@article{WinkelmannSchuettevonKleist2012, author = {Winkelmann, Stefanie and Sch{\"u}tte, Christof and von Kleist, Max}, title = {Markov Control with Rare State Observation}, series = {International Journal of Biomathematics and Biostatistics}, journal = {International Journal of Biomathematics and Biostatistics}, year = {2012}, language = {en} } @article{DuwalWinkelmannSchuetteetal., author = {Duwal, Sulav and Winkelmann, Stefanie and Sch{\"u}tte, Christof and von Kleist, Max}, title = {Optimal Treatment Strategies in the Context of 'Treatment for Prevention' against HIV/1 in Resource-Poor Settings}, series = {PloS Computational Biology}, volume = {11}, journal = {PloS Computational Biology}, number = {4}, doi = {10.1371/journal.pcbi.1004200}, abstract = {An estimated 2.7 million new HIV-1 infections occurred in 2010. `Treatment-for-prevention' may strongly prevent HIV-1 transmission. The basic idea is that immediate treatment initiation rapidly decreases virus burden, which reduces the number of transmittable viruses and thereby the probability of infection. However, HIV inevitably develops drug resistance, which leads to virus rebound and nullifies the effect of `treatment-for-prevention' for the time it remains unrecognized. While timely conducted treatment changes may avert periods of viral rebound, necessary treatment options and diagnostics may be lacking in resource-constrained settings. Within this work, we provide a mathematical platform for comparing different treatment paradigms that can be applied to many medical phenomena. We use this platform to optimize two distinct approaches for the treatment of HIV-1: (i) a diagnostic-guided treatment strategy, based on infrequent and patient-specific diagnostic schedules and (ii) a pro-active strategy that allows treatment adaptation prior to diagnostic ascertainment. Both strategies are compared to current clinical protocols (standard of care and the HPTN052 protocol) in terms of patient health, economic means and reduction in HIV-1 onward transmission exemplarily for South Africa. All therapeutic strategies are assessed using a coarse-grained stochastic model of within-host HIV dynamics and pseudo-codes for solving the respective optimal control problems are provided. Our mathematical model suggests that both optimal strategies (i)-(ii) perform better than the current clinical protocols and no treatment in terms of economic means, life prolongation and reduction of HIV-transmission. The optimal diagnostic-guided strategy suggests rare diagnostics and performs similar to the optimal pro-active strategy. Our results suggest that 'treatment-for-prevention' may be further improved using either of the two analyzed treatment paradigms.}, language = {en} } @article{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 silico cytotoxicity assessment on cultured rat intestinal cells deduced from cellular impedance measurements}, series = {Toxicology in Vitro}, volume = {41}, journal = {Toxicology in Vitro}, issn = {1438-0064}, pages = {179 -- 188}, 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 IC50 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. IC50 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{vonKleistSchuetteZhang, author = {von Kleist, Max and Sch{\"u}tte, Christof and Zhang, Wei}, title = {Statistical analysis of the first passage path ensemble of jump processes}, series = {Journal of Statistical Physics}, volume = {170}, journal = {Journal of Statistical Physics}, doi = {10.1007/s10955-017-1949-x}, pages = {809 -- 843}, abstract = {The transition mechanism of jump processes between two different subsets in state space reveals important dynamical information of the processes and therefore has attracted considerable attention in the past years. In this paper, we study the first passage path ensemble of both discrete-time and continuous-time jump processes on a finite state space. The main approach is to divide each first passage path into nonreactive and reactive segments and to study them separately. The analysis can be applied to jump processes which are non-ergodic, as well as continuous-time jump processes where the waiting time distributions are non-exponential. In the particular case that the jump processes are both Markovian and ergodic, our analysis elucidates the relations between the study of the first passage paths and the study of the transition paths in transition path theory. We provide algorithms to numerically compute statistics of the first passage path ensemble. The computational complexity of these algorithms scales with the complexity of solving a linear system, for which efficient methods are available. Several examples demonstrate the wide applicability of the derived results across research areas.