variety of module detection algorithms have been proposed, mostly oriented towards finding hard partitionings of undirected networks. Despite the increasing number of fuzzy clustering methods for directed networks, many of these approaches tend to neglect important directional information. In this paper, we present a novel random walk based approach for finding fuzzy partitions of directed, weighted networks, where edge directions play a crucial role in defining how well nodes in a module are interconnected. We will show that cycle decomposition of a random walk process connects the notion of network modules and information transport in a network, leading to a new, symmetric measure of node communication. Finally, we will use this measure to introduce a communication graph, for which we will show that although being undirected it inherits all necessary information about modular structures from the original network.}, language = {en} } @misc{WangSchuette2014, author = {Wang, Han and Sch{\"u}tte, Christof}, title = {Building Markov State Models for Periodically Driven Non-Equilibrium Systems}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-53167}, year = {2014}, abstract = {Recent years have seen an increased interest in non-equilibrium molecular dynamics (NEMD) simulations, especially for molecular systems with periodic forcing by external fields, e.g., in the context of studying effects of electromagnetic radiation on the human body tissue. Lately, an NEMD methods with local thermostating has been proposed that allows for studying non-equilibrium processes in a statistically reliable and thermodynamically consistent way. In this article, we demonstrate how to construct Markov State Models (MSMs) for such NEMD simulations. MSM building has been well-established for systems in equilibrium where MSMs with just a few (macro-)states allow for accurate reproduction of the essential kinetics of the molecular system under consideration. Non-equilibrium MSMs have been lacking so far. The article presents how to construct such MSMs and illustrates their validity and usefulness for the case of conformation dynamics of alanine dipeptide in an external electric field.}, language = {en} } @misc{GulSchuetteBernhard2015, author = {Gul, Raheem and Sch{\"u}tte, Christof and Bernhard, Stefan}, title = {Mathematical modeling and sensitivity analysis of arterial anastomosis in arm arteries}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-54339}, year = {2015}, abstract = {Cardiovascular diseases are one of the major problems in medicine today and the number of patients increases worldwide. To find the most efficient treatment, prior knowledge about function and dysfunction of the cardiovas- cular system is required and methods need to be developed that identify the disease in an early stage. Mathematical modeling is a powerful tool for prediction and investigation of cardiovascular diseases. It has been shown that the Windkessel model, being based on an analogy between electrical circuits and fluid flow, is a simple but effective method to model the human cardiovascular system. In this paper, we have applied parametric local sensitivity analysis (LSA) to a linear elastic model of the arm arteries, to find and rank sensitive param- eters that may be helpful in clinical diagnosis. A computational model for end-to-side anastomosis (superior ulnar collateral anastomosis with posterior ulnar recurrent, SUC-PUR) is carried out to study the effects of some clinically relevant haemodynamic parameters like blood flow resistance and terminal re- sistance on pressure and flow at different locations of the arm artery. In this context, we also discuss the spatio-temporal dependency of local sensitivities. The sensitivities with respect to cardiovascular parameters reveal the flow resistance and diameter of the vessels as most sensitive parameters. These parameters play a key role in diagnosis of severe stenosis and aneurysms. In contrast, wall thickness and elastic modulus are found to be less sensitive.}, language = {en} } @inproceedings{Mukhopadhyay2016, author = {Mukhopadhyay, Anirban}, title = {Total Variation Random Forest: Fully automatic MRI segmentation in congenital heart disease}, volume = {LNCS 10129}, booktitle = {RAMBO 2016, HVSMR 2016: Reconstruction, Segmentation, and Analysis of Medical Images}, doi = {10.1007/978-3-319-52280-7_17}, pages = {165 -- 171}, year = {2016}, language = {en} } @inproceedings{MukhopadhyayMorilloZachowetal.2016, author = {Mukhopadhyay, Anirban and Morillo, Oscar and Zachow, Stefan and Lamecker, Hans}, title = {Robust and Accurate Appearance Models Based on Joint Dictionary Learning Data from the Osteoarthritis Initiative}, volume = {9993}, booktitle = {Lecture Notes in Computer Science, Patch-Based Techniques in Medical Imaging. Patch-MI 2016}, doi = {10.1007/978-3-319-47118-1_4}, pages = {25 -- 33}, year = {2016}, abstract = {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.}, language = {en} } @article{SahuMukhopadhyaySzengeletal.2017, author = {Sahu, Manish and Mukhopadhyay, Anirban and Szengel, Angelika and Zachow, Stefan}, title = {Addressing multi-label imbalance problem of Surgical Tool Detection using CNN}, volume = {12}, journal = {International Journal of Computer Assisted Radiology and Surgery}, number = {6}, publisher = {Springer}, doi = {10.1007/s11548-017-1565-x}, pages = {1013 -- 1020}, year = {2017}, abstract = {Purpose: A fully automated surgical tool detection framework is proposed for endoscopic video streams. State-of-the-art surgical tool detection methods rely on supervised one-vs-all or multi-class classification techniques, completely ignoring the co-occurrence relationship of the tools and the associated class imbalance. Methods: In this paper, we formulate tool detection as a multi-label classification task where tool co-occurrences are treated as separate classes. In addition, imbalance on tool co-occurrences is analyzed and stratification techniques are employed to address the imbalance during Convolutional Neural Network (CNN) training. Moreover, temporal smoothing is introduced as an online post-processing step to enhance run time prediction. Results: Quantitative analysis is performed on the M2CAI16 tool detection dataset to highlight the importance of stratification, temporal smoothing and the overall framework for tool detection. Conclusion: The analysis on tool imbalance, backed by the empirical results indicates the need and superiority of the proposed framework over state-of-the-art techniques.