TY - JOUR A1 - Acevedo, Walter A1 - Reich, Sebastian A1 - Cubasch, Ulrich T1 - Towards the assimilation of tree-ring-width records using ensemble Kalman filtering techniques JF - Climate dynamics : observational, theoretical and computational research on the climate system N2 - This paper investigates the applicability of the Vaganov–Shashkin–Lite (VSL) forward model for tree-ring-width chronologies as observation operator within a proxy data assimilation (DA) setting. Based on the principle of limiting factors, VSL combines temperature and moisture time series in a nonlinear fashion to obtain simulated TRW chronologies. When used as observation operator, this modelling approach implies three compounding, challenging features: (1) time averaging, (2) “switching recording” of 2 variables and (3) bounded response windows leading to “thresholded response”. We generate pseudo-TRW observations from a chaotic 2-scale dynamical system, used as a cartoon of the atmosphere-land system, and attempt to assimilate them via ensemble Kalman filtering techniques. Results within our simplified setting reveal that VSL’s nonlinearities may lead to considerable loss of assimilation skill, as compared to the utilization of a time-averaged (TA) linear observation operator. In order to understand this undesired effect, we embed VSL’s formulation into the framework of fuzzy logic (FL) theory, which thereby exposes multiple representations of the principle of limiting factors. DA experiments employing three alternative growth rate functions disclose a strong link between the lack of smoothness of the growth rate function and the loss of optimality in the estimate of the TA state. Accordingly, VSL’s performance as observation operator can be enhanced by resorting to smoother FL representations of the principle of limiting factors. This finding fosters new interpretations of tree-ring-growth limitation processes. KW - Proxy forward modeling KW - Data assimilation KW - Fuzzy logic KW - Ensemble Kalman filter KW - Paleoclimate reconstruction Y1 - 2016 U6 - https://doi.org/10.1007/s00382-015-2683-1 SN - 0930-7575 SN - 1432-0894 VL - 46 SP - 1909 EP - 1920 PB - Springer CY - New York ER - TY - JOUR A1 - Shtrakov, Slavcho A1 - Koppitz, Jörg T1 - Stable varieties of semigroups and groupoids JF - Algebra universalis N2 - The paper deals with Sigma-composition and Sigma-essential composition of terms which lead to stable and s-stable varieties of algebras. A full description of all stable varieties of semigroups, commutative and idempotent groupoids is obtained. We use an abstract reduction system which simplifies the presentations of terms of type tau - (2) to study the variety of idempotent groupoids and s-stable varieties of groupoids. S-stable varieties are a variation of stable varieties, used to highlight replacement of subterms of a term in a deductive system instead of the usual replacement of variables by terms. KW - composition of terms KW - essential position in terms KW - stable variety Y1 - 2016 U6 - https://doi.org/10.1007/s00012-015-0359-7 SN - 0002-5240 SN - 1420-8911 VL - 75 SP - 85 EP - 106 PB - Springer CY - Basel ER - TY - JOUR A1 - Gregory, A. A1 - Cotter, C. J. A1 - Reich, Sebastian T1 - MULTILEVEL ENSEMBLE TRANSFORM PARTICLE FILTERING JF - SIAM journal on scientific computing N2 - This paper extends the multilevel Monte Carlo variance reduction technique to nonlinear filtering. In particular, multilevel Monte Carlo is applied to a certain variant of the particle filter, the ensemble transform particle filter (EPTF). A key aspect is the use of optimal transport methods to re-establish correlation between coarse and fine ensembles after resampling; this controls the variance of the estimator. Numerical examples present a proof of concept of the effectiveness of the proposed method, demonstrating significant computational cost reductions (relative to the single-level ETPF counterpart) in the propagation of ensembles. KW - multilevel Monte Carlo KW - sequential data assimilation KW - optimal transport Y1 - 2016 U6 - https://doi.org/10.1137/15M1038232 SN - 1064-8275 SN - 1095-7197 VL - 38 SP - A1317 EP - A1338 PB - Society for Industrial and Applied