TY - GEN A1 - Vu, Thi Huong A1 - Koch, Thorsten T1 - Clustering scientific publications: lessons learned through experiments with a real citation network N2 - Clustering scientific publications helps uncover research structures within bibliographic databases. Graph-based methods such as spectral, Louvain, and Leiden clustering are commonly used due to their ability to model citation networks. However, their effectiveness can diminish when applied to real-world data. This study evaluates these clustering algorithms on a citation graph of about 700,000 articles and 4.6 million citations from the Web of Science. The results show that while scalable methods like Louvain and Leiden perform efficiently, their default settings often yield poor partitioning. Meaningful outcomes require careful parameter tuning, especially for large networks with uneven structures, including a dense core and loosely connected papers. These findings highlight practical lessons about the challenges of large-scale data, method selection and tuning based on specific structures of bibliometric clustering tasks. T3 - ZIB-Report - 25-05 KW - graph clustering KW - citation networks KW - Web of Science KW - bibliometric analysis KW - unsupervised learning Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-100418 ER - TY - GEN A1 - Vu, Thi Huong A1 - Koch, Thorsten A1 - Xu, Hong-Kun T1 - The gradient projection method: Is the Polyak adaptive stepsize rule optimal? N2 - Not always! This is our answer to the question of whether the Polyak adaptive stepsize rule in the gradient projection method is optimal. The answer is based on revisiting the subgradient projection method by Polyak [USSR Computational Mathematics and Mathematical Physics 9 (1969)] for smooth and convex minimization problems where the objective function possesses a geometric property called flatness. Our results show that the method can be more flexible (the effective range for the parameter controlling the stepsize can be wider) and have sharper convergence rates. Applications to split feasibility/equality problems are presented, deriving for the first time the O(1/k) rate of convergence for the adaptive CQ method. A theoretical guarantee of the linear convergence of the gradient descent method with adaptive stepsizes for Google PageRank is provided. At the same time, numerical experiments are designed to spot the ``optimal" stepsize and to compare with other basic gradient methods. Y1 - 2024 ER - TY - JOUR A1 - Vu, Thi Huong A1 - Litzel, Ida A1 - Koch, Thorsten T1 - Similarity-based fuzzy clustering scientific articles: potentials and challenges from mathematical and computational perspectives JF - Journal of Nonlinear and Variational Analysis N2 - Fuzzy clustering, which allows an article to belong to multiple clusters with soft membership degrees, plays a vital role in analyzing publication data. This problem can be formulated as a constrained optimization model, where the goal is to minimize the discrepancy between the similarity observed from data and the similarity derived from a predicted distribution. While this approach benefits from leveraging state-of-the-art optimization algorithms, tailoring them to work with real, massive databases like OpenAlex or Web of Science - containing about 70 million articles and a billion citations - poses significant challenges. We analyze potentials and challenges of the approach from both mathematical and computational perspectives. Among other things, second-order optimality conditions are established, providing new theoretical insights, and practical solution methods are proposed by exploiting the structure of the problem. Specifically, we accelerate the gradient projection method using GPU-based parallel computing to efficiently handle large-scale data. Y1 - 2026 U6 - https://doi.org/https://doi.org/10.23952/jnva.10.2026.2.8 VL - 10 IS - 2 SP - 381 EP - 401 PB - Biemdas ER - TY - GEN A1 - Vu, Thi Huong A1 - Litzel, Ida A1 - Koch, Thorsten T1 - Similarity-based fuzzy clustering scientific articles: potentials and challenges from mathematical and computational perspectives N2 - Fuzzy clustering, which allows an article to belong to multiple clusters with soft membership degrees, plays a vital role in analyzing publication data. This problem can be formulated as a constrained optimization model, where the goal is to minimize the discrepancy between the similarity observed from data and the similarity derived from a predicted distribution. While this approach benefits from leveraging state-of-the-art optimization algorithms, tailoring them to work with real, massive databases like OpenAlex or Web of Science -- containing about 70 million articles and a billion citations -- poses significant challenges. We analyze potentials and challenges of the approach from both mathematical and computational perspectives. Among other things, second-order optimality conditions are established, providing new theoretical insights, and practical solution methods are proposed by exploiting the problem’s structure. Specifically, we accelerate the gradient projection method using GPU-based parallel computing to efficiently handle large-scale data. T3 - ZIB-Report - 25-09 KW - bibliometrics KW - fuzzy clustering KW - large-scale publication data KW - non-convex optimization KW - second-order optimality KW - gradient projection methods KW - Nesterov acceleration KW - GPU-based parallel computing Y1 - 2025 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/10036 ER - TY - JOUR A1 - Vu, Thi Huong A1 - Xu, Hong-Kun A1 - Nguyen, Dong Yen T1 - Stability analysis of split equality and split feasibility problems JF - Journal of Global Optimization N2 - In this paper, for the first time in the literature, we study the stability of solutions of two classes of feasibility (i.e., split equality and split feasibility) problems by set-valued and variational analysis techniques. Our idea is to equivalently reformulate the feasibility problems as parametric generalized equations to which set-valued and variational analysis techniques apply. Sufficient conditions, as well as necessary conditions, for the Lipschitz-likeness of the involved solution maps are proved by exploiting special structures of the problems and by using an advanced result of B.S. Mordukhovich [J. Global Optim. 