Recent Submissions

  • Journal Article

    An anisotropic interaction model for simulating fingerprints 

    Düring, Bertram; Gottschlich, Carsten; Huckemann, Stephan; Kreusser, Lisa Maria; Schönlieb, Carola-Bibiane
    Journal of Mathematical Biology
    Evidence suggests that both the interaction of so-called Merkel cells and the epidermal stress distribution play an important role in the formation of fingerprint patterns during pregnancy. To model the formation of fingerprint patterns in a biologically meaningful way these patterns have to become stationary. For the creation of synthetic fingerprints it is also very desirable that rescaling the model parameters leads to rescaled distances between the stationary fingerprint ridges. Based on these observations, as well as the model introduced by Kücken and Champod we propose a new model for the formation of fingerprint patterns during pregnancy. In this anisotropic interaction model the interaction forces not only depend on the distance vector between the cells and the model parameters, but additionally on an underlying tensor field, representing a stress field. This dependence on the tensor field leads to complex, anisotropic patterns. We study the resulting stationary patterns both analytically and numerically. In particular, we show that fingerprint patterns can be modeled as stationary solutions by choosing the underlying tensor field appropriately.
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  • Journal Article

    The Proximal Alternating Minimization Algorithm for Two-Block Separable Convex Optimization Problems with Linear Constraints 

    Bitterlich, Sandy; Boţ, Radu Ioan; Csetnek, Ernö Robert; Wanka, Gert
    Journal of Optimization Theory and Applications
    The Alternating Minimization Algorithm has been proposed by Paul Tseng to solve convex programming problems with two-block separable linear constraints and objectives, whereby (at least) one of the components of the latter is assumed to be strongly convex. The fact that one of the subproblems to be solved within the iteration process of this method does not usually correspond to the calculation of a proximal operator through a closed formula affects the implementability of the algorithm. In this paper, we allow in each block of the objective a further smooth convex function and propose a proximal version of the algorithm, which is achieved by equipping the algorithm with proximal terms induced by variable metrics. For suitable choices of the latter, the solving of the two subproblems in the iterative scheme can be reduced to the computation of proximal operators. We investigate the convergence of the proposed algorithm in a real Hilbert space setting and illustrate its numerical performances on two applications in image processing and machine learning.
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  • Journal Article

    Quantitative Convergence Analysis of Iterated Expansive, Set-Valued Mappings 

    Russell Luke, D.; Thao, Nguyen H.; Tam, Matthew K.
    Mathematics of Operations Research 2018; 43(4) p.1143-1176
    We develop a framework for quantitative convergence analysis of Picard iterations of expansive set-valued fixed point mappings. There are two key components of the analysis. The first is a natural generalization of single-valued averaged mappings to expansive set-valued mappings that characterizes a type of strong calmness of the fixed point mapping. The second component to this analysis is an extension of the well-established notion of metric subregularity—or inverse calmness—of the mapping at fixed points. Convergence of expansive fixed point iterations is proved using these two properties, and quantitative estimates are a natural by-product of the framework. To demonstrate the application of the theory, we prove, for the first time, a number of results showing local linear convergence of nonconvex cyclic projections for inconsistent (and consistent) feasibility problems, local linear convergence of the forward-backward algorithm for structured optimization without convexity, strong or otherwise, and local linear convergence of the Douglas-Rachford algorithm for structured nonconvex minimization. This theory includes earlier approaches for known results, convex and nonconvex, as special cases.
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  • Journal Article

    Latency-Sensitive Data Allocation and Workload Consolidation for Cloud Storage 

    Yang, Song; Wieder, Philipp; Aziz, Muzzamil; Yahyapour, Ramin; Fu, Xiaoming; Chen, Xu
    IEEE Access 2018; 6 p.76098-76110
    Customers often suffer from the variability of data access time in (edge) cloud storage service, caused by network congestion, load dynamics, and so on. One ef cient solution to guarantee a reliable latency-sensitive service (e.g., for industrial Internet of Things application) is to issue requests with multiple download/upload sessions which access the required data (replicas) stored in one or more servers, and use the earliest response from those sessions. In order to minimize the total storage costs, how to optimally allocate data in a minimum number of servers without violating latency guarantees remains to be a crucial issue for the cloud provider to deal with. In this paper, we study the latency-sensitive data allocation problem, the latency-sensitive data reallocation problem and the latency-sensitive workload consolidation problem for cloud storage. We model the data access time as a given distribution whose cumulative density function is known, and prove that these three problems are NP-hard. To solve them, we propose an exact integer nonlinear program (INLP) and a Tabu Search-based heuristic. The simulation results reveal that the INLP can always achieve the best performance in terms of lower number of used nodes and higher storage and throughput utilization, but this comes at the expense of much higher running time. The Tabu Searchbased heuristic, on the other hand, can obtain close-to-optimal performance, but in a much lower running time.
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  • Journal Article

