TY - JOUR A1 - Roos, Saskia T1 - The Dirac operator under collapse to a smooth limit space JF - Annals of global analysis and geometry N2 - Let (M-i, g(i))(i is an element of N) be a sequence of spin manifolds with uniform bounded curvature and diameter that converges to a lower-dimensional Riemannian manifold (B, h) in the Gromov-Hausdorff topology. Then, it happens that the spectrum of the Dirac operator converges to the spectrum of a certain first-order elliptic differential operator D-B on B. We give an explicit description of D-B and characterize the special case where D-B equals the Dirac operator on B. KW - Collapse KW - Dirac operator KW - Spin geometry Y1 - 2019 U6 - https://doi.org/10.1007/s10455-019-09691-8 SN - 0232-704X SN - 1572-9060 VL - 57 IS - 1 SP - 121 EP - 151 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Leung, Tsz Yan A1 - Leutbecher, Martin A1 - Reich, Sebastian A1 - Shepherd, Theodore G. T1 - Atmospheric Predictability: Revisiting the Inherent Finite-Time Barrier JF - Journal of the atmospheric sciences N2 - The accepted idea that there exists an inherent finite-time barrier in deterministically predicting atmospheric flows originates from Edward N. Lorenz’s 1969 work based on two-dimensional (2D) turbulence. Yet, known analytic results on the 2D Navier–Stokes (N-S) equations suggest that one can skillfully predict the 2D N-S system indefinitely far ahead should the initial-condition error become sufficiently small, thereby presenting a potential conflict with Lorenz’s theory. Aided by numerical simulations, the present work reexamines Lorenz’s model and reviews both sides of the argument, paying particular attention to the roles played by the slope of the kinetic energy spectrum. It is found that when this slope is shallower than −3, the Lipschitz continuity of analytic solutions (with respect to initial conditions) breaks down as the model resolution increases, unless the viscous range of the real system is resolved—which remains practically impossible. This breakdown leads to the inherent finite-time limit. If, on the other hand, the spectral slope is steeper than −3, then the breakdown does not occur. In this way, the apparent contradiction between the analytic results and Lorenz’s theory is reconciled. KW - Atmosphere KW - Turbulence KW - Error analysis KW - Spectral analysis KW - models KW - distribution KW - Numerical weather prediction KW - forecasting Y1 - 2019 U6 - https://doi.org/10.1175/JAS-D-19-0057.1 SN - 0022-4928 SN - 1520-0469 VL - 76 IS - 12 SP - 3883 EP - 3892 PB - American Meteorological Soc. CY - Boston ER - TY - JOUR A1 - Fernandes, Vitor H. A1 - Koppitz, Jörg A1 - Musunthia, Tiwadee T1 - The Rank of the Semigroup of All Order-Preserving Transformations on a Finite Fence JF - Bulletin of the Malaysian Mathematical Sciences Society volume N2 - A zig-zag (or fence) order is a special partial order on a (finite) set. In this paper, we consider the semigroup TFn of all order-preserving transformations on an n-element zig-zag-ordered set. We determine the rank of TFn and provide a minimal generating set for TFn. Moreover, a formula for the number of idempotents in TFn is given. KW - Transformation semigroups KW - Rank of semigroup KW - Idempotents KW - Order-preserving KW - Fence KW - Zig-zag order Y1 - 2019 U6 - https://doi.org/10.1007/s40840-017-0598-1 SN - 0126-6705 SN - 2180-4206 VL - 42 IS - 5 SP - 2191 EP - 2211 PB - Malaysian mathematical sciences sciences soc CY - Pulau Punang ER - TY - JOUR A1 - Shcherbakov, Robert A1 - Zhuang, Jiancang A1 - Zöller, Gert A1 - Ogata, Yosihiko T1 - Forecasting the magnitude of the largest expected earthquake JF - Nature Communications N2 - The majority of earthquakes occur unexpectedly and can trigger subsequent sequences of events that can culminate in more powerful earthquakes. This self-exciting nature of seismicity generates complex clustering of earthquakes in space and time. Therefore, the problem of constraining the magnitude of the largest expected earthquake during a future time interval is of critical importance in mitigating earthquake hazard. We address this problem by developing a methodology to compute the probabilities for such extreme earthquakes to be above certain magnitudes. We combine the Bayesian methods with the extreme value theory and assume that the occurrence of earthquakes can be described by the Epidemic Type Aftershock Sequence process. We analyze in detail the application of this methodology to the 2016 Kumamoto, Japan, earthquake sequence. We are able to estimate retrospectively the probabilities of having large subsequent earthquakes during several stages of the evolution of this sequence. Y1 - 2019 U6 - https://doi.org/10.1038/s41467-019-11958-4 SN - 2041-1723 VL - 10 PB - Nature Publishing Group CY - London ER - TY - JOUR A1 - Conforti, Giovanni A1 - Kosenkova, Tetiana A1 - Roelly, Sylvie T1 - Conditioned Point Processes with Application to Levy Bridges JF - Journal of theoretical probability N2 - Our first result concerns a characterization by means of a functional equation of Poisson point processes conditioned by the value of their first moment. It leads to a generalized version of Mecke’s formula. En passant, it also allows us to gain quantitative results about stochastic domination for Poisson point processes under linear constraints. Since bridges of a pure jump Lévy process in Rd with a height a can be interpreted as a Poisson point process on space–time conditioned by pinning its first moment to a, our approach allows us to characterize bridges of Lévy processes by means of a functional equation. The latter result has two direct applications: First, we obtain a constructive and simple way to sample Lévy bridge dynamics; second, it allows us to estimate the number of jumps for such bridges. We finally show that our method remains valid for linearly perturbed Lévy processes like periodic Ornstein–Uhlenbeck processes driven by Lévy noise. KW - Ornstein-Uhlenbeck Y1 - 2019 U6 - https://doi.org/10.1007/s10959-018-0863-8 SN - 0894-9840 SN - 1572-9230 VL - 32 IS - 4 SP - 2111 EP - 2134 PB - Springer CY - New York ER - TY - JOUR A1 - Salamat, Mona A1 - Zöller, Gert A1 - Amini, Morteza T1 - Prediction of the Maximum Expected Earthquake Magnitude in Iran: BT - from a Catalog with Varying Magnitude of Completeness and Uncertain Magnitudes JF - Pure and applied geophysics N2 - This paper concerns the problem of predicting the maximum expected earthquake magnitude μ in a future time interval Tf given a catalog covering a time period T in the past. Different studies show the divergence of the confidence interval of the maximum possible earthquake magnitude m_{ max } for high levels of confidence (Salamat et al. 2017). Therefore, m_{ max } should be better replaced by μ (Holschneider et al. 2011). In a previous study (Salamat et al. 2018), μ is estimated for an instrumental earthquake catalog of Iran from 1900 onwards with a constant level of completeness ( {m0 = 5.5} ). In the current study, the Bayesian methodology developed by Zöller et al. (2014, 2015) is applied for the purpose of predicting μ based on the catalog consisting of both historical and instrumental parts. The catalog is first subdivided into six subcatalogs corresponding to six seismotectonic zones, and each of those zone catalogs is subsequently subdivided according to changes in completeness level and magnitude uncertainty. For this, broad and small error distributions are considered for historical and instrumental earthquakes, respectively. We assume that earthquakes follow a Poisson process in time and Gutenberg-Richter law in the magnitude domain with a priori