Mathematics CY - Philadelphia ER - TY - JOUR A1 - Menne, Ulrich T1 - Weakly Differentiable Functions on Varifolds JF - Indiana University mathematics journal N2 - The present paper is intended to provide the basis for the study of weakly differentiable functions on rectifiable varifolds with locally bounded first variation. The concept proposed here is defined by means of integration-by-parts identities for certain compositions with smooth functions. In this class, the idea of zero boundary values is realised using the relative perimeter of superlevel sets. Results include a variety of Sobolev Poincare-type embeddings, embeddings into spaces of continuous and sometimes Holder-continuous functions, and point wise differentiability results both of approximate and integral type as well as coarea formulae. As a prerequisite for this study, decomposition properties of such varifolds and a relative isoperimetric inequality are established. Both involve a concept of distributional boundary of a set introduced for this purpose. As applications, the finiteness of the geodesic distance associated with varifolds with suitable summability of the mean curvature and a characterisation of curvature varifolds are obtained. KW - Rectifiable varifold KW - (generalised) wealdy differentiable function KW - distributional boundary KW - decomposition KW - relative isoperimetric inequality KW - Sobolev Poincare inequality KW - approximate differentiability KW - coarea formula KW - geodesic distance KW - curvature varifold Y1 - 2016 U6 - https://doi.org/10.1512/iumj.2016.65.5829 SN - 0022-2518 SN - 1943-5258 VL - 65 SP - 977 EP - 1088 PB - Indiana University, Department of Mathematics CY - Bloomington ER - TY - JOUR A1 - Bomanson, Jori A1 - Janhunen, Tomi A1 - Schaub, Torsten H. A1 - Gebser, Martin A1 - Kaufmann, Benjamin T1 - Answer Set Programming Modulo Acyclicity JF - Fundamenta informaticae N2 - Acyclicity constraints are prevalent in knowledge representation and applications where acyclic data structures such as DAGs and trees play a role. Recently, such constraints have been considered in the satisfiability modulo theories (SMT) framework, and in this paper we carry out an analogous extension to the answer set programming (ASP) paradigm. The resulting formalism, ASP modulo acyclicity, offers a rich set of primitives to express constraints related to recursive structures. In the technical results of the paper, we relate the new generalization with standard ASP by showing (i) how acyclicity extensions translate into normal rules, (ii) how weight constraint programs can be instrumented by acyclicity extensions to capture stability in analogy to unfounded set checking, and (iii) how the gap between supported and stable models is effectively closed in the presence of such an extension. Moreover, we present an efficient implementation of acyclicity constraints by incorporating a respective propagator into the state-of-the-art ASP solver CLASP. The implementation provides a unique combination of traditional unfounded set checking with acyclicity propagation. In the experimental part, we evaluate the interplay of these orthogonal checks by equipping logic programs with supplementary acyclicity constraints. The performance results show that native support for acyclicity constraints is a worthwhile addition, furnishing a complementary modeling construct in ASP itself as well as effective means for translation-based ASP solving. Y1 - 2016 U6 - https://doi.org/10.3233/FI-2016-1398 SN - 0169-2968 SN - 1875-8681 VL - 147 SP - 63 EP - 91 PB - IOS Press CY - Amsterdam ER - TY - JOUR A1 - Tinpun, Kittisak A1 - Koppitz, Jörg T1 - Generating sets of infinite full transformation semigroups with restricted range JF - Acta scientiarum mathematicarum N2 - In the present paper, we consider minimal generating sets of infinite full transformation semigroups with restricted range modulo specific subsets. In particular, we determine relative ranks. KW - generating sets KW - transformation semigroups KW - restricted range KW - relative ranks Y1 - 2016 U6 - https://doi.org/10.14232/actasm-015-502-4 SN - 0001-6969 VL - 82 SP - 55 EP - 63 PB - Institutum Bolyaianum Universitatis Szegediensis