}, language = {en} } @misc{GuptaGramatkeEinspanieretal., 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}, 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} } @misc{WinkelmannSchuettevonKleist, 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}, issn = {1438-0064}, doi = {10.4310/CMS.2014.v12.n5.a4}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-41955}, 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 immunodefficiency 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{WinkelmannSchuettevonKleist, author = {Winkelmann, Stefanie and Sch{\"u}tte, Christof and von Kleist, Max}, title = {Markov Control Processes with Rare State Observation: Sensitivity Analysis with Respect to Optimal Treatment Strategies against HIV-1}, series = {International Journal of Biomathematics and Biostatistics}, volume = {2}, journal = {International Journal of Biomathematics and Biostatistics}, number = {1}, abstract = {We present the theory of "Markov decision processes (MDP) with rare state observation" and apply it to optimal treatment scheduling and diagnostic testing to mitigate HIV-1 drug resistance development in resource-poor countries. The developed theory assumes that the state of the process is hidden and can only be determined by making an examination. Each examination produces costs which enter into the considered cost functional so that the resulting optimization problem includes finding optimal examination times. This is a realistic ansatz: In many real world applications, like HIV-1 treatment scheduling, the information about the disease evolution involves substantial costs, such that examination and control are intimately connected. However, a perfect compliance with the optimal strategy can rarely be achieved. This may be particularly true for HIV-1 resistance testing in resource-constrained countries. In the present work, we therefore analyze the sensitivity of the costs with respect to deviations from the optimal examination times both analytically and for the considered application. We discover continuity in the cost-functional with respect to the examination times. For the HIV-application, moreover, sensitivity towards small deviations from the optimal examination rule depends on the disease state. Furthermore, we compare the optimal rare-control strategy to (i) constant control strategies (one action for the remaining time) and to (ii) the permanent control of the original, fully observed MDP. This comparison is done in terms of expected costs and in terms of life-prolongation. The proposed rare-control strategy offers a clear benefit over a constant control, stressing the usefulness of medical testing and informed decision making. This indicates that lower-priced medical tests could improve HIV treatment in resource-constrained settings and warrants further investigation.}, language = {en} } @article{WangSchuetteCiccottietal., author = {Wang, Han and Sch{\"u}tte, Christof and Ciccotti, Giovanni and von Kleist, Max}, title = {Exploring the conformational dynamics of alanine dipeptide in solution subjected to an external electric field: A nonequilibrium molecular dynamics simulation}, series = {Journal of Chemical Theory and Computation}, volume = {10}, journal = {Journal of Chemical Theory and Computation}, number = {4}, doi = {10.1021/ct400993e}, pages = {1376 -- 1386}, abstract = {In this paper, we investigate the conformational dynamics of alanine dipeptide under an external electric field by nonequilibrium molecular dynamics simulation. We consider the case of a constant and of an oscillatory field. In this context, we propose a procedure to implement the temperature control, which removes the irrelevant thermal effects of the field. For the constant field different time-scales are identified in the conformational, dipole moment, and orientational dynamics. Moreover, we prove that the solvent structure only marginally changes when the external field is switched on. In the case of oscillatory field, the conformational changes are shown to be as strong as in the previous case, and nontrivial nonequilibrium circular paths in the conformation space are revealed by calculating the integrated net probability fluxes.}, language = {en} } @article{WinkelmannSchuettevonKleist, 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}, series = {Communications in Mathematical Sciences}, volume = {12}, journal = {Communications in Mathematical Sciences}, number = {5}, doi = {10.4310/CMS.2014.v12.n5.a4}, pages = {859 -- 877}, 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{HaaseSunkaraKohletal., author = {Haase, Tobias and Sunkara, Vikram and Kohl, Benjamin and Meier, Carola and Bußmann, Patricia and Becker, Jessica and Jagielski, Michal and von Kleist, Max and Ertel, Wolfgang}, title = {Discerning the spatio-temporal disease patterns of surgically induced OA mouse models}, series = {PLOS One}, volume = {14}, journal = {PLOS One}, number = {4}, publisher = {PLOS