unknown a and b values which are first estimated by Bayes' theorem and subsequently used to estimate μ. Imposing different values of m_{ max } for different seismotectonic zones namely Alborz, Azerbaijan, Central Iran, Zagros, Kopet Dagh and Makran, the results show considerable probabilities for the occurrence of earthquakes with Mw ≥ 7.5 in short Tf , whereas for long Tf, μ is almost equal to m_{ max } KW - Maximum expected earthquake magnitude KW - completeness levels KW - magnitude errors KW - Bayesian method KW - Iran Y1 - 2019 U6 - https://doi.org/10.1007/s00024-019-02141-3 SN - 0033-4553 SN - 1420-9136 VL - 176 IS - 8 SP - 3425 EP - 3438 PB - Springer CY - Basel ER - TY - JOUR A1 - Bär, Christian A1 - Strohmaier, Alexander T1 - An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary JF - American Journal of Mathematics N2 - We show that the Dirac operator on a compact globally hyperbolic Lorentzian spacetime with spacelike Cauchy boundary is a Fredholm operator if appropriate boundary conditions are imposed. We prove that the index of this operator is given by the same expression as in the index formula of Atiyah-Patodi-Singer for Riemannian manifolds with boundary. The index is also shown to equal that of a certain operator constructed from the evolution operator and a spectral projection on the boundary. In case the metric is of product type near the boundary a Feynman parametrix is constructed. Y1 - 2019 U6 - https://doi.org/10.1353/ajm.2019.0037 SN - 0002-9327 SN - 1080-6377 VL - 141 IS - 5 SP - 1421 EP - 1455 PB - Johns Hopkins Univ. Press CY - Baltimore ER - TY - JOUR A1 - Denecke, Klaus-Dieter T1 - The partial clone of linear formulas JF - Siberian mathematical journal N2 - A term t is linear if no variable occurs more than once in t. An identity s ≈ t is said to be linear if s and t are linear terms. Identities are particular formulas. As for terms superposition operations can be defined for formulas too. We define the arbitrary linear formulas and seek for a condition for the set of all linear formulas to be closed under superposition. This will be used to define the partial superposition operations on the set of linear formulas and a partial many-sorted algebra Formclonelin(τ, τ′). This algebra has similar properties with the partial many-sorted clone of all linear terms. We extend the concept of a hypersubstitution of type τ to the linear hypersubstitutions of type (τ, τ′) for algebraic systems. The extensions of linear hypersubstitutions of type (τ, τ′) send linear formulas to linear formulas, presenting weak endomorphisms of Formclonelin(τ, τ′). KW - term KW - formula KW - superposition KW - linear term KW - linear formula KW - clone KW - partial clone KW - linear hypersubstitution Y1 - 2019 U6 - https://doi.org/10.1134/S0037446619040037 SN - 0037-4466 SN - 1573-9260 VL - 60 IS - 4 SP - 572 EP - 584 PB - Pleiades Publ. CY - New York ER - TY - JOUR A1 - Lekkoksung, Nareupanat A1 - Denecke, Klaus-Dieter T1 - The partial clone of linear tree languages JF - Siberian mathematical journal N2 - A term, also called a tree, is said to be linear, if each variable occurs in the term only once. The linear terms and sets of linear terms, the so-called linear tree languages, play some role in automata theory and in the theory of formal languages in connection with recognizability. We define a partial superposition operation on sets of linear trees of a given type and study the properties of some many-sorted partial clones that have sets of linear trees as elements and partial superposition operations as fundamental operations. The endomorphisms of those algebras correspond to nondeterministic linear hypersubstitutions. KW - linear term KW - linear tree language KW - clone KW - partial clone KW - linear hypersubstitution KW - nondeterministic linear hypersubstitution Y1 - 2019 U6 - https://doi.org/10.1134/S0037446619030121 SN - 0037-4466 SN - 1573-9260 VL - 60 IS - 3 SP - 497 EP - 507 PB - Pleiades Publ. CY - New York ER - TY - JOUR A1 - Clavier, Pierre J. A1 - Guo, Li A1 - Paycha, Sylvie A1 - Zhang, Bin T1 - An algebraic formulation of the locality principle in renormalisation JF - European Journal of Mathematics N2 - We study the mathematical structure underlying the concept of locality which lies at the heart of classical and quantum field theory, and develop a machinery used to preserve locality during the renormalisation procedure. Viewing renormalisation in the framework of Connes and Kreimer as the algebraic Birkhoff factorisation of characters on a Hopf algebra with values in a Rota-Baxter algebra, we build locality variants of these algebraic structures, leading to a locality variant of the algebraic Birkhoff factorisation. This provides an algebraic formulation of the conservation of locality while renormalising. As an application in the context of the Euler-Maclaurin formula on lattice cones, we renormalise the exponential generating function which sums over the lattice points in a lattice cone. As a consequence, for a suitable multivariate regularisation, renormalisation from the algebraic Birkhoff factorisation amounts to composition by a projection onto holomorphic multivariate germs. KW - Locality KW - Renormalisation KW - Algebraic Birkhoff factorisation KW - Partial algebra KW - Hopf algebra KW - Rota-Baxter algebra KW - Multivariate meromorphic functions KW - Lattice cones Y1 - 2019 U6 - https://doi.org/10.1007/s40879-018-0255-8 SN - 2199-675X SN - 2199-6768 VL - 5 IS - 2 SP - 356 EP - 394 PB - Springer CY - Cham ER - TY - JOUR A1 - Koltai, Peter A1 - Lie, Han Cheng A1 - Plonka, Martin T1 - Frechet differentiable drift dependence of Perron-Frobenius and Koopman operators for non-deterministic dynamics JF - Nonlinearity N2 - We prove the Fréchet differentiability with respect to the drift of Perron–Frobenius and Koopman operators associated to time-inhomogeneous ordinary stochastic differential equations. This result relies on a similar differentiability result for pathwise expectations of path functionals of the solution of the stochastic differential equation, which we establish using Girsanov's formula. We demonstrate the significance of our result in the context of dynamical systems and operator theory, by proving continuously differentiable drift dependence of the simple eigen- and singular values and the corresponding eigen- and singular functions of the stochastic Perron–Frobenius and Koopman operators. KW - stochastic differential equations KW - transfer operator KW - Koopman operator KW - Perron-Frobenius operator KW - smooth drift dependence KW - linear response KW - pathwise expectations Y1 - 2019 U6 - https://doi.org/10.1088/1361-6544/ab1f2a SN - 0951-7715 SN - 1361-6544 VL - 32 IS - 11 SP - 4232 EP - 4257 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Gerlach, Moritz Reinhardt A1 - Glück, Jochen T1 - Convergence of positive operator semigroups JF - Transactions of the American Mathematical Society N2 - We present new conditions for semigroups of positive operators to converge strongly as time tends to infinity. Our proofs are based on a novel approach combining the well-known splitting theorem by Jacobs, de Leeuw, and Glicksberg with a purely algebraic result about positive group representations. Thus, we obtain convergence theorems not only for one-parameter semigroups but also for a much larger class of semigroup representations. Our results allow for a unified treatment of various theorems from the literature that, under technical assumptions, a bounded positive C-0-semigroup containing or dominating a kernel operator converges strongly as t ->infinity. We gain new insights into the structure theoretical