@article{AcevedoDeWiljesReich2017, author = {Acevedo, Walter and De Wiljes, Jana and Reich, Sebastian}, title = {Second-order accurate ensemble transform particle filters}, series = {SIAM journal on scientific computing}, volume = {39}, journal = {SIAM journal on scientific computing}, number = {5}, publisher = {Society for Industrial and Applied Mathematics}, address = {Philadelphia}, issn = {1064-8275}, doi = {10.1137/16M1095184}, pages = {A1834 -- A1850}, year = {2017}, abstract = {Particle filters (also called sequential Monte Carlo methods) are widely used for state and parameter estimation problems in the context of nonlinear evolution equations. The recently proposed ensemble transform particle filter (ETPF) [S. Reich, SIAM T. Sci. Comput., 35, (2013), pp. A2013-A2014[ replaces the resampling step of a standard particle filter by a linear transformation which allows for a hybridization of particle filters with ensemble Kalman filters and renders the resulting hybrid filters applicable to spatially extended systems. However, the linear transformation step is computationally expensive and leads to an underestimation of the ensemble spread for small and moderate ensemble sizes. Here we address both of these shortcomings by developing second order accurate extensions of the ETPF. These extensions allow one in particular to replace the exact solution of a linear transport problem by its Sinkhorn approximation. It is also demonstrated that the nonlinear ensemble transform filter arises as a special case of our general framework. We illustrate the performance of the second-order accurate filters for the chaotic Lorenz-63 and Lorenz-96 models and a dynamic scene-viewing model. The numerical results for the Lorenz-63 and Lorenz-96 models demonstrate that significant accuracy improvements can be achieved in comparison to a standard ensemble Kalman filter and the ETPF for small to moderate ensemble sizes. The numerical results for the scene-viewing model reveal, on the other hand, that second-order corrections can lead to statistically inconsistent samples from the posterior parameter distribution.}, language = {en} } @article{AcevedoFallahReichetal.2017, author = {Acevedo, Walter and Fallah, Bijan and Reich, Sebastian and Cubasch, Ulrich}, title = {Assimilation of pseudo-tree-ring-width observations into an atmospheric general circulation model}, series = {Climate of the past : an interactive open access journal of the European Geosciences Union}, volume = {13}, journal = {Climate of the past : an interactive open access journal of the European Geosciences Union}, publisher = {Copernicus}, address = {G{\"o}ttingen}, issn = {1814-9324}, doi = {10.5194/cp-13-545-2017}, pages = {545 -- 557}, year = {2017}, abstract = {Paleoclimate data assimilation (DA) is a promising technique to systematically combine the information from climate model simulations and proxy records. Here, we investigate the assimilation of tree-ring-width (TRW) chronologies into an atmospheric global climate model using ensemble Kalman filter (EnKF) techniques and a process-based tree-growth forward model as an observation operator. Our results, within a perfect-model experiment setting, indicate that the "online DA" approach did not outperform the "off-line" one, despite its considerable additional implementation complexity. On the other hand, it was observed that the nonlinear response of tree growth to surface temperature and soil moisture does deteriorate the operation of the time-averaged EnKF methodology. Moreover, for the first time we show that this skill loss appears significantly sensitive to the structure of the growth rate function, used to represent the principle of limiting factors (PLF) within the forward model. In general, our experiments showed that the error reduction achieved by assimilating pseudo-TRW chronologies is modulated by the magnitude of the yearly internal variability in themodel. This result might help the dendrochronology community to optimize their sampling efforts.}, language = {en} } @article{AcevedoReichCubasch2016, author = {Acevedo, Walter and Reich, Sebastian and Cubasch, Ulrich}, title = {Towards the assimilation of tree-ring-width records using ensemble Kalman filtering techniques}, series = {Climate dynamics : observational, theoretical and computational research on the climate system}, volume = {46}, journal = {Climate dynamics : observational, theoretical and computational research on the climate system}, publisher = {Springer}, address = {New York}, issn = {0930-7575}, doi = {10.1007/s00382-015-2683-1}, pages = {1909 -- 1920}, year = {2016}, abstract = {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.}, language = {en} } @article{AfshariMoeinSomogyvariValleyetal.2018, author = {Afshari Moein, Mohammad J. and Somogyv{\´a}ri, M{\´a}rk and Valley, Beno{\^i}t and Jalali, Mohammadreza and L{\"o}w, Simon and Bayer, Peter}, title = {Fracture network characterization using stress-based tomography}, series = {Journal of geophysical research : JGR}, volume = {123}, journal = {Journal of geophysical research : JGR}, number = {11}, publisher = {American Geophysical Union}, address = {Washington}, issn = {2169-9313}, doi = {10.1029/2018JB016438}, pages = {9324 -- 9340}, year = {2018}, abstract = {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.}, language = {en} } @article{AizingerKornGiorgettaetal.2015, author = {Aizinger, Vadym and Korn, Peter and Giorgetta, Marco and Reich, Sebastian}, title = {Large-scale turbulence modelling via alpha-regularisation for atmospheric simulations}, series = {Journal of turbulence}, volume = {16}, journal = {Journal of turbulence}, number = {4}, publisher = {Routledge, Taylor \& Francis Group}, address = {Abingdon}, issn = {1468-5248}, doi = {10.1080/14685248.2014.991443}, pages = {367 -- 391}, year = {2015}, abstract = {We study the possibility of obtaining a computational turbulence model by means of non-dissipative regularisation of the compressible atmospheric equations for climate-type applications. We use an -regularisation (Lagrangian averaging) of the atmospheric equations. For the hydrostatic and compressible atmospheric equations discretised using a finite volume method on unstructured grids, deterministic and non-deterministic numerical experiments are conducted to compare the individual solutions and the statistics of the regularised equations to those of the original model. The impact of the regularisation parameter is investigated. Our results confirm the principal compatibility of -regularisation with atmospheric dynamics and encourage further investigations within atmospheric model including complex physical parametrisations.}, language = {en} } @article{AkhmatskayaBouRabeeReich2009, author = {Akhmatskaya, Elena and Bou-Rabee, Nawaf and Reich, Sebastian}, title = {A comparison of generalized hybrid Monte Carlo methods with and without momentum flip}, issn = {0021-9991}, doi = {10.1016/j.jcp.2008.12.014}, year = {2009}, abstract = {The generalized hybrid Monte Carlo (GHMC) method combines Metropolis corrected constant energy simulations with a partial random refreshment step in the particle momenta. The standard detailed balance condition requires that momenta are negated upon rejection of a molecular dynamics proposal step. The implication is a trajectory reversal upon rejection, which is undesirable when interpreting GHMC as thermostated molecular dynamics. We show that a modified detailed balance condition can be used to implement GHMC without momentum flips. The same modification can be applied to the generalized shadow hybrid Monte Carlo (GSHMC) method. Numerical results indicate that GHMC/GSHMC implementations with momentum flip display a favorable behavior in terms of sampling efficiency, i.e., the traditional GHMC/GSHMC implementations with momentum flip got the advantage of a higher acceptance rate and faster decorrelation of Monte Carlo samples. The difference is more pronounced for GHMC. We also numerically investigate the behavior of the GHMC method as a Langevin-type thermostat. We find that the GHMC method without momentum flip interferes less with the underlying stochastic molecular dynamics in terms of autocorrelation functions and it to be preferred over the GHMC method with momentum flip. The same finding applies to GSHMC.}, language = {en} } @article{AkhmatskayaBouRabeeReich2009, author = {Akhmatskaya, Elena and Bou-Rabee, Nawaf and Reich, Sebastian}, title = {Erratum to "A comparison of generalized hybrid Monte Carlo methods with and without momentum flip" [J. Comput. Phys. 228 (2009), S. 2256 - 2265]}, issn = {0021-9991}, doi = {10.1016/j.jcp.2009.06.039}, year = {2009}, abstract = {The generalized hybrid Monte Carlo (GHMC) method combines Metropolis corrected constant energy simulations with a partial random refreshment step in the particle momenta. The standard detailed balance condition requires that momenta are negated upon rejection of a molecular dynamics proposal step. The implication is a trajectory reversal upon rejection, which is undesirable when interpreting GHMC as thermostated molecular dynamics. We show that a modified detailed balance condition can be used to implement GHMC without momentum flips. The same modification can be applied to the generalized shadow hybrid Monte Carlo (GSHMC) method. Numerical results indicate that GHMC/GSHMC implementations with momentum flip display a favorable behavior in terms of sampling efficiency, i.e., the traditional GHMC/GSHMC implementations with momentum flip got the advantage of a higher acceptance rate and faster decorrelation of Monte Carlo samples. The difference is more pronounced for GHMC. We also numerically investigate the behavior of the GHMC method as a Langevin-type thermostat. We find that the GHMC method without momentum flip interferes less with the underlying stochastic molecular dynamics in terms of autocorrelation functions and it to be preferred over the GHMC method with momentum flip. The same finding applies to GSHMC.}, language = {en} } @article{AlSaedyTarchanov2020, author = {Al-Saedy, Ammar Jaffar Muhesin and Tarchanov, Nikolaj Nikolaevič}, title = {A degree theory for Lagrangian boundary value problems}, series = {Žurnal Sibirskogo Federalʹnogo Universiteta = Journal of Siberian Federal University; mathematics \& physics}, volume = {13}, journal = {Žurnal Sibirskogo Federalʹnogo Universiteta = Journal of Siberian Federal University; mathematics \& physics}, number = {1}, publisher = {Sibirskij Federalʹnyj Universitet}, address = {Krasnojarsk}, issn = {1997-1397}, doi = {10.17516/1997-1397-2020-13-1-5-25}, pages = {5 -- 25}, year = {2020}, abstract = {We study those nonlinear partial differential equations which appear as Euler-Lagrange equations of variational problems. On defining weak boundary values of solutions to such equations we initiate the theory of Lagrangian boundary value problems in spaces of appropriate smoothness. We also analyse if the concept of mapping degree of current importance applies to Lagrangian problems.}, language = {en} } @article{AlbeverioBrascheNeidhardt1998, author = {Albeverio, Sergio and Brasche, Johannes F. and Neidhardt, Hagen}, title = {On inverse spectral theory: mixed types of spectra.}, year = {1998}, language = {en} } @article{AlsaedyTarkhanov2014, author = {Alsaedy, Ammar and Tarkhanov, Nikolai Nikolaevich}, title = {Normally solvable nonlinear boundary value problems}, series = {Nonlinear analysis : theory, methods \& applications ; an international multidisciplinary journal}, volume = {95}, journal = {Nonlinear analysis : theory, methods \& applications ; an international multidisciplinary journal}, publisher = {Elsevier}, address = {Oxford}, issn = {0362-546X}, doi = {10.1016/j.na.2013.09.024}, pages = {468 -- 482}, year = {2014}, abstract = {We investigate nonlinear problems which appear as Euler-Lagrange equations for a variational problem. They include in particular variational boundary value problems for nonlinear elliptic equations studied by F. Browder in the 1960s. We establish a solvability criterion of such problems and elaborate an efficient orthogonal projection method for constructing approximate solutions.}, language = {en} } @article{AltundagBoeckmannTaseli2015, author = {Altundag, H{\"u}seyin and B{\"o}ckmann, Christine and Taseli, Hasan}, title = {Inverse Sturm-Liouville problems with pseudospectral methods}, series = {International journal of computer mathematics}, volume = {92}, journal = {International journal of computer mathematics}, number = {7}, publisher = {Routledge, Taylor \& Francis Group}, address = {Abingdon}, issn = {0020-7160}, doi = {10.1080/00207160.2014.939646}, pages = {1373 -- 1384}, year = {2015}, abstract = {In this paper a technique to obtain a first approximation for singular inverse Sturm-Liouville problems with a symmetrical potential is introduced. The singularity, as a result of unbounded domain (-infinity, infinity), is treated by considering numerically the asymptotic limit of the associated problem on a finite interval (-L, L). In spite of this treatment, the problem has still an ill-conditioned structure unlike the classical regular ones and needs regularization techniques. Direct computation of eigenvalues in iterative solution procedure is made by means of pseudospectral methods. A fairly detailed description of the numerical algorithm and its applications to specific examples are presented to illustrate the accuracy and convergence behaviour of the proposed approach.}, language = {en} } @article{AmendolaBattagliaMayerCapozzielloetal.1992, author = {Amendola, Luca and Battaglia Mayer, Alexandra and Capozziello, Salvatore and Gottl{\"o}ber, Stefan and M{\"u}ller, Volker and Occhionero, Franco and Schmidt, Hans-J{\"u}rgen}, title = {Generalized sixth-order gravity and inflation}, series = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik}, volume = {1992, 04}, journal = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik}, publisher = {Univ.}, address = {Potsdam}, pages = {7 S.}, year = {1992}, language = {en} } @article{AmezcuaIdeKalnayetal.2014, author = {Amezcua, Javier and Ide, Kayo and Kalnay, Eugenia and Reich, Sebastian}, title = {Ensemble transform Kalman-Bucy filters}, series = {Quarterly journal of the Royal Meteorological Society}, volume = {140}, journal = {Quarterly journal of the Royal Meteorological Society}, number = {680}, publisher = {Wiley-Blackwell}, address = {Hoboken}, issn = {0035-9009}, doi = {10.1002/qj.2186}, pages = {995 -- 1004}, year = {2014}, abstract = {Two recent works have adapted the Kalman-Bucy filter into an ensemble setting. In the first formulation, the ensemble of perturbations is updated by the solution of an ordinary differential equation (ODE) in pseudo-time, while the mean is updated as in the standard Kalman filter. In the second formulation, the full ensemble is updated in the analysis step as the solution of single set of ODEs in pseudo-time. Neither requires matrix inversions except for the frequently diagonal observation error covariance. We analyse the behaviour of the ODEs involved in these formulations. We demonstrate that they stiffen for large magnitudes of the ratio of background error to observational error variance, and that using the integration scheme proposed in both formulations can lead to failure. A numerical integration scheme that is both stable and is not computationally expensive is proposed. We develop transform-based alternatives for these Bucy-type approaches so that the integrations are computed in ensemble space where the variables are weights (of dimension equal to the ensemble size) rather than model variables. Finally, the performance of our ensemble transform Kalman-Bucy implementations is evaluated using three models: the 3-variable Lorenz 1963 model, the 40-variable Lorenz 1996 model, and a medium complexity atmospheric general circulation model known as SPEEDY. The results from all three models are encouraging and warrant further exploration of these assimilation techniques.}, language = {en} } @article{AnderssonMetzger2010, author = {Andersson, Lars and Metzger, Jan}, title = {Curvature estimates for stable marginally trapped surfaces}, issn = {0022-040X}, year = {2010}, abstract = {We derive local integral and sup-estimates for the curvature of stable marginally outer trapped surfaces in a sliced space-time. The estimates bound the shear of a marginally outer trapped surface in terms of the intrinsic and extrinsic curvature of a slice containing the surface. These estimates are well adapted to situations of physical interest, such as dynamical horizons.}, language = {en} } @article{AntoniniAzzaliSkandalis2016, author = {Antonini, Paolo and Azzali, Sara and Skandalis, Georges}, title = {Bivariant K-theory with R/Z-coefficients and rho classes of unitary representations}, series = {Journal of functional analysis}, volume = {270}, journal = {Journal of functional analysis}, publisher = {Elsevier}, address = {San Diego}, issn = {0022-1236}, doi = {10.1016/j.jfa.2015.06.017}, pages = {447 -- 481}, year = {2016}, abstract = {We construct equivariant KK-theory with coefficients in and R/Z as suitable inductive limits over II1-factors. We show that the Kasparov product, together with its usual functorial properties, extends to KK-theory with real coefficients. Let Gamma be a group. We define a Gamma-algebra A to be K-theoretically free and proper (KFP) if the group trace tr of Gamma acts as the unit element in KKR Gamma (A, A). We show that free and proper Gamma-algebras (in the sense of Kasparov) have the (KFP) property. Moreover, if Gamma is torsion free and satisfies the KK Gamma-form of the Baum-Connes conjecture, then every Gamma-algebra satisfies (KFP). If alpha : Gamma -> U-n is a unitary representation and A satisfies property (KFP), we construct in a canonical way a rho class rho(A)(alpha) is an element of KKR/Z1,Gamma (A A) This construction generalizes the Atiyah-Patodi-Singer K-theory class with R/Z-coefficients associated to alpha. (C) 2015 Elsevier Inc. All rights reserved.}, language = {en} } @article{AntonioukKiselevTarkhanov2015, author = {Antoniouk, Alexandra Viktorivna and Kiselev, Oleg M. and Tarkhanov, Nikolai Nikolaevich}, title = {Asymptotic Solutions of the Dirichlet Problem for the Heat Equation at a Characteristic Point}, series = {Ukrainian mathematical journal}, volume = {66}, journal = {Ukrainian mathematical journal}, number = {10}, publisher = {Springer}, address = {New York}, issn = {0041-5995}, doi = {10.1007/s11253-015-1038-8}, pages = {1455 -- 1474}, year = {2015}, abstract = {The Dirichlet problem for the heat equation in a bounded domain aS, a"e (n+1) is characteristic because there are boundary points at which the boundary touches a characteristic hyperplane t = c, where c is a constant. For the first time, necessary and sufficient conditions on the boundary guaranteeing that the solution is continuous up to the characteristic point were established by Petrovskii (1934) under the assumption that the Dirichlet data are continuous. The appearance of Petrovskii's paper was stimulated by the existing interest to the investigation of general boundary-value problems for parabolic equations in bounded domains. We contribute to the study of this problem by finding a formal solution of the Dirichlet problem for the heat equation in a neighborhood of a cuspidal characteristic boundary point and analyzing its asymptotic behavior.}, language = {en} } @article{ArwornDenecke1999, author = {Arworn, Srichan and Denecke, Klaus-Dieter}, title = {Left-edges solid varieties of differential groupoids}, year = {1999}, language = {en} } @article{ArwornDenecke1997, author = {Arworn, Srichan and Denecke, Klaus-Dieter}, title = {Groupoids of hypersubstitutions and G-solid varieties}, year = {1997}, language = {en} } @article{ArwornDenecke1997, author = {Arworn, Srichan and Denecke, Klaus-Dieter}, title = {A new methods to study subvariety lattices of semigroup varieties}, year = {1997}, language = {en} } @article{ArwornDenecke2001, author = {Arworn, