TY - JOUR A1 - Lewandowski, Max T1 - Hadamard states for bosonic quantum field theory on globally hyperbolic spacetimes JF - Journal of mathematical physics N2 - According to Radzikowski’s celebrated results, bisolutions of a wave operator on a globally hyperbolic spacetime are of the Hadamard form iff they are given by a linear combination of distinguished parametrices i2(G˜aF−G˜F+G˜A−G˜R) in the sense of Duistermaat and Hörmander [Acta Math. 128, 183–269 (1972)] and Radzikowski [Commun. Math. Phys. 179, 529 (1996)]. Inspired by the construction of the corresponding advanced and retarded Green operator GA, GR as done by Bär, Ginoux, and Pfäffle {Wave Equations on Lorentzian Manifolds and Quantization [European Mathematical Society (EMS), Zürich, 2007]}, we construct the remaining two Green operators GF, GaF locally in terms of Hadamard series. Afterward, we provide the global construction of i2(G˜aF−G˜F), which relies on new techniques such as a well-posed Cauchy problem for bisolutions and a patching argument using Čech cohomology. This leads to global bisolutions of the Hadamard form, each of which can be chosen to be a Hadamard two-point-function, i.e., the smooth part can be adapted such that, additionally, the symmetry and the positivity condition are exactly satisfied. Y1 - 2022 U6 - https://doi.org/10.1063/5.0055753 SN - 0022-2488 SN - 1089-7658 VL - 63 IS - 1 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Malass, Ihsane A1 - Tarkhanov, Nikolaj Nikolaevič T1 - A perturbation of the de Rham complex T1 - Возмущение комплекса де Рама JF - Journal of Siberian Federal University : Mathematics & Physics JF - Žurnal Sibirskogo Federalʹnogo Universiteta : Matematika i fizika N2 - We consider a perturbation of the de Rham complex on a compact manifold with boundary. This perturbation goes beyond the framework of complexes, and so cohomology does not apply to it. On the other hand, its curvature is "small", hence there is a natural way to introduce an Euler characteristic and develop a Lefschetz theory for the perturbation. This work is intended as an attempt to develop a cohomology theory for arbitrary sequences of linear mappings. N2 - Рассмотрим возмущение комплекса де Рама на компактном многообразии с краем. Это возмущение выходит за рамки комплексов, и поэтому когомологии к нему не относятся. С другой стороны, его кривизна "мала", поэтому существует естественный способ ввести характеристику Эйлера и разработать теорию Лефшеца для возмущения. Данная работа предназначена для попытки разработать теорию когомологий для произвольных последовательностей линейных отображений. KW - de Rham complex KW - cohomology KW - Hodge theory KW - Neumann problem KW - комплекс де Рама KW - когомологии KW - теория Ходжа KW - проблема Неймана Y1 - 2020 U6 - https://doi.org/10.17516/1997-1397-2020-13-5-519-532 SN - 1997-1397 SN - 2313-6022 VL - 13 IS - 5 SP - 519 EP - 532 PB - Siberian Federal University CY - Krasnojarsk ER - TY - THES A1 - Rudorf, Sophia T1 - Protein Synthesis by Ribosomes Y1 - 2014 ER - TY - INPR A1 - Böckmann, Christine A1 - Niebsch, Jenny T1 - Examination of the nonlinear LIDAR-operator : the influence of inhomogeneous absorbing spheres on the operator N2 - The determination of the atmospheric aerosol size distribution is an inverse illposed problem. The shape and the material composition of the air-carried particles are two substantial model parameters. Present evaluation algorithms only used an approximation with spherical homogeneous particles. In this paper we propose a new numerically efficient recursive algorithm for inhomogeneous multilayered coated and absorbing particles. Numerical results of real existing particles show that the influence of the two parameters on the model is very important and therefore cannot be ignored. T3 - NLD Preprints - 47 KW - multiwavelength lidar KW - aerosol size distribution KW - inverse ill-posed problem KW - multilayered coated and absorbing aerosol KW - new recursive algorithm Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14725 ER - TY - INPR A1 - Böckmann, Christine A1 - Biele, Jens A1 - Neuber, Roland A1 - Niebsch, Jenny T1 - Retrieval of multimodal aerosol size distribution by inversion of multiwavelength data N2 - The ill-posed