Publications at the Institute of Mathematics

Results: 1976
Created on: Tue, 06 Jun 2023 23:12:55 +0200 in 0.0647 sec

Faulwasser, Timm; Ou, Ruchuan; Pan, Guanru; Schmitz, Philipp; Worthmann, Karl
Behavioral theory for stochastic systems? A data-driven journey from Willems to Wiener and back again. - In: Annual reviews in control, ISSN 1872-9088, Bd. 55 (2023), S. 92-117

The fundamental lemma by Jan C. Willems and co-workers is deeply rooted in behavioral systems theory and it has become one of the supporting pillars of the recent progress on data-driven control and system analysis. This tutorial-style paper combines recent insights into stochastic and descriptor-system formulations of the lemma to further extend and broaden the formal basis for behavioral theory of stochastic linear systems. We show that series expansions - in particular Polynomial Chaos Expansions (PCE) of L2-random variables, which date back to Norbert Wiener’s seminal work - enable equivalent behavioral characterizations of linear stochastic systems. Specifically, we prove that under mild assumptions the behavior of the dynamics of the L2-random variables is equivalent to the behavior of the dynamics of the series expansion coefficients and that it entails the behavior composed of sampled realization trajectories. We also illustrate the short-comings of the behavior associated to the time-evolution of the statistical moments. The paper culminates in the formulation of the stochastic fundamental lemma for linear time-invariant systems, which in turn enables numerically tractable formulations of data-driven stochastic optimal control combining Hankel matrices in realization data (i.e. in measurements) with PCE concepts.
Chan, Tsz Lung; Kriesell, Matthias; Schmidt, Jens M.
Contractible edges in longest cycles. - In: Journal of graph theory, ISSN 1097-0118, Bd. 103 (2023), 3, S. 542-563
Reis, Timo; Stykel, Tatjana
Passivity, port-Hamiltonian formulation and solution estimates for a coupled magneto-quasistatic system. - In: Evolution equations and control theory, ISSN 2163-2480, Bd. 12 (2023), 4, S. 1208-1232

In this paper, we study a quasilinear coupled magneto-quasistatic model from a systems theoretic perspective. First, by taking the injected voltages as input and the associated currents as output, we prove that the magneto-quasistatic system is passive. Moreover, by defining suitable Dirac and resistive structures, we show that it admits a representation as a port-Hamiltonian system. Thereafter, we consider dependence of the solution on initial and input data. We show that the current and the magnetic vector potential can be estimated by means of the initial magnetic vector potential and the voltage. We also analyse the free dynamics of the system and study the asymptotic behavior of the solutions for $ t\to\infty $.
Sherratt, Katharine; Gruson, Hugo; Grah, Rok; Johnson, Helen; Niehus, Rene; Prasse, Bastian; Sandmann, Frank; Deuschel, Jannik; Wolffram, Daniel; Abbott, Sam; Ullrich, Alexander; Gibson, Graham; Ray, Evan L.; Reich, Nicholas G.; Sheldon, Daniel; Wang, Yijin; Wattanachit, Nutcha; Wang, Lijing; Trnka, Jan; Obozinski, Guillaume; Sun, Tao; Thanou, Dorina; Pottier, Loic; Krymova, Ekaterina; Meinke, Jan H.; Barbarossa, Maria Vittoria; Leithäuser, Neele; Mohring, Jan; Schneider, Johanna; Wlazło, Jarosław; Fuhrmann, Jan; Lange, Berit; Rodiah, Isti; Baccam, Prasith; Gurung, Heidi; Stage, Steven; Suchoski, Bradley; Budzinski, Jozef; Walraven, Robert; Villanueva, Inmaculada; Tucek, Vit; Smid, Martin; Zajíček, Milan; Pérez Álvarez, Cesar; Reina, Borja; Bosse, Nikos I.; Meakin, Sophie R.; Castro, Lauren; Fairchild, Geoffrey; Michaud, Isaac; Osthus, Dave; Alaimo Di Loro, Pierfrancesco; Maruotti, Antonello; Eclerová, Veronika; Kraus, Andrea; Kraus, David; Pribylova, Lenka; Dimitris, Bertsimas; Li, Michael Lingzhi; Saksham, Soni; Dehning, Jonas; Mohr, Sebastian; Priesemann, Viola; Redlarski, Grzegorz; Bejar Haro, Benjamin; Ardenghi, Giovanni; Parolini, Nicola; Ziarelli, Giovanni; Bock, Wolfgang; Heyder, Stefan; Hotz, Thomas; Singh, David E.; Guzman-Merino, Miguel; Aznarte, Jose L.; Moriña, David; Alonso, Sergio; Álvarez, Enric; López, Daniel; Prats, Clara; Burgard, Jan Pablo; Rodloff, Arne; Zimmermann, Tom; Kuhlmann, Alexander; Zibert, Janez; Pennoni, Fulvia; Divino, Fabio; Català, Marti; Lovison, Gianfranco; Giudici, Paolo; Tarantino, Barbara; Bartolucci, Francesco; Jona Lasinio, Giovanna; Mingione, Marco; Farcomeni, Alessio; Srivastava, Ajitesh; Montero-Manso, Pablo; Adiga, Aniruddha; Hurt, Benjamin; Lewis, Bryan; Marathe, Madhav; Porebski, Przemyslaw; Venkatramanan, Srinivasan; Bartczuk, Rafal P.; Dreger, Filip; Gambin, Anna; Gogolewski, Krzysztof; Gruziel-Słomka, Magdalena; Krupa, Bartosz; Moszyânski, Antoni; Niedzielewski, Karol; Nowosielski, Jedrzej; Radwan, Maciej; Rakowski, Franciszek; Semeniuk, Marcin; Szczurek, Ewa; Zieliânski, Jakub; Kisielewski, Jan; Pabjan, Barbara; Kirsten, Holger; Kheifetz, Yuri; Scholz, Markus; Biecek, Przemysław; Bodych, Marcin; Filinski, Maciej; Idzikowski, Radoslaw; Krueger, Tyll; Ozanski, Tomasz; Bracher, Johannes; Funk, Sebastian
Predictive performance of multi-model ensemble forecasts of COVID-19 across European nations. - In: eLife, ISSN 2050-084X, Bd. 12 (2023), e81916, S. 1-23

Background: Short-term forecasts of infectious disease contribute to situational awareness and capacity planning. Based on best practice in other fields and recent insights in infectious disease epidemiology, one can maximise forecasts’ predictive performance by combining independent models into an ensemble. Here we report the performance of ensemble predictions of COVID-19 cases and deaths across Europe from March 2021 to March 2022. Methods: We created the European COVID-19 Forecast Hub, an online open-access platform where modellers upload weekly forecasts for 32 countries with results publicly visualised and evaluated. We created a weekly ensemble forecast from the equally-weighted average across individual models' predictive quantiles. We measured forecast accuracy using a baseline and relative Weighted Interval Score (rWIS). We retrospectively explored ensemble methods, including weighting by past performance. Results: We collected weekly forecasts from 48 models, of which we evaluated 29 models alongside the ensemble model. The ensemble had a consistently strong performance across countries over time, performing better on rWIS than 91% of forecasts for deaths (N=763 predictions from 20 models), and 83% forecasts for cases (N=886 predictions from 23 models). Performance remained stable over a 4-week horizon for death forecasts but declined with longer horizons for cases. Among ensemble methods, the most influential choice came from using a median average instead of the mean, regardless of weighting component models. Conclusions: Our results support combining independent models into an ensemble forecast to improve epidemiological predictions, and suggest that median averages yield better performance than methods based on means. We highlight that forecast consumers should place more weight on incident death forecasts than case forecasts at horizons greater than two weeks. Funding: European Commission, Ministerio de Ciencia, Innovación y Universidades, FEDER; Agència de Qualitat i Avaluació Sanitàries de Catalunya; Netzwerk Universitätsmedizin; Health Protection Research Unit; Wellcome Trust; European Centre for Disease Prevention and Control; Ministry of Science and Higher Education of Poland; Federal Ministry of Education and Research; Los Alamos National Laboratory; German Free State of Saxony; NCBiR; FISR 2020 Covid-19 I Fase; Spanish Ministry of Health / REACT-UE (FEDER); National Institutes of General Medical Sciences; Ministerio de Sanidad/ISCIII; PERISCOPE European H2020; PERISCOPE European H2021; InPresa; National Institutes of Health, NSF, US Centers for Disease Control and Prevention, Google, University of Virginia, Defense Threat Reduction Agency.
Behrndt, Jussi; Schmitz, Philipp; Teschl, Gerald; Trunk, Carsten
Perturbations of periodic Sturm-Liouville operators. - In: Advances in mathematics, ISSN 1090-2082, Bd. 422 (2023), 109022, S. 1-22
Kleyman, Viktoria; Schaller, Manuel; Mordmüller, Mario; Wilson, Mitsuru; Brinkmann, Ralf; Worthmann, Karl; Müller, Matthias A.
State and parameter estimation for retinal laser treatment. - In: IEEE transactions on control systems technology, ISSN 1558-0865, Bd. 31 (2023), 3, S. 1366-1378

Adequate therapeutic retinal laser irradiation needs to be adapted to local absorption. This leads to time-consuming treatments as the laser power needs to be successively adjusted to avoid undertreatment and overtreatment caused by too low or too high temperatures. Closed-loop control can overcome this burden by means of temperature measurements. To allow for model predictive control schemes, the current state and the spot-dependent absorption need to be estimated. In this article, we thoroughly compare moving horizon estimator (MHE) and extended Kalman filter (EKF) designs for joint state and parameter estimation. We consider two different scenarios, the estimation of one or two unknown absorption coefficients. For one unknown parameter, both estimators perform very similarly. For two unknown parameters, we found that the MHE benefits from active parameter constraints at the beginning of the estimation, whereas after a settling time, both estimators perform again very similarly as long as the parameters are inside the considered parameter bounds.
Caragea, Andrei; Lee, Dae Gwan; Philipp, Friedrich; Voigtlaender, Felix
A Balian-Low type theorem for Gabor Riesz sequences of arbitrary density. - In: Mathematische Zeitschrift, ISSN 1432-1823, Bd. 303 (2023), 2, 48, S. 1-22
Eichfelder, Gabriele; Warnow, Leo
Advancements in the computation of enclosures for multi-objective optimization problems. - In: European journal of operational research, ISSN 0377-2217, Bd. 310 (2023), 1, S. 315-327

A central goal for multi-objective optimization problems is to compute their nondominated sets. In most cases these sets consist of infinitely many points and it is not a practical approach to compute them exactly. One solution to overcome this problem is to compute an enclosure, a special kind of coverage, of the nondominated set. For that computation one often makes use of so-called local upper bounds. In this paper we present a generalization of this concept. For the first time, this allows to apply a warm start strategy to the computation of an enclosure. We also show how this generalized concept allows to remove empty areas of an enclosure by deleting certain parts of the lower and upper bound sets which has not been possible in the past. We demonstrate how to apply our ideas to the box approximation algorithm, a general framework to compute an enclosure, as recently used in the solver called BAMOP. We show how that framework can be simplified and improved significantly, especially concerning its practical numerical use. In fact, we show for selected numerical instances that our new approach is up to eight times faster than the original one. Hence, our new framework is not only of theoretical but also of practical use, for instance for continuous convex or mixed-integer quadratic optimization problems.
âCurgus, Branko; Derkach, Volodymyr; Trunk, Carsten
Indefinite Sturm-Liouville operators in polar form. - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2023. - 1 Online-Ressource (49 Seiten). - (Preprint ; M23,03)
Chill, Ralph; Reis, Timo; Stykel, Tatjana
Analysis of a quasilinear coupled magneto-quasistatic model: solvability and regularity of solutions. - In: Journal of mathematical analysis and applications, ISSN 1096-0813, Bd. 523 (2023), 2, 127033

We consider a quasilinear model arising from dynamical magnetization. This model is described by a magneto-quasistatic (MQS) approximation of Maxwell's equations. Assuming that the medium consists of a conducting and a non-conducting part, the derivative with respect to time is not fully entering, whence the system can be described by an abstract differential-algebraic equation. Furthermore, via magnetic induction, the system is coupled with an equation which contains the induced electrical currents along the associated voltages, which form the input of the system. The aim of this paper is to study well-posedness of the coupled MQS system and regularity of its solutions. Thereby, we rely on the classical theory of gradient systems on Hilbert spaces combined with the concept of E-subgradients using in particular the magnetic energy. The coupled MQS system precisely fits into this general framework.