@inproceedings{RuehrupSchindelhauerVolbert, author = {R{\"u}hrup, Stefan and Schindelhauer, Christian and Volbert, Klaus}, title = {Performance analysis of the hierarchical layer graph for wireless networks}, series = {4th International Conference, ADHOC-NOW 2005, Cancun, Mexico, October 6-8, 2005}, booktitle = {4th International Conference, ADHOC-NOW 2005, Cancun, Mexico, October 6-8, 2005}, publisher = {Springer}, address = {Berlin ; Heidelberg}, isbn = {978-3-540-29132-9}, doi = {10.1007/11561354_21}, pages = {244 -- 257}, abstract = {The Hierarchical Layer Graph (HL graph) is a promising network topology for wireless networks with variable transmission ranges. It was introduced and analyzed by Meyer auf der Heide et al. 2004. In this paper we present a distributed, localized and resource-efficient algorithm for constructing this graph. The qualtiy of the HL graph depends on the domination radius and the publication radius, which affect the amount of interference in the network. These parameters also determine whether the HL graph is a c-spanner, which implies an energy-efficient topology. We investigate the performance on randomly distributed node sets and show that the restrictions on these parameters derived from a worst case analysis are not so tight using realistic settings. Here, we present the results of our extensive experimental evaluation, measuring congestion, dilation and energy. Congestion includes the load that is induced by interfering edges. We distinguish between congestion and realistic congestion where we also take the signal-to-interference ratio into account. Our experiments show that the HL graph contains energy-efficient paths as well as paths with a few number of hops while preserving a low congestion.}, language = {en} } @inproceedings{ReinhardtKucera, author = {Reinhardt, Dominik and Kucera, Markus}, title = {Domain controlled architecture: A new approach for large scale software integrated automotive systems}, series = {PECCS 2013 - Proceedings of the 3rd International Conference on Pervasive Embedded Computing and Communication Systems, 19 - 21 February 2013, Barcelona, Spain}, booktitle = {PECCS 2013 - Proceedings of the 3rd International Conference on Pervasive Embedded Computing and Communication Systems, 19 - 21 February 2013, Barcelona, Spain}, publisher = {IEEE}, pages = {221 -- 226}, abstract = {Electric and electronic functionalities increase exponentially in every mobility domain. The automotive in-dustry is confronted with a rising system complexity and several restricting requirements and standards (likeAUTOSAR), in particular to design embedded software for electronic control units. To stand against rampantfunctionalities software units could be restructured according to their affiliation and should not be attached toa certain place. This can be effected by integration on single controllers. On the one hand the system wideamount of hardware controllers could such be limited. On the other hand the workload for integration CPUswill rise. To support this paradigm, multi-core systems can provide enough processing power in an efficientway. This paper shows a first approach to combine automotive functionality on such a single controller.}, language = {en} } @inproceedings{SchaeferSchildgenDessloch, author = {Sch{\"a}fer, Marc and Schildgen, J{\"u}rgen and Deßloch, Stefan}, title = {Sampling with Incremental MapReduce}, series = {Datenbanksysteme f{\"u}r Business, Technologie und Web (BTW 2015) : Workshopband ; 02. - 03. M{\"a}rz 2015 in Hamburg}, volume = {242}, booktitle = {Datenbanksysteme f{\"u}r Business, Technologie und Web (BTW 2015) : Workshopband ; 02. - 03. M{\"a}rz 2015 in Hamburg}, publisher = {Gesellschaft f{\"u}r Informatik e.V.}, pages = {121 -- 130}, abstract = {The goal of this paper is to increase the computation speed of MapReduce jobs by reducing the accuracy of the result. Often, the timely processing is more important than the precision of the result. Hadoop has no built-in functionality for such an approximation technique, so the user has to implement sampling techniques manually. We introduce an automatic system for computing arithmetic approximations. The sampling is based on techniques from statistics and the extrapolation is done generically. This system is also extended by an incremental component which enables the reuse of already computed results to enlarge the sampling size. This can be used iteratively to further increase the sampling size and also the precision of the approximation. We present a transparent incremental sampling approach, so the developed components can be integrated in the Hadoop framework in a non-invasive manner.