Fakultät für Mathematik und Informatik
Browse by
Recent Submissions

Journal ArticleView Document Abstract
Analyzing Dynamic Change in Social Network Based on DistributionFree Multivariate Process Control Method
Computers, Materials & Continua 2019; 60(3) p.11231139Social organizations can be represented by social network because it can mathematically quantify and represent complex interrelated organizational behavior. Exploring the change in dynamic social network is essential for the situation awareness of the corresponding social organization. Social network usually evolves gradually and slightly, which is hard to be noticed. The statistical process control techniques in industry field have been used to distinguish the statistically significant change of social network. But the original method is narrowed due to some limitation on measures. This paper presents a generic framework to address the change detection problem in dynamic social network and introduces a distributionfree multivariate control charts to supervise the changing of social network. Three groups of network parameters are integrated together in order to achieve a comprehensive view of the dynamic tendency. The proposed approaches handle the nonGaussian data based on categorizing and ranking. Experiments indicate that nonparametric multivariate procedure is promising to be applied to social network analysis. 
Journal ArticleView Document Abstract
Asymptotic Distribution and Simultaneous Confidence Bands for Ratios of Quantile Functions
Electronic Journal of Statistics 2019; 13(2) p.43914415Ratios of medians or other suitable quantiles of two distributions are widely used in medical research to compare treatment and control groups or in economics to compare various economic variables when repeated crosssectional data are available. Inspired by the socalled growth incidence curves introduced in poverty research, we argue that the ratio of quantile functions is a more appropriate and informative tool to compare two distributions. We present an estimator for the ratio of quantile functions and develop corresponding simultaneous confidence bands, which allow to assess significance of certain features of the quantile functions ratio. Derived simultaneous confidence bands rely on the asymptotic distribution of the quantile functions ratio and do not require resampling techniques. The performance of the simultaneous confidence bands is demonstrated in simulations. Analysis of expenditure data from Uganda in years 1999, 2002 and 2005 illustrates the relevance of our approach. 
Journal ArticleView Document Abstract
Multiscale changepoint segmentation: beyond step functions
Electronic Journal of Statistics 2019; 13(2) p.32543296Modern multiscale type segmentation methods are known to detect multiple changepoints with high statistical accuracy, while allowing for fast computation. Underpinning (minimax) estimation theory has been developed mainly for models that assume the signal as a piecewise constant function. In this paper, for a large collection of multiscale segmentation methods (including various existing procedures), such theory will be extended to certain function classes beyond step functions in a nonparametric regression setting. This extends the interpretation of such methods on the one hand and on the other hand reveals these methods as robust to deviation from piecewise constant functions. Our main finding is the adaptation over nonlinear approximation classes for a universal thresholding, which includes bounded variation functions, and (piecewise) Hölder functions of smoothness order 0<α≤1 as special cases. From this we derive statistical guarantees on feature detection in terms of jumps and modes. Another key finding is that these multiscale segmentation methods perform nearly (up to a logfactor) as well as the oracle piecewise constant segmentation estimator (with known jump locations), and the best piecewise constant approximants of the (unknown) true signal. Theoretical findings are examined by various numerical simulations. 
Journal ArticleView Document Abstract
Tests for qualitative features in the random coefficients model
Electronic Journal of Statistics 2019; 13(2) p.22572306The random coefficients model is an extension of the linear regression model that allows for unobserved heterogeneity in the population by modeling the regression coefficients as random variables. Given data from this model, the statistical challenge is to recover information about the joint density of the random coefficients which is a multivariate and illposed problem. Because of the curse of dimensionality and the illposedness, nonparametric estimation of the joint density is difficult and suffers from slow convergence rates. Larger features, such as an increase of the density along some direction or a wellaccentuated mode can, however, be much easier detected from data by means of statistical tests. In this article, we follow this strategy and construct tests and confidence statements for qualitative features of the joint density, such as increases, decreases and modes. We propose a multiple testing approach based on aggregating single tests which are designed to extract shape information on fixed scales and directions. Using recent tools for Gaussian approximations of multivariate empirical processes, we derive xpressions for the critical value. We apply our method to simulated and real data. 