background of those theorems and generalize them in several respects; especially we drop any kind of continuity or regularity assumption with respect to the time parameter. KW - Positive semigroups KW - semigroup representations KW - asymptotic behavior KW - kernel operator Y1 - 2019 U6 - https://doi.org/10.1090/tran/7836 SN - 0002-9947 SN - 1088-6850 VL - 372 IS - 9 SP - 6603 EP - 6627 PB - American Mathematical Soc. CY - Providence ER - TY - JOUR A1 - Sanchez, S. A1 - Wicht, J. A1 - Baerenzung, Julien A1 - Holschneider, Matthias T1 - Sequential assimilation of geomagnetic observations BT - perspectives for the reconstruction and prediction of core dynamics JF - Geophysical journal international N2 - High-precision observations of the present-day geomagnetic field by ground-based observatories and satellites provide unprecedented conditions for unveiling the dynamics of the Earth’s core. Combining geomagnetic observations with dynamo simulations in a data assimilation (DA) framework allows the reconstruction of past and present states of the internal core dynamics. The essential information that couples the internal state to the observations is provided by the statistical correlations from a numerical dynamo model in the form of a model covariance matrix. Here we test a sequential DA framework, working through a succession of forecast and analysis steps, that extracts the correlations from an ensemble of dynamo models. The primary correlations couple variables of the same azimuthal wave number, reflecting the predominant axial symmetry of the magnetic field. Synthetic tests show that the scheme becomes unstable when confronted with high-precision geomagnetic observations. Our study has identified spurious secondary correlations as the origin of the problem. Keeping only the primary correlations by localizing the covariance matrix with respect to the azimuthal wave number suffices to stabilize the assimilation. While the first analysis step is fundamental in constraining the large-scale interior state, further assimilation steps refine the smaller and more dynamical scales. This refinement turns out to be critical for long-term geomagnetic predictions. Increasing the assimilation steps from one to 18 roughly doubles the prediction horizon for the dipole from about  tree to six centuries, and from 30 to about  60 yr for smaller observable scales. This improvement is also reflected on the predictability of surface intensity features such as the South Atlantic Anomaly. Intensity prediction errors are decreased roughly by a half when assimilating long observation sequences. KW - Magnetic field variations through time KW - Core dynamics KW - Dynamo: theories and simulations KW - Inverse theory KW - Probabilistic forecasting Y1 - 2019 U6 - https://doi.org/10.1093/gji/ggz090 SN - 0956-540X SN - 1365-246X VL - 217 IS - 2 SP - 1434 EP - 1450 PB - Oxford Univ. Press CY - Oxford ER - TY - JOUR A1 - Bandara, Menaka Lashitha A1 - Rosen, Andreas T1 - Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of local boundary conditions JF - Communications in partial differential equations N2 - On a smooth complete Riemannian spin manifold with smooth compact boundary, we demonstrate that Atiyah-Singer Dirac operator in depends Riesz continuously on perturbations of local boundary conditions The Lipschitz bound for the map depends on Lipschitz smoothness and ellipticity of and bounds on Ricci curvature and its first derivatives as well as a lower bound on injectivity radius away from a compact neighbourhood of the boundary. More generally, we prove perturbation estimates for functional calculi of elliptic operators on manifolds with local boundary conditions. KW - Boundary value problems KW - Dirac operator KW - functional calculus KW - real-variable harmonic analysis KW - Riesz continuity KW - spectral flow Y1 - 2019 U6 - https://doi.org/10.1080/03605302.2019.1611847 SN - 0360-5302 SN - 1532-4133 VL - 44 IS - 12 SP - 1253 EP - 1284 PB - Taylor & Francis Group CY - Philadelphia ER - TY - JOUR A1 - Ringel, Lisa Maria A1 - Somogyvári, Márk A1 - Jalali, Mohammadreza A1 - Bayer, Peter T1 - Comparison of hydraulic and tracer tomography for discrete fracture network inversion JF - Geosciences N2 - Fractures serve as highly conductive preferential flow paths for fluids in rocks, which are difficult to exactly reconstruct in numerical models. Especially, in low-conductive rocks, fractures are often the only pathways for advection of solutes and heat. The presented study compares the results from hydraulic and tracer tomography applied to invert a theoretical discrete fracture network (DFN) that is based on data from synthetic cross-well testing. For hydraulic tomography, pressure pulses in various injection intervals are induced and the pressure responses in the monitoring intervals of a nearby observation well are recorded. For tracer tomography, a conservative tracer is injected in different well levels and the depth-dependent breakthrough of the tracer is monitored. A recently introduced transdimensional Bayesian inversion procedure is applied for both tomographical methods, which adjusts the fracture positions, orientations, and numbers based on given geometrical fracture statistics. The used Metropolis-Hastings-Green algorithm is refined by the simultaneous estimation of the measurement error’s variance, that is, the measurement noise. Based on the presented application to invert the two-dimensional cross-section between source and the receiver well, the hydraulic tomography reveals itself to be more suitable for reconstructing the original DFN. This is based on a probabilistic representation of the inverted results by means of fracture probabilities. KW - hydraulic tomography KW - tracer tomography KW - DFN KW - Bayesian inversion KW - heterogeneity KW - fracture KW - hydrogeophysics Y1 - 2019 U6 - https://doi.org/10.3390/geosciences9060274 SN - 2076-3263 VL - 9 IS - 6 PB - MDPI CY - Basel ER - TY - JOUR A1 - Beckus, Siegfried A1 - Bellissard, Jean A1 - Cornean, Horia T1 - Holder Continuity of the Spectra for Aperiodic Hamiltonians JF - Annales de l'Institut Henri Poincaré N2 - We study the spectral location of a strongly pattern equivariant Hamiltonians arising through configurations on a colored lattice. Roughly speaking, two configurations are "close to each other" if, up to a translation, they "almost coincide" on a large fixed ball. The larger this ball, the more similar they are, and this induces a metric on the space of the corresponding dynamical systems. Our main result states that the map which sends a given configuration into the spectrum of its associated Hamiltonian, is Holder (even Lipschitz) continuous in the usual Hausdorff metric. Specifically, the spectral distance of two Hamiltonians is estimated by the distance of the corresponding dynamical systems. Y1 - 2019 U6 - https://doi.org/10.1007/s00023-019-00848-6 SN - 1424-0637 SN - 1424-0661 VL - 20 IS - 11 SP - 3603 EP - 3631 PB - Springer CY - Cham ER - TY - JOUR A1 - Blanchard, Gilles A1 - Zadorozhnyi, Oleksandr T1 - Concentration of weakly dependent Banach-valued sums and applications to statistical learning methods JF - Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability N2 - We obtain a Bernstein-type inequality for sums of Banach-valued random variables satisfying a weak dependence assumption of general type and under certain smoothness assumptions of the underlying Banach norm. We use this inequality in order to investigate in the asymptotical regime the error upper bounds for the broad family of spectral regularization methods for reproducing kernel decision rules, when trained on a