}, language = {en} } @inproceedings{SchildgenDessloch, author = {Schildgen, Johannes and Deßloch, Stefan}, title = {NotaQL is not a query language! It's for data transformation on wide-column stores}, series = {Data Science : 30th British International Conference on Databases, BICOD 2015 Edingburgh, UK, July 6-8, 2015, Proceedings}, volume = {9147}, booktitle = {Data Science : 30th British International Conference on Databases, BICOD 2015 Edingburgh, UK, July 6-8, 2015, Proceedings}, editor = {Maneth, Sebastian}, publisher = {Springer Nature}, isbn = {978-3-319-20423-9}, issn = {1611-3349}, doi = {10.1007/978-3-319-20424-6_14}, pages = {139 -- 151}, abstract = {It is simple to query a relational database because all columns of the tables are known and the language SQL is easily applicable. In NoSQL, there usually is no fixed schema and no query language. In this article, we present NotaQL, a data-transformation language for wide-column stores. NotaQL is easy to use and powerful. Many MapReduce algorithms like filtering, grouping, aggregation and even breadth-first-search, PageRank and other graph and text algorithms can be expressed in two or three short lines of code.}, language = {en} } @inproceedings{SchildgenLottermannDessloch, author = {Schildgen, Johannes and Lottermann, Thomas and Deßloch, Stefan}, title = {Cross-system NoSQL data transformations with NotaQL}, series = {BeyondMR '16: Proceedings of the 3rd ACM SIGMOD Workshop on Algorithms and Systems for MapReduce and BeyondJune 2016}, booktitle = {BeyondMR '16: Proceedings of the 3rd ACM SIGMOD Workshop on Algorithms and Systems for MapReduce and BeyondJune 2016}, publisher = {ACM}, doi = {10.1145/2926534.2926535}, pages = {1 -- 10}, abstract = {The rising adoption of NoSQL technology in enterprises causes a heterogeneous landscape of different data stores. Different stores provide distinct advantages and disadvantages, making it necessary for enterprises to facilitate multiple systems for specific purposes. This resulting polyglot persistence is difficult to handle for developers since some data needs to be replicated and aggregated between different and within the same stores. Currently, there are no uniform tools to perform these data transformations since all stores feature different APIs and data models. In this paper, we present the transformation language NotaQL that allows cross-system data transformations. These transformations are output-oriented, meaning that the structure of a transformation script is similar to that of the output. Besides, we provide an aggregation-centric approach, which makes aggregation operations as easy as possible.}, language = {en} } @article{SchildgenJoergDossingeretal., author = {Schildgen, Johannes and J{\"o}rg, Thomas and Dossinger, Manuel and Deßloch, Stefan}, title = {Marimba: A framework for making MapReduce jobs incremental}, series = {Proceedings - 2014 IEEE International Congress on Big Data, BigData Congress 2014, 27 June 2014 - 02 July 2014, Anchorage, AK, USA}, journal = {Proceedings - 2014 IEEE International Congress on Big Data, BigData Congress 2014, 27 June 2014 - 02 July 2014, Anchorage, AK, USA}, publisher = {IEEE}, doi = {10.1109/BigData.Congress.2014.27}, abstract = {Many MapReduce jobs for analyzing Big Data require many hours and have to be repeated again and again because the base data changes continuously. In this paper we propose Marimba, a framework for making MapReduce jobs incremental. Thus, a recomputation of a job only needs to process the changes since the last computation. This accelerates the execution and enables more frequent recomputations, which leads to results which are more up-to-date. Our approach is based on concepts that are popular in the area of materialized views in relational database systems where a view can be updated only by aggregating changes in base data upon the previous result.