Journal ArticleView Document Abstract
The Protein‐Coding Human Genome: Annotating High‐Hanging Fruits
BioEssays 2019; 41(11): Art. 1900066The major transcript variants of human proteincoding genes are annotated to a certain degree of accuracy combining manual curation, transcript data, and proteomics evidence. However, there is considerable disagreement on the annotation of about 2000 genesthey can be proteincoding, noncoding, or pseudogenesand on the annotation of most of the predicted alternative transcripts. Pure transcriptome mapping approaches seem to be limited in discriminating functional expression from noise. These limitations have partially been overcome by dedicated algorithms to detect alternative spliced microexons and wobble splice variants. Recently, knowledge about splice mechanism and protein structure are incorporated into an algorithm to predict neighboring homologous exons, often spliced in a mutually exclusive manner. Predicted exons are evaluated by transcript data, structural compatibility, and evolutionary conservation, revealing hundreds of novel coding exons and splice mechanism reassignments. The emerging human pangenome is necessitating distinctive annotations incorporating differences between individuals and between populations. 
Journal ArticleView Document Abstract
Molecular contribution function in RESOLFT nanoscopy
Optics Express 2019; 27(15): Art. 21956The ultimate objective of a microscope of the highest resolution is to map the molecules of interest in the sample. Traditionally, linear imaging systems are characterized by their spatial frequency transfer function, which is given, in real space, by the point spread function (PSF). By extending the concept of the PSF towards the molecular contribution function (MCF), that quantifies the average contribution of a single fluorophore to the image, a straightforward concept for counting fluorophores is obtained. Using reversible saturable optical fluorescence transitions (RESOLFT), fluorophores are effectively activated only in a small, subdiffractionsized volume before they are read out. During readout the signal exhibits an increased variance due to the stochastic nature of prior activation, which scales quadratically with the brightness of the active fluorophores while the mean of the signal scales only linearly with it. Using a twostate Markov model for the activation, showing comparable behavior to the switching kinetics of the switchable fluorescent protein rsEGFP2, we can approximate quantitatively the MCF of RESOLFT nanoscopy allowing to count the number of fluorophores within a subdiffractionsized region of the sample. The method is validated on measurements of tubulin structures in Drosophila melagonaster larvae. Modeling and estimation of the MCF is a promising approach to quantitative microscopy. 
Journal ArticleView Document Abstract
THE EXPLICIT MORDELL CONJECTURE FOR FAMILIES OF CURVES
Forum of Mathematics, Sigma 2019; 7: Art. e31In this article we prove the explicit Mordell Conjecture for large families of curves. In addition, we introduce a method, of easy application, to compute all rational points on curves of quite general shape and increasing genus. The method bases on some explicit and sharp estimates for the height of such rational points, and the bounds are small enough to successfully implement a computer search. As an evidence of the simplicity of its application, we present a variety of explicit examples and explain how to produce many others. In the appendix our method is compared in detail to the classical method of Manin–Demjanenko and the analysis of our explicit examples is carried to conclusion. 
Journal ArticleView Document Abstract
Semisupervised triAdaboost algorithm for network intrusion detection
International Journal of Distributed Sensor Networks 2019; 15(6)Network intrusion detection is a relatively mature research topic, but one that remains challenging particular as technologies and threat landscape evolve. Here, a semisupervised triAdaboost (STA) algorithm is proposed. In the algorithm, three different Adaboost algorithms are used as the weak classifiers (both for continuous and categorical data), constituting the decision stumps in the tritraining method. In addition, the chisquare method is used to reduce the dimension of feature and improve computational efficiency. We then conduct extensive numerical studies using different training and testing samples in the KDDcup99 dataset and discover the flows demonstrated that (1) high accuracy can be obtained using a training dataset which consists of a small number of labeled and a large number of unlabeled samples. (2) The algorithm proposed is reproducible and consistent over different runs. (3) The proposed algorithm outperforms other existing learning algorithms, even with only a small amount of labeled data in the training phase. (4) The proposed algorithm has a short execution time and a low false positive rate, while providing a desirable detection rate. 
Journal ArticleView Document Abstract
Direct characterization of cytoskeletal reorganization during blood platelet spreading
Progress in Biophysics and Molecular Biology 2019; 144 p.166176Blood platelets are the key cellular players in blood clotting and thus of great biomedical importance. While spreading at the site of injury, they reorganize their cytoskeleton within minutes and assume a flat appearance. As platelets possess no nucleus, many standard methods for visualizing cytoskeletal components by means of fluorescence tags fail. Here we employ siliconrhodamine actin and tubulin probes for imaging these important proteins in a timeresolved manner. We find two distinct timescales for platelet spread area development and for cytoskeletal reorganization, indicating that although cell spreading is most likely associated with actin polymerization at the cell edges, distinct, stressfiberlike actin structures within the cell, which may be involved in the generation of contractile forces, form on their own timescale. Following microtubule dynamics allows us to distinguish the role of myosin, microtubules and actin during early spreading. 