One}, doi = {10.1371/journal.pone.0213734}, abstract = {Osteoarthritis (OA) is the most common cause of disability in ageing societies, with no effective therapies available to date. Two preclinical models are widely used to validate novel OA interventions (MCL-MM and DMM). Our aim is to discern disease dynamics in these models to provide a clear timeline in which various pathological changes occur. OA was surgically induced in mice by destabilisation of the medial meniscus. Analysis of OA progression revealed that the intensity and duration of chondrocyte loss and cartilage lesion formation were significantly different in MCL-MM vs DMM. Firstly, apoptosis was seen prior to week two and was narrowly restricted to the weight bearing area. Four weeks post injury the magnitude of apoptosis led to a 40-60\% reduction of chondrocytes in the non-calcified zone. Secondly, the progression of cell loss preceded the structural changes of the cartilage spatio-temporally. Lastly, while proteoglycan loss was similar in both models, collagen type II degradation only occurred more prominently in MCL-MM. Dynamics of chondrocyte loss and lesion formation in preclinical models has important implications for validating new therapeutic strategies. Our work could be helpful in assessing the feasibility and expected response of the DMM- and the MCL-MM models to chondrocyte mediated therapies.}, language = {en} } @article{RettigHaasePletnyovetal., author = {Rettig, Anika and Haase, Tobias and Pletnyov, Alexandr and Kohl, Benjamin and Ertel, Wolfgang and von Kleist, Max and Sunkara, Vikram}, title = {SLCV - A Supervised Learning - Computer Vision combined strategy for automated muscle fibre detection in cross sectional images}, series = {PeerJ}, journal = {PeerJ}, publisher = {PeerJ}, address = {PeerJ}, doi = {10.7717/peerj.7053}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-72639}, abstract = {Muscle fibre cross sectional area (CSA) is an important biomedical measure used to determine the structural composition of skeletal muscle, and it is relevant for tackling research questions in many different fields of research. To date, time consuming and tedious manual delineation of muscle fibres is often used to determine the CSA. Few methods are able to automatically detect muscle fibres in muscle fibre cross sections to quantify CSA due to challenges posed by variation of bright- ness and noise in the staining images. In this paper, we introduce SLCV, a robust semi-automatic pipeline for muscle fibre detection, which combines supervised learning (SL) with computer vision (CV). SLCV is adaptable to different staining methods and is quickly and intuitively tunable by the user. We are the first to perform an error analysis with respect to cell count and area, based on which we compare SLCV to the best purely CV-based pipeline in order to identify the contribution of SL and CV steps to muscle fibre detection. Our results obtained on 27 fluorescence-stained cross sectional images of varying staining quality suggest that combining SL and CV performs signifi- cantly better than both SL based and CV based methods with regards to both the cell separation- and the area reconstruction error. Furthermore, applying SLCV to our test set images yielded fibre detection results of very high quality, with average sensitivity values of 0.93 or higher on different cluster sizes and an average Dice Similarity Coefficient (DSC) of 0.9778.}, language = {en} } @article{GuptaPeterJungetal., author = {Gupta, Pooja and Peter, Sarah and Jung, Markus and Lewin, Astrid and Hemmrich-Stanisak, Georg and Franke, Andre and von Kleist, Max and Sch{\"u}tte, Christof and Einspanier, Ralf and Sharbati, Soroush and zur Bruegge, Jennifer}, title = {Analysis of long non-coding RNA and mRNA expression in bovine macrophages brings up novel 2 aspects of Mycobacterium avium subspecies paratuberculosis infections}, series = {Scientific Reports in Nature}, volume = {9}, journal = {Scientific Reports in Nature}, doi = {10.1038/s41598-018-38141-x}, abstract = {Paratuberculosis is a major disease in cattle that severely affects animal welfare and causes huge economic losses worldwide. Development of alternative diagnostic methods is of urgent need to control the disease. Recent studies suggest that long non-coding RNAs (lncRNAs) play a crucial role in regulating immune function and may confer valuable information about the disease. However, their role has not yet been investigated in cattle with respect to infection towards Paratuberculosis. Therefore, we investigated the alteration in genomic expression profiles of mRNA and lncRNA in bovine macrophages in response to Paratuberculosis infection using RNA-Seq. We identified 397 potentially novel lncRNA candidates in macrophages of which 38 were differentially regulated by the infection. A total of 820 coding genes were also significantly altered by the infection. Co-expression analysis of lncRNAs and their neighbouring coding genes suggest regulatory functions of lncRNAs in pathways related to immune response. For example, this included protein coding genes such as TNIP3, TNFAIP3 and NF-κB2 that play a role in NF-κB2 signalling, a pathway associated with immune response. This study advances our understanding of lncRNA roles during Paratuberculosis infection.