}, language = {en} } @article{SchindelhauerVolbertZiegler, author = {Schindelhauer, Christian and Volbert, Klaus and Ziegler, Martin}, title = {Geometric spanners with applications in wireless networks}, series = {Computational Geometry: Theory and Applications}, volume = {36}, journal = {Computational Geometry: Theory and Applications}, number = {3}, doi = {10.1016/j.comgeo.2006.02.001}, pages = {197 -- 214}, abstract = {In this paper we investigate the relations between spanners, weak spanners, and power spanners in for any dimension and apply our results to topology control in wireless networks. For , a c-spanner is a subgraph of the complete Euclidean graph satisfying the condition that between any two vertices there exists a path of length at most c-times their Euclidean distance. Based on this ability to approximate the complete Euclidean graph, sparse spanners have found many applications, e.g., in FPTAS, geometric searching, and radio networks. In a weak c-spanner, this path may be arbitrarily long, but must remain within a disk or sphere of radius c-times the Euclidean distance between the vertices. Finally in a c-power spanner, the total energy consumed on such a path, where the energy is given by the sum of the squares of the edge lengths on this path, must be at most c-times the square of the Euclidean distance of the direct edge or communication link. While it is known that any c-spanner is also both a weak -spanner and a -power spanner for appropriate , depending only on c but not on the graph under consideration, we show that the converse is not true: there exists a family of -power spanners that are not weak C-spanners and also a family of weak -spanners that are not C-spanners for any fixed C. However a main result of this paper reveals that any weak c-spanner is also a C-power spanner for an appropriate constant C. We further generalize the latter notion by considering -power spanners where the sum of the δth powers of the lengths has to be bounded; so ()-power spanners coincide with the usual power spanners and ()-power spanners are classical spanners. Interestingly, these ()-power spanners form a strict hierarchy where the above results still hold for any some even hold for while counter-examples exist for . We show that every self-similar curve of fractal dimension is not a -power spanner for any fixed C, in general. Finally, we consider the sparsified Yao-graph (SparsY-graph or YY) that is a well-known sparse topology for wireless networks. We prove that all SparsY-graphs are weak c-spanners for a constant c and hence they allow us to approximate energy-optimal wireless networks by a constant factor.}, language = {en} } @article{Frikel, author = {Frikel, J{\"u}rgen}, title = {Sparse regularization in limited angle tomography}, series = {Applied and Computational Harmonic Analysis}, volume = {34}, journal = {Applied and Computational Harmonic Analysis}, number = {1}, publisher = {Elsevier}, doi = {10.1016/j.acha.2012.03.005}, pages = {117 -- 141}, abstract = {We investigate the reconstruction problem of limited angle tomography. Such problems arise naturally in applications like digital breast tomosynthesis, dental tomography, electron microscopy, etc. Since the acquired tomographic data is highly incomplete, the reconstruction problem is severely ill-posed and the traditional reconstruction methods, e.g. filtered backprojection (FBP), do not perform well in such situations. To stabilize the reconstruction procedure additional prior knowledge about the unknown object has to be integrated into the reconstruction process. In this work, we propose the use of the sparse regularization technique in combination with curvelets. We argue that this technique gives rise to an edge-preserving reconstruction. Moreover, we show that the dimension of the problem can be significantly reduced in the curvelet domain. To this end, we give a characterization of the kernel of the limited angle Radon transform in terms of curvelets and derive a characterization of solutions obtained through curvelet sparse regularization. In numerical experiments, we will show that the theoretical results directly translate into practice and that the proposed method outperforms classical reconstructions.