TY - JOUR A1 - Nitze, Ingmar A1 - Grosse, Guido A1 - Jones, Benjamin M. A1 - Romanovsky, Vladimir E. A1 - Boike, Julia T1 - Remote sensing quantifies widespread abundance of permafrost region disturbances across the Arctic and Subarctic JF - Nature Communications N2 - Local observations indicate that climate change and shifting disturbance regimes are causing permafrost degradation. However, the occurrence and distribution of permafrost region disturbances (PRDs) remain poorly resolved across the Arctic and Subarctic. Here we quantify the abundance and distribution of three primary PRDs using time-series analysis of 30-m resolution Landsat imagery from 1999 to 2014. Our dataset spans four continental-scale transects in North America and Eurasia, covering similar to 10% of the permafrost region. Lake area loss (-1.45%) dominated the study domain with enhanced losses occurring at the boundary between discontinuous and continuous permafrost regions. Fires were the most extensive PRD across boreal regions (6.59%), but in tundra regions (0.63%) limited to Alaska. Retrogressive thaw slumps were abundant but highly localized (< 10(-5)%). Our analysis synergizes the global-scale importance of PRDs. The findings highlight the need to include PRDs in next-generation land surface models to project the permafrost carbon feedback. Y1 - 2018 U6 - https://doi.org/10.1038/s41467-018-07663-3 SN - 2041-1723 VL - 9 PB - Nature Publ. Group CY - London ER - TY - JOUR A1 - Güneysu, Batu A1 - Keller, Matthias T1 - Scattering the Geometry of Weighted Graphs JF - Mathematical physics, analysis and geometry : an international journal devoted to the theory and applications of analysis and geometry to physics N2 - Given two weighted graphs (X, b(k), m(k)), k = 1, 2 with b(1) similar to b(2) and m(1) similar to m(2), we prove a weighted L-1-criterion for the existence and completeness of the wave operators W-+/- (H-2, H-1, I-1,I-2), where H-k denotes the natural Laplacian in l(2)(X, m(k)) w.r.t. (X, b(k), m(k)) and I-1,I-2 the trivial identification of l(2)(X, m(1)) with l(2) (X, m(2)). In particular, this entails a general criterion for the absolutely continuous spectra of H-1 and H-2 to be equal. KW - Graphs KW - Laplacian KW - Scattering theory Y1 - 2018 U6 - https://doi.org/10.1007/s11040-018-9285-1 SN - 1385-0172 SN - 1572-9656 VL - 21 IS - 3 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Salamat, Mona A1 - Zöller, Gert A1 - Zare, Mehdi A1 - Amini, Mortaza T1 - The maximum expected earthquake magnitudes in different future time intervals of six seismotectonic zones of Iran and its surroundings JF - Journal of seismology N2 - One of the crucial components in seismic hazard analysis is the estimation of the maximum earthquake magnitude and associated uncertainty. In the present study, the uncertainty related to the maximum expected magnitude mu is determined in terms of confidence intervals for an imposed level of confidence. Previous work by Salamat et al. (Pure Appl Geophys 174:763-777, 2017) shows the divergence of the confidence interval of the maximum possible magnitude m(max) for high levels of confidence in six seismotectonic zones of Iran. In this work, the maximum expected earthquake magnitude mu is calculated in a predefined finite time interval and imposed level of confidence. For this, we use a conceptual model based on a doubly truncated Gutenberg-Richter law for magnitudes with constant b-value and calculate the posterior distribution of mu for the time interval T-f in future. We assume a stationary Poisson process in time and a Gutenberg-Richter relation for magnitudes. The upper bound of the magnitude confidence interval is calculated for different time intervals of 30, 50, and 100 years and imposed levels of confidence alpha = 0.5, 0.1, 0.05, and 0.01. The posterior distribution of waiting times T-f to the next earthquake with a given magnitude equal to 6.5, 7.0, and7.5 are calculated in each zone. In order to find the influence of declustering, we use the original and declustered version of the catalog. The earthquake catalog of the territory of Iran and surroundings are subdivided into six seismotectonic zones Alborz, Azerbaijan, Central Iran, Zagros, Kopet Dagh, and Makran. We assume the maximum possible magnitude m(max) = 8.5 and calculate the upper bound of the confidence interval of mu in each zone. The results indicate that for short time intervals equal to 30 and 50 years and imposed levels of confidence 1 - alpha = 0.95 and 0.90, the probability distribution of mu is around mu = 7.16-8.23 in all seismic zones. KW - Maximum expected earthquake magnitude KW - Future time interval KW - Level of confidence KW - Iran Y1 - 2018 U6 - https://doi.org/10.1007/s10950-018-9780-7 SN - 1383-4649 SN - 1573-157X VL - 22 IS - 6 SP - 1485 EP - 1498 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Afshari Moein, Mohammad J. A1 - Somogyvári, Márk A1 - Valley, Benoît A1 - Jalali, Mohammadreza A1 - Löw, Simon A1 - Bayer, Peter T1 - Fracture network characterization using stress-based tomography JF - Journal of geophysical research : JGR N2 - Information on structural features of a fracture network at early stages of Enhanced Geothermal System development is mostly restricted to borehole images and, if available, outcrop data. However, using this information to image discontinuities in deep reservoirs is difficult. Wellbore failure data provides only some information on components of the in situ stress state and its heterogeneity. Our working hypothesis is that slip on natural fractures primarily controls these stress heterogeneities. Based on this, we introduce stress-based tomography in a Bayesian framework to characterize the fracture network and its heterogeneity in potential Enhanced Geothermal System reservoirs. In this procedure, first a random initial discrete fracture network (DFN) realization is generated based on prior information about the network. The observations needed to calibrate the DFN are based on local variations of the orientation and magnitude of at least one principal stress component along boreholes. A Markov Chain Monte Carlo sequence is employed to update the DFN iteratively by a fracture translation within the domain. The Markov sequence compares the simulated stress profile with the observed stress profiles in the borehole, evaluates each iteration with Metropolis-Hastings acceptance criteria, and stores acceptable DFN realizations in an ensemble. Finally, this obtained ensemble is used to visualize the potential occurrence of fractures in a probability map, indicating possible fracture locations and lengths. We test this methodology to reconstruct simple synthetic and more complex outcrop-based fracture networks and successfully image the significant fractures in the domain. KW - fracture network KW - Bayesian inversion KW - stress variability KW - rock mechanics Y1 - 2018 U6 - https://doi.org/10.1029/2018JB016438 SN - 2169-9313 SN - 2169-9356 VL - 123 IS - 11 SP - 9324 EP - 9340 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Chang, Der-Chen A1 - Mahmoudi, Mahdi Hedayat A1 - Schulze, Bert-Wolfgang T1 - Volterra operators in the edge-calculus JF - Analysis and Mathematical Physics N2 - We study the Volterra property of a class of anisotropic pseudo-differential operators on R x B for a manifold B with edge Y and time-variable t. This exposition belongs to a program for studying parabolicity in such a situation. In the present consideration we establish non-smoothing elements in a subalgebra with anisotropic operator-valued symbols of Mellin type with holomorphic symbols in the complex Mellin covariable from the cone theory, where the covariable t of t extends to symbolswith respect to t to the lower complex v half-plane. The resulting space ofVolterra operators enlarges an approach of Buchholz (Parabolische Pseudodifferentialoperatoren mit operatorwertigen Symbolen. Ph. D. thesis, Universitat Potsdam, 1996) by necessary elements to a new operator algebra containing Volterra parametrices under an appropriate condition of anisotropic ellipticity. Our approach avoids some difficulty in choosing Volterra quantizations in the edge case by generalizing specific achievements from the isotropic edge-calculus, obtained by Seiler (Pseudodifferential calculus on manifolds with non-compact edges, Ph. D. thesis, University of Potsdam, 1997), see also Gil et al. (in: Demuth et al (eds) Mathematical research, vol 100. Akademic Verlag, Berlin, pp 113-137, 1997; Osaka J Math 37: 221-260, 2000). KW - Volterra operator KW - Anisotropic pseudo-differential operators KW - Edge calculus KW - Operator-valued symbols of Mellin type Y1 - 2018 U6 - https://doi.org/10.1007/s13324-018-0238-4 SN - 1664-2368 SN - 1664-235X VL - 8 IS - 4 SP - 551 EP - 570 PB - Springer CY - Basel ER - TY - JOUR A1 - Siddiqui, Tarique Adnan A1 - Maute, Astrid A1 - Pedatella, Nick A1 - Yamazaki, Yosuke A1 - Lühr, Hermann A1 - Stolle, Claudia T1 - On