TY - JOUR A1 - Shaki, Samuel A1 - Pinhas, Michal A1 - Fischer, Martin H. T1 - Heuristics and biases in mental arithmetic BT - revisiting and reversing operational momentum JF - Thinking & Reasoning N2 - Mental arithmetic is characterised by a tendency to overestimate addition and to underestimate subtraction results: the operational momentum (OM) effect. Here, motivated by contentious explanations of this effect, we developed and tested an arithmetic heuristics and biases model that predicts reverse OM due to cognitive anchoring effects. Participants produced bi-directional lines with lengths corresponding to the results of arithmetic problems. In two experiments, we found regular OM with zero problems (e.g., 3+0, 3-0) but reverse OM with non-zero problems (e.g., 2+1, 4-1). In a third experiment, we tested the prediction of our model. Our results suggest the presence of at least three competing biases in mental arithmetic: a more-or-less heuristic, a sign-space association and an anchoring bias. We conclude that mental arithmetic exhibits shortcuts for decision-making similar to traditional domains of reasoning and problem-solving. KW - Heuristics KW - mental arithmetic KW - mental number line KW - operational momentum KW - problem-solving Y1 - 2017 U6 - https://doi.org/10.1080/13546783.2017.1348987 SN - 1354-6783 SN - 1464-0708 VL - 24 IS - 2 SP - 138 EP - 156 PB - Routledge, Taylor & Francis Group CY - Abingdon ER - TY - JOUR A1 - Bandara, Lashi A1 - McIntosh, Alan A1 - Rosen, Andreas T1 - Riesz continuity of the Atiyah BT - singer dirac operator under perturbations of the metric JF - Mathematische Annalen N2 - We prove that the Atiyah–Singer Dirac operator in L2 depends Riesz continuously on L∞ perturbations of complete metrics g on a smooth manifold. The Lipschitz bound for the map depends on bounds on Ricci curvature and its first derivatives as well as a lower bound on injectivity radius. Our proof uses harmonic analysis techniques related to Calderón’s first commutator and the Kato square root problem. We also show perturbation results for more general functions of general Dirac-type operators on vector bundles. Y1 - 2017 U6 - https://doi.org/10.1007/s00208-017-1610-7 SN - 0025-5831 SN - 1432-1807 VL - 370 IS - 1-2 SP - 863 EP - 915 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Gerlach, Moritz Reinhardt A1 - Glück, Jochen T1 - On a convergence theorem for semigroups of positive integral operators JF - Comptes Rendus Mathematique N2 - We give a new and very short proof of a theorem of Greiner asserting that a positive and contractive -semigroup on an -space is strongly convergent in case it has a strictly positive fixed point and contains an integral operator. Our proof is a streamlined version of a much more general approach to the asymptotic theory of positive semigroups developed recently by the authors. Under the assumptions of Greiner's theorem, this approach becomes particularly elegant and simple. We also give an outlook on several generalisations of this result. Y1 - 2017 U6 - https://doi.org/10.1016/j.crma.2017.07.017 SN - 1631-073X SN - 1778-3569 VL - 355 SP - 973 EP - 976 PB - Elsevier CY - Paris ER - TY - JOUR A1 - Taghvaei, Amirhossein A1 - de Wiljes, Jana A1 - Mehta, Prashant G. A1 - Reich, Sebastian T1 - Kalman filter and its modern extensions for the continuous-time nonlinear filtering problem JF - Journal of dynamic systems measurement and control N2 - This paper is concerned with the filtering problem in continuous time. Three algorithmic solution approaches for this problem are reviewed: (i) the classical Kalman-Bucy filter, which provides an exact solution for the linear Gaussian problem; (ii) the ensemble Kalman-Bucy filter (EnKBF), which is an approximate filter and represents an extension of the Kalman-Bucy filter to nonlinear problems; and (iii) the feedback particle filter (FPF), which represents an extension of the EnKBF and furthermore provides for a consistent solution in the general nonlinear, non-Gaussian case. The common feature of the three algorithms is the gain times error formula to implement the update