}, language = {en} } @article{Frikel, author = {Frikel, J{\"u}rgen}, title = {Short communication: Dimensionality reduction of curvelet sparse regularizations in limited angle tomography}, series = {Proceedings in applied mathematics and mechanics : PAMM}, volume = {11}, journal = {Proceedings in applied mathematics and mechanics : PAMM}, number = {1}, publisher = {Wiley-VCH}, address = {Weinheim}, issn = {1617-7061}, doi = {10.1002/pamm.201110412}, pages = {847 -- 848}, abstract = {We investigate the reconstruction problem for limited angle tomography. Such problems arise naturally in applications like digital breast tomosynthesis, dental tomography, etc. Since the acquired tomographic data is highly incomplete, the reconstruction problem is severely ill-posed and the traditional reconstruction methods, such as filtered backprojection (FBP), do not perform well in such situations. To stabilize the inversion we propose the use of a sparse regularization technique in combination with curvelets. We argue that this technique has the ability to preserve edges. As our main result, we present a characterization of the kernel of the limited angle Radon transform in terms of curvelets. Moreover, we characterize reconstructions which are obtained via curvelet sparse regularizations at a limited angular range. As a result, we show that the dimension of the limited angle problem can be significantly reduced in the curvelet domain.}, language = {en} } @article{FrikelQuinto, author = {Frikel, J{\"u}rgen and Quinto, Eric Todd}, title = {Artifacts in Incomplete Data Tomography with Applications to Photoacoustic Tomography and Sonar}, series = {SIAM Journal on Applied Mathematics}, volume = {75}, journal = {SIAM Journal on Applied Mathematics}, number = {2}, publisher = {Society for Industrial and Applied Mathematics}, address = {Philadelphia, Pa.}, issn = {1095-712X}, doi = {10.1137/140977709}, pages = {703 -- 725}, abstract = {We develop a paradigm using microlocal analysis that allows one to characterize the visible and added singularities in a broad range of incomplete data tomography problems. We give precise characterizations for photoacoustic and thermoacoustic tomography and sonar, and provide artifact reduction strategies. In particular, our theorems show that it is better to arrange sonar detectors so that the boundary of the set of detectors does not have corners and is smooth. To illustrate our results, we provide reconstructions from synthetic spherical mean data as well as from experimental photoacoustic data.}, language = {en} } @article{FrikelQuinto, author = {Frikel, J{\"u}rgen and Quinto, Eric Todd}, title = {Characterization and reduction of artifacts in limited angle tomography}, series = {Inverse Problems}, volume = {29}, journal = {Inverse Problems}, number = {12}, publisher = {IOP Publishing}, address = {Bristol}, issn = {0266-5611}, doi = {10.1088/0266-5611/29/12/125007}, abstract = {We consider the reconstruction problem for limited angle tomography using filtered backprojection (FBP) and lambda tomography. We use microlocal analysis to explain why the well-known streak artifacts are present at the end of the limited angular range. We explain how to mitigate the streaks and prove that our modified FBP and lambda operators are standard pseudodifferential operators, and so they do not add artifacts. We provide reconstructions to illustrate our mathematical results.}, language = {en} } @unpublished{FrikelQuinto, author = {Frikel, J{\"u}rgen and Quinto, Eric Todd}, title = {A paradigm for the characterization of artifacts in tomography}, doi = {10.48550/arXiv.1409.4103}, abstract = {We present a paradigm for characterization of artifacts in limited data tomography problems. In particular, we use this paradigm to characterize artifacts that are generated in reconstructions from limited angle data with generalized Radon transforms and general filtered backprojection type operators. In order to find when visible singularities are imaged, we calculate the symbol of our reconstruction operator as a pseudodifferential operator.