    Extended Object Tracking: Introduction, Overview, and Applications 

    Granström, Karl; Baum, Marcus; Reuter, Stephan
    Journal of Advances in Information Fusion 2017; 12(2)
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  • Journal Article

    Topology determines force distributions in one-dimensional random spring networks 

    Heidemann, Knut M.; Sageman-Furnas, Andrew O.; Sharma, Abhinav; Rehfeldt, Florian; Schmidt, Christoph F.; Wardetzky, Max
    Physical Review E 2018; 97(2): Art. 022306
    etworks of elastic fibers are ubiquitous in biological systems and often provide mechanical stability to cells and tissues. Fiber-reinforced materials are also common in technology. An important characteristic of such materials is their resistance to failure under load. Rupture occurs when fibers break under excessive force and when that failure propagates. Therefore, it is crucial to understand force distributions. Force distributions within such networks are typically highly inhomogeneous and are not well understood. Here we construct a simple one-dimensional model system with periodic boundary conditions by randomly placing linear springs on a circle. We consider ensembles of such networks that consist of N nodes and have an average degree of connectivity z but vary in topology. Using a graph-theoretical approach that accounts for the full topology of each network in the ensemble, we show that, surprisingly, the force distributions can be fully characterized in terms of the parameters (N,z). Despite the universal properties of such (N,z) ensembles, our analysis further reveals that a classical mean-field approach fails to capture force distributions correctly. We demonstrate that network topology is a crucial determinant of force distributions in elastic spring networks.
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  • Journal Article

    A Survey of Ant Colony Optimization Based Routing Protocols for Mobile Ad Hoc Networks 

    Zhang, Hang; Wang, Xi; Memarmoshrefi, Parisa; Hogrefe, Dieter
    IEEE Access 2017; 5 p.24139-24161
    eveloping highly efficient routing protocols for Mobile Ad hoc NETworks (MANETs) is a challenging task. In order to fulfill multiple routing requirements, such as low packet delay, high packet delivery rate, and effective adaptation to network topology changes with low control overhead, and so on, new ways to approximate solutions to the known NP-hard optimization problem of routing in MANETs have to be investigated. Swarm intelligence (SI)-inspired algorithms have attracted a lot of attention, because they can offer possible optimized solutions ensuring high robustness, flexibility, and low cost. Moreover, they can solve large-scale sophisticated problems without a centralized control entity. A successful example in the SI field is the ant colony optimization (ACO) meta-heuristic. It presents a common framework for approximating solutions to NP-hard optimization problems. ACO has been successfully applied to balance the various routing related requirements in dynamic MANETs. This paper presents a comprehensive survey and comparison of various ACO-based routing protocols in MANETs. The main contributions of this survey include: 1) introducing the ACO principles as applied in routing protocols for MANETs; 2) classifying ACO-based routing approaches reviewed in this paper into five main categories; 3) surveying and comparing the selected routing protocols from the perspective of design and simulation parameters; and 4) discussing open issues and future possible design directions of ACO-based routing protocols.
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  • Journal Article

    An evolutionarily conserved glycine-tyrosine motif forms a folding core in outer membrane proteins. 

    Michalik, Marcin; Orwick-Rydmark, Marcella; Habeck, Michael; Alva, Vikram; Arnold, Thomas; Linke, Dirk
    PloS one 2017; 12(8): Art. e0182016
    An intimate interaction between a pair of amino acids, a tyrosine and glycine on neighboring β-strands, has been previously reported to be important for the structural stability of autotransporters. Here, we show that the conservation of this interacting pair extends to nearly all major families of outer membrane β-barrel proteins, which are thought to have originated through duplication events involving an ancestral ββ hairpin. We analyzed the function of this motif using the prototypical outer membrane protein OmpX. Stopped-flow fluorescence shows that two folding processes occur in the millisecond time regime, the rates of which are reduced in the tyrosine mutant. Folding assays further demonstrate a reduction in the yield of folded protein for the mutant compared to the wild-type, as well as a reduction in thermal stability. Taken together, our data support the idea of an evolutionarily conserved 'folding core' that affects the folding, membrane insertion, and thermal stability of outer membrane protein β-barrels.
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  • Journal Article