the variability of the semidiurnal solar and lunar tides of the equatorial electrojet during sudden stratospheric warmings JF - Annales geophysicae N2 - The variabilities of the semidiurnal solar and lunar tides of the equatorial electrojet (EEJ) are investigated during the 2003, 2006, 2009 and 2013 major sudden stratospheric warming (SSW) events in this study. For this purpose, ground-magnetometer recordings at the equatorial observatories in Huancayo and Fuquene are utilized. Results show a major enhancement in the amplitude of the EEJ semidiurnal lunar tide in each of the four warming events. The EEJ semidiurnal solar tidal amplitude shows an amplification prior to the onset of warmings, a reduction during the deceleration of the zonal mean zonal wind at 60 degrees N and 10 hPa, and a second enhancement a few days after the peak reversal of the zonal mean zonal wind during all four SSWs. Results also reveal that the amplitude of the EEJ semidiurnal lunar tide becomes comparable or even greater than the amplitude of the EEJ semidiurnal solar tide during all these warming events. The present study also compares the EEJ semidiurnal solar and lunar tidal changes with the variability of the migrating semidiurnal solar (SW2) and lunar (M2) tides in neutral temperature and zonal wind obtained from numerical simulations at E-region heights. A better agreement between the enhancements of the EEJ semidiurnal lunar tide and the M2 tide is found in comparison with the enhancements of the EEJ semidiurnal solar tide and the SW2 tide in both the neutral temperature and zonal wind at the E-region altitudes. Y1 - 2018 U6 - https://doi.org/10.5194/angeo-36-1545-2018 SN - 0992-7689 SN - 1432-0576 VL - 36 IS - 6 SP - 1545 EP - 1562 PB - Copernicus CY - Göttingen ER - TY - JOUR A1 - Gerlach, Moritz Reinhardt A1 - Glück, Jochen T1 - Lower bounds and the asymptotic behaviour of positive operator semigroups JF - Ergodic theory and dynamical systems N2 - If (T-t) is a semigroup of Markov operators on an L-1-space that admits a nontrivial lower bound, then a well-known theorem of Lasota and Yorke asserts that the semigroup is strongly convergent as t -> infinity. In this article we generalize and improve this result in several respects. First, we give a new and very simple proof for the fact that the same conclusion also holds if the semigroup is merely assumed to be bounded instead of Markov. As a main result, we then prove a version of this theorem for semigroups which only admit certain individual lower bounds. Moreover, we generalize a theorem of Ding on semigroups of Frobenius-Perron operators. We also demonstrate how our results can be adapted to the setting of general Banach lattices and we give some counterexamples to show optimality of our results. Our methods combine some rather concrete estimates and approximation arguments with abstract functional analytical tools. One of these tools is a theorem which relates the convergence of a time-continuous operator semigroup to the convergence of embedded discrete semigroups. Y1 - 2017 U6 - https://doi.org/10.1017/etds.2017.9 SN - 0143-3857 SN - 1469-4417 VL - 38 SP - 3012 EP - 3041 PB - Cambridge Univ. Press CY - New York ER - TY - JOUR A1 - Flad, Heinz-Jürgen A1 - Flad-Harutyunyan, Gohar A1 - Schulze, Bert-Wolfgang T1 - Ellipticity of the quantum mechanical Hamiltonians BT - corner singularity of the helium atom JF - Journal of pseudo-differential operators and applications N2 - In paper (Flad and Harutyunyan in Discrete Contin Dyn Syst 420-429, 2011) is shown that the Hamiltonian of the helium atom in the Born-Oppenheimer approximation, in the case if two particles coincide, is an edge-degenerate operator, which is elliptic in the corresponding edge calculus. The aim of this paper is an analogous investigation in the case if all three particles coincide. More precisely, we show that the Hamiltonian in the mentioned case is a corner-degenerate operator, which is elliptic as an operator in the corner analysis. Y1 - 2018 U6 - https://doi.org/10.1007/s11868-017-0201-4 SN - 1662-9981 SN - 1662-999X VL - 9 IS - 3 SP - 451 EP - 467 PB - Springer CY - Basel ER - TY - JOUR A1 - Klein, Markus A1 - Rosenberger, Elke T1 - The tunneling effect for a class of difference operators JF - Reviews in Mathematical Physics N2 - We analyze a general class of self-adjoint difference operators H-epsilon = T-epsilon + V-epsilon on l(2)((epsilon Z)(d)), where V-epsilon is a multi-well potential and