step (to account for conditioning due to the observations) in the filter. In contrast to the commonly used sequential Monte Carlo methods, the EnKBF and FPF avoid the resampling of the particles in the importance sampling update step. Moreover, the feedback control structure provides for error correction potentially leading to smaller simulation variance and improved stability properties. The paper also discusses the issue of nonuniqueness of the filter update formula and formulates a novel approximation algorithm based on ideas from optimal transport and coupling of measures. Performance of this and other algorithms is illustrated for a numerical example. Y1 - 2017 U6 - https://doi.org/10.1115/1.4037780 SN - 0022-0434 SN - 1528-9028 VL - 140 IS - 3 PB - ASME CY - New York ER - TY - JOUR A1 - Lesur, Vincent A1 - Wardinski, Ingo A1 - Bärenzung, Julien A1 - Holschneider, Matthias T1 - On the frequency spectra of the core magnetic field Gauss coefficients JF - Physics of the earth and planetary interiors N2 - From monthly mean observatory data spanning 1957-2014, geomagnetic field secular variation values were calculated by annual differences. Estimates of the spherical harmonic Gauss coefficients of the core field secular variation were then derived by applying a correlation based modelling. Finally, a Fourier transform was applied to the time series of the Gauss coefficients. This process led to reliable temporal spectra of the Gauss coefficients up to spherical harmonic degree 5 or 6, and down to periods as short as 1 or 2 years depending on the coefficient. We observed that a k(-2) slope, where k is the frequency, is an acceptable approximation for these spectra, with possibly an exception for the dipole field. The monthly estimates of the core field secular variation at the observatory sites also show that large and rapid variations of the latter happen. This is an indication that geomagnetic jerks are frequent phenomena and that significant secular variation signals at short time scales - i.e. less than 2 years, could still be extracted from data to reveal an unexplored part of the core dynamics. KW - Geomagnetism KW - Core field KW - Secular variation rate of change KW - Geomagnetic jerks KW - Correlation based modelling Y1 - 2017 U6 - https://doi.org/10.1016/j.pepi.2017.05.017 SN - 0031-9201 SN - 1872-7395 VL - 276 SP - 145 EP - 158 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Pathiraja, Sahani Darschika A1 - Anghileri, Daniela A1 - Burlando, P. A1 - Sharma, A. A1 - Marshall, L. A1 - Moradkhani, H. T1 - Insights on the impact of systematic model errors on data assimilation performance in changing catchments JF - Advances in water resources N2 - The global prevalence of rapid and extensive land use change necessitates hydrologic modelling methodologies capable of handling non-stationarity. This is particularly true in the context of Hydrologic Forecasting using Data Assimilation. Data Assimilation has been shown to dramatically improve forecast skill in hydrologic and meteorological applications, although such improvements are conditional on using bias-free observations and model simulations. A hydrologic model calibrated to a particular set of land cover conditions has the potential to produce biased simulations when the catchment is disturbed. This paper sheds new light on the impacts of bias or systematic errors in hydrologic data assimilation, in the context of forecasting in catchments with changing land surface conditions and a model calibrated to pre-change conditions. We posit that in such cases, the impact of systematic model errors on assimilation or forecast quality is dependent on the inherent prediction uncertainty that persists even in pre-change conditions. Through experiments on a range of catchments, we develop a conceptual relationship between total prediction uncertainty and the impacts of land cover changes on the hydrologic regime to demonstrate how forecast quality is affected when using state estimation Data Assimilation with no modifications to account for land cover changes. This work shows that systematic model