sample coming from a tau-mixing process. KW - Banach-valued process KW - Bernstein inequality KW - concentration KW - spectral regularization KW - weak dependence Y1 - 2019 U6 - https://doi.org/10.3150/18-BEJ1095 SN - 1350-7265 SN - 1573-9759 VL - 25 IS - 4B SP - 3421 EP - 3458 PB - International Statistical Institute CY - Voorburg ER - TY - JOUR A1 - Azzali, Sara A1 - Wahl, Charlotte T1 - Two-cocycle twists and Atiyah-Patodi-Singer index theory JF - Mathematical Proceedings of the Cambridge Philosophical Society N2 - We construct eta- and rho-invariants for Dirac operators, on the universal covering of a closed manifold, that are invariant under the projective action associated to a 2-cocycle of the fundamental group. We prove an Atiyah-Patodi-Singer index theorem in this setting, as well as its higher generalisation. Applications concern the classification of positive scalar curvature metrics on closed spin manifolds. We also investigate the properties of these twisted invariants for the signature operator and the relation to the higher invariants. Y1 - 2019 U6 - https://doi.org/10.1017/S0305004118000427 SN - 0305-0041 SN - 1469-8064 VL - 167 IS - 3 SP - 437 EP - 487 PB - Cambridge Univ. Press CY - New York ER - TY - JOUR A1 - Ty, Alexander J. A. A1 - Fang, Zheng A1 - Gonzalez, Rivver A. A1 - Rozdeba, Paul J. A1 - Abarbanel, Henry D. T1 - Machine learning of time series using time-delay embedding and precision annealing JF - Neural Computation N2 - Tasking machine learning to predict segments of a time series requires estimating the parameters of a ML model with input/output pairs from the time series. We borrow two techniques used in statistical data assimilation in order to accomplish this task: time-delay embedding to prepare our input data and precision annealing as a training method. The precision annealing approach identifies the global minimum of the action (-log[P]). In this way, we are able to identify the number of training pairs required to produce good generalizations (predictions) for the time series. We proceed from a scalar time series s(tn);tn=t0+n Delta t and, using methods of nonlinear time series analysis, show how to produce a DE>1-dimensional time-delay embedding space in which the time series has no false neighbors as does the observed s(tn) time series. In that DE-dimensional space, we explore the use of feedforward multilayer perceptrons as network models operating on DE-dimensional input and producing DE-dimensional outputs. Y1 - 2019 U6 - https://doi.org/10.1162/neco_a_01224 SN - 0899-7667 SN - 1530-888X VL - 31 IS - 10 SP - 2004 EP - 2024 PB - MIT Press CY - Cambridge ER - TY - JOUR A1 - Bär, Christian T1 - The curl operator on odd-dimensional manifolds JF - Journal of mathematical physics N2 - We study the spectral properties of curl, a linear differential operator of first order acting on differential forms of appropriate degree on an odd-dimensional closed oriented Riemannian manifold. In three dimensions, its eigenvalues are the electromagnetic oscillation frequencies in vacuum without external sources. In general, the spectrum consists of the eigenvalue 0 with infinite multiplicity and further real discrete eigenvalues of finite multiplicity. We compute the Weyl asymptotics and study the zeta-function. We give a sharp lower eigenvalue bound for positively curved manifolds and analyze the equality case. Finally, we compute the spectrum for flat tori, round spheres, and 3-dimensional spherical space forms. Published under license by AIP Publishing. Y1 - 2019 U6 - https://doi.org/10.1063/1.5082528 SN - 0022-2488 SN - 1089-7658 VL - 60 IS - 3 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Becker, Christian A1 - Benini, Marco A1 - Schenkel, Alexander A1 - Szabo, Richard J. T1 - Cheeger-Simons differential characters with compact support and Pontryagin duality JF - Communications in analysis and geometry N2 - By adapting the Cheeger-Simons approach to differential cohomology, we establish a notion of differential cohomology with compact support. We show that it is functorial with respect to open embeddings and that it fits into a natural diagram of exact sequences which compare it to compactly supported singular cohomology and differential forms with compact support, in full analogy to ordinary differential cohomology. We prove an excision theorem for differential cohomology using a suitable relative version. Furthermore, we use our model to give an independent proof of Pontryagin duality for differential cohomology recovering a result of [Harvey, Lawson, Zweck - Amer. J. Math. 125 (2003), 791]: On any oriented manifold, ordinary differential cohomology is isomorphic to the smooth Pontryagin dual of compactly supported differential cohomology. For manifolds of finite-type, a similar result is obtained interchanging ordinary with compactly supported differential cohomology. Y1 - 2019 U6 - https://doi.org/10.4310/CAG.2019.v27.n7.a2 SN - 1019-8385 SN - 1944-9992 VL - 27 IS - 7 SP - 1473 EP - 1522 PB - International Press of Boston CY - Somerville ER - TY - JOUR A1 - Reich, Sebastian T1 - Data assimilation BT - the Schrödinger perspective JF - Acta numerica N2 - Data assimilation addresses the general problem of how to combine model-based predictions with partial and noisy observations of the process in an optimal manner. This survey focuses on sequential data assimilation techniques using probabilistic particle-based algorithms. In addition to surveying recent developments for discrete- and continuous-time data assimilation, both in terms of mathematical foundations and algorithmic implementations, we also provide a unifying framework from the perspective of coupling of measures, and Schrödinger’s boundary value problem for stochastic processes in particular. Y1 - 2019 U6 - https://doi.org/10.1017/S0962492919000011 SN - 0962-4929 SN - 1474-0508 VL - 28 SP - 635 EP - 711 PB - Cambridge Univ. Press CY - New York ER - TY - JOUR A1 - Edeko, Nikolai A1 - Gerlach, Moritz Reinhardt A1 - Kühner, Viktoria T1 - Measure-preserving semiflows and one-parameter Koopman semigroups JF - Semigroup forum N2 - For a finite measure space X, we characterize strongly continuous Markov lattice semigroups on Lp(X) by showing that their generator A acts as a derivation on the dense subspace D(A)L(X). We then use this to characterize Koopman semigroups on Lp(X) if X is a standard probability space. In addition, we show that every measurable and measure-preserving flow on a standard probability space is isomorphic to a continuous flow on a compact Borel probability space. KW - Measure-preserving semiflow KW - Koopman semigroup KW - Derivation KW - Topological model Y1 - 2019 U6 - https://doi.org/10.1007/s00233-018-9960-3 SN - 0037-1912 SN - 1432-2137 VL - 98 IS - 1 SP - 48 EP - 63 PB - Springer CY - New York ER - TY - JOUR A1 - Mera, Azal A1 - Shlapunov, Alexander A. A1 - Tarkhanov, Nikolai Nikolaevich T1 - Navier-Stokes Equations for Elliptic Complexes JF - Journal of Siberian Federal University. Mathematics & Physics N2 - We continue our study of invariant forms of the classical equations of mathematical physics, such as the Maxwell equations or the Lam´e system, on manifold with boundary. To this end we interpret them in terms of the de Rham complex at a certain step. On using the structure of the complex we get an insight to predict a degeneracy deeply encoded in the equations. In the present paper we develop an invariant approach to the classical Navier-Stokes equations. KW - Navier-Stokes equations KW - classical solution Y1 - 2019 U6 - https://doi.org/10.17516/1997-1397-2019-12-1-3-27 SN - 1997-1397 SN - 2313-6022 VL - 12 IS - 1 SP - 3 EP - 27 PB - Sibirskij Federalʹnyj Universitet CY - Krasnojarsk ER - TY - JOUR A1 - Nüsken, Nikolas A1 - Pavhotis, Grigorios A. T1 - Constructing Sampling Schemes via Coupling BT - Markov Semigroups and Optimal Transport JF - SIAM ASA journal on uncertainty quantification / Society for Industrial and Applied Mathematics ; American Statistical Association N2 - In this paper we develop a general framework for constructing and analyzing coupled Markov chain Monte Carlo samplers, allowing for both (possibly degenerate) diffusion and piecewise deterministic Markov processes. For many performance criteria of interest, including the asymptotic variance, the task of finding efficient couplings can be phrased in terms of problems related to optimal transport theory. We investigate general structural properties, proving a singularity theorem that has both geometric and probabilistic interpretations. Moreover, we show that those problems can often be solved approximately and support our findings with numerical experiments. For the particular objective of estimating the variance of a Bayesian posterior, our analysis suggests using novel techniques in the spirit of antithetic variates. Addressing the convergence to equilibrium of coupled processes we furthermore derive a modified Poincare inequality. KW - sampling KW - optimal transport KW - particle methods KW - Markov semigroups KW - MCMC Y1 - 2019 U6 - https://doi.org/10.1137/18M119896X SN - 2166-2525 VL - 7 IS - 1 SP - 324 EP - 382 PB - Society for Industrial and Applied Mathematics CY - Philadelphia ER - TY - JOUR A1 - Katz-Samuels, Julian A1 - Blanchard, Gilles A1 - Scott, Clayton T1 - Decontamination of Mutual Contamination Models JF - Journal of machine learning research N2 - Many machine learning problems can be characterized by mutual contamination models. In these problems, one observes several random samples from different convex combinations of a set of unknown base distributions and the goal is to infer these base distributions. This paper considers the general setting where the base distributions are defined on arbitrary probability spaces. We examine three popular machine learning problems that arise in this general setting: multiclass classification with label noise, demixing of mixed membership models, and classification with partial labels. In each case, we give sufficient conditions for identifiability and present algorithms for the infinite and finite sample settings, with associated performance guarantees. KW - multiclass classification with label noise KW - classification with partial labels KW - mixed membership models KW - topic modeling KW - mutual contamination models Y1 - 2019 UR - http://arxiv.org/abs/1710.01167 SN - 1532-4435 VL - 20 PB - Microtome Publishing CY - Cambridge, Mass. ER - TY - JOUR A1 - Malass, Ihsane A1 - Tarkhanov, Nikolai Nikolaevich T1 - The de Rham Cohomology through Hilbert Space Methods JF - Journal of Siberian Federal University. Mathematics & physics N2 - We discuss canonical representations of the de Rham cohomology on a compact manifold with boundary. They are obtained by minimising the energy integral in a Hilbert space of differential forms that belong along with the exterior derivative to the domain of the adjoint operator. The corresponding Euler-Lagrange equations reduce to an elliptic boundary value problem on the manifold, which is usually referred to as the Neumann problem after Spencer. KW - De Rham complex KW - cohomology KW - Hodge theory KW - Neumann problem Y1 - 2019 U6 - https://doi.org/10.17516/1997-1397-2019-12-4-455-465 SN - 1997-1397 SN - 2313-6022 VL - 12 IS - 4 SP - 455 EP - 465 PB - Sibirskij Federalʹnyj Universitet CY - Krasnoyarsk ER - TY - JOUR A1 - Gerlach, Moritz Reinhardt A1 - Glück, Jochen T1 - Mean ergodicity vs weak almost periodicity JF - Studia mathematica N2 - We provide explicit examples of positive and power-bounded operators on c(0) and l(infinity) which are mean ergodic but not weakly almost periodic. As a consequence we prove that a countably order complete Banach lattice on which every positive and power-bounded mean ergodic operator is weakly almost periodic is necessarily a KB-space. This answers several open questions from the literature. Finally, we prove that if T is a positive mean ergodic operator with zero fixed space on an arbitrary Banach lattice, then so is every power of T . KW - positive operators KW - weakly almost periodic KW - order continuous norm KW - KB-space KW - mean ergodic Y1 - 2019 U6 - https://doi.org/10.4064/sm170918-20-3 SN - 0039-3223 SN - 1730-6337 VL - 248 IS - 1 SP - 45 EP - 56 PB - Polska Akademia Nauk, Instytut Matematyczny CY - Warszawa ER - TY - JOUR A1 - Dombrowsky, Charlotte A1 - Und, Myriam Fradon A1 - Roelly, Sylvie T1 - Packungen aus Kreisscheiben BT - Wie eine wahrscheinlichkeitstheoretische Sichtweise eine geometrische Analyse vervollständigen kann JF - Elemente der Mathematik N2 - Der englische Seefahrer Sir Walter Raleigh fragte sich einst, wie er in seinem Schiffsladeraum moeglichst viele Kanonenkugeln stapeln koennte. Johannes Kepler entwickelte daraufhin 1611 eine Vermutung ueber die optimale Anordnung der Kugeln. Diese Vermutung sollte sich als eine der haertesten mathematischen Nuesse der Geschichte erweisen. Selbst in der Ebene sind dichteste Packungen kongruenter Kreise eine Herausforderung. 1892 und 1910 veroeffentlichte Axel Thue (kritisierte) Beweise, dass die hexagonale Kreispackung optimal sei. Erst 1940 lieferte Laszlo Fejes Toth schliesslich einen wasserdichten Beweis fuer diese Tatsache. Eine Variante des Problems verlangt, Packungen mit endlich vielen kongruenten Kugeln zu finden, die eine gewisse quadratische Energie minimieren: Diese spannende geometrische Aufgabe wurde 1967 von Toth gestellt. Sie ist auch heute noch nicht vollstaendig gelaest. In diesem Beitrag schlagen die Autorinnen eine originelle wahrscheinlichkeitstheoretische Methode vor, um in der Ebene Näherungen der Lösung zu konstruieren. Y1 - 2019 U6 - https://doi.org/10.4171/EM/381 SN - 0013-6018 SN - 1420-8962 VL - 74 IS - 2 SP - 45 EP - 62 PB - EMS Publ. CY - Zürich ER - TY - JOUR A1 - Nüsken, Nikolas A1 - Reich, Sebastian A1 - Rozdeba, Paul J. T1 - State and parameter estimation from observed signal increments JF - Entropy : an international and interdisciplinary journal of entropy and information studies N2 - The success of the ensemble Kalman filter has triggered a strong interest in expanding its scope beyond classical state estimation problems. In this paper, we focus on continuous-time data assimilation where the model and measurement errors are correlated and both states and parameters need to be identified. Such scenarios arise from noisy and partial observations of Lagrangian particles which move under a stochastic velocity field involving unknown parameters. We take an appropriate class of McKean-Vlasov equations as the starting point to derive ensemble Kalman-Bucy filter algorithms for combined state and parameter estimation. We demonstrate their performance through a series of increasingly complex multi-scale model systems. KW - parameter estimation KW - continuous-time data assimilation KW - ensemble Kalman filter KW - correlated noise KW - multi-scale diffusion processes Y1 - 2019 U6 - https://doi.org/10.3390/e21050505 SN - 1099-4300 VL - 21 IS - 5 PB - MDPI CY - Basel ER - TY - JOUR A1 - Keller, Matthias A1 - Pinchover, Yehuda A1 - Pogorzelski, Felix T1 - Criticality theory for Schrödinger operators on graphs JF - Journal of spectral theory N2 - We study Schrodinger operators given by positive quadratic forms on infinite graphs. From there, we develop a criticality theory for Schrodinger operators on general weighted graphs. KW - green function KW - ground state KW - positive solutions KW - discrete Schrodinger KW - operators KW - weighted graphs Y1 - 2019 U6 - https://doi.org/10.4171/JST/286 SN - 1664-039X SN - 1664-0403 VL - 10 IS - 1 SP - 73 EP - 114 PB - European Mathematical Society CY - Zürich ER - TY - JOUR A1 - Keller, Matthias A1 - Münch, Florentin T1 - A new discrete Hopf-Rinow theorem JF - Discrete Mathematics N2 - We prove a version of the Hopf-Rinow theorem with respect to path metrics on discrete spaces. The novel aspect is that we do not a priori assume local finiteness but isolate a local finiteness type condition, called essentially locally finite, that is indeed necessary. As a side product we identify the maximal weight, called the geodesic weight, generating the path metric in the situation when the space is complete with respect to any of the equivalent notions of completeness proven in the Hopf-Rinow theorem. As an application we characterize the graphs for which the resistance metric is a path metric induced by the graph structure. Y1 - 2019 U6 - https://doi.org/10.1016/j.disc.2019.03.014 SN - 0012-365X SN - 1872-681X VL - 342 IS - 9 SP - 2751 EP - 2757 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Keller, Matthias A1 - Lenz, Daniel A1 - Schmidt, Marcel A1 - Schwarz, Michael T1 - Boundary representation of Dirichlet forms on discrete spaces JF - Journal de Mathématiques Pures et Appliquées N2 - We describe the set of all Dirichlet forms associated to a given infinite graph in terms of Dirichlet forms on its Royden boundary. Our approach is purely analytical and uses form methods. (C) 2018 Elsevier Masson SAS. KW - Dirichlet form KW - Royden boundary KW - Infinite graph KW - Harmonic measure KW - Trace Dirichlet form Y1 - 2019 U6 - https://doi.org/10.1016/j.matpur.2018.10.005 SN - 0021-7824 SN - 1776-3371 VL - 126 SP - 109 EP - 143 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Grott, Matthias A1 - Knollenberg, J. A1 - Hamm, M. A1 - Ogawa, K. A1 - Jaumann, R. A1 - Otto, Katharina Alexandra A1 - Delbo, M. A1 - Michel, Patrick A1 - Biele, J. A1 - Neumann, Wladimir A1 - Knapmeyer, Martin A1 - Kührt, E. A1 - Senshu, H. A1 - Okada, T. A1 - Helbert, Jorn A1 - Maturilli, A. A1 - Müller, N. A1 - Hagermann, A. A1 - Sakatani, Naoya A1 - Tanaka, S. A1 - Arai, T. A1 - Mottola, Stefano A1 - Tachibana, Shogo A1 - Pelivan, Ivanka A1 - Drube, Line A1 - Vincent, J-B A1 - Yano, Hajime A1 - Pilorget, C. A1 - Matz, K. D. A1 - Schmitz, N. A1 - Koncz, A. A1 - Schröder, Stefan E. A1 - Trauthan, F. A1 - Schlotterer, Markus A1 - Krause, C. A1 - Ho, T-M A1 - Moussi-Soffys, A. T1 - Low thermal conductivity boulder with high porosity identified on C-type asteroid (162173) Ryugu JF - Nature astronomy N2 - C-type asteroids are among the most pristine objects in the Solar System, but little is known about their interior structure and surface properties. Telescopic thermal infrared observations have so far been interpreted in terms of a regolith-covered surface with low thermal conductivity and particle sizes in the centimetre range. This includes observations of C-type asteroid (162173) Ryugu1,2,3. However, on arrival of the Hayabusa2 spacecraft at Ryugu, a regolith cover of sand- to pebble-sized particles was found to be absent4,5 (R.J. et al., manuscript in preparation). Rather, the surface is largely covered by cobbles and boulders, seemingly incompatible with the remote-sensing infrared observations. Here we report on in situ thermal infrared observations of a boulder on the C-type asteroid Ryugu. We found that the boulder’s thermal inertia was much lower than anticipated based on laboratory measurements of meteorites, and that a surface covered by such low-conductivity boulders would be consistent with remote-sensing observations. Our results furthermore indicate high boulder porosities as well as a low tensile strength in the few hundred kilopascal range. The predicted low tensile strength confirms the suspected observational bias6 in our meteorite collections, as such asteroidal material would be too frail to survive atmospheric entry7 Y1 - 2019 U6 - https://doi.org/10.1038/s41550-019-0832-x SN - 2397-3366 VL - 3 IS - 11 SP - 971 EP - 976 PB - Nature Publishing Group CY - London ER - TY - JOUR A1 - Grott, Matthias A1 - Knollenberg, J. A1 - Hamm, M. A1 - Ogawa, K. A1 - Jaumann, R. A1 - Otto, Katharina Alexandra A1 - Delbo, M. A1 - Michel, P. A1 - Biele, J. A1 - Neumann, W. A1 - Knapmeyer, M. A1 - Kuehrt, E. A1 - Senshu, H. A1 - Okada, T. A1 - Helbert, J. A1 - Maturilli, A. A1 - Müller, N. A1 - Hagermann, A. A1 - Sakatani, N. A1 - Tanaka, S. A1 - Arai, T. A1 - Mottola, S. A1 - Tachibana, S. A1 - Pelivan, Ivanka A1 - Drube, L. A1 - Vincent, J-B A1 - Yano, H. A1 - Pilorget, C. A1 - Matz, K. D. A1 - Schmitz, N. A1 - Koncz, A. A1 - Schröder, S. E. A1 - Trauthan, F. A1 - Schlotterer, M. A1 - Krause, C. A1 - Ho, T-M A1 - Moussi-Soffys, A. T1 - Low thermal conductivity boulder with high porosity identified on C-type asteroid (162173) Ryugu JF - Nature astronomy N2 - C-type asteroids are among the most pristine objects in the Solar System, but little is known about their interior structure and surface properties. Telescopic thermal infrared observations have so far been interpreted in terms of a regolith-covered surface with low thermal conductivity and particle sizes in the centimetre range. This includes observations of C-type asteroid (162173) Ryugu1,2,3. However, on arrival of the Hayabusa2 spacecraft at Ryugu, a regolith cover of sand- to pebble-sized particles was found to be absent4,5 (R.J. et al., manuscript in preparation). Rather, the surface is largely covered by cobbles and boulders, seemingly incompatible with the remote-sensing infrared observations. Here we report on in situ thermal infrared observations of a boulder on the C-type asteroid Ryugu. We found that the boulder’s thermal inertia was much lower than anticipated based on laboratory measurements of meteorites, and that a surface covered by such low-conductivity boulders would be consistent with remote-sensing observations. Our results furthermore indicate high boulder porosities as well as a low tensile strength in the few hundred kilopascal range. The predicted low tensile strength confirms the suspected observational bias6 in our meteorite collections, as such asteroidal material would be too frail to survive atmospheric entry7. Y1 - 2020 U6 - https://doi.org/10.1038/s41550-019-0832-x SN - 2397-3366 VL - 3 IS - 11 SP - 971 EP - 976 PB - Nature Publishing Group CY - London ER - TY - JOUR A1 - Kuckelkorn, Ulrike A1 - Stübler, Sabine A1 - Textoris-Taube, Kathrin A1 - Kilian, Christiane A1 - Niewienda, Agathe A1 - Henklein, Petra A1 - Janek, Katharina A1 - Stumpf, Michael P. H. A1 - Mishto, Michele A1 - Liepe, Juliane T1 - Proteolytic dynamics of human 20S thymoproteasome JF - The journal of biological chemistry N2 - An efficient immunosurveillance of CD8(+) T cells in the periphery depends on positive/negative selection of thymocytes and thus on the dynamics of antigen degradation and epitope production by thymoproteasome and immunoproteasome in the thymus. Although studies in mouse systems have shown how thymoproteasome activity differs from that of immunoproteasome and strongly impacts the T cell repertoire, the proteolytic dynamics and the regulation of human thymoproteasome are unknown. By combining biochemical and computational modeling approaches, we show here that human 20S thymoproteasome and immunoproteasome differ not only in the proteolytic activity of the catalytic sites but also in the peptide transport. These differences impinge upon