28, 347–362 (2004)]. These conditions stand on a solid interaction among all the input data by means of their dual counterparts, which are transposes of matrices and regular/limiting normal cones to sets. Several examples are presented to illustrate how the obtained results work in practice and also show that the assumption on the existence of a nonzero solution used in the necessity conditions cannot be lifted. Y1 - 2025 U6 - https://doi.org/10.1007/s10898-025-01469-6 SN - 0925-5001 VL - 92 SP - 411 EP - 429 PB - Springer Science and Business Media LLC ER - TY - JOUR A1 - Vu, Thi Huong A1 - Xu, Hong-Kun A1 - Nguyen, Dong Yen T1 - Stability of nonhomogeneous split equality and split feasibility problems with possibly nonconvex constraint sets JF - Optimization N2 - By applying some techniques of set-valued and variational analysis, we study solution stability of nonhomogeneous split equality problems and nonhomogeneous split feasibility problems, where the constraint sets need not be convex. Necessary and sufficient conditions for the Lipschitz-likeness of the solution maps of the problems are given and illustrated by concrete examples. The obtained results complement those given in [Huong VT, Xu HK, Yen ND. Stability analysis of split equality and split feasibility problems. arXiv:2410.16856.], where classical split equality problems and split feasibility problems have been considered. Y1 - 2025 U6 - https://doi.org/10.1080/02331934.2025.2508499 SP - 1 EP - 19 ER - TY - JOUR A1 - Vu-Han, Tu-Lan A1 - Schettino, Rodrigo Bermudez A1 - Weiß, Claudia A1 - Perka, Carsten A1 - Winkler, Tobias A1 - Sunkara, Vikram A1 - Pumberger, Matthias T1 - An interpretable data-driven prediction model to anticipate scoliosis in spinal muscular atrophy in the era of (gene-) therapies JF - Scientific Reports N2 - 5q-spinal muscular atrophy (SMA) is a neuromuscular disorder (NMD) that has become one of the first 5% treatable rare diseases. The efficacy of new SMA therapies is creating a dynamic SMA patient landscape, where disease progression and scoliosis development play a central role, however, remain difficult to anticipate. New approaches to anticipate disease progression and associated sequelae will be needed to continuously provide these patients the best standard of care. Here we developed an interpretable machine learning (ML) model that can function as an assistive tool in the anticipation of SMA-associated scoliosis based on disease progression markers. We collected longitudinal data from 86 genetically confirmed SMA patients. We selected six features routinely assessed over time to train a random forest classifier. The model achieved a mean accuracy of 0.77 (SD 0.2) and an average ROC AUC of 0.85 (SD 0.17). For class 1 ‘scoliosis’ the average precision was 0.84 (SD 0.11), recall 0.89 (SD 0.22), F1-score of 0.85 (SD 0.17), respectively. Our trained model could predict scoliosis using selected disease progression markers and was consistent with the radiological measurements. During post validation, the model could predict scoliosis in patients who were unseen during training. We also demonstrate that rare disease data sets can be wrangled to build predictive ML models. Interpretable ML models can function as assistive tools in a changing disease landscape and have the potential to democratize expertise that is otherwise clustered at specialized centers. Y1 - 2024 U6 - https://doi.org/10.1038/s41598-024-62720-w VL - 14 IS - 11838 ER - TY - JOUR A1 - Vu‐Han, Tu‐Lan A1 - Sunkara, Vikram A1 - Bermudez‐Schettino, Rodrigo A1 - Schwechten, Jakob A1 - Runge, Robin A1 - Perka, Carsten A1 - Winkler, Tobias A1 - Pokutta, Sebastian A1 - Weiß, Claudia A1 - Pumberger, Matthias T1 - Feature Engineering for the Prediction of Scoliosis in 5q‐Spinal Muscular Atrophy JF - Journal of Cachexia, Sarcopenia and Muscle Y1 - 2025 U6 - https://doi.org/10.1002/jcsm.13599 VL - 16 IS - 1 SP - e13599 ER - TY - THES A1 - Wachsmann, Ole T1 - Computational Models for the prediction of drug-induced Nephrotoxicity Y1 - 2019 ER - TY - THES A1 - Wade, Moritz T1 - Automatic Textbook-Like Layout of Biological Networks Y1 - 2008 ER - TY - JOUR A1 - Wagendorf, Oliver A1 - Nahles, Susanne A1 - Vach, Kirstin A1 - Kernen, Florian A1 - Zachow, Stefan A1 - Heiland, Max A1 - Flügge, Tabea T1 - The impact of teeth and dental restorations on gray value distribution in cone-beam computer tomography - a pilot study JF - International Journal of Implant Dentistry N2 - Purpose: To investigate the influence of teeth and dental restorations on the facial skeleton's gray value distributions in cone-beam computed tomography (CBCT). Methods: Gray value selection for the upper and lower jaw segmentation was performed in 40 patients. In total, CBCT data of 20 maxillae and 20 mandibles, ten partial edentulous and ten fully edentulous in each jaw, respectively, were evaluated using two different gray value selection procedures: manual lower threshold selection and automated lower threshold selection. Two sample t tests, linear regression models, linear mixed models, and Pearson's correlation coefficients were computed to evaluate the influence of teeth, dental restorations, and threshold selection procedures on gray value distributions. Results: Manual threshold selection resulted in significantly different gray values in the fully and partially edentulous mandible. (p = 