}, language = {en} } @article{KlusSchuette2016, author = {Klus, Stefan and Sch{\"u}tte, Christof}, title = {Towards tensor-based methods for the numerical approximation of the Perron-Frobenius and Koopman operator}, volume = {3}, journal = {Journal of Computational Dynamics}, number = {2}, doi = {10.3934/jcd.2016007}, pages = {139 -- 161}, year = {2016}, abstract = {The global behavior of dynamical systems can be studied by analyzing the eigenvalues and corresponding eigenfunctions of linear operators associated with the system. Two important operators which are frequently used to gain insight into the system's behavior are the Perron-Frobenius operator and the Koopman operator. Due to the curse of dimensionality, computing the eigenfunctions of high-dimensional systems is in general infeasible. We will propose a tensor-based reformulation of two numerical methods for computing finite-dimensional approximations of the aforementioned infinite-dimensional operators, namely Ulam's method and Extended Dynamic Mode Decomposition (EDMD). The aim of the tensor formulation is to approximate the eigenfunctions by low-rank tensors, potentially resulting in a significant reduction of the time and memory required to solve the resulting eigenvalue problems, provided that such a low-rank tensor decomposition exists. Typically, not all variables of a high-dimensional dynamical system contribute equally to the system's behavior, often the dynamics can be decomposed into slow and fast processes, which is also reflected in the eigenfunctions. Thus, the weak coupling between different variables might be approximated by low-rank tensor cores. We will illustrate the efficiency of the tensor-based formulation of Ulam's method and EDMD using simple stochastic differential equations.}, language = {en} } @article{KlusKoltaiSchuette2016, author = {Klus, Stefan and Koltai, Peter and Sch{\"u}tte, Christof}, title = {On the numerical approximation of the Perron-Frobenius and Koopman operator}, volume = {3}, journal = {Journal of Computational Dynamics}, number = {1}, doi = {10.3934/jcd.2016003}, pages = {51 -- 77}, year = {2016}, abstract = {Information about the behavior of dynamical systems can often be obtained by analyzing the eigenvalues and corresponding eigenfunctions of linear operators associated with a dynamical system. Examples of such operators are the Perron-Frobenius and the Koopman operator. In this paper, we will review di� fferent methods that have been developed over the last decades to compute � infinite-dimensional approximations of these in� finite-dimensional operators - in particular Ulam's method and Extended Dynamic Mode Decomposition (EDMD) - and highlight the similarities and di� fferences between these approaches. The results will be illustrated using simple stochastic di� fferential equations and molecular dynamics examples.}, language = {en} } @article{HuttaryGoubergritsSchuetteetal.2017, author = {Huttary, Rudolf and Goubergrits, Leonid and Sch{\"u}tte, Christof and Bernhard, Stefan}, title = {Simulation, Identification and Statistical Variation in Cardiovascular Analysis (SISCA) - a Software Framework for Multi-compartment Lumped Modeling}, volume = {87}, journal = {Computers in Biology and Medicine}, doi = {10.1016/j.compbiomed.2017.05.021}, pages = {104 -- 123}, year = {2017}, language = {en} } @misc{GuptaGramatkeEinspanieretal.2017, author = {Gupta, Pooja and Gramatke, Annika and Einspanier, Ralf and Sch{\"u}tte, Christof and von Kleist, Max and Sharbati, Jutta}, title = {In silicio cytotoxicity assessment on cultured rat intestinal cells deduced from cellular impedance measurements}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-62666}, year = {2017}, abstract = {Early and reliable identification of chemical toxicity is of utmost importance. At the same time, reduction of animal testing is paramount. Therefore, methods that improve the interpretability and usability of in vitro assays are essential. xCELLigence's real-time cell analyzer (RTCA) provides a novel, fast and cost effective in vitro method to probe compound toxicity. We developed a simple mathematical framework for the qualitative and quantitative assessment of toxicity for RTCA measurements. Compound toxicity, in terms of its 50\% inhibitory concentration IC_{50} on cell growth, and parameters related to cell turnover were estimated on cultured IEC-6 cells exposed to 10 chemicals at varying concentrations. Our method estimated IC50 values of 113.05, 7.16, 28.69 and 725.15 μM for the apparently toxic compounds 2-acetylamino-fluorene, aflatoxin B1, benzo-[a]-pyrene and chloramphenicol in the tested cell line, in agreement with literature knowledge. IC_{50} values of all apparent in vivo non-toxic compounds were estimated to be non-toxic by our method. Corresponding estimates from RTCA's in-built model gave false positive (toxicity) predictions in 5/10 cases. Taken together, our proposed method reduces false positive predictions and reliably identifies chemical toxicity based on impedance measurements. The source code for the developed method including instructions is available at https://git.zib.de/bzfgupta/toxfit/tree/master.}, language = {en} } @article{KlusNueskeKoltaietal.2018, author = {Klus, Stefan and N{\"u}ske, Feliks and Koltai, Peter and Wu, Hao and Kevrekidis, Ioannis and Sch{\"u}tte, Christof and No{\´e}, Frank}, title = {Data-driven model reduction and transfer operator approximation}, volume = {28}, journal = {Journal of Nonlinear Science}, number = {3}, doi = {10.1007/s00332-017-9437-7}, pages = {985 -- 1010}, year = {2018}, language = {en} } @article{KoltaiCiccottiSchuette2016, author = {Koltai, Peter and Ciccotti, Giovanni and Sch{\"u}tte, Christof}, title = {On Markov state models for non-equilibrium molecular dynamics}, volume = {145}, journal = {The Journal of Chemical Physics}, number = {174103}, doi = {10.1063/1.4966157}, year = {2016}, language = {en} }