the quantity of peptide products rather than where the substrates are cleaved. The comparison of the two human 20S proteasome isoforms depicts different processing of antigens that are associated to tumors and autoimmune diseases. KW - proteasome KW - protein degradation KW - antigen processing KW - computational biology KW - bioinformatics KW - thymoproteasome KW - thymus KW - proteolysis Y1 - 2019 U6 - https://doi.org/10.1074/jbc.RA118.007347 SN - 1083-351X VL - 294 IS - 19 SP - 7740 EP - 7754 PB - American Society for Biochemistry and Molecular Biology CY - Bethesda ER - TY - JOUR A1 - Rosenblum, Michael A1 - Frühwirth, Martha A1 - Moser, Maximilian A1 - Pikovskij, Arkadij T1 - Dynamical disentanglement in an analysis of oscillatory systems: an application to respiratory sinus arrhythmia JF - Philosophical Transactions of the Royal Society of London, Series A : Mathematical, Physical and Engineering Sciences N2 - We develop a technique for the multivariate data analysis of perturbed self-sustained oscillators. The approach is based on the reconstruction of the phase dynamics model from observations and on a subsequent exploration of this model. For the system, driven by several inputs, we suggest a dynamical disentanglement procedure, allowing us to reconstruct the variability of the system's output that is due to a particular observed input, or, alternatively, to reconstruct the variability which is caused by all the inputs except for the observed one. We focus on the application of the method to the vagal component of the heart rate variability caused by a respiratory influence. We develop an algorithm that extracts purely respiratory-related variability, using a respiratory trace and times of R-peaks in the electrocardiogram. The algorithm can be applied to other systems where the observed bivariate data can be represented as a point process and a slow continuous signal, e.g. for the analysis of neuronal spiking. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'. KW - phase dynamics KW - point process KW - vagal sympathetic activity KW - autonomic nervous system Y1 - 2019 U6 - https://doi.org/10.1098/rsta.2019.0045 SN - 1364-503X SN - 1471-2962 VL - 377 IS - 2160 PB - Royal Society CY - London ER - TY - JOUR A1 - Lie, Han Cheng A1 - Stuart, A. M. A1 - Sullivan, Tim J. T1 - Strong convergence rates of probabilistic integrators for ordinary differential equations JF - Statistics and Computing N2 - Probabilistic integration of a continuous dynamical system is a way of systematically introducing discretisation error, at scales no larger than errors introduced by standard numerical discretisation, in order to enable thorough exploration of possible responses of the system to inputs. It is thus a potentially useful approach in a number of applications such as forward uncertainty quantification, inverse problems, and data assimilation. We extend the convergence analysis of probabilistic integrators for deterministic ordinary differential equations, as proposed by Conrad et al. (Stat Comput 27(4):1065-1082, 2017. ), to establish mean-square convergence in the uniform norm on discrete- or continuous-time solutions under relaxed regularity assumptions on the driving vector fields and their induced flows. Specifically, we show that randomised high-order integrators for globally Lipschitz flows and randomised Euler integrators for dissipative vector fields with polynomially bounded local Lipschitz constants all have the same mean-square convergence rate as their deterministic counterparts, provided that the variance of the integration noise is not of higher order than the corresponding deterministic integrator. These and similar results are proven for probabilistic integrators where the random perturbations may be state-dependent, non-Gaussian, or non-centred random variables. KW - Probabilistic numerical methods KW - Ordinary differential equations KW - Convergence rates KW - Uncertainty quantification Y1 - 2019 U6 - https://doi.org/10.1007/s11222-019-09898-6 SN - 0960-3174 SN - 1573-1375 VL - 29 IS - 6 SP - 1265 EP - 1283 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Perera, Upeksha A1 - Böckmann, Christine T1 - Solutions of Direct and Inverse Even-Order Sturm-Liouville Problems Using Magnus Expansion JF - Mathematics N2 - In this paper Lie group method in combination with Magnus expansion is utilized to develop a universal method applicable to solving a Sturm–Liouville problem (SLP) of any order with arbitrary boundary conditions. It is shown that the method has ability to solve direct regular (and some singular) SLPs of even orders (tested for up to eight), with a mix of (including non-separable and finite singular endpoints) boundary conditions, accurately and efficiently. The present technique is successfully applied to overcome the difficulties in finding suitable sets of eigenvalues so that the inverse SLP problem can be effectively solved. The inverse SLP algorithm proposed by Barcilon (1974) is utilized in combination with the Magnus method so that a direct SLP of any (even) order and an inverse SLP of order two can be solved effectively. KW - higher-order Sturm–Liouville problems KW - inverse Sturm–Liouville problems KW - Magnus expansion Y1 - 2019 U6 - https://doi.org/10.3390/math7060544 SN - 2227-7390 VL - 7 IS - 6 PB - MDPI CY - Basel, Schweiz ER - TY - JOUR A1 - Pornsawad, Pornsarp A1 - Sapsakul, Nantawan A1 - Böckmann, Christine T1 - A modified asymptotical regularization of nonlinear ill-posed problems JF - Mathematics N2 - In this paper, we investigate the continuous version of modified iterative Runge–Kutta-type methods for nonlinear inverse ill-posed problems proposed in a previous work. The convergence analysis is proved under the tangential cone condition, a modified discrepancy principle, i.e., the stopping time T is a solution of ∥𝐹(𝑥𝛿(𝑇))−𝑦𝛿∥=𝜏𝛿+ for some 𝛿+>𝛿, and an appropriate source condition. We yield the optimal rate of convergence. KW - nonlinear operator KW - regularization KW - discrepancy principle KW - asymptotic method KW - optimal rate Y1 - 2019 U6 - https://doi.org/10.3390/math7050419 SN - 2227-7390 VL - 7 PB - MDPI CY - Basel, Schweiz ET - 5 ER - TY - JOUR A1 - Khalil, Sara A1 - Schulze, Bert-Wolfgang T1 - Calculus on a Manifold with Edge and Boundary JF - Complex analysis and operator theory N2 - We study elements of the calculus of boundary value problems in a variant of Boutet de Monvel’s algebra (Acta Math 126:11–51, 1971) on a manifold N with edge and boundary. If the boundary is empty then the approach corresponds to Schulze (Symposium on partial differential equations (Holzhau, 1988), BSB Teubner, Leipzig, 1989) and other papers from the subsequent development. For non-trivial boundary we study Mellin-edge quantizations and compositions within the structure in terms a new Mellin-edge quantization, compared with a more traditional technique. Similar structures in the closed case have been studied in Gil et al. KW - algebra KW - Mellin quantization Y1 - 2019 U6 - https://doi.org/10.1007/s11785-018-0800-y SN - 1661-8254 SN - 1661-8262 VL - 13 IS - 6 SP - 2627 EP - 2670 PB - Springer CY - Basel ER - TY - JOUR A1 - Schulze, Bert-Wolfgang A1 - Seiler, Jörg T1 - Elliptic complexes on manifolds with boundary JF - The journal of geometric analysis N2 - We show that elliptic complexes of (pseudo) differential operators on smooth compact manifolds with boundary can always be complemented to a Fredholm problem by boundary conditions involving global pseudodifferential projections on the boundary (similarly as the spectral boundary conditions of Atiyah, Patodi, and Singer for a single operator). We prove