0.015, difference 123). In automated threshold selection, only tendencies to different gray values in fully edentulous compared to partially edentulous jaws were observed (difference: 58–75). Significantly different gray values were evaluated for threshold selection approaches, independent of the dental situation of the analyzed jaw. No significant correlation between the number of teeth and gray values was assessed, but a trend towards higher gray values in patients with more teeth was noted. Conclusions: Standard gray values derived from CT imaging do not apply for threshold-based bone segmentation in CBCT. Teeth influence gray values and segmentation results. Inaccurate bone segmentation may result in ill-fitting surgical guides produced on CBCT data and misinterpreting bone density, which is crucial for selecting surgical protocols. Y1 - 2023 U6 - https://doi.org/10.1186/s40729-023-00493-z VL - 9 IS - 27 ER - TY - GEN A1 - Wagler, Annegret T1 - On Critically Perfect Graphs N2 - A perfect graph is critical if the deletion of any edge results in an imperfect graph. We give examples of such graphs and prove some basic properties. We investigate the relationship of critically perfect graphs to well-known classes of perfect graphs and study operations preserving critical perfectness. T3 - ZIB-Report - SC-96-50 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2609 ER - TY - GEN A1 - Wagler, Annegret T1 - Critical Edges in Perfect Graphs and Some Polyhedral Consequences N2 - An edge $e$ of a perfect graph $G$ is called critical if $G-e$ is imperfect. For certain graphs $G-e$ of this type, we determine all minimally imperfect subgraphs. We use this knowledge to describe inequalities inducing facets of the stable set polytope associated with $G-e$.\\ T3 - ZIB-Report - SC-97-46 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3153 ER - TY - GEN A1 - Wagler, Annegret T1 - Critical and Anticritical Edges with respect to Perfectness N2 - We call an edge $e$ of a perfect graph $G$ critical if $G-e$ is imperfect and call $e$ anticritical if $G+e$ is imperfect. The present paper surveys several questions in this context. We ask in which perfect graphs critical and anticritical edges occur and how to detect such edges. The main result by [{\sl Wagler, PhD thesis 2000}] shows that a graph does not admit any critical edge if and only if it is Meyniel. The goal is to order the edges resp.~non-edges of certain perfect graphs s.t. deleting resp.~adding all edges in this order yields a sequence of perfect graphs only. Results of [{\sl Hayward 1985}] and [{\sl Spinrad & Sritharan 1995}] show the existence of such edge orders for weakly triangulated graphs; the line-perfect graphs are precisely these graphs where all edge orders are perfect [{\sl Wagler 2001}]. Such edge orders cannot exist for every subclass of perfect graphs that contains critically resp.~anticritically perfect graphs where deleting resp.~adding an arbitrary edge yields an imperfect graph. We present several examples and properties of such graphs, discuss constructions and characterizations from [{\sl Wagler 1999, Wagler PhD thesis 2000}]. An application of the concept of critically and anticritically perfect graphs is a result due to [{\sl Hougardy & Wagler 2002}] showing that perfectness is an elusive graph property. T3 - ZIB-Report - 03-22 KW - Perfect graphs KW - critical edges KW - perfect edge orders KW - critically perfect graphs Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7446 ER - TY - GEN A1 - Wagler, Annegret T1 - The Normal Graph Conjecture is true for Circulants N2 - Normal graphs are defined in terms of cross-intersecting set families: a graph is normal if it admits a clique cover $\cal Q$ and a stable set cover $\cal S$ s.t.~every clique in $\cal Q$ intersects every stable set in $\cal S$. Normal graphs can be considered as closure of perfect graphs by means of co-normal products (Körner 1973) and graph entropy (Czisz\'ar et al. 1990). Perfect graphs have been recently characterized as those graphs without odd holes and odd antiholes as induced subgraphs (Strong Perfect Graph Theorem, Chudnovsky et al. 2002). Körner and de Simone observed that $C_5$, $C_7$, and $\overline C_7$ are minimal not normal and conjectured, as generalization of the Strong Perfect Graph Theorem, that every $C_5$, $C_7$, $\overline C_7$- free graph is normal (Normal Graph Conjecture, Körner and de Simone 1999). We prove this conjecture for a first class of graphs that generalize both odd holes and odd antiholes, the circulants, by characterizing all the normal circulants. T3 - ZIB-Report - 04-06 KW - perfect graphs KW - normal graphs KW - circulants Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7813 ER - TY - GEN A1 - Wagler, Annegret T1 - Rank-Perfect and Weakly Rank-Perfect Graphs N2 - An edge of a perfect graph $G$ is critical if $G-e$ is imperfect. We would like to decide whether $G - e$ is still {\sl almost perfect} or already {\sl very imperfect}. Via relaxations of the stable set polytope of a graph, we define two superclasses of perfect graphs: rank-perfect and weakly rank-perfect graphs. Membership in those two classes indicates how far an imperfect graph is away from being perfect. We study the cases, when a critical edge is removed from the line graph of a bipartite graph or from the complement of such a graph. T3 - ZIB-Report - 01-18 KW - perfect graphs KW - rank-perfect graphs KW - weakly rank-perfect graphs KW - stable set polytope KW - critical edges Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6448 ER - TY - GEN A1 - Wagler, Annegret T1 - The Classes of Critically and Anticritically Perfect Graphs N2 - We focus on two new types of extremal graphs with respect to perfectness: critically and anticritically perfect graphs that lose their perfectness by simply deleting and adding an arbitrary