errors as a result of changing or changed catchment conditions do not always necessitate adjustments to the modelling or assimilation methodology, for instance through re-calibration of the hydrologic model, time varying model parameters or revised offline/online bias estimation. Y1 - 2017 U6 - https://doi.org/10.1016/j.advwatres.2017.12.006 SN - 0309-1708 SN - 1872-9657 VL - 113 SP - 202 EP - 222 PB - Elsevier CY - Oxford ER - TY - JOUR A1 - Brungs, Hans H. A1 - Gräter, Joachim T1 - On central extensions of SL(2, F) admitting left-orderings JF - Journal of Algebra N2 - For an arbitrary euclidean field F we introduce a central extension (G(F), Phi) of SL(2, F) admitting a left-ordering and study its algebraic properties. The elements of G(F) are order preserving bijections of the convex hull of Q in F. If F = R then G(F) is isomorphic to the classical universal covering group of the Lie group SL(2, R). Among other results we show that G(F) is a perfect group which possesses a rank 1 cone of exceptional type. We also prove that its centre is an infinite cyclic group and investigate its normal subgroups. KW - Universal covering group KW - Central extensions of groups KW - Perfect groups KW - Ordered fields KW - Left-ordered groups KW - Order-preserving bijections KW - Euclidean fields Y1 - 2017 U6 - https://doi.org/10.1016/j.jalgebra.2017.05.025 SN - 0021-8693 SN - 1090-266X VL - 486 SP - 288 EP - 327 PB - Elsevier CY - San Diego ER - TY - JOUR A1 - Elin, Mark A1 - Shoikhet, David A1 - Tarkhanov, Nikolai Nikolaevich T1 - Analytic Semigroups of Holomorphic Mappings and Composition Operators JF - Computational Methods and Function Theory N2 - In this manuscript we provide a review on the classical and resent results related to the problem of analytic extension in parameter for a semigroup of holomorphic self-mappings of the unit ball in a complex Banach space and its relation to the linear continuous semigroup of composition operators. KW - Non-linear semigroups KW - Composition operators KW - Analytic extension KW - Holomorphic mappings Y1 - 2017 U6 - https://doi.org/10.1007/s40315-017-0227-x SN - 1617-9447 SN - 2195-3724 VL - 18 IS - 2 SP - 269 EP - 294 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Gairing, Jan A1 - Högele, Michael A1 - Kosenkova, Tetiana T1 - Transportation distances and noise sensitivity of multiplicative Levy SDE with applications JF - Stochastic processes and their application N2 - This article assesses the distance between the laws of stochastic differential equations with multiplicative Levy noise on path space in terms of their characteristics. The notion of transportation distance on the set of Levy kernels introduced by Kosenkova and Kulik yields a natural and statistically tractable upper bound on the noise sensitivity. This extends recent results for the additive case in terms of coupling distances to the multiplicative case. The strength of this notion is shown in a statistical implementation for simulations and the example of a benchmark time series in paleoclimate. KW - Stochastic differential equations KW - Multiplicative Levy noise KW - Levy type processes KW - Heavy-tailed distributions KW - Model selection KW - Wasserstein distance KW - Time series Y1 - 2017 U6 - https://doi.org/10.1016/j.spa.2017.09.003 SN - 0304-4149 SN - 1879-209X VL - 128 IS - 7 SP - 2153 EP - 2178 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Fedchenko, Dmitry A1 - Tarkhanov, Nikolai Nikolaevich T1 - A Rado theorem for the porous medium equation JF - Boletin de la Sociedad Matemática Mexicana N2 - We prove that if u is a locally Lipschitz continuous function on an open set chi subset of Rn + 1 satisfying the nonlinear heat equation partial derivative(t)u = Delta(vertical bar u vertical bar(p-1) u), p > 1, weakly away from the zero set u(-1) (0) in chi, then u is a weak solution to this equation in all of chi. KW - Quasilinear equations KW - Removable sets KW - Porous medium equation Y1 - 2017 U6 - https://doi.org/10.1007/s40590-017-0169-3 SN - 1405-213X SN - 2296-4495 VL - 24 IS - 2 SP - 427 EP - 437 PB - Springer CY - Cham ER -