Journal ArticleView Document Abstract
An anisotropic interaction model for simulating fingerprints
Journal of Mathematical BiologyEvidence suggests that both the interaction of socalled 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. 
Journal ArticleView Document Abstract
The Proximal Alternating Minimization Algorithm for TwoBlock Separable Convex Optimization Problems with Linear Constraints
Journal of Optimization Theory and ApplicationsThe Alternating Minimization Algorithm has been proposed by Paul Tseng to solve convex programming problems with twoblock 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. 
Journal ArticleView Document Abstract
Quantitative Convergence Analysis of Iterated Expansive, SetValued Mappings
Mathematics of Operations Research 2018; 43(4) p.11431176We develop a framework for quantitative convergence analysis of Picard iterations of expansive setvalued fixed point mappings. There are two key components of the analysis. The first is a natural generalization of singlevalued averaged mappings to expansive setvalued mappings that characterizes a type of strong calmness of the fixed point mapping. The second component to this analysis is an extension of the wellestablished 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 byproduct 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 forwardbackward algorithm for structured optimization without convexity, strong or otherwise, and local linear convergence of the DouglasRachford algorithm for structured nonconvex minimization. This theory includes earlier approaches for known results, convex and nonconvex, as special cases. 
Journal ArticleView Document Abstract
LatencySensitive Data Allocation and Workload Consolidation for Cloud Storage
IEEE Access 2018; 6 p.7609876110Customers 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 latencysensitive 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 latencysensitive data allocation problem, the latencysensitive data reallocation problem and the latencysensitive 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 NPhard. To solve them, we propose an exact integer nonlinear program (INLP) and a Tabu Searchbased 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 closetooptimal performance, but in a much lower running time. 
Journal ArticleView Document
Extended Object Tracking: Introduction, Overview, and Applications
Journal of Advances in Information Fusion 2017; 12(2) 
Journal ArticleView Document Abstract
Topology determines force distributions in onedimensional random spring networks
Physical Review E 2018; 97(2): Art. 022306etworks of elastic fibers are ubiquitous in biological systems and often provide mechanical stability to cells and tissues. Fiberreinforced 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 onedimensional 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 graphtheoretical 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 meanfield approach fails to capture force distributions correctly. We demonstrate that network topology is a crucial determinant of force distributions in elastic spring networks. 
Journal ArticleView Document Abstract
A Survey of Ant Colony Optimization Based Routing Protocols for Mobile Ad Hoc Networks
IEEE Access 2017; 5 p.2413924161eveloping 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 NPhard 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 largescale sophisticated problems without a centralized control entity. A successful example in the SI ﬁeld is the ant colony optimization (ACO) metaheuristic. It presents a common framework for approximating solutions to NPhard 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 ACObased 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 ACObased 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 ACObased routing protocols. 
Journal ArticleView Document Abstract
An evolutionarily conserved glycinetyrosine motif forms a folding core in outer membrane proteins.
PloS one 2017; 12(8): Art. e0182016An intimate interaction between a pair of amino acids, a tyrosine and glycine on neighboring βstrands, 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 βbarrel 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. Stoppedflow 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 wildtype, 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 βbarrels. 
Journal ArticleView Document Abstract
ESTIMATION OF PARAMETERS IN A PLANAR SEGMENT PROCESS WITH A BIOLOGICAL APPLICATION
Image Analysis & Stereology 2017; 36(1) p.2533The 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 TakaczFiksel 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 degreeoffit testing of the model using various characteristics yields quite satisfactory results. 
Journal ArticleView Document Abstract
Double Lie algebroids and representations up to homotopy
Journal of Homotopy and Related StructuresWe showthat a double Lie algebroid, together with a chosen decomposition, is equivalent to a pair of 2term 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. 
Journal ArticleView Document Abstract
The Quantum SineGordon Model in Perturbative AQFT
Communications in Mathematical PhysicsWe study the SineGordon 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 Smatrix and the interacting current or the field respectively converge, both given as formal power series.