edge, respectively. We present examples and study properties in order to compare critically and anticritically perfect graphs with minimally imperfect graphs, another type of extremal graphs with respect to perfectness. We discuss two attempts to characterize the classes of all critically and anticritically perfect graphs and give a brief overview on classes of perfect graphs which contain critically or anticritically perfect graphs. T3 - ZIB-Report - 00-29 KW - perfect graphs KW - critically perfect graphs KW - anticritically perfect graphs Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5975 ER - TY - GEN A1 - Wagler, Annegret T1 - Critical and Anticritical Edges in Perfect Graphs N2 - We call an edge $e$ of a perfect graph $G$ critical if $G-e$ is imperfect and say further that $e$ is anticritical with respect to the complementary graph $\overline G$. We ask in which perfect graphs critical and anticritical edges occur and how to find critical and anticritical edges in perfect graphs. Finally, we study whether we can order the edges of certain perfect graphs such that deleting all the edges yields a sequence of perfect graphs ending up with a stable set. T3 - ZIB-Report - 00-49 KW - perfect graphs KW - critical edges KW - anticritical edges Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6174 ER - TY - GEN A1 - Wagler, Annegret T1 - Relaxing Perfectness: Which Graphs are 'Almost' Perfect? N2 - For all perfect graphs, the stable set polytope STAB$(G)$ coincides with the fractional stable set polytope QSTAB$(G)$, whereas STAB$(G) \subset$ QSTAB$(G)$ holds iff $G$ is imperfect. Padberg asked in the early seventies for ``almost'' perfect graphs. He characterized those graphs for which the difference between STAB$(G)$ and QSTAB$(G)$ is smallest possible. We develop this idea further and define three polytopes between STAB$(G)$ and QSTAB$(G)$ by allowing certain sets of cutting planes only to cut off all the fractional vertices of QSTAB$(G)$. The difference between QSTAB$(G)$ and the largest of the three polytopes coinciding with STAB$(G)$ gives some information on the stage of imperfectness of the graph~$G$. We obtain a nested collection of three superclasses of perfect graphs and survey which graphs are known to belong to one of those three superclasses. This answers the question: which graphs are ``almost'' perfect? T3 - ZIB-Report - 02-03 KW - perfect graph KW - stable set polytope KW - relaxations Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6700 ER - TY - GEN A1 - Wagler, Annegret T1 - Antiwebs are Rank-Perfect N2 - \We discuss a nested collection of three superclasses of perfect graphs: near-perfect, rank-perfect, and weakly rank-perfect graphs. For that, we start with the description of the stable set polytope for perfect graphs and allow stepwise more general facets for the stable set polytopes of the graphs in each superclass. Membership in those three classes indicates how far a graph is away from being perfect. We investigate for webs and antiwebs to which of the three classes they belong. We provide a complete description of the facets of the stable set polytope for antiwebs (with help of a result due to Shepherd on near-bipartite graphs). The main result is that antiwebs are rankperfect. T3 - ZIB-Report - 02-07 KW - relaxations of perfect graphs KW - antiwebs KW - stable set polytope Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6742 ER - TY - THES A1 - Wagler, Annegret T1 - Critical Edges in Perfect Graphs Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10220 ER - TY - JOUR A1 - Wagner, Sabine A1 - Zapata, Carlos A1 - Wan, Wei A1 - Gawlitza, Kornelia A1 - Weber, Marcus A1 - Rurack, Knut T1 - Role of Counterions in Molecularly Imprinted Polymers for Anionic Species JF - Langmuir N2 - Small-molecule oxoanions are often imprinted noncovalently as carboxylates into molecularly imprinted polymers (MIPs), requiring the use of an organic counterion. Popular species are either pentamethylpiperidine (PMP) as a protonatable cation or tetraalkylammonium (TXA) ions as permanent cations. The present work explores the influence of the TXA as a function of their alkyl chain length, from methyl to octyl, using UV/vis absorption, fluorescence titrations, and HPLC as well as MD simulations. Protected phenylalanines (Z-L/D-Phe) served as templates/analytes. While the influence of the counterion on the complex stability constants and anion-induced spectral changes shows a monotonous trend with increasing alkyl chain length at the prepolymerization stage, the cross-imprinting/rebinding studies showed a unique pattern that suggested the presence of adaptive cavities in the MIP matrix, related to the concept of induced fit of enzyme–substrate interaction. Larger cavities formed in the presence of larger counterions can take up pairs of Z-x-Phe and smaller TXA, eventually escaping spectroscopic detection. Correlation of the experimental data with the MD simulations revealed that counterion mobility, the relative distances between the three partners, and the hydrogen bond lifetimes are more decisive for the response features observed than actual distances between interacting atoms in a complex or the orientation of binding moieties. TBA has been found to yield the highest imprinting factor, also showing a unique dual behavior regarding the interaction with template and fluorescent monomer. Finally, interesting differences between both enantiomers have been observed in both theory and experiment, suggesting true control of enantioselectivity. The contribution concludes with suggestions for translating the findings into actual MIP development. Y1 - 2018 U6 - https://doi.org/10.1021/acs.langmuir.8b00500 VL - 34 IS - 23 SP - 6963 EP - 6975 ER - TY - GEN A1 - Wakabayashi, Yoshiko T1 - Medians of Binary Relations: Computational Complexity. N2 - Let $\Re$ be the set of all binary relations on a finite set $N$ and $d$ be the symmetric difference distance defined on $\Re$. For a given profile $\Pi = (R_1,...,R_m) \in R^m$, a relation $R* \in \Re $ that minimizes the function $\sum^m_{k=1} d(R_k,R) $ is called a median relation of $\Pi$. A number of problems occuring in the social sciences, in qualitative data analysis and in multicriteria decision making can be modelled as problems of finding medians of a profile of binary relations. In these contexts the profile $\Pi$ represents collected data (preferences, similarities, games) and the objective is that of finding a median relation of $\Pi$ with some special feature (representing e. g., consensus of preferences, clustering of similar objects, ranking of teams, etc.). In this paper we analyse the computational complexity of all such problems in which the median is required to satisfy one or more of the properties: reflexitivity, symmetry, antisymmetry, transitivity and completeness. We prove that whenever transitivity is required (except when symmetry and completeness are also simultaneously required) then the corresponding median problem is $NP$-hard. In some cases we prove that they remain $NP$-hard when the profile $\Pi$ has a fixed number of binary relations. T3 - ZIB-Report - SC-92-04 Y1 - 1992 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-746 ER - TY - JOUR A1 - Wakayama, Yuki A1 - Yokoyama, Ryohei A1 - Shinano, Yuji A1 - Wakui, Tetsuya T1 - エネルギー供給システムの設計および運用の階層的関係を考慮した最適化(時間集約によるモデル縮約とその効果) T1 - Optimization of Energy Supply Systems in Consideration of Hierarchical Relationship Between Design and Operation(Model Reduction by Time Aggregation and Its Effect) JF - エネルギー・資源学会第34回エネルギーシステム・経済・環境コンファレンス講演論文集 N2 - A hierarchical mixed-integer linear programming method to solve optimal design problems of energy supply systems efficiently has been proposed. The original problem is solved by dividing it into a relaxed optimal design problem at the upper level and optimal operation problems which are independent of each other at the lower level. In this paper, a method of reducing model by time aggregation is proposed to search design solution candidates efficiently in the relaxed optimal design problem at the upper level. This method is realized only by clustering periods and averaging energy demands for clustered periods, while it guarantees to derive the optimal solution. On one hand, the method may decrease the number of design variables and costraints at the upper level, and thus the computation time at the upper level. On the other hand, it may increase the numbers of generated design solution candidates and solved optimal operation problems, and thus the computation time at both the levels. Though a case study on the optimal design of a cogeneration system, it is clarified how the model reduction is effective to enhance the computation efficiency. Y1 - 2018 SP - 401 EP - 404 ER - TY - JOUR A1 - Wakayama, Yuki A1 - Yokoyama, Ryohei A1 - Shinano, Yuji A1 - Wakui, Tetsuya T1 - 階層的最適化によるエネルギ ー供給システムの最適設計・運用 (期間のクラスタリングに よるモデル縮約とその効果) T1 - Optimal Design and Operation of Energy Supply Systems by Hierarchical Optimization (Model Reduction by Clustering Periods and Its Effect) JF - 日本機械学会関西支部第93期定時総会講演会講演論文集 N2 - Ahierarchical mixed-integer linear programmingmethod has been proposed to solve optimal design problems of energy supply systems efficiently. In this paper, a method of reducing model by clustering periods is proposed to search design solution candidates efficiently in the relaxed optimal design problem at the upper level. This method is realized only by clustering periods and averaging energy demands for clustered periods, while it guarantees to derive the optimal solution. Through acase study on the optimaldesign of a cogeneration system, ti is clarified how the model reduction si effective ot enhance the computation efficiency. Y1 - 2018 SP - 259 EP - 260 ER - TY - GEN A1 - Walter, Artur T1 - Sparse Secant Methods for the Iterative Solution of Large Nonsymmetric Linear Systems. N2 - A variety of secant methods has been revisited in view of the construction of iterative solvers for large nonsymmetric linear systems $ Ax = b $ stemming from the discretization of convection diffusion equations. In the first section, we tried to approximate $ A ^{-1} $ directly. Since the sparsity structure of A- is not known, additional storage vectors are needed during the iteration. In the next section, an incomplete factorization $ LU $ of $ A $ is the starting point and we tried to improve this easy invertible approximation of $ A $. The update is constructed in such a way that the sparsity structure of $ L $ and $ U $ is maintained. Two different sparsity preserving updates are investigated from theoretical and practical point of view. Numerical experiments on discretized PDEs of convection diffusion type in 2- D with internal layers and on "arbitrary" matrices with symmetric sparsity structure are given. {\bf Key words:} nonsymmetric linear system, sparse secant method, Broyden's method, incomplete factorization. T3 - ZIB-Report - SC-90-20 Y1 - 1990 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-483 ER - TY - GEN A1 - Walter, Artur T1 - Improvement of Incomplete Factorizations by a Sparse Secant Method. N2 - In the present paper, the improvement of an incomplete factorization of a non-symmetric matrix A is discussed. Starting from the ideas of sparsity preserving quasi-Newton methods, an algorithm is developed which improves the approximation of A by the incomplete factorization maintaining the sparsity structure of the matrices. No renumbering of the unknowns or the admittance of additional fill-in is necessary. The linear convergence of the algorithm is proved under the assumption, that $ L $ and $ U $* have the same sparsity structure and an