}, language = {en} } @misc{SunkaraRaharinirinaPeppertetal., author = {Sunkara, Vikram and Raharinirina, N. Alexia and Peppert, Felix and von Kleist, Max and Sch{\"u}tte, Christof}, title = {Inferring Gene Regulatory Networks from Single Cell RNA-seq Temporal Snapshot Data Requires Higher Order Moments}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-79664}, abstract = {Due to the increase in accessibility and robustness of sequencing technology, single cell RNA-seq (scRNA-seq) data has become abundant. The technology has made significant contributions to discovering novel phenotypes and heterogeneities of cells. Recently, there has been a push for using single-- or multiple scRNA-seq snapshots to infer the underlying gene regulatory networks (GRNs) steering the cells' biological functions. To date, this aspiration remains unrealised. In this paper, we took a bottom-up approach and curated a stochastic two gene interaction model capturing the dynamics of a complete system of genes, mRNAs, and proteins. In the model, the regulation was placed upstream from the mRNA on the gene level. We then inferred the underlying regulatory interactions from only the observation of the mRNA population through~time. We could detect signatures of the regulation by combining information of the mean, covariance, and the skewness of the mRNA counts through time. We also saw that reordering the observations using pseudo-time did not conserve the covariance and skewness of the true time course. The underlying GRN could be captured consistently when we fitted the moments up to degree three; however, this required a computationally expensive non-linear least squares minimisation solver. There are still major numerical challenges to overcome for inference of GRNs from scRNA-seq data. These challenges entail finding informative summary statistics of the data which capture the critical regulatory information. Furthermore, the statistics have to evolve linearly or piece-wise linearly through time to achieve computational feasibility and scalability.}, language = {en} } @article{RaharinirinaPeppertvonKleistetal., author = {Raharinirina, Alexia N. and Peppert, Felix and von Kleist, Max and Sch{\"u}tte, Christof and Sunkara, Vikram}, title = {Inferring gene regulatory networks from single-cell RNA-seq temporal snapshot data requires higher-order moments}, series = {Patterns}, volume = {2}, journal = {Patterns}, number = {9}, doi = {10.1016/j.patter.2021.100332}, abstract = {Single-cell RNA sequencing (scRNA-seq) has become ubiquitous in biology. Recently, there has been a push for using scRNA-seq snapshot data to infer the underlying gene regulatory networks (GRNs) steering cellular function. To date, this aspiration remains unrealized due to technical and computational challenges. In this work we focus on the latter, which is under-represented in the literature. We took a systemic approach by subdividing the GRN inference into three fundamental components: data pre-processing, feature extraction, and inference. We observed that the regulatory signature is captured in the statistical moments of scRNA-seq data and requires computationally intensive minimization solvers to extract it. Furthermore, current data pre-processing might not conserve these statistical moments. Although our moment-based approach is a didactic tool for understanding the different compartments of GRN inference, this line of thinking—finding computationally feasible multi-dimensional statistics of data—is imperative for designing GRN inference methods.}, language = {en} } @misc{OezelKulkarniHasanetal., author = {{\"O}zel, M. Neset and Kulkarni, Abhishek and Hasan, Amr and Brummer, Josephine and Moldenhauer, Marian and Daumann, Ilsa-Maria and Wolfenberg, Heike and Dercksen, Vincent J. and Kiral, F. Ridvan and Weiser, Martin and Prohaska, Steffen and von Kleist, Max and Hiesinger, Peter Robin}, title = {Serial synapse formation through filopodial competition for synaptic seeding factors}, issn = {1438-0064}, doi = {10.1016/j.devcel.2019.06.014}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-74397}, abstract = {Following axon pathfinding, growth cones transition from stochastic filopodial exploration to the formation of a limited number of synapses. How the interplay of filopodia and synapse assembly ensures robust connectivity in the brain has remained a challenging problem. Here, we developed a