CY - Szeged ER - TY - JOUR A1 - Zöller, Gert A1 - Holschneider, Matthias T1 - The Maximum Possible and the Maximum Expected Earthquake Magnitude for Production-Induced Earthquakes at the Gas Field in Groningen, The Netherlands JF - Bulletin of the Seismological Society of America N2 - The Groningen gas field serves as a natural laboratory for production-induced earthquakes, because no earthquakes were observed before the beginning of gas production. Increasing gas production rates resulted in growing earthquake activity and eventually in the occurrence of the 2012M(w) 3.6 Huizinge earthquake. At least since this event, a detailed seismic hazard and risk assessment including estimation of the maximum earthquake magnitude is considered to be necessary to decide on the future gas production. In this short note, we first apply state-of-the-art methods of mathematical statistics to derive confidence intervals for the maximum possible earthquake magnitude m(max). Second, we calculate the maximum expected magnitude M-T in the time between 2016 and 2024 for three assumed gas-production scenarios. Using broadly accepted physical assumptions and 90% confidence level, we suggest a value of m(max) 4.4, whereas M-T varies between 3.9 and 4.3, depending on the production scenario. Y1 - 2016 U6 - https://doi.org/10.1785/0120160220 SN - 0037-1106 SN - 1943-3573 VL - 106 SP - 2917 EP - 2921 PB - Seismological Society of America CY - Albany ER - TY - JOUR A1 - Menne, Ulrich T1 - Sobolev functions on varifolds JF - Proceedings of the London Mathematical Society N2 - This paper introduces first-order Sobolev spaces on certain rectifiable varifolds. These complete locally convex spaces are contained in the generally non-linear class of generalised weakly differentiable functions and share key functional analytic properties with their Euclidean counterparts. Assuming the varifold to satisfy a uniform lower density bound and a dimensionally critical summability condition on its mean curvature, the following statements hold. Firstly, continuous and compact embeddings of Sobolev spaces into Lebesgue spaces and spaces of continuous functions are available. Secondly, the geodesic distance associated to the varifold is a continuous, not necessarily Holder continuous Sobolev function with bounded derivative. Thirdly, if the varifold additionally has bounded mean curvature and finite measure, then the present Sobolev spaces are isomorphic to those previously available for finite Radon measures yielding many new results for those classes as well. Suitable versions of the embedding results obtained for Sobolev functions hold in the larger class of generalised weakly differentiable functions. Y1 - 2016 U6 - https://doi.org/10.1112/plms/pdw023 SN - 0024-6115 SN - 1460-244X VL - 113 SP - 725 EP - 774 PB - Oxford Univ. Press CY - Oxford ER - TY - JOUR A1 - Keller, Matthias A1 - Lenz, Daniel A1 - Münch, Florentin A1 - Schmidt, Marcel A1 - Telcs, Andras T1 - Note on short-time behavior of semigroups associated to self-adjoint operators JF - Bulletin of the London Mathematical Society N2 - We present a simple observation showing that the heat kernel on a locally finite graph behaves for short times t roughly like t(d), where d is the combinatorial distance. This is very different from the classical Varadhan-type behavior on manifolds. Moreover, this also gives that short-time behavior and global behavior of the heat kernel are governed by two different metrics whenever the degree of the graph is not uniformly bounded. Y1 - 2016 U6 - https://doi.org/10.1112/blms/bdw054 SN - 0024-6093 SN - 1469-2120 VL - 48 SP - 935 EP - 944 PB - Oxford Univ. Press CY - Oxford ER - TY - JOUR A1 - Wichitsa-Nguan, Korakot A1 - Läuter, Henning A1 - Liero, Hannelore T1 - Estimability in Cox models JF - Statistical Papers N2 - Our procedure of estimating is the maximum partial likelihood estimate (MPLE) which is the appropriate estimate in the Cox model with a general censoring distribution, covariates and an unknown baseline hazard rate . We find conditions for estimability and asymptotic estimability. The asymptotic variance matrix of the MPLE is represented and properties are discussed. KW - Cox