v(epsilon) is a small parameter. We give a coherent review of our results on tunneling up to new sharp results on the level of complete asymptotic expansions (see [30-35]). Our emphasis is on general ideas and strategy, possibly of interest for a broader range of readers, and less on detailed mathematical proofs. The wells are decoupled by introducing certain Dirichlet operators on regions containing only one potential well. Then the eigenvalue problem for the Hamiltonian H-epsilon is treated as a small perturbation of these comparison problems. After constructing a Finslerian distance d induced by H-epsilon, we show that Dirichlet eigenfunctions decay exponentially with a rate controlled by this distance to the well. It follows with microlocal techniques that the first n eigenvalues of H-epsilon converge to the first n eigenvalues of the direct sum of harmonic oscillators on R-d located at several wells. In a neighborhood of one well, we construct formal asymptotic expansions of WKB-type for eigenfunctions associated with the low-lying eigenvalues of H-epsilon. These are obtained from eigenfunctions or quasimodes for the operator H-epsilon acting on L-2(R-d), via restriction to the lattice (epsilon Z)(d). Tunneling is then described by a certain interaction matrix, similar to the analysis for the Schrodinger operator (see [22]), the remainder is exponentially small and roughly quadratic compared with the interaction matrix. We give weighted l(2)-estimates for the difference of eigenfunctions of Dirichlet-operators in neighborhoods of the different wells and the associated WKB-expansions at the wells. In the last step, we derive full asymptotic expansions for interactions between two "wells" (minima) of the potential energy, in particular for the discrete tunneling effect. Here we essentially use analysis on phase space, complexified in the momentum variable. These results are as sharp as the classical results for the Schrodinger operator in [22]. KW - Semiclassical difference operator KW - tunneling KW - interaction matrix KW - asymptotic expansion KW - multi-well potential KW - Finsler distance KW - Agmon estimates Y1 - 2018 U6 - https://doi.org/10.1142/S0129055X18300029 SN - 0129-055X SN - 1793-6659 VL - 30 IS - 4 PB - World Scientific CY - Singapore ER - TY - GEN A1 - Zöller, Gert A1 - Holschneider, Matthias T1 - Reply to “Comment on ‘The Maximum Possible and the Maximum Expected Earthquake Magnitude for Production‐Induced Earthquakes at the Gas Field in Groningen, The Netherlands’ by Gert Zöller and Matthias Holschneider” by Mathias Raschke T2 - Bulletin of the Seismological Society of America Y1 - 2018 U6 - https://doi.org/10.1785/0120170131 SN - 0037-1106 SN - 1943-3573 VL - 108 IS - 2 SP - 1029 EP - 1030 PB - Seismological Society of America CY - Albany ER - TY - JOUR A1 - Gerlach, Moritz Reinhardt T1 - Convergence of dynamics and the Perron-Frobenius operator JF - Israel Journal of Mathematics N2 - We complete the picture how the asymptotic behavior of a dynamical system is reflected by properties of the associated Perron-Frobenius operator. Our main result states that strong convergence of the powers of the Perron-Frobenius operator is equivalent to setwise convergence of the underlying dynamic in the measure algebra. This situation is furthermore characterized by uniform mixing-like properties of the system. Y1 - 2018 U6 - https://doi.org/10.1007/s11856-018-1671-7 SN - 0021-2172 SN - 1565-8511 VL - 225 IS - 1 SP - 451 EP - 463 PB - Hebrew univ magnes press CY - Jerusalem ER - TY - JOUR A1 - Liu, Shiping A1 - Münch, Florentin A1 - Peyerimhoff, Norbert T1 - Bakry-Emery curvature and diameter bounds on graphs JF - Calculus of variations and partial differential equations N2 - We prove finiteness and diameter bounds for graphs having a positive Ricci-curvature bound in the Bakry–Émery sense. Our first result using only curvature and maximal vertex degree is sharp in the case of hypercubes. The second result depends on an additional dimension bound, but is independent of the vertex degree. In particular, the second result is the first Bonnet–Myers type theorem for unbounded graph Laplacians. Moreover, our results improve diameter bounds from Fathi and Shu (Bernoulli 24(1):672–698, 2018) and Horn et al. (J für die reine und angewandte Mathematik (Crelle’s J), 2017, https://doi.org/10.1515/crelle-2017-0038) and solve a conjecture from Cushing et al. (Bakry–Émery curvature functions of graphs, 2016). Y1 - 2018 U6 - https://doi.org/10.1007/s00526-018-1334-x SN - 0944-2669 SN - 1432-0835 VL - 57 IS - 2 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Keller, Matthias A1 - Schwarz, Michael T1 - The Kazdan-Warner equation on canonically compactifiable graphs JF - Calculus of variations and partial differential equations N2 - We study the Kazdan-Warner equation on canonically compactifiable graphs. These graphs are distinguished as analytic properties of Laplacians on these graphs carry a strong resemblance to Laplacians on open pre-compact manifolds. Y1 - 2018 U6 - https://doi.org/10.1007/s00526-018-1329-7 SN - 0944-2669 SN - 1432-0835 VL - 57 IS - 2 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - de Wiljes, Jana A1 - Reich, Sebastian A1 - Stannat, Wilhelm T1 - Long-Time stability and accuracy of the ensemble Kalman-Bucy Filter for fully observed processes and small measurement noise JF - SIAM Journal on Applied Dynamical Systems N2 - The ensemble Kalman filter has become a popular data assimilation technique in the geosciences. However, little is known theoretically about its long term stability and accuracy. In this paper, we investigate the behavior of an ensemble Kalman-Bucy filter applied to continuous-time filtering problems. We derive mean field limiting equations as the ensemble size goes to infinity as well as uniform-in-time accuracy and stability results for finite ensemble sizes. The later results require that the process is fully observed and that the measurement noise is small. We also demonstrate that our ensemble Kalman-Bucy filter is consistent with the classic Kalman-Bucy filter for linear systems and Gaussian processes. We finally verify our theoretical findings for the Lorenz-63 system. KW - data assimilation KW - Kalman Bucy filter KW - ensemble Kalman filter KW - stability KW - accuracy KW - asymptotic behavior Y1 - 2018 U6 - https://doi.org/10.1137/17M1119056 SN - 1536-0040 VL - 17 IS - 2 SP - 1152 EP - 1181 PB - Society for Industrial and Applied Mathematics CY - Philadelphia ER - TY - JOUR A1 - Vidal-Garcia, Marta A1 - Bandara, Lashi A1 - Keogh, J. Scott T1 - ShapeRotator BT - an R tool for standardized rigid rotations of articulated three-dimensional structures with application for geometric morphometrics JF - Ecology and evolution N2 - The quantification of complex morphological patterns typically involves comprehensive shape and size analyses, usually obtained by gathering morphological data from all the structures that capture the phenotypic diversity of an organism or object. Articulated structures are a critical component of overall phenotypic diversity, but data gathered from these structures are difficult to incorporate into modern analyses because of the complexities associated with jointly quantifying 3D shape in multiple structures. While there are existing methods for analyzing shape variation in articulated structures in two-dimensional (2D) space, these methods do not work in 3D, a rapidly growing area of capability and research. Here, we describe a simple geometric rigid rotation approach that removes the effect of random translation and rotation, enabling the morphological analysis of 3D articulated structures. Our method is based on Cartesian coordinates in 3D space, so it can be applied to any morphometric problem that also uses 3D coordinates (e.g., spherical harmonics). We demonstrate the method by applying it to a landmark-based dataset for analyzing shape variation using geometric morphometrics. We have developed an R tool (ShapeRotator) so that the method can be easily implemented in the commonly used R package geomorph and MorphoJ software. This method will be a valuable tool for 3D morphological analyses in articulated structures by allowing an exhaustive examination of shape and size diversity. KW - articulation KW - morphology KW - motion correction KW - multi-modular morphology Y1 - 2018 U6 - https://doi.org/10.1002/ece3.4018 SN - 2045-7758 VL - 8 IS - 9 SP - 4669 EP - 4675 PB - Wiley CY - Hoboken ER - TY - JOUR A1 - Zöller, Gert T1 - A statistical model for earthquake recurrence based on the assimilation of paleoseismicity, historic seismicity, and instrumental seismicity JF - Journal of geophysical research : Solid earth N2 - Paleoearthquakes and historic earthquakes are the most important source of information for the estimation of long-term earthquake recurrence intervals in fault zones, because corresponding sequences cover more than one seismic cycle. However, these