    ESTIMATION OF PARAMETERS IN A PLANAR SEGMENT PROCESS WITH A BIOLOGICAL APPLICATION 

    Beneš, Viktor; Večeřa, Jakub; Eltzner, Benjamin; Wollnik, Carina; Rehfeldt, Florian; Králová, Veronika; Huckemann, Stephan
    Image Analysis & Stereology 2017; 36(1) p.25-33
    The paper deals with modeling of segment systems in a bounded planar set (a cell) by means of random segment processes. Two models with a density with respect to the Poisson process are presented. In model I interactions are given by the number of intersections, model II includes the length distribution and takes into account distances from the centre of the cell. The estimation of parameters of the models is suggested based on Takacz-Fiksel method. The method is tested first using simulated data. Further the real data from fluorescence imaging of stress fibres in mesenchymal human stem cells are evaluated. We apply model II which is inhomogeneous. The degree-of-fit testing of the model using various characteristics yields quite satisfactory results.
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  • Journal Article

    Double Lie algebroids and representations up to homotopy 

    Gracia-Saz, A.; Jotz Lean, M.; Mackenzie, K. C. H.; Mehta, R. A.
    Journal of Homotopy and Related Structures
    We showthat a double Lie algebroid, together with a chosen decomposition, is equivalent to a pair of 2-term representations up to homotopy satisfying compatibility conditions which extend the notion of matched pair of Lie algebroids. We discuss in detail the double Lie algebroids arising from the tangent bundle of a Lie algebroid and the cotangent bundle of a Lie bialgebroid.
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  • Journal Article

    The Quantum Sine-Gordon Model in Perturbative AQFT 

    Bahns, Dorothea; Rejzner, Kasia
    Communications in Mathematical Physics
    We study the Sine-Gordon model with Minkowski signature in the framework of perturbative algebraic quantum field theory.We calculate the vertex operator algebra braiding property.We prove that in the finite regime of themodel, the expectation value— with respect to the vacuum or a Hadamard state—of the Epstein Glaser S-matrix and the interacting current or the field respectively converge, both given as formal power series.
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  • Journal Article

    Data-driven coarse graining of large biomolecular structures. 

    Chen, Yi-Ling; Habeck, Michael
    PloS one 2017; 12(8): Art. e0183057
    Advances in experimental and computational techniques allow us to study the structure and dynamics of large biomolecular assemblies at increasingly higher resolution. However, with increasing structural detail it can be challenging to unravel the mechanism underlying the function of molecular machines. One reason is that atomistic simulations become computationally prohibitive. Moreover it is difficult to rationalize the functional mechanism of systems composed of tens of thousands to millions of atoms by following each atom's movements. Coarse graining (CG) allows us to understand biological structures from a hierarchical perspective and to gradually zoom into the adequate level of structural detail. This article introduces a Bayesian approach for coarse graining biomolecular structures. We develop a probabilistic model that aims to represent the shape of an experimental structure as a cloud of bead particles. The particles interact via a pairwise potential whose parameters are estimated along with the bead positions and the CG mapping between atoms and beads. Our model can also be applied to density maps obtained by cryo-electron microscopy. We illustrate our approach on various test systems.
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  • Journal Article

    Distribution and evolution of stable single α-helices (SAH domains) in myosin motor proteins 

    Simm, Dominic; Hatje, Klas; Kollmar, Martin
    PLOS ONE 2017; 12(4): Art. e0174639
    Stable single-alpha helices (SAHs) are versatile structural elements in many prokaryotic and eukaryotic proteins acting as semi-flexible linkers and constant force springs. This way SAH-domains function as part of the lever of many different myosins. Canonical myosin levers consist of one or several IQ-motifs to which light chains such as calmodulin bind. SAH-domains provide flexibility in length and stiffness to the myosin levers, and may be particularly suited for myosins working in crowded cellular environments. Although the function of the SAH-domains in human class-6 and class-10 myosins has well been characterised, the distribution of the SAH-domain in all myosin subfamilies and across the eukaryotic tree of life remained elusive. Here, we analysed the largest available myosin sequence dataset consisting of 7919 manually annotated myosin sequences from 938 species representing all major eukaryotic branches using the SAH-prediction algorithm of Waggawagga, a recently developed tool for the identification of SAH-domains. With this approach we identified SAH-domains in more than one third of the supposed 79 myosin subfamilies. Depending on the myosin class, the presence of SAH-domains can range from a few to almost all class members indicating complex patterns of independent and taxon-specific SAH-domain gain and loss.
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  • Journal Article