problem of aerosol size distribution determination from a small number of backscatter and extinction measurements was solved successfully with a mollifier method which is advantageous since the ill-posed part is performed on exactly given quantities, the points r where n(r) is evaluated may be freely selected. A new twodimensional model for the troposphere is proposed. T3 - NLD Preprints - 38 KW - Multiwavelength LIDAR KW - aerosol size distribution KW - ill-posed problem KW - inversion KW - mollifier method KW - coated and absorbing aerosols Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14360 ER - TY - INPR A1 - Dicken, Volker T1 - Simultaneous activity and attenuation reconstruction in emission tomography N2 - In single photon emission computed tomography (SPECT) one is interested in reconstructing the activity distribution f of some radiopharmaceutical. The data gathered suffer from attenuation due to the tissue density µ. Each imaged slice incorporates noisy sample values of the nonlinear attenuated Radon transform (formular at this place in the original abstract) Traditional theory for SPECT reconstruction treats µ as a known parameter. In practical applications, however, µ is not known, but either crudely estimated, determined in costly additional measurements or plainly neglected. We demonstrate that an approximation of both f and µ from SPECT data alone is feasible, leading to quantitatively more accurate SPECT images. The result is based on nonlinear Tikhonov regularization techniques for parameter estimation problems in differential equations combined with Gauss-Newton-CG minimization. T3 - NLD Preprints - 50 KW - SPECT KW - tomogrphy KW - attenuated Radon transform KW - nonlinear invers problem KW - Tikhonov regularization KW - nonlinear optimization Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14747 ER - TY - JOUR A1 - Klein, Markus A1 - Rosenberger, Elke T1 - The tunneling effect for Schrödinger operators on a vector bundle JF - Analysis and mathematical physics N2 - In the semiclassical limit (h) over bar -> 0, we analyze a class of self-adjoint Schrodinger operators H-(h) over bar = (h) over bar L-2 + (h) over barW + V center dot id(E) acting on sections of a vector bundle E over an oriented Riemannian manifold M where L is a Laplace type operator, W is an endomorphism field and the potential energy V has non-degenerate minima at a finite number of points m(1),... m(r) is an element of M, called potential wells. Using quasimodes of WKB-type near m(j) for eigenfunctions associated with the low lying eigenvalues of H-(h) over bar, we analyze the tunneling effect, i.e. the splitting between low lying eigenvalues, which e.g. arises in certain symmetric configurations. Technically, we treat the coupling between different potential wells by an interaction matrix and we consider the case of a single minimal geodesic (with respect to the associated Agmon metric) connecting two potential wells and the case of a submanifold of minimal geodesics of dimension l + 1. This dimension l determines the polynomial prefactor for exponentially small eigenvalue splitting. KW - Laplace-type operator KW - Vector bundle KW - WKB-expansion KW - Quasimodes KW - Tunneling KW - Spectral gap KW - Complete asymptotics Y1 - 2021 U6 - https://doi.org/10.1007/s13324-021-00485-5 SN - 1664-2368 SN - 1664-235X VL - 11 IS - 2 PB - Springer International Publishing AG CY - Cham (ZG) ER - TY - JOUR A1 - Park, Jaeheung A1 - Lühr, Hermann A1 - Kervalishvili, Guram A1 - Rauberg, Jan A1 - Stolle, Claudia A1 - Kwak, Young-Sil A1 - Lee, Woo Kyoung T1 - Morphology of high-latitude plasma density perturbations as deduced from the total electron content measurements onboard the Swarm constellation JF - Journal of geophysical research : A, Space physics N2 - In this study, we investigate the climatology of high-latitude total electron content (TEC) variations as observed by the dual-frequency Global Navigation Satellite Systems (GNSS) receivers onboard the Swarm satellite constellation. The distribution of TEC perturbations as a function of geographic/magnetic coordinates and seasons reasonably agrees with that of the Challenging Minisatellite Payload observations published earlier. Categorizing the high-latitude