incomplete factorization with some reasonable approximation property exits. In combination with this algorithm, the method of incomplete factorization and its several modifications are applicable to a wider class of problems with improved convergence qualities. This is shown by a numerical example. {\bf Key Words:} non-symmetric linear system, sparse secant method, incomplete factorization. AMS(MOS) {\bf Subject Classifications:} 65F10, 65N20, 65N30. T3 - ZIB-Report - SC-90-12 KW - non-symmetric linear systems KW - sparse secant method KW - incomplete factorization Y1 - 1990 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-401 ER - TY - GEN A1 - Walter, Artur T1 - Ein Finite-Element-Verfahren zur numerischen Lösung von Erhaltungsgleichungen. N2 - A new approach for the discretisation of hyperbolic conservation laws via a finite element method is developed and analysed. Appropriate forms of the Eulers equation of gas dynamic are considered to employ the algorithm in a reasonable way for this system of nonlinear equations. Both mathematical and physical stability results are obtained. A main part of the paper is devoted to the convergence proof with energy methods under strong regularity of the solution of a scalar nonlinear conservation law. Some hints on the implementation and numerical results for the calculation of transonic gasflow through a Laval nozzle are given. The necessary amount of numerical work is compared to an established finite difference method and the efficiency of the algorithm is shown. A survey on recent literature about finite element methods for hyperbolic problem is included. T3 - ZIB-Report - TR-89-03 Y1 - 1989 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4597 ER - TY - CHAP A1 - Walter, J. A1 - Schütte, Christof ED - Mielke, A. T1 - Conditional Averaging for Diffusive Fast-Slow Systems T2 - Analysis, Modeling and Simulation of Multiscale Problems Y1 - 2006 UR - http://publications.imp.fu-berlin.de/117/ U6 - https://doi.org/10.1007/3-540-35657-6_24 SP - 647 EP - 682 PB - Springer ER - TY - JOUR A1 - Walter, J. A1 - Schütte, Christof A1 - Pavliotis, G. A1 - Stuart, Andrew T1 - Averaging of Stochastic Differential Equations JF - preprint Y1 - 2004 UR - http://publications.imp.fu-berlin.de/63/ ER - TY - GEN A1 - Walter, Lionel A1 - Weber, Marcus T1 - ConfJump : a fast biomolecular sampling method which drills tunnels through high mountains N2 - In order to compute the thermodynamic weights of the different metastable conformations of a molecule, we want to approximate the molecule's Boltzmann distribution in a reasonable time. This is an essential issue in computational drug design. The energy landscape of active biomolecules is generally very rough with a lot of high barriers and low regions. Many of the algorithms that perform such samplings (e.g. the hybrid Monte Carlo method) have difficulties with such landscapes. They are trapped in low-energy regions for a very long time and cannot overcome high barriers. Moving from one low-energy region to another is a very rare event. For these reasons, the distribution of the generated sampling points converges very slowly against the thermodynamically correct distribution of the molecule. The idea of ConfJump is to use $a~priori$ knowledge of the localization of low-energy regions to enhance the sampling with artificial jumps between these low-energy regions. The artificial jumps are combined with the hybrid Monte Carlo method. This allows the computation of some dynamical properties of the molecule. In ConfJump, the detailed balance condition is satisfied and the mathematically correct molecular distribution is sampled. T3 - ZIB-Report - 06-26 KW - Monte Carlo simulation KW - rare events KW - rough potential energy function KW - molecular dynamics Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9204 ER - TY - THES A1 - Walther, Tom T1 - A SCIP Constraint Handler for Piecewise Linear Functions N2 - In this thesis, we study different modelling approaches for piecewise linear functions, in particular with respect to their occurrence in mathematical optimization problems. Reviewing the quality of the classical MIP models from the literature, we will see that all but the disaggregated convex combination method yield both sharp and locally ideal formulations. In the main part, we will present an alternative approach for modelling constraints involving piecewise linear functions, based on ideas of constraint programming and using a convex hull relaxation. For the purpose of developing a branch-and-bound procedure specifically adapted to our constraint formulation within SCIP, all required components such as propagation, branching and separation will be discussed. In particular, we will focus on adapting well-known MIP strategies for the selection of branching variables to our type of piecewise linear constraints. Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-49112 ER - TY - GEN A1 - Walther, Tom A1 - Hiller, Benjamin A1 - Saitenmacher, René T1 - Polyhedral 3D Models for compressors in gas networks N2 - Compressor machines are crucial elements in a gas transmission network, required to compensate for the pressure loss caused by friction in the pipes. Modelling all physical and technical details of a compressor machine involves a large amount of nonlinearity, which makes it hard to use such models in the optimization of large-scale gas networks. In this paper, we are going to describe a modelling approach for the operating range of a compressor machine, starting from a physical reference model and resulting in a polyhedral representation in the 3D space of mass flow throughput as well as in- and outlet pressure. T3 - ZIB-Report - 17-66 KW - gas compressor modeling, polyhedral model, accuracy, z factor Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-65864 SN - 1438-0064 ER - TY - GEN A1 - Wang, Daoliu T1 - Symplectic Difference Schemes for Perturbed Hamiltonian Systems. N2 - In this paper we consider symplectic difference schemes for perturbed Hamiltonian systems of integrable ones, which can cover many important problems. Symplectic difference schemes for general Hamiltonian systems can also be used to these problems. But the perturbation property has not been paid proper attention to, which is important in the method proposed here. Numerical simulation shows that, for this method the time step size can be taken quite large and the qualitative property , such as preserving invariant tori, is also better than usual symplectic difference schemes. T3 - ZIB-Report - SC-90-17 Y1 - 1990 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-456 ER - TY - GEN A1 - Wang, Daoliu T1 - On Symplectic Difference Schemes for Hamiltonian Systems. N2 - Symplectic difference schemes have been shown to be a right formalism for numerical computation of Hamiltonian systems. They are suitable to long time computation and of good qualitative properties. These properties are ensured by the fact that a symplectic difference scheme approximating to a time-independent Hamiltonian system can be regarded as a perturbed time-dependent Hamiltonian system of the original one. That is, a solution of a symplectic difference scheme is a solution of a certain perturbed time dependent Hamiltonian system evaluated at discrete (time) points. This is the main result of the paper. Moreover, linear symplectic difference schemes approximating to a linear time-independent Hamiltonian system can be regarded as a perturbed time-independent Hamiltonian system. So it has all properties that a linear Hamiltonian system has. Based on these results, stochastic webs and chaos in symplectic difference schemes are also discussed. They will appear in numerical simulation for Hamiltonian systems, even with one degree of freedom. T3 - ZIB-Report - SC-90-06 Y1 - 1990 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-345 ER - TY - JOUR A1 - Wang, Han A1 - Hartmann, Carsten A1 - Schütte, Christof T1 - Linear response theory and optimal control for a molecular system under nonequilibrium conditions JF - Molecular Physics Y1 - 2013 UR - http://publications.imp.fu-berlin.de/1297/ U6 - https://doi.org/10.1080/00268976.2013.844370 VL - 111 SP - 3555 EP - 3564 ER - TY - GEN A1 - Wang, Han A1 - Hartmann, Carsten A1 - Schütte, Christof T1 - Linear response theory and optimal control for a molecular system under nonequilibrium conditions N2 - In this paper, we propose a straightforward generalization of linear response theory to systems in nonequilibrium that are subject to nonequilibrium driving. We briefly revisit the standard linear response result for equilibrium systems, where we consider Langevin dynamics as a special case, and then give an alternative derivation using a change-of-measure argument that does not rely on any stationarity or reversibility assumption. This procedure moreover easily enables us to calculate the second order correction to the linear response formula (which may or may not be useful in practice). Furthermore, we outline how the novel nonequilibirum linear response formula can be used to compute optimal controls of molecular systems for cases in which one wants to steer the system to maximize a certain target expectation value. We illustrate our approach with simple numerical examples. T3 - ZIB-Report - 13-33 KW - nonequilibrium molecular dynamics KW - linear response KW - Girsanov transformation KW - stochastic control Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-18944 ER - TY - JOUR A1 - Wang, Han A1 - Hartmann, Carsten A1 - Schütte, Christof A1 - Site, Luigi Delle T1 - Grand-canonical-like molecular-dynamics simulations by using an adaptive-resolution technique JF - Phys. Rev. X Y1 - 2013 U6 - https://doi.org/10.1103/PhysRevX.3.011018 VL - 3 SP - 011018 ER - TY - GEN A1 - Wang, Han A1 - Schütte, Christof T1 - Building Markov State Models for Periodically Driven Non-Equilibrium Systems N2 - Recent years have seen an increased interest in non-equilibrium molecular dynamics (NEMD) simulations, especially for molecular systems with periodic forcing by external fields, e.g., in the context of studying effects of electromagnetic radiation on the human body tissue. Lately, an NEMD methods with local thermostating has been proposed that allows for studying non-equilibrium processes in a statistically reliable and thermodynamically consistent way. In this article, we demonstrate how to construct Markov State Models (MSMs) for such NEMD simulations. MSM building has been well-established for systems in equilibrium where MSMs with just a few (macro-)states allow for accurate reproduction of the essential kinetics of the molecular system under consideration. Non-equilibrium MSMs have been lacking so far. The article presents how to construct such MSMs and illustrates their validity and usefulness for the case of conformation dynamics of alanine dipeptide in an external electric field. T3 - ZIB-Report - 14-46 KW - Non-equilibrium KW - Markov states model KW - Alanine dipeptide KW - Electric field KW - Floquet theory Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-53167 SN - 1438-0064 N1 - To appear in: Journal of Chemical Theory and Computation ER - TY - JOUR A1 - Wang, Han A1 - Schütte, Christof A1 - Ciccotti, Giovanni A1 - Delle Site, Luigi T1 - Exploring the conformational dynamics of alanine dipeptide in solution subjected to an external electric field: A nonequilibrium molecular dynamics simulation JF - Journal of Chemical Theory and Computation Y1 - 2014 U6 - https://doi.org/10.1186/s12859-017-1565-4 VL - 10 IS - 4 SP - 1376 EP - 1386 ER - TY - JOUR A1 - Wang, Han A1 - Schütte, Christof A1 - Ciccotti, Giovanni A1 - von Kleist, Max T1 - Exploring the conformational