    Model-based testing as a service 

    Herbold, Steffen; Hoffmann, Andreas
    International Journal on Software Tools for Technology Transfer
    The quality ofWeb services is an important factor for businesses that advertise or sell their services in the Internet. Failures can directly lead to fewer costumers or security problems. However, the testing of complexWeb services that are organized in service-oriented architectures is a difficult and complex problem. Model-based testing (MBT) is one solution to deal with the complexity of the testing. With MBT, testers do not define the tests directly, but rather specify the structure and behavior of the System Under Test using models. Then, a test strategy is used to derive test cases automatically from the models. However, MBT yields a large amount of tests for complex systems which require lots of resources for their execution, thereby limiting its potential. Within this article, we discuss how cloud computing can be used to provide the required resources for scaling up test campaigns with large amounts of test cases derived using MBT.
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  • Journal Article

    Directional global three-part image decomposition 

    Thai, D. H.; Gottschlich, C.
    EURASIP Journal on Image and Video Processing 2016; 2016(1): Art. 12
    We consider the task of image decomposition, and we introduce a new model coined directional global three-part decomposition (DG3PD) for solving it. As key ingredients of the DG3PD model, we introduce a discrete multi-directional total variation norm and a discrete multi-directional G-norm. Using these novel norms, the proposed discrete DG3PD model can decompose an image into two or three parts. Existing models for image decomposition by Vese and Osher (J. Sci. Comput. 19(1–3):553–572, 2003), by Aujol and Chambolle (Int. J. Comput. Vis. 63(1):85–104, 2005), by Starck et al. (IEEE Trans. Image Process. 14(10):1570–1582, 2005), and by Thai and Gottschlich are included as special cases in the new model. Decomposition of an image by DG3PD results in a cartoon image, a texture image, and a residual image. Advantages of the DG3PD model over existing ones lie in the properties enforced on the cartoon and texture images. The geometric objects in the cartoon image have a very smooth surface and sharp edges. The texture image yields oscillating patterns on a defined scale which are both smooth and sparse. Moreover, the DG3PD method achieves the goal of perfect reconstruction by summation of all components better than the other considered methods. Relevant applications of DG3PD are a novel way of image compression as well as feature extraction for applications such as latent fingerprint processing and optical character recognition.
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  • Journal Article

    Modelling modal gating of ion channels with hierarchical Markov models 

    Siekmann, Ivo; Fackrell, Mark; Crampin, Edmund J.; Taylor, Peter
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science 2016; 472(2192)
    Many ion channels spontaneously switch between different levels of activity. Although this behaviour known as modal gating has been observed for a long time it is currently not well understood. Despite the fact that appropriately representing activity changes is essential for accurately capturing time course data from ion channels, systematic approaches for modelling modal gating are currently not available. In this paper, we develop a modular approach for building such a model in an iterative process. First, stochastic switching between modes and stochastic opening and closing within modes are represented in separate aggregated Markov models. Second, the continuous-time hierarchical Markov model, a new modelling framework proposed here, then enables us to combine these components so that in the integrated model both mode switching as well as the kinetics within modes are appropriately represented. A mathematical analysis reveals that the behaviour of the hierarchical Markov model naturally depends on the properties of its components. We also demonstrate how a hierarchical Markov model can be parametrized using experimental data and show that it provides a better representation than a previous model of the same dataset. Because evidence is increasing that modal gating reflects underlying molecular properties of the channel protein, it is likely that biophysical processes are better captured by our new approach than in earlier models.
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  • Journal Article

    DOTmark - A Benchmark for Discrete Optimal Transport 

    Schrieber, Jorn; Schuhmacher, Dominic; Gottschlich, Carsten
    IEEE Access p.1-12
    The Wasserstein metric or earth mover’s distance (EMD) is a useful tool in statistics, computer science and engineering with many applications to biological or medical imaging, among others. Especially in the light of increasingly complex data, the computation of these distances via optimal transport is often the limiting factor. Inspired by this challenge, a variety of new approaches to optimal transport has been proposed in recent years and along with these new methods comes the need for a meaningful comparison. In this paper, we introduce a benchmark for discrete optimal transport, called DOTmark, which is designed to serve as a neutral collection of problems, where discrete optimal transport methods can be tested, compared to one another, and brought to their limits on large-scale instances. It consists of a variety of grayscale images, in various resolutions and classes, such as several types of randomly generated images, classical test images and real data from microscopy. Along with the DOTmark we present a survey and a performance test for a cross section of established methods ranging from more traditional algorithms, such as the transportation simplex, to recently developed approaches, such as the shielding neighborhood method, and including also a comparison with commercial solvers.
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  • Journal Article

    Inferential Structure Determination of Chromosomes from Single-Cell Hi-C Data 

    Carstens, Simeon; Nilges, Michael; Habeck, Michael
    PLOS Computational Biology 2016; 12(12): Art. e1005292
    Chromosome conformation capture (3C) techniques have revealed many fascinating insights into the spatial organization of genomes. 3C methods typically provide information about chromosomal contacts in a large population of cells, which makes it difficult to draw conclusions about the three-dimensional organization of genomes in individual cells. Recently it became possible to study single cells with Hi-C, a genome-wide 3C variant, demonstrating a high cell-to-cell variability of genome organization. In principle, restraint-based modeling should allow us to infer the 3D structure of chromosomes from single-cell contact data, but suffers from the sparsity and low resolution of chromosomal contacts. To address these challenges, we adapt the Bayesian Inferential Structure Determination (ISD) framework, originally developed for NMR structure determination of proteins, to infer statistical ensembles of chromosome structures from single-cell data. Using ISD, we are able to compute structural error bars and estimate model parameters, thereby eliminating potential bias imposed by ad hoc parameter choices. We apply and compare different models for representing the chromatin fiber and for incorporating singe-cell contact information. Finally, we extend our approach to the analysis of diploid chromosome data.
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  • Journal Article

    A Novel Sequence-Based Feature for the Identification of DNA-Binding Sites in Proteins Using Jensen–Shannon Divergence 

    Dang, Truong; Meckbach, Cornelia; Tacke, Rebecca; Waack, Stephan; Gültas, Mehmet
    Entropy 2016; 18(10)
    The knowledge of protein-DNA interactions is essential to fully understand the molecular activities of life. Many research groups have developed various tools which are either structure- or sequence-based approaches to predict the DNA-binding residues in proteins. The structure-based methods usually achieve good results, but require the knowledge of the 3D structure of protein; while sequence-based methods can be applied to high-throughput of proteins, but require good features. In this study, we present a new information theoretic feature derived from Jensen–Shannon Divergence (JSD) between amino acid distribution of a site and the background distribution of non-binding sites. Our new feature indicates the difference of a certain site from a non-binding site, thus it is informative for detecting binding sites in proteins. We conduct the study with a five-fold cross validation of 263 proteins utilizing the Random Forest classifier. We evaluate the functionality of our new features by combining them with other popular existing features such as position-specific scoring matrix (PSSM), orthogonal binary vector (OBV), and secondary structure (SS). We notice that by adding our features, we can significantly boost the performance of Random Forest classifier, with a clear increment of sensitivity and Matthews correlation coefficient (MCC).
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  • Journal Article

    Interpretable Multiclass Models for Corporate Credit Rating Capable of Expressing Doubt 

    Obermann, Lennart; Waack, Stephan
    Frontiers in Applied Mathematics and Statistics 2016; 2: Art. 16
    Corporate credit rating is a process to classify commercial enterprises based on their creditworthiness. Machine learning algorithms can construct classification models, but in general they do not tend to be 100% accurate. Since they can be used as decision support for experts, interpretable models are desirable. Unfortunately, interpretable models are provided by only few machine learners. Furthermore, credit rating often is a multiclass problem with more than two rating classes. Due to this fact, multiclass classification is often achieved via meta-algorithms using multiple binary learners. However, most state-of-the-art meta-algorithms destroy the interpretability of binary models. In this study, we present Thresholder, a binary interpretable threshold-based disjunctive normal form (DNF) learning algorithm in addition to modifications of popular multiclass meta-algorithms which maintain the interpretability of our binary classifier. Furthermore, we present an approach to express doubt in the decision of our model. Performance and model size are compared with other interpretable approaches for learning DNFs (RIPPER) and decision trees (C4.5) as well as non-interpretable models like random forests, artificial neural networks, and support vector machines. We evaluate their performances on three real-life data sets divided into three rating classes. In this case study all threshold-based and interpretable models perform equally well and significantly better than other methods. Our new Thresholder algorithm builds the smallest models while its performance is as good as the best methods of our case study. Furthermore, Thresholder marks many potential misclassifications in advance with a doubt label without increasing the classification error.
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