TEC perturbations according to line-of-sight directions between Swarm and GNSS satellites, we can deduce their morphology with respect to the geomagnetic field lines. In the Northern Hemisphere, the perturbation shapes are mostly aligned with the L shell surface, and this anisotropy is strongest in the nightside auroral (substorm) and subauroral regions and weakest in the central polar cap. The results are consistent with the well-known two-cell plasma convection pattern of the high-latitude ionosphere, which is approximately aligned with L shells at auroral regions and crossing different L shells for a significant part of the polar cap. In the Southern Hemisphere, the perturbation structures exhibit noticeable misalignment to the local L shells. Here the direction toward the Sun has an additional influence on the plasma structure, which we attribute to photoionization effects. The larger offset between geographic and geomagnetic poles in the south than in the north is responsible for the hemispheric difference. Y1 - 2017 U6 - https://doi.org/10.1002/2016JA023086 SN - 2169-9380 SN - 2169-9402 VL - 122 IS - 1 SP - 1338 EP - 1359 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Beckus, Siegfried A1 - Pinchover, Yehuda T1 - Shnol-type theorem for the Agmon ground state JF - Journal of spectral theory N2 - LetH be a Schrodinger operator defined on a noncompact Riemannianmanifold Omega, and let W is an element of L-infinity (Omega; R). Suppose that the operator H + W is critical in Omega, and let phi be the corresponding Agmon ground state. We prove that if u is a generalized eigenfunction ofH satisfying vertical bar u vertical bar <= C-phi in Omega for some constant C > 0, then the corresponding eigenvalue is in the spectrum of H. The conclusion also holds true if for some K is an element of Omega the operator H admits a positive solution in (Omega) over bar = Omega \ K, and vertical bar u vertical bar <= C psi in (Omega) over bar for some constant C > 0, where psi is a positive solution of minimal growth in a neighborhood of infinity in Omega. Under natural assumptions, this result holds also in the context of infinite graphs, and Dirichlet forms. KW - Shnol theorem KW - Caccioppoli inequality KW - Schrodinger operators KW - generalized eigenfunction KW - ground state KW - positive solutions KW - weighted KW - graphs Y1 - 2020 U6 - https://doi.org/10.4171/JST/296 SN - 1664-039X SN - 1664-0403 VL - 10 IS - 2 SP - 355 EP - 377 PB - EMS Publishing House CY - Zürich ER - TY - THES A1 - Berner, Nadine T1 - Deciphering multiple changes in complex climate time series using Bayesian inference T1 - Bayes'sche Inferenz als diagnostischer Ansatz zur Untersuchung multipler Übergänge in komplexen Klimazeitreihen N2 - Change points in time series are perceived as heterogeneities in the statistical or dynamical characteristics of the observations. Unraveling such transitions yields essential information for the understanding of the observed system’s intrinsic evolution and potential external influences. A precise detection of multiple changes is therefore of great importance for various research disciplines, such as environmental sciences, bioinformatics and economics. The primary purpose of the detection approach introduced in this thesis is the investigation of transitions underlying direct or indirect climate observations. In order to develop a diagnostic approach capable to capture such a variety of natural processes, the generic statistical features in terms of central tendency and dispersion are employed in the light of Bayesian inversion. In contrast to established Bayesian approaches to multiple changes, the generic approach proposed in this thesis is not formulated in the framework of specialized partition models of high dimensionality requiring prior specification, but as a robust kernel-based approach of low dimensionality employing least informative prior distributions. First of all, a local Bayesian inversion approach is developed to robustly infer on the location and the generic patterns of a single transition. The analysis of synthetic time series comprising changes of different observational evidence, data loss and outliers validates the performance, consistency and sensitivity of