that boundary conditions without projections can be chosen if, and only if, the topological Atiyah-Bott obstruction vanishes. These results make use of a Fredholm theory for complexes of operators in algebras of generalized pseudodifferential operators of Toeplitz type which we also develop in the present paper. KW - Elliptic complexes KW - Manifolds with boundary KW - Atiyah-Bott obstruction KW - Toeplitz-type pseudodifferential operators Y1 - 2018 U6 - https://doi.org/10.1007/s12220-018-0014-6 SN - 1050-6926 SN - 1559-002X VL - 29 IS - 1 SP - 656 EP - 706 PB - Springer CY - New York ER - TY - JOUR A1 - Biskaborn, Boris A1 - Smith, Sharon L. A1 - Noetzli, Jeannette A1 - Matthes, Heidrun A1 - Vieira, Goncalo A1 - Streletskiy, Dmitry A. A1 - Schoeneich, Philippe A1 - Romanovsky, Vladimir E. A1 - Lewkowicz, Antoni G. A1 - Abramov, Andrey A1 - Allard, Michel A1 - Boike, Julia A1 - Cable, William L. A1 - Christiansen, Hanne H. A1 - Delaloye, Reynald A1 - Diekmann, Bernhard A1 - Drozdov, Dmitry A1 - Etzelmueller, Bernd A1 - Grosse, Guido A1 - Guglielmin, Mauro A1 - Ingeman-Nielsen, Thomas A1 - Isaksen, Ketil A1 - Ishikawa, Mamoru A1 - Johansson, Margareta A1 - Johannsson, Halldor A1 - Joo, Anseok A1 - Kaverin, Dmitry A1 - Kholodov, Alexander A1 - Konstantinov, Pavel A1 - Kroeger, Tim A1 - Lambiel, Christophe A1 - Lanckman, Jean-Pierre A1 - Luo, Dongliang A1 - Malkova, Galina A1 - Meiklejohn, Ian A1 - Moskalenko, Natalia A1 - Oliva, Marc A1 - Phillips, Marcia A1 - Ramos, Miguel A1 - Sannel, A. Britta K. A1 - Sergeev, Dmitrii A1 - Seybold, Cathy A1 - Skryabin, Pavel A1 - Vasiliev, Alexander A1 - Wu, Qingbai A1 - Yoshikawa, Kenji A1 - Zheleznyak, Mikhail A1 - Lantuit, Hugues T1 - Permafrost is warming at a global scale JF - Nature Communications N2 - Permafrost warming has the potential to amplify global climate change, because when frozen sediments thaw it unlocks soil organic carbon. Yet to date, no globally consistent assessment of permafrost temperature change has been compiled. Here we use a global data set of permafrost temperature time series from the Global Terrestrial Network for Permafrost to evaluate temperature change across permafrost regions for the period since the International Polar Year (2007-2009). During the reference decade between 2007 and 2016, ground temperature near the depth of zero annual amplitude in the continuous permafrost zone increased by 0.39 +/- 0.15 degrees C. Over the same period, discontinuous permafrost warmed by 0.20 +/- 0.10 degrees C. Permafrost in mountains warmed by 0.19 +/- 0.05 degrees C and in Antarctica by 0.37 +/- 0.10 degrees C. Globally, permafrost temperature increased by 0.29 +/- 0.12 degrees C. The observed trend follows the Arctic amplification of air temperature increase in the Northern Hemisphere. In the discontinuous zone, however, ground warming occurred due to increased snow thickness while air temperature remained statistically unchanged. Y1 - 2019 U6 - https://doi.org/10.1038/s41467-018-08240-4 SN - 2041-1723 VL - 10 PB - Nature Publ. Group CY - London ER - TY - JOUR A1 - Kucharski, Maciej A1 - Ergintav, Arzu A1 - Ahmad, Wael Abdullah A1 - Krstić, Miloš A1 - Ng, Herman Jalli A1 - Kissinger, Dietmar T1 - A Scalable 79-GHz Radar Platform Based on Single-Channel Transceivers JF - IEEE Transactions on Microwave Theory and Techniques N2 - This paper presents a scalable E-band radar platform based on single-channel fully integrated transceivers (TRX) manufactured using 130-nm silicon-germanium (SiGe) BiCMOS technology. The TRX is suitable for flexible radar systems exploiting massive multiple-input-multipleoutput (MIMO) techniques for multidimensional sensing. A fully integrated fractional-N phase-locked loop (PLL) comprising a 39.5-GHz voltage-controlled oscillator is used to generate wideband frequency-modulated continuous-wave (FMCW) chirp for E-band radar front ends. The TRX is equipped with a vector modulator (VM) for high-speed carrier modulation and beam-forming techniques. A single TRX achieves 19.2-dBm maximum output power and 27.5-dB total conversion gain with input-referred 1-dB compression point of -10 dBm. It consumes 220 mA from 3.3-V supply and occupies 3.96 mm(2) silicon area. A two-channel radar platform based on full-custom TRXs and PLL was fabricated to demonstrate high-precision and high-resolution FMCW sensing. The radar enables up to 10-GHz frequency ramp generation in 74-84-GHz range, which results in 1.5-cm spatial resolution. Due to high output power, thus high signal-to-noise ratio (SNR), a ranging precision of 7.5 mu m for a target at 2 m was achieved. The proposed architecture supports scalable multichannel applications for automotive FMCW using a single local oscillator (LO). KW - Automotive KW - E-band KW - frequency-modulated continuous-wave (FMCW) KW - patch antenna KW - phase-locked loop (PLL) KW - power amplifier (PA) KW - radar KW - scalable KW - transceiver (TRX) Y1 - 2019 U6 - https://doi.org/10.1109/TMTT.2019.2914104 SN - 0018-9480 SN - 1557-9670 VL - 67 IS - 9 SP - 3882 EP - 3896 PB - Inst. of Electr. and Electronics Engineers CY - Piscataway ER - TY - JOUR A1 - Edlund, Helena A1 - Grisic, Ana-Marija A1 - Steenholdt, Casper A1 - Ainsworth, Mark Andrew A1 - Brynskov, Torn A1 - Huisinga, Wilhelm A1 - Kloft, Charlotte T1 - Absence of Relationship Between Crohn's Disease Activity Index or C-Reactive Protein and Infliximab Exposure Calls for Objective Crohn's Disease Activity Measures for the Evaluation of Treatment Effects at Treatment Failure JF - Therapeutic drug monitoring : official journal of the International Association of Therapeutic Drug Monitoring and Clinical Toxicology N2 - Background: Circulating infliximab (IFX) concentrations correlate with clinical outcomes, forming the basis of the IFX concentration monitoring in patients with Crohn's disease. This study aims to investigate and refine the exposure-response relationship by linking the disease activity markers "Crohn's disease activity index" (CDAI) and C-reactive protein (CRP) to IFX exposure. In addition, we aim to explore the correlations between different disease markers and exposure metrics. Methods: Data from 47 Crohn's disease patients of a randomized controlled trial were analyzed post hoc. All patients had secondary treatment failure at inclusion and had received intensified IFX of 5 mg/kg every 4 weeks for up to 20 weeks. Graphical analyses were performed to explore exposure-response relationships. Metrics of exposure included area under the concentration-time curve (AUC) and trough concentrations (Cmin). Disease activity was measured by CDAI and CRP values, their change from baseline/last visit, and response/remission outcomes at week 12. Results: Although trends toward lower Cmin and lower AUC in nonresponders were observed, neither CDAI nor CRP showed consistent trends of lower disease activity with higher IFX exposure across the 30 evaluated relationships. As can be expected, Cmin and AUC were strongly correlated with each other. Contrarily, the disease activity markers were only weakly correlated with each other. Conclusions: No significant relationship between disease activity, as evaluated by CDAI or CRP, and IFX exposure was identified. AUC did not add benefit compared with Cmin. These findings support the continued use of Cmin and call for stringent objective disease activity (bio-)markers (eg, endoscopy) to form the basis of personalized IFX therapy for Crohn's disease patients with IFX treatment failure. Y1 - 2019 U6 - https://doi.org/10.1097/FTD.0000000000000590 SN - 0163-4356 SN - 1536-3694 VL - 41 IS - 2 SP - 235 EP - 242 PB - Lippincott Williams & Wilkins CY - Philadelphia ER -