new 4D analysis method for filopodial dynamics and a data-driven computational model of synapse formation for R7 photoreceptor axons in developing Drosophila brains. Our live data support a 'serial synapse formation' model, where at any time point only a single 'synaptogenic' filopodium suppresses the synaptic competence of other filopodia through competition for synaptic seeding factors. Loss of the synaptic seeding factors Syd-1 and Liprin-α leads to a loss of this suppression, filopodial destabilization and reduced synapse formation, which is sufficient to cause the destabilization of entire axon terminals. Our model provides a filopodial 'winner-takes-all' mechanism that ensures the formation of an appropriate number of synapses.}, language = {en} } @article{OzelKulkarniHasanetal., author = {Ozel, Mehmet Neset and Kulkarni, Abhishek and Hasan, Amr and Brummer, Josephine and Moldenhauer, Marian and Daumann, Ilsa-Maria and Wolfenberg, Heike and Dercksen, Vincent J. and Kiral, Ferdi Ridvan and Weiser, Martin and Prohaska, Steffen and von Kleist, Max and Hiesinger, Peter Robin}, title = {Serial synapse formation through filopodial competition for synaptic seeding factors}, series = {Developmental Cell}, volume = {50}, journal = {Developmental Cell}, number = {4}, doi = {10.1016/j.devcel.2019.06.014}, pages = {447 -- 461}, abstract = {Following axon pathfinding, growth cones transition from stochastic filopodial exploration to the formation of a limited number of synapses. How the interplay of filopodia and synapse assembly ensures robust connectivity in the brain has remained a challenging problem. Here, we developed a new 4D analysis method for filopodial dynamics and a data-driven computational model of synapse formation for R7 photoreceptor axons in developing Drosophila brains. Our live data support a 'serial synapse formation' model, where at any time point only a single 'synaptogenic' filopodium suppresses the synaptic competence of other filopodia through competition for synaptic seeding factors. Loss of the synaptic seeding factors Syd-1 and Liprin-α leads to a loss of this suppression, filopodial destabilization and reduced synapse formation, which is sufficient to cause the destabilization of entire axon terminals. Our model provides a filopodial 'winner-takes-all' mechanism that ensures the formation of an appropriate number of synapses.}, language = {en} } @article{PeppertvonKleistSchuetteetal., author = {Peppert, Felix and von Kleist, Max and Sch{\"u}tte, Christof and Sunkara, Vikram}, title = {On the Sufficient Condition for Solving the Gap-Filling Problem Using Deep Convolutional Neural Networks}, series = {IEEE Transactions on Neural Networks and Learning Systems}, volume = {33}, journal = {IEEE Transactions on Neural Networks and Learning Systems}, number = {11}, doi = {10.1109/TNNLS.2021.3072746}, pages = {6194 -- 6205}, abstract = {Deep convolutional neural networks (DCNNs) are routinely used for image segmentation of biomedical data sets to obtain quantitative measurements of cellular structures like tissues. These cellular structures often contain gaps in their boundaries, leading to poor segmentation performance when using DCNNs like the U-Net. The gaps can usually be corrected by post-hoc computer vision (CV) steps, which are specific to the data set and require a disproportionate amount of work. As DCNNs are Universal Function Approximators, it is conceivable that the corrections should be obsolete by selecting the appropriate architecture for the DCNN. In this article, we present a novel theoretical framework for the gap-filling problem in DCNNs that allows the selection of architecture to circumvent the CV steps. Combining information-theoretic measures of the data set with a fundamental property of DCNNs, the size of their receptive field, allows us to formulate statements about the solvability of the gap-filling problem independent of the specifics of model training. In particular, we obtain mathematical proof showing that the maximum proficiency of filling a gap by a DCNN is achieved if its receptive field is larger than the gap length. We then demonstrate the consequence of this result using numerical experiments on a synthetic and real data set and compare the gap-filling ability of the ubiquitous U-Net architecture with variable depths. Our code is available at https://github.com/ai-biology/dcnn-gap-filling.}, language = {en} } @article{ConradRathTiefetal., author = {Conrad, Tim and Rath, Barbara and Tief, Franziska and Karsch, K. and Muehlhans, S. and Obermeier, Patrick and Adamou, E. and Chen, X. and Seeber, L. and Peiser, Ch. and Hoppe, Christian and von Kleist, Max and Schweiger, Brunhilde}, title = {Towards a personalized approach to managing of influenza infections in infants and children - food for thought and a note on oseltamivir}, series = {Infectious Disorders - Drug Targets}, volume = {13}, journal = {Infectious Disorders - Drug Targets}, number = {1}, pages = {25 -- 33}, language = {en} } @article{RathYousefKatzensteinetal., author = {Rath, Barbara and Yousef, Kaveh and Katzenstein, D. and Shafer, R. and Sch{\"u}tte, Christof and von Kleist, Max and Merigan, T.