the inference algorithm. To systematically investigate time series for multiple changes, the Bayesian inversion is extended to a kernel-based inference approach. By introducing basic kernel measures, the weighted kernel inference results are composed into a proxy probability to a posterior distribution of multiple transitions. The detection approach is applied to environmental time series from the Nile river in Aswan and the weather station Tuscaloosa, Alabama comprising documented changes. The method’s performance confirms the approach as a powerful diagnostic tool to decipher multiple changes underlying direct climate observations. Finally, the kernel-based Bayesian inference approach is used to investigate a set of complex terrigenous dust records interpreted as climate indicators of the African region of the Plio-Pleistocene period. A detailed inference unravels multiple transitions underlying the indirect climate observations, that are interpreted as conjoint changes. The identified conjoint changes coincide with established global climate events. In particular, the two-step transition associated to the establishment of the modern Walker-Circulation contributes to the current discussion about the influence of paleoclimate changes on the environmental conditions in tropical and subtropical Africa at around two million years ago. N2 - Im Allgemeinen stellen punktuelle Veränderungen in Zeitreihen (change points) eine Heterogenität in den statistischen oder dynamischen Charakteristika der Observablen dar. Das Auffinden und die Beschreibung solcher Übergänge bietet grundlegende Informationen über das beobachtete System hinsichtlich seiner intrinsischen Entwicklung sowie potentieller externer Einflüsse. Eine präzise Detektion von Veränderungen ist daher für die verschiedensten Forschungsgebiete, wie den Umweltwissenschaften, der Bioinformatik und den Wirtschaftswissenschaften von großem Interesse. Die primäre Zielsetzung der in der vorliegenden Doktorarbeit vorgestellten Detektionsmethode ist die Untersuchung von direkten als auch indirekten Klimaobservablen auf Veränderungen. Um die damit verbundene Vielzahl an möglichen natürlichen Prozessen zu beschreiben, werden im Rahmen einer Bayes’schen Inversion die generischen statistischen Merkmale Zentraltendenz und Dispersion verwendet. Im Gegensatz zu etablierten Bayes’schen Methoden zur Analyse von multiplen Übergängen, die im Rahmen von Partitionsmodellen hoher Dimensionalität formuliert sind und die Spezifikation von Priorverteilungen erfordern, wird in dieser Doktorarbeit ein generischer, Kernel-basierter Ansatz niedriger Dimensionalität mit minimal informativen Priorverteilungen vorgestellt. Zunächst wird ein lokaler Bayes’scher Inversionsansatz entwickelt, der robuste Rückschlüsse auf die Position und die generischen Charakteristika einer einzelnen Veränderung erlaubt. Durch die Analyse von synthetischen Zeitreihen die dem Einfluss von Veränderungen unterschiedlicher Signifikanz, Datenverlust und Ausreißern unterliegen wird die Leistungsfähigkeit, Konsistenz und Sensitivität der Inversionmethode begründet. Um Zeitreihen auch auf multiple Veränderungen systematisch untersuchen zu können, wird die Methode der Bayes’schen Inversion zu einem Kernel-basierten Ansatz erweitert. Durch die Einführung grundlegender Kernel-Maße können die Kernel-Resultate zu einer gewichteten Wahrscheinlichkeit kombiniert werden die als Proxy einer Posterior-Verteilung multipler Veränderungen dient. Der Detektionsalgorithmus wird auf reale Umweltmessreihen vom Nil-Fluss in Aswan und von der Wetterstation Tuscaloosa, Alabama, angewendet, die jeweils dokumentierte Veränderungen enthalten. Das Ergebnis dieser Analyse bestätigt den entwickelten Ansatz als eine leistungsstarke diagnostische Methode zur Detektion multipler Übergänge in Zeitreihen. Abschließend wird der generische Kernel-basierte Bayes’sche Ansatz verwendet, um eine Reihe von komplexen terrigenen Staubdaten zu untersuchen, die als Klimaindikatoren der afrikanischen Region des Plio-Pleistozän interpretiert werden. Eine detaillierte Untersuchung deutet auf multiple Veränderungen in den indirekten Klimaobservablen hin, von denen einige als gemeinsame Übergänge interpretiert werden. Diese gemeinsam auftretenden