model KW - Estimability KW - Asymptotic variance of maximum partial likelihood estimate Y1 - 2016 U6 - https://doi.org/10.1007/s00362-016-0755-x SN - 0932-5026 SN - 1613-9798 VL - 57 SP - 1121 EP - 1140 PB - Springer CY - New York ER - TY - JOUR A1 - Müller, Detlef A1 - Böckmann, Christine A1 - Kolgotin, Alexei A1 - Schneidenbach, Lars A1 - Chemyakin, Eduard A1 - Rosemann, Julia A1 - Znak, Pavel A1 - Romanov, Anton T1 - Microphysical particle properties derived from inversion algorithms developed in the framework of EARLINET JF - Atmospheric measurement techniques : an interactive open access journal of the European Geosciences Union N2 - We present a summary on the current status of two inversion algorithms that are used in EARLINET (European Aerosol Research Lidar Network) for the inversion of data collected with EARLINET multiwavelength Raman lidars. These instruments measure backscatter coefficients at 355, 532, and 1064 nm, and extinction coefficients at 355 and 532 nm. Development of these two algorithms started in 2000 when EARLINET was founded. The algorithms are based on a manually controlled inversion of optical data which allows for detailed sensitivity studies. The algorithms allow us to derive particle effective radius as well as volume and surface area concentration with comparably high confidence. The retrieval of the real and imaginary parts of the complex refractive index still is a challenge in view of the accuracy required for these parameters in climate change studies in which light absorption needs to be known with high accuracy. It is an extreme challenge to retrieve the real part with an accuracy better than 0.05 and the imaginary part with accuracy better than 0.005-0.1 or +/- 50 %. Single-scattering albedo can be computed from the retrieved microphysical parameters and allows us to categorize aerosols into high-and low-absorbing aerosols. On the basis of a few exemplary simulations with synthetic optical data we discuss the current status of these manually operated algorithms, the potentially achievable accuracy of data products, and the goals for future work. One algorithm was used with the purpose of testing how well microphysical parameters can be derived if the real part of the complex refractive index is known to at least 0.05 or 0.1. The other algorithm was used to find out how well microphysical parameters can be derived if this constraint for the real part is not applied. The optical data used in our study cover a range of Angstrom exponents and extinction-to-backscatter (lidar) ratios that are found from lidar measurements of various aerosol types. We also tested aerosol scenarios that are considered highly unlikely, e.g. the lidar ratios fall outside the commonly accepted range of values measured with Raman lidar, even though the underlying microphysical particle properties are not uncommon. The goal of this part of the study is to test the robustness of the algorithms towards their ability to identify aerosol types that have not been measured so far, but cannot be ruled out based on our current knowledge of aerosol physics. We computed the optical data from monomodal logarithmic particle size distributions, i.e. we explicitly excluded the more complicated case of bimodal particle size distributions which is a topic of ongoing research work. Another constraint is that we only considered particles of spherical shape in our simulations. We considered particle radii as large as 7-10 mu m in our simulations where the Potsdam algorithm is limited to the lower value. We considered optical-data errors of 15% in the simulation studies. We target 50% uncertainty as a reasonable threshold for our data products, though we attempt to obtain data products with less uncertainty in future work. Y1 - 2016 U6 - https://doi.org/10.5194/amt-9-5007-2016 SN - 1867-1381 SN - 1867-8548 VL - 9 SP - 5007 EP - 5035 PB - Copernicus CY - Göttingen ER - TY - JOUR A1 - Bär, Christian A1 - Strohmaier, Alexander T1 - A Rigorous Geometric Derivation of the Chiral Anomaly in Curved Backgrounds JF - Communications in mathematical physics N2 - We discuss the chiral anomaly for a Weyl field in a curved background and show that a novel index theorem for the Lorentzian Dirac operator can be applied to describe the gravitational chiral anomaly. A formula for the total charge generated by the gravitational and gauge field background is derived directly in Lorentzian signature and in a mathematically rigorous manner. It contains a term identical to the integrand in the Atiyah-Singer index theorem and another term involving the.