events are often rare, dating uncertainties are enormous, and missing or misinterpreted events lead to additional problems. In the present study, I assume that the time to the next major earthquake depends on the rate of small and intermediate events between the large ones in terms of a clock change model. Mathematically, this leads to a Brownian passage time distribution for recurrence intervals. I take advantage of an earlier finding that under certain assumptions the aperiodicity of this distribution can be related to the Gutenberg-Richter b value, which can be estimated easily from instrumental seismicity in the region under consideration. In this way, both parameters of the Brownian passage time distribution can be attributed with accessible seismological quantities. This allows to reduce the uncertainties in the estimation of the mean recurrence interval, especially for short paleoearthquake sequences and high dating errors. Using a Bayesian framework for parameter estimation results in a statistical model for earthquake recurrence intervals that assimilates in a simple way paleoearthquake sequences and instrumental data. I present illustrative case studies from Southern California and compare the method with the commonly used approach of exponentially distributed recurrence times based on a stationary Poisson process. KW - statistical seismology KW - paleoearthquakes KW - stochastic models KW - seismic hazard Y1 - 2018 U6 - https://doi.org/10.1029/2017JB015099 SN - 2169-9313 SN - 2169-9356 VL - 123 IS - 6 SP - 4906 EP - 4921 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Lonnemann, Jan A1 - Hasselhorn, Marcus T1 - Frühe mathematische Bildung T1 - Early Mathematics Education BT - Aktuelle Forschungstrends und Perspektiven BT - Current Research Trends and Perspectives JF - Frühe Bildung N2 - Im vorliegenden Beitrag werden aktuelle Forschungstrends im Bereich der frühen mathematischen Bildung im Kontext jüngst formulierter Zieldimensionen für die frühe mathematische Bildung (siehe Benz et al., 2017) dargestellt. Es wird auf spielbasierte Fördermaßnahmen, Kompetenzen im Bereich „Raum und Form“, den Einfluss sprachlicher Parameter auf die Entwicklung mathematischer Kompetenzen sowie auf mathematikbezogene Kompetenzen frühpädagogischer Fachkräfte eingegangen. Darüber hinaus werden die Ergebnisse einer aktuellen Feldstudie zur Förderung früher mathematischer Kompetenzen (siehe Dillon, Kannan, Dean, Spelke & Duflo, 2017) vorgestellt. Abschließend wird die Entwicklung und Implementierung anschlussfähiger Bildungskonzepte als eine der zentralen Herausforderungen zukünftiger Forschungs- und Bildungsbemühungen diskutiert N2 - Current research trends in the field of early mathematical education are presented in the context of recently formulated target dimensions of early mathematical education (see Benz et al., 2017). Game-based approaches, competencies in the field of “space and form”, the influence of language skills on the development of mathematical competencies, as well as mathematics-related competencies of early childhood educators are discussed. In addition, the results of a recent field study on a preschool intervention intended to enhance children's early mathematical skills (see Dillon, Kannan, Dean, Spelke, & Duflo, 2017) are presented. Finally, we discuss the development and implementation of aligned educational concepts as one of the central challenges of future research and educational activities. KW - early mathematical education KW - target dimensions KW - conditions of success KW - alignment Y1 - 2018 U6 - https://doi.org/10.1026/2191-9186/a000379 SN - 2191-9186 SN - 2191-9194 VL - 7 IS - 3 SP - 129 EP - 134 PB - Hogrefe CY - Göttingen ER - TY - JOUR A1 - Carpentier, Alexandra A1 - Kim, Arlene K. H. T1 - An iterative hard thresholding estimator for low rank matrix recovery with explicit limiting distribution JF - Statistica Sinica N2 - We consider the problem of low rank matrix recovery in a stochastically noisy high-dimensional setting. We propose a new estimator for the low rank matrix, based on the iterative hard thresholding method, that is computationally efficient and simple. We prove that our estimator is optimal in terms of the Frobenius risk and in terms of the entry-wise risk uniformly over any change of orthonormal basis, allowing us to provide the limiting distribution of the estimator. When the design is Gaussian, we prove that the entry-wise bias of the limiting distribution