}, title = {HIV-1 Evolution in Response to Triple Reverse Transcriptase Inhibitor Induced Selective Pressure in vitro}, series = {PLoS ONE}, volume = {8}, journal = {PLoS ONE}, number = {4}, publisher = {Public Library of Science}, doi = {10.1371/journal.pone.0061102}, pages = {e61102}, language = {en} } @article{DuwalSchuettevonKleist2012, author = {Duwal, Sulav and Sch{\"u}tte, Christof and von Kleist, Max}, title = {Pharmacokinetics and Pharmacodynamics of the Reverse Transcriptase Inhibitor Tenofovir \& Prophylactic Efficacy against HIV-1 Infection.}, series = {PLoS One}, volume = {7}, journal = {PLoS One}, number = {7}, doi = {10.1371/journal.pone.0040382}, pages = {e40382}, year = {2012}, language = {en} } @article{FrankvonKleistKunzetal.2011, author = {Frank, M. and von Kleist, Max and Kunz, A. and Harms, G. and Sch{\"u}tte, Christof and Kloft, Ch.}, title = {Quantifying the impact of nevirapine-based prophylaxis strategies to prevent mother-to-child transmission of HIV-1}, series = {Antimicrob. Agents Chemother.}, volume = {55}, journal = {Antimicrob. Agents Chemother.}, number = {12}, pages = {5529 -- 5540}, year = {2011}, language = {en} } @article{vonKleistMenzStockeretal.2011, author = {von Kleist, Max and Menz, Stephan and Stocker, Hartmut and Arasteh, Keikawus and Huisinga, Wilhelm and Sch{\"u}tte, Christof}, title = {HIV Quasispecies Dynamics during Pro-active Treatment Switching}, series = {Plos One}, volume = {6}, journal = {Plos One}, number = {3}, publisher = {Public Library of Science}, doi = {10.1371/journal.pone.0018204}, pages = {e18204}, year = {2011}, language = {en} } @article{vonKleistMetznerMarquetetal.2012, author = {von Kleist, Max and Metzner, Ph. and Marquet, R. and Sch{\"u}tte, Christof}, title = {Polymerase Inhibition by Nucleoside Analogs}, series = {Plos Computational Biology}, volume = {8}, journal = {Plos Computational Biology}, number = {1}, doi = {10.1371/journal.pcbi.1002359}, pages = {e1002359}, year = {2012}, language = {en} } @article{WinkelmannSchuettevonKleist2012, author = {Winkelmann, Stefanie and Sch{\"u}tte, Christof and von Kleist, Max}, title = {Markov Control Processes with Rare State Observation}, series = {Communications in Mathematical Sciences}, volume = {12}, journal = {Communications in Mathematical Sciences}, number = {859}, year = {2012}, language = {en} } @article{ZhangHartmannvonKleist, author = {Zhang, Wei and Hartmann, Carsten and von Kleist, Max}, title = {Optimal control of Markov jump processes: Asymptotic analysis, algorithms and applications to the modeling of chemical reaction systems}, series = {Communications in Mathematical Sciences}, journal = {Communications in Mathematical Sciences}, doi = {10.4310/CMS.2018.v16.n2.a1}, pages = {293 -- 331}, abstract = {Markov jump processes are widely used to model natural and engineered processes. In the context of biological or chemical applications one typically refers to the chemical master equation (CME), which models the evolution of the probability mass of any copy-number combination of the interacting particles. When many interacting particles ("species") are considered, the complexity of the CME quickly increases, making direct numerical simulations impossible. This is even more problematic when one aims at controlling the Markov jump processes defined by the CME. In this work, we study both open loop and feedback optimal control problems of the Markov jump processes in the case that the controls can only be switched at fixed control stages. Based on Kurtz's limit theorems, we prove the convergence of the respective control value functions of the underlying Markov decision problem as the copy numbers of the species go to infinity. In the case of the optimal control problem on a finite time-horizon, we propose a hybrid control policy algorithm to overcome the difficulties due to the curse of dimensionality when the copy number of the involved species is large. Two numerical examples demonstrate the suitability of both the analysis and the proposed algorithms.}, language = {en} } @article{RaharinirinaSunkaravonKleistetal., author = {Raharinirina, Nomenjanahary Alexia and Sunkara, Vikram and von Kleist, Max and Fackeldey, Konstantin and Weber, Marcus}, title = {Multi-Input data ASsembly for joint Analysis (MIASA): A framework for the joint analysis of disjoint sets of variables}, series = {PLOS ONE}, volume = {19}, journal = {PLOS ONE}, number = {5}, publisher = {Public Library of Science}, doi = {10.1371/journal.pone.0302425}, pages = {26}, language = {en} }