-invariant of the Cauchy hypersurfaces. Y1 - 2016 U6 - https://doi.org/10.1007/s00220-016-2664-1 SN - 0010-3616 SN - 1432-0916 VL - 347 SP - 703 EP - 721 PB - Springer CY - New York ER - TY - JOUR A1 - Beinrucker, Andre A1 - Dogan, Urun A1 - Blanchard, Gilles T1 - Extensions of stability selection using subsamples of observations and covariates JF - Statistics and Computing N2 - We introduce extensions of stability selection, a method to stabilise variable selection methods introduced by Meinshausen and Buhlmann (J R Stat Soc 72:417-473, 2010). We propose to apply a base selection method repeatedly to random subsamples of observations and subsets of covariates under scrutiny, and to select covariates based on their selection frequency. We analyse the effects and benefits of these extensions. Our analysis generalizes the theoretical results of Meinshausen and Buhlmann (J R Stat Soc 72:417-473, 2010) from the case of half-samples to subsamples of arbitrary size. We study, in a theoretical manner, the effect of taking random covariate subsets using a simplified score model. Finally we validate these extensions on numerical experiments on both synthetic and real datasets, and compare the obtained results in detail to the original stability selection method. KW - Variable selection KW - Stability selection KW - Subsampling Y1 - 2016 U6 - https://doi.org/10.1007/s11222-015-9589-y SN - 0960-3174 SN - 1573-1375 VL - 26 SP - 1059 EP - 1077 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Kröncke, Klaus T1 - Rigidity and Infinitesimal Deformability of Ricci Solitons JF - The journal of geometric analysis N2 - In this paper, an obstruction against the integrability of certain infinitesimal solitonic deformations is given. Using this obstruction, we show that the complex projective spaces of even complex dimension are rigid as Ricci solitons although they have infinitesimal solitonic deformations. KW - Ricci solitons KW - Moduli space KW - Linearized equation KW - Integrability Y1 - 2016 U6 - https://doi.org/10.1007/s12220-015-9608-4 SN - 1050-6926 SN - 1559-002X VL - 26 SP - 1795 EP - 1807 PB - Springer CY - New York ER - TY - JOUR A1 - Mieth, Bettina A1 - Kloft, Marius A1 - Rodriguez, Juan Antonio A1 - Sonnenburg, Soren A1 - Vobruba, Robin A1 - Morcillo-Suarez, Carlos A1 - Farre, Xavier A1 - Marigorta, Urko M. A1 - Fehr, Ernst A1 - Dickhaus, Thorsten A1 - Blanchard, Gilles A1 - Schunk, Daniel A1 - Navarro, Arcadi A1 - Müller, Klaus-Robert T1 - Combining Multiple Hypothesis Testing with Machine Learning Increases the Statistical Power of Genome-wide Association Studies JF - Scientific reports N2 - The standard approach to the analysis of genome-wide association studies (GWAS) is based on testing each position in the genome individually for statistical significance of its association with the phenotype under investigation. To improve the analysis of GWAS, we propose a combination of machine learning and statistical testing that takes correlation structures within the set of SNPs under investigation in a mathematically well-controlled manner into account. The novel two-step algorithm, COMBI, first trains a support vector machine to determine a subset of candidate SNPs and then performs hypothesis tests for these SNPs together with an adequate threshold correction. Applying COMBI to data from a WTCCC study (2007) and measuring performance as replication by independent GWAS published within the 2008-2015 period, we show that our method outperforms ordinary raw p-value thresholding as well as other state-of-the-art methods. COMBI presents higher power and precision than the examined alternatives while yielding fewer false (i.e. non-replicated) and more true (i.e. replicated) discoveries when its results are validated on later GWAS studies. More than 80% of the