of the estimator is small, which is of interest for constructing tests and confidence sets for low-dimensional subsets of entries of the low rank matrix. KW - High dimensional statistical inference KW - inverse problem KW - limiting distribution KW - low rank matrix recovery KW - numerical methods KW - uncertainty quantification Y1 - 2018 U6 - https://doi.org/10.5705/ss.202016.0103 SN - 1017-0405 SN - 1996-8507 VL - 28 IS - 3 SP - 1371 EP - 1393 PB - Statistica Sinica, Institute of Statistical Science, Academia Sinica CY - Taipei ER - TY - JOUR A1 - Blanchard, Gilles A1 - Mücke, Nicole T1 - Optimal rates for regularization of statistical inverse learning problems JF - Foundations of Computational Mathematics N2 - We consider a statistical inverse learning (also called inverse regression) problem, where we observe the image of a function f through a linear operator A at i.i.d. random design points X-i , superposed with an additive noise. The distribution of the design points is unknown and can be very general. We analyze simultaneously the direct (estimation of Af) and the inverse (estimation of f) learning problems. In this general framework, we obtain strong and weak minimax optimal rates of convergence (as the number of observations n grows large) for a large class of spectral regularization methods over regularity classes defined through appropriate source conditions. This improves on or completes previous results obtained in related settings. The optimality of the obtained rates is shown not only in the exponent in n but also in the explicit dependency of the constant factor in the variance of the noise and the radius of the source condition set. KW - Reproducing kernel Hilbert space KW - Spectral regularization KW - Inverse problem KW - Statistical learning KW - Minimax convergence rates Y1 - 2018 U6 - https://doi.org/10.1007/s10208-017-9359-7 SN - 1615-3375 SN - 1615-3383 VL - 18 IS - 4 SP - 971 EP - 1013 PB - Springer CY - New York ER - TY - JOUR A1 - Omori, Toshihiro A1 - Winter, Katja A1 - Shinohara, Kyosuke A1 - Hamada, Hiroshi A1 - Ishikawa, Takuji T1 - Simulation of the nodal flow of mutant embryos with a small number of cilia BT - comparison of mechanosensing and vesicle transport hypotheses JF - Royal Society Open Science N2 - Left-right (L-R) asymmetry in the body plan is determined by nodal flow in vertebrate embryos. Shinohara et al. (Shinohara K et al. 2012 Nat. Commun. 3, 622 (doi:10.1038/ncomms1624)) used Dpcd and Rfx3 mutant mouse embryos and showed that only a few cilia were sufficient to achieve L-R asymmetry. However, the mechanism underlying the breaking of symmetry by such weak ciliary flow is unclear. Flow-mediated signals associated with the L-R asymmetric organogenesis have not been clarified, and two different hypotheses-vesicle transport and mechanosensing-are now debated in the research field of developmental biology. In this study, we developed a computational model of the node system reported by Shinohara et al. and examined the feasibilities of the two hypotheses with a small number of cilia. With the small number of rotating cilia, flow was induced locally and global strong flow was not observed in the node. Particles were then effectively transported only when they were close to the cilia, and particle transport was strongly dependent on the ciliary positions. Although the maximum wall shear rate was also influenced by ciliary position, the mean wall shear rate at the perinodal wall increased monotonically with the number of cilia. We also investigated the membrane tension of immotile cilia, which is relevant to the regulation of mechanotransduction. The results indicated that tension of about 0.1 mu Nm(-1) was exerted at the base even when the fluid shear rate was applied at about 0.1 s(-1). The area of high tension was also localized at the upstream side, and negative tension appeared at the downstream side. Such localization may be useful to sense the flow direction at the periphery, as time-averaged anticlockwise circulation was induced in the node by rotation of a few cilia. Our numerical results support the mechanosensing hypothesis, and we expect that our study will stimulate further experimental investigations of mechanotransduction in the near future. KW - nodal flow KW - left-right asymmetry KW - boundary element method KW - fluid-structure interaction Y1 - 2018 U6 - https://doi.org/10.1098/rsos.180601 SN - 2054-5703 VL - 5 IS - 8 PB - Royal Society CY - London ER -