}, language = {en} } @article{StorathWeinmannFrikeletal., author = {Storath, Martin and Weinmann, Andreas and Frikel, J{\"u}rgen and Unser, Michael}, title = {Joint image reconstruction and segmentation using the Potts model}, series = {Inverse Problems}, volume = {31}, journal = {Inverse Problems}, number = {2}, publisher = {IOP Publishing}, address = {Bristol}, issn = {0266-5611}, doi = {10.1088/0266-5611/31/2/025003}, abstract = {We propose a new algorithmic approach to the non-smooth and non-convex Potts problem (also called piecewise-constant Mumford-Shah problem) for inverse imaging problems. We derive a suitable splitting into specific subproblems that can all be solved efficiently. Our method does not require a priori knowledge on the gray levels nor on the number of segments of the reconstruction. Further, it avoids anisotropic artifacts such as geometric staircasing. We demonstrate the suitability of our method for joint image reconstruction and segmentation. We focus on Radon data, where we in particular consider limited data situations. For instance, our method is able to recover all segments of the Shepp-Logan phantom from seven angular views only. We illustrate the practical applicability on a real positron emission tomography dataset. As further applications, we consider spherical Radon data as well as blurred data.}, language = {en} } @article{WieczorekFrikelVogeletal., author = {Wieczorek, Matthias and Frikel, J{\"u}rgen and Vogel, Jakob and Eggl, Elena and Kopp, Felix and No{\"e}l, Peter B. and Pfeiffer, Franz and Demaret, Laurent and Lasser, Tobias}, title = {X-ray computed tomography using curvelet sparse regularization}, series = {Medical physics}, volume = {42}, journal = {Medical physics}, number = {4}, publisher = {American Association of Physicists in Medicine}, issn = {0094-2405}, doi = {10.1118/1.4914368}, pages = {1555 -- 1565}, abstract = {PURPOSE Reconstruction of x-ray computed tomography (CT) data remains a mathematically challenging problem in medical imaging. Complementing the standard analytical reconstruction methods, sparse regularization is growing in importance, as it allows inclusion of prior knowledge. The paper presents a method for sparse regularization based on the curvelet frame for the application to iterative reconstruction in x-ray computed tomography. METHODS In this work, the authors present an iterative reconstruction approach based on the alternating direction method of multipliers using curvelet sparse regularization. RESULTS Evaluation of the method is performed on a specifically crafted numerical phantom dataset to highlight the method's strengths. Additional evaluation is performed on two real datasets from commercial scanners with different noise characteristics, a clinical bone sample acquired in a micro-CT and a human abdomen scanned in a diagnostic CT. The results clearly illustrate that curvelet sparse regularization has characteristic strengths. In particular, it improves the restoration and resolution of highly directional, high contrast features with smooth contrast variations. The authors also compare this approach to the popular technique of total variation and to traditional filtered backprojection. CONCLUSIONS The authors conclude that curvelet sparse regularization is able to improve reconstruction quality by reducing noise while preserving highly directional features.}, language = {en} } @inproceedings{WieczorekFrikelVogeletal., author = {Wieczorek, Matthias and Frikel, J{\"u}rgen and Vogel, Jakob and Pfeiffer, Franz and Demaret, Laurent and Lasser, Tobias}, title = {Curvelet sparse regularization for differential phase-contrast X-ray imaging}, series = {Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine : Proceedings ; June 16-21, 2013, Granlibakken Resort, Lake Tahoe, California}, booktitle = {Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine : Proceedings ; June 16-21, 2013, Granlibakken Resort, Lake Tahoe, California}, pages = {489 -- 492}, abstract = {Differential phase contrast imaging (DPCI) enables the visualization of soft tissue contrast using X-rays. In this work we introduce a reconstruction framework based on curvelet expansion and sparse regularization for DPCI. We will show that curvelets provide a suitable data representation for DPCI reconstruction that allows preservation of edges as well as an exact analytic representation of the system matrix. As a first evaluation, we show results using simulated phantom data}, language = {en} } @article{FroeseJainRymaretal., author = {Froese, Vincent and Jain, Brijnesh and Rymar, Maciej and Welle, Mathias}, title = {Fast Exact Dynamic Time Warping on Run-Length Encoded Time Series}, series = {Algorithmica}, journal = {Algorithmica}, publisher = {Springer Nature}, doi = {10.1007/s00453-022-01038-3}, pages = {17}, abstract = {Dynamic Time Warping (DTW) is a well-known similarity measure for time series. The standard dynamic programming approach to compute the DTW distance of two length-n time series, however, requires