discoveries made by COMBI upon WTCCC data have been validated by independent studies. Implementations of the COMBI method are available as a part of the GWASpi toolbox 2.0. Y1 - 2016 U6 - https://doi.org/10.1038/srep36671 SN - 2045-2322 VL - 6 PB - Nature Publ. Group CY - London ER - TY - JOUR A1 - Keller, Matthias A1 - Mugnolo, Delio T1 - General Cheeger inequalities for p-Laplacians on graphs JF - Theoretical ecology N2 - We prove Cheeger inequalities for p-Laplacians on finite and infinite weighted graphs. Unlike in previous works, we do not impose boundedness of the vertex degree, nor do we restrict ourselves to the normalized Laplacian and, more generally, we do not impose any boundedness assumption on the geometry. This is achieved by a novel definition of the measure of the boundary which uses the idea of intrinsic metrics. For the non-normalized case, our bounds on the spectral gap of p-Laplacians are already significantly better for finite graphs and for infinite graphs they yield non-trivial bounds even in the case of unbounded vertex degree. We, furthermore, give upper bounds by the Cheeger constant and by the exponential volume growth of distance balls. (C) 2016 Elsevier Ltd. All rights reserved. KW - Cheeger inequalities KW - Spectral theory of graphs KW - Intrinsic metrics for Dirichlet forms Y1 - 2016 U6 - https://doi.org/10.1016/j.na.2016.07.011 SN - 0362-546X SN - 1873-5215 VL - 147 SP - 80 EP - 95 PB - Elsevier CY - Oxford ER - TY - JOUR A1 - Blanchard, Gilles A1 - Kraemer, Nicole T1 - Convergence rates of Kernel Conjugate Gradient for random design regression JF - Analysis and applications N2 - We prove statistical rates of convergence for kernel-based least squares regression from i.i.d. data using a conjugate gradient (CG) algorithm, where regularization against over-fitting is obtained by early stopping. This method is related to Kernel Partial Least Squares, a regression method that combines supervised dimensionality reduction with least squares projection. Following the setting introduced in earlier related literature, we study so-called "fast convergence rates" depending on the regularity of the target regression function (measured by a source condition in terms of the kernel integral operator) and on the effective dimensionality of the data mapped into the kernel space. We obtain upper bounds, essentially matching known minimax lower bounds, for the L-2 (prediction) norm as well as for the stronger Hilbert norm, if the true regression function belongs to the reproducing kernel Hilbert space. If the latter assumption is not fulfilled, we obtain similar convergence rates for appropriate norms, provided additional unlabeled data are available. KW - Nonparametric regression KW - reproducing kernel Hilbert space KW - conjugate gradient KW - partial least squares KW - minimax convergence rates Y1 - 2016 U6 - https://doi.org/10.1142/S0219530516400017 SN - 0219-5305 SN - 1793-6861 VL - 14 SP - 763 EP - 794 PB - World Scientific CY - Singapore ER - TY - JOUR A1 - Hermann, Andreas A1 - Humbert, Emmanuel T1 - About the mass of certain second order elliptic operators JF - Advances in mathematics N2 - Let (M, g) be a closed Riemannian manifold of dimension n >= 3 and let f is an element of C-infinity (M), such that the operator P-f := Delta g + f is positive. If g is flat near some point p and f vanishes around p, we can define the mass of P1 as the constant term in the expansion of the Green function of P-f at p. In this paper, we establish many results on the mass of such operators. In particular, if f := n-2/n(n-1)s(g), i.e. if P-f is the Yamabe operator, we show the following result: assume that there exists a closed simply connected non-spin manifold M such that the mass is non-negative for every metric g as above on M, then the mass is non-negative for every such metric on every closed manifold of the same dimension as M. (C) 2016 Elsevier Inc. All rights reserved. KW - Yamabe operator KW - Surgery KW - Positive mass theorem Y1 - 2016 U6 - https://doi.org/10.1016/j.aim.2016.03.008 SN - 0001-8708 SN - 1090-2082 VL - 294 SP - 596 EP - 633 PB - Elsevier CY - San Diego ER - TY - JOUR A1 - Becker, Christian T1 - Cheeger-Chern-Simons