dynamics of alanine dipeptide in solution subjected to an external electric field: A nonequilibrium molecular dynamics simulation JF - Journal of Chemical Theory and Computation N2 - 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. Y1 - 2014 U6 - https://doi.org/10.1021/ct400993e VL - 10 IS - 4 SP - 1376 EP - 1386 ER - TY - JOUR A1 - Wang, Han A1 - Schütte, Christof A1 - Site, Luigi Delle T1 - Adaptive Resolution Simulation (AdResS): A Smooth Thermodynamic and Structural Transition from Atomistic to Coarse Grained Resolution and Vice Versa in a Grand Canonical Fashion. JF - J. Chem. Theo. Comp. Y1 - 2012 UR - http://publications.imp.fu-berlin.de/1182/ U6 - https://doi.org/10.1021/ct3003354 VL - 8 IS - 8 SP - 2878 EP - 2887 ER - TY - JOUR A1 - Wang, Han A1 - Schütte, Christof A1 - Zhang, P. T1 - Error Estimate of Short-Range Force Calculation in the Inhomogeneous Molecular Systems JF - Phys. Rev. E Y1 - 2012 UR - http://publications.imp.fu-berlin.de/1125/ U6 - https://doi.org/10.1103/PhysRevE.86.026704 VL - 86 IS - 02 SP - 026704 ER - TY - JOUR A1 - Wang, Han A1 - Zhang, P. A1 - Schütte, Christof T1 - On the Numerical Accuracy of Ewald, Smooth Particle Mesh Ewald, and Staggered Mesh Ewald Methods for Correlated Molecular Systems JF - J. Chem. Theo. Comp. Y1 - 2012 UR - http://publications.imp.fu-berlin.de/1181/ U6 - https://doi.org/10.1021/ct300343y VL - 8 IS - 9 SP - 3243 EP - 3256 ER - TY - JOUR A1 - Wang, Junyang A1 - Cockayne, Jon A1 - Chkrebtii, Oksana A1 - Sullivan, T. J. A1 - Oates, Chris T1 - Bayesian numerical methods for nonlinear partial differential equations JF - Statistics and Computing Y1 - 2021 U6 - https://doi.org/10.1007/s11222-021-10030-w VL - 31 IS - 5 ER - TY - JOUR A1 - Wang, Yujing A1 - Vannucci, Luca A1 - Burger, Sven A1 - Gregersen, Niels T1 - Near-unity efficiency in ridge waveguide-based, on-chip single-photon sources JF - Mater. Quantum Technol. Y1 - 2022 U6 - https://doi.org/10.1088/2633-4356/aca8e8 VL - 2 SP - 045004 ER - TY - CHAP A1 - Wardetzky, Max ED - I. Bobenko, Alexander ED - Sullivan, John ED - Ziegler, Günter T1 - Convergence of the Cotan formula - an overview T2 - Discrete Differential Geometry Y1 - 2008 U6 - https://doi.org/10.1007/978-3-7643-8621-4 SP - 275 EP - 286 PB - Birkhäuser Basel ER - TY - THES A1 - Warszawski, Maciej T1 - Lagrange-Relaxierungen der Multi-Fluss-Formulierung für das Distance-Constrained-Vehicle-Routing-Problem und das Travelling-Salesman-Problem Y1 - 2010 ER - TY - THES A1 - Weber, Britta T1 - Merkmalskurven auf triangulierten Oberflächen Y1 - 2008 ER - TY - THES A1 - Weber, Britta T1 - Reconstruction of Microtubule Centerlines from Electron Tomograms N2 - The organization of the mitotic spindle, a structure that separates the chromosomes during cell division, is an active research topic in molecular cell biology. It is composed of microtubules, elongated tubular macromolecules with a diameter of 25 nm. The only volumetric imaging technique that is available to a wide community and provides the required resolution to capture details about microtubules is electron tomography. However, the automatic detection of microtubules in electron tomograms is a difficult task due to the low contrast of the data. Furthermore, thick samples have to be cut into 300 nm thin sections before electron tomography can be applied. Software for automatically segmentation and stitching of the microtubules are not available and therefore these tasks have to be performed manually. Unfortunately, manual segmentation is time consuming for large samples and manual stitching of the tomograms is often infeasible due to the lack of prominent features for registration. Conclusions drawn from electron tomographic data is currently mostly based on either small samples containing few microtubules or single sections of complex structures. Consequently, simple properties, such as the length of microtubules in the spindle or their number, are still unknown for most model organisms. In this thesis, we present methods for 1) an automatic segmentation of microtubule centerlines in electron tomograms, and 2) an automatic stitching of the lines extracted from serial sections. For the centerline segmentation, we use 3D template matching and exploit knowledge about shape of microtubules and microscopy artifacts to design the templates. For the registration of the lines, we present a way to model the orientation of lines as a mixture of Fisher-Mises distributions where we estimate transformation parameters with the expectation maximization algorithm. The final line matching problem is formulated in terms of a probabilistic graphical model. To find the correct correspondences of line ends, we use belief propagation. We handle the poor convergence properties of this algorithm by detecting ambiguous and conflicting assignments of lines automatically. An expert can then influence the final output of the algorithm by solving conflicts manually. A detailed error analysis on true biological data and assessment of the reliability of the results is the prerequisite for analyzing the resulting line representations of the microtubules. To this end, the developed workflow for segmenting and stitching of microtubule centerlines is evaluated on plasticembedded samples of C. elegans early embryos and of spindles from X. laevis egg extracts. Our results suggest that the output of the presented algorithms together with little manual correction is of sufficient quality to allow a detailed analysis of dense microtubule networks. Finally, we exemplarily show results for the centrosome of a C. elegans mitotic spindle. KW - microtubules KW - electron tomography KW - c.elegans KW - image processing KW - graphical model KW - gaussian mixture model KW - template matching Y1 - 2015 UR - http://www.diss.fu-berlin.de/diss/receive/FUDISS_thesis_000000100915 ER -