@article{Lewandowski2022,
  author    = {Lewandowski, Max},
  title     = {Hadamard states for bosonic quantum field theory on globally hyperbolic spacetimes},
  series = {Journal of mathematical physics},
  volume    = {63},
  journal   = {Journal of mathematical physics},
  number    = {1},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {0022-2488},
  doi       = {10.1063/5.0055753},
  pages     = {34},
  year      = {2022},
  abstract  = {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 H{\"o}rmander [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 B{\"a}r, Ginoux, and Pf{\"a}ffle {Wave Equations on Lorentzian Manifolds and Quantization [European Mathematical Society (EMS), Z{\"u}rich, 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.},
  language  = {en}
}
@article{MalassTarkhanov2020,
  author    = {Malass, Ihsane and Tarkhanov, Nikolaj Nikolaevič},
  title     = {A perturbation of the de Rham complex},
  series = {Journal of Siberian Federal University : Mathematics \& Physics},
  volume    = {13},
  journal   = {Journal of Siberian Federal University : Mathematics \& Physics},
  number    = {5},
  publisher = {Siberian Federal University},
  address   = {Krasnojarsk},
  issn      = {1997-1397},
  doi       = {10.17516/1997-1397-2020-13-5-519-532},
  pages     = {519 -- 532},
  year      = {2020},
  abstract  = {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.},
  language  = {en}
}
@phdthesis{Rudorf2014,
  author    = {Rudorf, Sophia},
  title     = {Protein Synthesis by Ribosomes},
  pages     = {xii, 145},
  year      = {2014},
  language  = {en}
}
@article{KleinRosenberger2021,
  author    = {Klein, Markus and Rosenberger, Elke},
  title     = {The tunneling effect for Schr{\"o}dinger operators on a vector bundle},
  series = {Analysis and mathematical physics},
  volume    = {11},
  journal   = {Analysis and mathematical physics},
  number    = {2},
  publisher = {Springer International Publishing AG},
  address   = {Cham (ZG)},
  issn      = {1664-2368},
  doi       = {10.1007/s13324-021-00485-5},
  pages     = {35},
  year      = {2021},
  abstract  = {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.},
  language  = {en}
}
@article{ParkLuehrKervalishvilietal.2017,
  author    = {Park, Jaeheung and L{\"u}hr, Hermann and Kervalishvili, Guram and Rauberg, Jan and Stolle, Claudia and Kwak, Young-Sil and Lee, Woo Kyoung},
  title     = {Morphology of high-latitude plasma density perturbations as deduced from the total electron content measurements onboard the Swarm constellation},
  series = {Journal of geophysical research : A, Space physics},
  volume    = {122},
  journal   = {Journal of geophysical research : A, Space physics},
  number    = {1},
  publisher = {American Geophysical Union},
  address   = {Washington},
  issn      = {2169-9380},
  doi       = {10.1002/2016JA023086},
  pages     = {1338 -- 1359},
  year      = {2017},
  abstract  = {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.},
  language  = {en}
}
@article{BeckusPinchover2020,
  author    = {Beckus, Siegfried and Pinchover, Yehuda},
  title     = {Shnol-type theorem for the Agmon ground state},
  series = {Journal of spectral theory},
  volume    = {10},
  journal   = {Journal of spectral theory},
  number    = {2},
  publisher = {EMS Publishing House},
  address   = {Z{\"u}rich},
  issn      = {1664-039X},
  doi       = {10.4171/JST/296},
  pages     = {355 -- 377},
  year      = {2020},
  abstract  = {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.},
  language  = {en}
}
@article{BaerMazzeo2021,
  author    = {B{\"a}r, Christian and Mazzeo, Rafe},
  title     = {Manifolds with many Rarita-Schwinger fields},
  series = {Communications in mathematical physics},
  volume    = {384},
  journal   = {Communications in mathematical physics},
  number    = {1},
  publisher = {Springer},
  address   = {Berlin},
  issn      = {0010-3616},
  doi       = {10.1007/s00220-021-04030-0},
  pages     = {533 -- 548},
  year      = {2021},
  abstract  = {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.},
  language  = {en}
}
@article{GottwaldReich2021,
  author    = {Gottwald, Georg A. and Reich, Sebastian},
  title     = {Combining machine learning and data assimilation to forecast dynamical systems from noisy partial observations},
  series = {Chaos : an interdisciplinary journal of nonlinear science},
  volume    = {31},
  journal   = {Chaos : an interdisciplinary journal of nonlinear science},
  number    = {10},
  publisher = {AIP},
  address   = {Melville},
  issn      = {1054-1500},
  doi       = {10.1063/5.0066080},
  pages     = {8},
  year      = {2021},
  abstract  = {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.},
  language  = {en}
}
@article{Clavier2021,
  author    = {Clavier, Pierre J.},
  title     = {Borel-{\´E}calle resummation of a two-point function},
  series = {Annales Henri Poincar{\´e} : a journal of theoretical and mathematical physics / ed. jointly by the Institut Henri Poincar{\´e} and by the Swiss Physical Society},
  volume    = {22},
  journal   = {Annales Henri Poincar{\´e} : a journal of theoretical and mathematical physics / ed. jointly by the Institut Henri Poincar{\´e} and by the Swiss Physical Society},
  number    = {6},
  publisher = {Springer},
  address   = {Cham},
  issn      = {1424-0637},
  doi       = {10.1007/s00023-021-01057-w},
  pages     = {2103 -- 2136},
  year      = {2021},
  abstract  = {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.},
  language  = {en}
}
@article{GottwaldReich2021,
  author    = {Gottwald, Georg A. and Reich, Sebastian},
  title     = {Supervised learning from noisy observations},
  series = {Physica : D, Nonlinear phenomena},
  volume    = {423},
  journal   = {Physica : D, Nonlinear phenomena},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0167-2789},
  doi       = {10.1016/j.physd.2021.132911},
  pages     = {15},
  year      = {2021},
  abstract  = {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.},
  language  = {en}
}