Theory and Differential String Classes JF - Annales de l'Institut Henri Poincaré N2 - We construct new concrete examples of relative differential characters, which we call Cheeger-Chern-Simons characters. They combine the well-known Cheeger-Simons characters with Chern-Simons forms. In the same way as Cheeger-Simons characters generalize Chern-Simons invariants of oriented closed manifolds, Cheeger-Chern-Simons characters generalize Chern-Simons invariants of oriented manifolds with boundary. We study the differential cohomology of compact Lie groups G and their classifying spaces BG. We show that the even degree differential cohomology of BG canonically splits into Cheeger-Simons characters and topologically trivial characters. We discuss the transgression in principal G-bundles and in the universal bundle. We introduce two methods to lift the universal transgression to a differential cohomology valued map. They generalize the Dijkgraaf-Witten correspondence between 3-dimensional Chern-Simons theories and Wess-Zumino-Witten terms to fully extended higher-order Chern-Simons theories. Using these lifts, we also prove two versions of a differential Hopf theorem. Using Cheeger-Chern-Simons characters and transgression, we introduce the notion of differential trivializations of universal characteristic classes. It generalizes well-established notions of differential String classes to arbitrary degree. Specializing to the class , we recover isomorphism classes of geometric string structures on Spin (n) -bundles with connection and the corresponding spin structures on the free loop space. The Cheeger-Chern-Simons character associated with the class together with its transgressions to loop space and higher mapping spaces defines a Chern-Simons theory, extended down to points. Differential String classes provide trivializations of this extended Chern-Simons theory. This setting immediately generalizes to arbitrary degree: for any universal characteristic class of principal G-bundles, we have an associated Cheeger-Chern-Simons character and extended Chern-Simons theory. Differential trivialization classes yield trivializations of this extended Chern-Simons theory. Y1 - 2016 U6 - https://doi.org/10.1007/s00023-016-0485-6 SN - 1424-0637 SN - 1424-0661 VL - 17 SP - 1529 EP - 1594 PB - Springer CY - Basel ER - TY - JOUR A1 - Bärenzung, Julien A1 - Holschneider, Matthias A1 - Lesur, Vincent T1 - constraints JF - Journal of geophysical research : Solid earth N2 - Prior information in ill-posed inverse problem is of critical importance because it is conditioning the posterior solution and its associated variability. The problem of determining the flow evolving at the Earth's core-mantle boundary through magnetic field models derived from satellite or observatory data is no exception to the rule. This study aims to estimate what information can be extracted on the velocity field at the core-mantle boundary, when the frozen flux equation is inverted under very weakly informative, but realistic, prior constraints. Instead of imposing a converging spectrum to the flow, we simply assume that its poloidal and toroidal energy spectra are characterized by power laws. The parameters of the spectra, namely, their magnitudes, and slopes are unknown. The connection between the velocity field, its spectra parameters, and the magnetic field model is established through the Bayesian formulation of the problem. Working in two steps, we determined the time-averaged spectra of the flow within the 2001–2009.5 period, as well as the flow itself and its associated uncertainties in 2005.0. According to the spectra we obtained, we can conclude that the large-scale approximation of the velocity field is not an appropriate assumption within the time window we considered. For the flow itself, we show that although it is dominated by its equatorial symmetric component, it is very unlikely to be perfectly symmetric. We also demonstrate that its geostrophic state is questioned in different locations of the outer core. Y1 - 2016 U6 - https://doi.org/10.1002/2015JB012464 SN - 2169-9313 SN - 2169-9356 VL - 121 SP - 1343 EP - 1364 PB - American Geophysical Union CY - Washington ER -