O(n2) time, which is often too slow for real-world applications. Therefore, many heuristics have been proposed to speed up the DTW computation. These are often based on lower bounding techniques, approximating the DTW distance, or considering special input data such as binary or piecewise constant time series. In this paper, we present a first exact algorithm to compute the DTW distance of two run-length encoded time series whose running time only depends on the encoding lengths of the inputs. The worst-case running time is cubic in the encoding length. In experiments we show that our algorithm is indeed fast for time series with short encoding lengths.}, language = {en} } @inproceedings{WinterspergerSafiMauerer, author = {Wintersperger, Karen and Safi, Hila and Mauerer, Wolfgang}, title = {QPU-System Co-Design for Quantum HPC Accelerators?}, series = {Architecture of Computing Systems: 35th International Conference, ARCS 2022, Heilbronn, Germany, September 13-15, 2022, Proceedings}, booktitle = {Architecture of Computing Systems: 35th International Conference, ARCS 2022, Heilbronn, Germany, September 13-15, 2022, Proceedings}, publisher = {Springer}, isbn = {978-3-031-21866-8}, doi = {10.1007/978-3-031-21867-5_7}, pages = {100 -- 114}, abstract = {The use of quantum processing units (QPUs) promises speed-ups for solving computational problems, but the quantum devices currently available possess only a very limited number of qubits and suffer from considerable imperfections. One possibility to progress towards practical utility is to use a co-design approach: Problem formulation and algorithm, but also the physical QPU properties are tailored to the specific application. Since QPUs will likely be used as accelerators for classical computers, details of systemic integration into existing architectures are another lever to influence and improve the practical utility of QPUs. In this work, we investigate the influence of different parameters on the runtime of quantum programs on tailored hybrid CPU-QPU-systems. We study the influence of communication times between CPU and QPU, how adapting QPU designs influences quantum and overall execution performance, and how these factors interact. Using a simple model that allows for estimating which design choices should be subjected to optimisation for a given task, we provide an intuition to the HPC community on potentials and limitations of co-design approaches. We also discuss physical limitations for implementing the proposed changes on real quantum hardware devices.}, language = {en} } @incollection{Kiesl, author = {Kiesl, Hans}, title = {Gewichtung}, series = {Handbuch Methoden der empirischen Sozialforschung}, booktitle = {Handbuch Methoden der empirischen Sozialforschung}, editor = {Baur, Nina and Blasius, J{\"o}rg}, publisher = {Springer Nature}, doi = {10.1007/978-3-658-37985-8_30}, pages = {473 -- 481}, abstract = {Ziel einer Analyse quantitativer Daten ist die Verallgemeinerung der Stichprobenergebnisse auf die interessierende Grundgesamtheit (H{\"a}der/H{\"a}der, Kapitel 27 in diesem Band). Tats{\"a}chlich unterscheiden sich Stichproben in bestimmter Hinsicht aber fast immer von der Grundgesamtheit; sei es durch ein geplantes „Oversampling" einer bestimmten Teilpopulation (die Genauigkeit einer Sch{\"a}tzung wird im Wesentlichen von der Fallzahl in der Stichprobe bestimmt, weshalb seltene Teilpopulationen, f{\"u}r die valide Sch{\"a}tzungen m{\"o}glich sein sollen, mit einem gr{\"o}ßeren Auswahlsatz in die Erhebung aufgenommen werden) oder durch selektiven Nonresponse (Engel/Schmidt, Kapitel 29 in diesem Band). Viele Befragungen weisen etwa einen so genannten „Mittelschichtsbias" auf; Personen mit mittlerem bis gehobenem Bildungsniveau (gemessen durch den h{\"o}chsten Schulabschluss) zeigen sich am {\"o}ftesten bereit, an Umfragen teilzunehmen, sie sind in den Erhebungsdaten daher {\"u}berrepr{\"a}sentiert.