Ereignisse stimmen mit etablierten globalen Klimaereignissen überein. Insbesondere der gefundene Zwei-Stufen-Übergang, der mit der Ausbildung der modernen Walker-Zirkulation assoziiert wird, liefert einen wichtigen Beitrag zur aktuellen Diskussion über den Einfluss von paläoklimatischen Veränderungen auf die Umweltbedingungen im tropischen und subtropischen Afrika vor circa zwei Millionen Jahren. KW - kernel-based Bayesian inference KW - multi-change point detection KW - direct and indirect climate observations KW - Plio-Pleistocene KW - (sub-) tropical Africa KW - terrigenous dust KW - kernel-basierte Bayes'sche Inferenz KW - Detektion multipler Übergänge KW - direkte und indirekte Klimaobservablen KW - Plio-Pleistozän KW - (sub-) tropisches Afrika KW - terrigener Staub Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-100065 ER - TY - JOUR A1 - Bär, Christian A1 - Mazzeo, Rafe T1 - Manifolds with many Rarita-Schwinger fields JF - Communications in mathematical physics N2 - The Rarita-Schwinger operator is the twisted Dirac operator restricted to 3/2-spinors. Rarita-Schwinger fields are solutions of this operator which are in addition divergence-free. This is an overdetermined problem and solutions are rare; it is even more unexpected for there to be large dimensional spaces of solutions. In this paper we prove the existence of a sequence of compact manifolds in any given dimension greater than or equal to 4 for which the dimension of the space of Rarita-Schwinger fields tends to infinity. These manifolds are either simply connected Kahler-Einstein spin with negative Einstein constant, or products of such spaces with flat tori. Moreover, we construct Calabi-Yau manifolds of even complex dimension with more linearly independent Rarita-Schwinger fields than flat tori of the same dimension. Y1 - 2021 U6 - https://doi.org/10.1007/s00220-021-04030-0 SN - 0010-3616 SN - 1432-0916 VL - 384 IS - 1 SP - 533 EP - 548 PB - Springer CY - Berlin ER - TY - GEN A1 - Grisic, A. -M. A1 - Huisinga, Wilhelm A1 - Reinisch, W. A1 - Kloft, Charlotte T1 - P485 Dosing infliximab in Crohn's disease BT - is adjustment for body size justified? T2 - Journal of Crohn's and Colitis N2 - Background: Infliximab (IFX), an anti-TNF monoclonal antibody approved for the treatment of inflammatory bowel disease, is dosed per kg body weight (BW). However, the rationale for body size adjustment has not been unequivocally demonstrated [1], and first attempts to improve IFX therapy have been undertaken [2]. The aim of our study was to assess the impact of different dosing strategies (i.e. body size-adjusted and fixed dosing) on drug exposure and pharmacokinetic (PK) target attainment. For this purpose, a comprehensive simulation study was performed, using patient characteristics (n=116) from an in-house clinical database. Methods: IFX concentration-time profiles of 1000 virtual, clinically representative patients were generated using a previously published PK model for IFX in patients with Crohn's disease [3]. For each patient 1000 profiles accounting for PK variability were considered. The IFX exposure during maintenance treatment after the following dosing strategies was compared: i) fixed dose, and per ii) BW, iii) lean BW (LBW), iv) body surface area (BSA), v) height (HT), vi) body mass index (BMI) and vii) fat-free mass (FFM)). For each dosing strategy the variability in maximum concentration Cmax, minimum concentration Cmin (= C8weeks) and area under the concentration-time curve (AUC), as well as percent of patients achieving the PK target, Cmin=3 μg/mL [4] were assessed. Results: For all dosing strategies the variability of Cmin (CV ≈110%) was highest, compared to Cmax and AUC, and was of similar extent regardless of dosing strategy. The proportion of patients reaching the PK target (≈⅓ was approximately equal for all dosing strategies. Y1 - 2017 U6 - https://doi.org/10.1093/ecco-jcc/jjx002.609 SN - 1873-9946 SN - 1876-4479 VL - 11 IS - 1 SP - S325 EP - S326 PB - Oxford Univ. Press CY - Oxford ER - TY - JOUR A1 - Gottwald, Georg A. A1 - Reich, Sebastian T1 - Combining machine learning and data assimilation to forecast dynamical systems from noisy partial observations JF - Chaos : an interdisciplinary journal of