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  - 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  - Rodríguez Zuluaga, Juan
A1  - Stolle, Claudia
A1  - Yamazaki, Yosuke
A1  - Xiong, Chao
A1  - England, Scott L.
T1  - A synoptic-scale wavelike structure in the nighttime equatorial ionization anomaly
JF  - Earth and Space Science : ESS
N2  - Both ground- and satellite-based airglow imaging have significantly contributed to understanding the low-latitude ionosphere, especially the morphology and dynamics of the equatorial ionization anomaly (EIA). The NASA Global-scale Observations of the Limb and Disk (GOLD) mission focuses on far-ultraviolet airglow images from a geostationary orbit at 47.5 degrees W. This region is of particular interest at low magnetic latitudes because of the high magnetic declination (i.e., about -20 degrees) and proximity of the South Atlantic magnetic anomaly. In this study, we characterize an exciting feature of the nighttime EIA using GOLD observations from October 5, 2018 to June 30, 2020. It consists of a wavelike structure of a few thousand kilometers seen as poleward and equatorward displacements of the EIA-crests. Initial analyses show that the synoptic-scale structure is symmetric about the dip equator and appears nearly stationary with time over the night. In quasi-dipole coordinates, maxima poleward displacements of the EIA-crests are seen at about +/- 12 degrees latitude and around 20 and 60 degrees longitude (i.e., in geographic longitude at the dip equator, about 53 degrees W and 14 degrees W). The wavelike structure presents typical zonal wavelengths of about 6.7 x 10(3) km and 3.3 x 10(3) km. The structure's occurrence and wavelength are highly variable on a day-to-day basis with no apparent dependence on geomagnetic activity. In addition, a cluster or quasi-periodic wave train of equatorial plasma depletions (EPDs) is often detected within the synoptic-scale structure. We further outline the difference in observing these EPDs from FUV images and in situ measurements during a GOLD and Swarm mission conjunction.
KW  - equatorial ionization anomaly
KW  - equatorial ionosphere
KW  - equatorial plasma bubbles
KW  - wave structure
KW  - forcing from below
Y1  - 2021
U6  - https://doi.org/10.1029/2020EA001529
SN  - 2333-5084
VL  - 8
IS  - 2
PB  - American Geophysical Union
CY  - Malden, Mass.
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  - 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  - 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  - 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  - 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  - 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  - 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  - 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  - 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  - 
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  - 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  - 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  -