}, language = {de} } @inproceedings{Frikel, author = {Frikel, J{\"u}rgen}, title = {A new framework for sparse regularization in limited angle x-ray tomography}, series = {2010 7th IEEE International Symposium on Biomedical Imaging: From Nano to Macro ; Rotterdam 14.04.2010 - 17.04.2010}, booktitle = {2010 7th IEEE International Symposium on Biomedical Imaging: From Nano to Macro ; Rotterdam 14.04.2010 - 17.04.2010}, publisher = {IEEE}, address = {Piscataway, NJ}, isbn = {978-1-4244-4125-9}, issn = {1945-7928}, doi = {10.1109/ISBI.2010.5490113}, pages = {824 -- 827}, abstract = {We propose a new framework for limited angle tomographic reconstruction. Our approach is based on the observation that for a given acquisition geometry only a few (visible) structures of the object can be reconstructed reliably using a limited angle data set. By formulating this problem in the curvelet domain, we can characterize those curvelet coefficients which correspond to visible structures in the image domain. The integration of this information into the formulation of the reconstruction problem leads to a considerable dimensionality reduction and yields a speedup of the corresponding reconstruction algorithms.}, language = {en} } @article{TrostClausHerrmann, author = {Trost, Marco and Claus, Thorsten and Herrmann, Frank}, title = {Social Sustainability in Production Planning: A Systematic Literature Review}, series = {Sustainability}, volume = {14}, journal = {Sustainability}, number = {13}, publisher = {MDPI}, address = {Basel}, doi = {10.3390/su14138198}, pages = {1 -- 31}, abstract = {Sustainable production includes economic, environmental, and social aspects. However, social sustainability has received less attention, especially compared to the economic aspects. Next to technical and organizational measures, social improvements within supply chains can also be achieved through suitable production planning. Within production planning, production programs are determined, and the assignment of available resources (e.g., employees) is specified. Thus, the utilization and workload of employees are defined. This systematic literature review investigates to what extent such employee-related social aspects are reflected in production planning and discusses whether economic aspects dominate them. For this, a Scopus database search was carried out and 76 identified approaches were analyzed and categorized regarding the occurring employee-related social aspects and their implementation. Thus far, the approaches mainly consider single aspects on single planning levels. A consideration of a broad set of aspects along the entire production planning has rarely been studied. In particular, health and safety aspects are considered on the levels of assembly line balancing and job rotation. However, their impact is primarily determined by the specific settings of the decision-maker. To support decision-makers, only a few studies have investigated the effects based on real application scenarios. Further potential might be an extended modeling of social and economic interdependencies and a consideration of employee-related social aspects in medium- to long-term production planning.}, language = {en} } @techreport{GoeppelFrikelHaltmeier, author = {G{\"o}ppel, Simon and Frikel, J{\"u}rgen and Haltmeier, Markus}, title = {Translation invariant diagonal frame decomposition of inverse problems and their regularization}, doi = {10.48550/arXiv.2208.08500}, abstract = {Solving inverse problems is central to a variety of important applications, such as biomedical image reconstruction and non-destructive testing. These problems are characterized by the sensitivity of direct solution methods with respect to data perturbations. To stabilize the reconstruction process, regularization methods have to be employed. Well-known regularization methods are based on frame expansions, such as the wavelet-vaguelette (WVD) decomposition, which are well adapted to the underlying signal class and the forward model and allow efficient implementation. However, it is well known that the lack of translational invariance of wavelets and related systems leads to specific artifacts in the reconstruction. To overcome this problem, in this paper we introduce and analyze the concept of translation invariant diagonal frame decomposition (TI-DFD) of linear operators. We prove that a TI-DFD combined with a regularizing filter leads to a convergent regularization method with optimal convergence rates. As illustrative example, we construct a wavelet-based TI-DFD for one-dimensional integration, where we also investigate our approach numerically. The results indicate that filtered TI-DFDs eliminate the typical wavelet artifacts when using standard wavelets and provide a fast, accurate, and stable solution scheme for inverse problems.}, language = {en} }