nonlinear science N2 - We present a supervised learning method to learn the propagator map of a dynamical system from partial and noisy observations. In our computationally cheap and easy-to-implement framework, a neural network consisting of random feature maps is trained sequentially by incoming observations within a data assimilation procedure. By employing Takens's embedding theorem, the network is trained on delay coordinates. We show that the combination of random feature maps and data assimilation, called RAFDA, outperforms standard random feature maps for which the dynamics is learned using batch data. Y1 - 2021 U6 - https://doi.org/10.1063/5.0066080 SN - 1054-1500 SN - 1089-7682 VL - 31 IS - 10 PB - AIP CY - Melville ER - TY - JOUR A1 - Clavier, Pierre J. T1 - Borel-Écalle resummation of a two-point function JF - Annales Henri Poincaré : a journal of theoretical and mathematical physics / ed. jointly by the Institut Henri Poincaré and by the Swiss Physical Society N2 - We provide an overview of the tools and techniques of resurgence theory used in the Borel-ecalle resummation method, which we then apply to the massless Wess-Zumino model. Starting from already known results on the anomalous dimension of the Wess-Zumino model, we solve its renormalisation group equation for the two-point function in a space of formal series. We show that this solution is 1-Gevrey and that its Borel transform is resurgent. The Schwinger-Dyson equation of the model is then used to prove an asymptotic exponential bound for the Borel transformed two-point function on a star-shaped domain of a suitable ramified complex plane. This proves that the two-point function of the Wess-Zumino model is Borel-ecalle summable. Y1 - 2021 U6 - https://doi.org/10.1007/s00023-021-01057-w SN - 1424-0637 SN - 1424-0661 VL - 22 IS - 6 SP - 2103 EP - 2136 PB - Springer CY - Cham ER - TY - JOUR A1 - Gottwald, Georg A. A1 - Reich, Sebastian T1 - Supervised learning from noisy observations BT - Combining machine-learning techniques with data assimilation JF - Physica : D, Nonlinear phenomena N2 - Data-driven prediction and physics-agnostic machine-learning methods have attracted increased interest in recent years achieving forecast horizons going well beyond those to be expected for chaotic dynamical systems. In a separate strand of research data-assimilation has been successfully used to optimally combine forecast models and their inherent uncertainty with incoming noisy observations. The key idea in our work here is to achieve increased forecast capabilities by judiciously combining machine-learning algorithms and data assimilation. We combine the physics-agnostic data -driven approach of random feature maps as a forecast model within an ensemble Kalman filter data assimilation procedure. The machine-learning model is learned sequentially by incorporating incoming noisy observations. We show that the obtained forecast model has remarkably good forecast skill while being computationally cheap once trained. Going beyond the task of forecasting, we show that our method can be used to generate reliable ensembles for probabilistic forecasting as well as to learn effective model closure in multi-scale systems. (C) 2021 Elsevier B.V. All rights reserved. KW - Data-driven modelling KW - Random feature maps KW - Data assimilation Y1 - 2021 U6 - https://doi.org/10.1016/j.physd.2021.132911 SN - 0167-2789 SN - 1872-8022 VL - 423 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Beckus, Siegfried A1 - Eliaz, Latif T1 - Eigenfunctions growth of R-limits on graphs JF - Journal of spectral theory / European Mathematical Society N2 - A characterization of the essential spectrum of Schrodinger operators on infinite graphs is derived involving the concept of R-limits. This concept, which was introduced previously for operators on N and Z(d) as "right-limits," captures the behaviour of the operator at infinity. For graphs with sub-exponential growth rate, we show that each point in sigma(ss)(H) corresponds to a bounded generalized eigenfunction of a corresponding R-limit of H. If, additionally, the graph is of uniform sub-exponential growth, also the converse inclusion holds. KW - Essential spectrum KW - Schrodinger operators KW - graphs KW - right limits KW - generalized eigenfunctions Y1 - 2021 U6 - https://doi.org/10.4171/JST/389 SN - 1664-039X SN - 1664-0403 VL - 11 IS - 4 SP - 1895 EP - 1933 PB - EMS Press, an imprint of the European Mathematical Society - EMS - Publishing House GmbH, Institut für Mathematik, Technische Universität CY - Berlin ER - TY - JOUR A1 - Saggioro, Elena A1 - de Wiljes, Jana A1 - Kretschmer, Marlene A1 - Runge, Jakob T1 - Reconstructing regime-dependent causal relationships from observational time series JF - Chaos : an interdisciplinary journal of nonlinear science N2 - Inferring causal relations from observational time series data is a key problem across science and engineering whenever experimental interventions are infeasible or unethical. Increasing data availability over the past few decades has spurred the development of a plethora of causal discovery methods, each addressing particular challenges of this difficult task. In this paper, we focus on an important challenge that is at the core of time series causal discovery: regime-dependent causal relations. Often dynamical systems feature transitions depending on some, often persistent, unobserved background regime, and different regimes may exhibit different causal relations. Here, we assume a persistent and discrete regime variable leading to a finite number of regimes within which we may assume stationary causal relations. To detect regime-dependent causal relations, we combine the conditional independence-based PCMCI method [based on a condition-selection step (PC) followed by the momentary conditional independence (MCI) test] with a regime learning optimization approach. PCMCI allows for causal discovery from high-dimensional and highly correlated time series. Our method, Regime-PCMCI, is evaluated on a number of numerical experiments demonstrating that it can distinguish regimes with different causal directions, time lags, and sign of causal links, as well as changes in the variables' autocorrelation. Furthermore, Regime-PCMCI is employed to observations of El Nino Southern Oscillation and Indian rainfall, demonstrating skill also in real-world datasets. Y1 - 2020 U6 - https://doi.org/10.1063/5.0020538 SN - 1054-1500 SN - 1089-7682 SN - 1527-2443 VL - 30 IS - 11 PB - American Institute of Physics CY - Melville ER - TY - GEN A1 - Wiljes, Jana de A1 - Tong, Xin T. T1 - Analysis of a localised nonlinear ensemble Kalman Bucy filter with complete and accurate observations T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - Concurrent observation technologies have made high-precision real-time data available in large quantities. Data assimilation (DA) is concerned with how to combine this data with physical models to produce accurate predictions. For spatial-temporal models, the ensemble Kalman filter with proper localisation techniques is considered to be a state-of-the-art DA methodology. This article proposes and investigates a localised ensemble Kalman Bucy filter for nonlinear models with short-range interactions. We derive dimension-independent and component-wise error bounds and show the long time path-wise error only has logarithmic dependence on the time range. The theoretical results are verified through some simple numerical tests. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1221 KW - data assimilation KW - stability and accuracy KW - dimension independent bound KW - localisation KW - high dimensional KW - filter KW - nonlinear Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-540417 SN - 1866-8372 VL - 33 IS - 9 SP - 4752 EP - 4782 PB - IOP Publ. CY - Bristol ER - TY - JOUR A1 - Hanisch, Florian A1 - Ludewig, Matthias T1 - A rigorous construction of the supersymmetric path integral associated to a compact spin manifold JF - Communications in mathematical physics N2 - We give a rigorous construction of the path integral in N = 1/2 supersymmetry as an integral map for differential forms on the loop space of a compact spin manifold. It is defined on the space of differential forms which can be represented by extended iterated integrals in the sense of Chen and Getzler-Jones-Petrack. Via the iterated integral map, we compare our path integral to the non-commutative loop space Chern character of Guneysu and the second author. Our theory provides a rigorous background to various formal proofs of the Atiyah-Singer index theorem for twisted Dirac operators using supersymmetric path integrals, as investigated by Alvarez-Gaume, Atiyah, Bismut and Witten. Y1 - 2022 U6 - https://doi.org/10.1007/s00220-022-04336-7 SN - 0010-3616 SN - 1432-0916 VL - 391 IS - 3 SP - 1209 EP - 1239 PB - Springer CY - Berlin ; Heidelberg ER - TY - JOUR A1 - Wiljes, Jana de A1 - Tong, Xin T. T1 - Analysis of a localised nonlinear ensemble Kalman Bucy filter with complete and accurate observations JF - Nonlinearity N2 - Concurrent observation technologies have made high-precision real-time data available in large quantities. Data assimilation (DA) is concerned with how to combine this data with physical models to produce accurate predictions. For spatial-temporal models, the ensemble Kalman filter with proper localisation techniques is considered to be a state-of-the-art DA methodology. This article proposes and investigates a localised ensemble Kalman Bucy filter for nonlinear models with short-range interactions. We derive dimension-independent and component-wise error bounds and show the long time path-wise error only has logarithmic dependence on the time range. The theoretical results are verified through some simple numerical tests. KW - data assimilation KW - stability and accuracy KW - dimension independent bound KW - localisation KW - high dimensional KW - filter KW - nonlinear Y1 - 2020 U6 - https://doi.org/10.1088/1361-6544/ab8d14 SN - 0951-7715 SN - 1361-6544 VL - 33 IS - 9 SP - 4752 EP - 4782 PB - IOP Publ. CY - Bristol ER - TY - JOUR A1 - Dereudre, David A1 - Houdebert, Pierre T1 - Sharp phase transition for the continuum Widom-Rowlinson model JF - Annales de l'Institut Henri Poincaré. B, Probability and statistics N2 - The Widom-Rowlinson model (or the Area-interaction model) is a Gibbs point process in R-d with the formal Hamiltonian defined as the volume of Ux epsilon omega B1(x), where. is a locally finite configuration of points and B-1(x) denotes the unit closed ball centred at x. The model is also tuned by two other parameters: the activity z > 0 related to the intensity of the process and the inverse temperature beta >= 0 related to the strength of the interaction. In the present paper we investigate the phase transition of the model in the point of view of percolation theory and the liquid-gas transition. First, considering the graph connecting points with distance smaller than 2r > 0, we show that for any beta >= 0, there exists 0 <(similar to a)(zc) (beta, r) < +infinity such that an exponential decay of connectivity at distance n occurs in the subcritical phase (i.e. z <(similar to a)(zc) (beta, r)) and a linear lower bound of the connection at infinity holds in the supercritical case (i.e. z >(similar to a)(zc) (beta, r)). These results are in the spirit of recent works using the theory of randomised tree algorithms (Probab. Theory Related Fields 173 (2019) 479-490, Ann. of Math. 189 (2019) 75-99, Duminil-Copin, Raoufi and Tassion (2018)). Secondly we study a standard liquid-gas phase transition related to the uniqueness/non-uniqueness of Gibbs states depending on the parameters z, beta. Old results (Phys. Rev. Lett. 27 (1971) 1040-1041, J. Chem. Phys. 52 (1970) 1670-1684) claim that a non-uniqueness regime occurs for z = beta large enough and it is conjectured that the uniqueness should hold outside such an half line ( z = beta >= beta(c) > 0). We solve partially this conjecture in any dimension by showing that for beta large enough the non-uniqueness holds if and only if z = beta. We show also that this critical value z = beta corresponds to the percolation threshold (similar to a)(zc) (beta, r) = beta for beta large enough, providing a straight connection between these two notions of phase transition. KW - Gibbs point process KW - DLR equations KW - Boolean model KW - Continuum KW - percolation KW - Random cluster model KW - Fortuin-Kasteleyn representation KW - Randomised tree algorithm KW - OSSS inequality Y1 - 2018 U6 - https://doi.org/10.1214/20-AIHP1082 SN - 0246-0203 SN - 1778-7017 VL - 57 IS - 1 SP - 387 EP - 407 PB - Association des Publications de l'Institut Henri Poincaré CY - Bethesda, Md. ER -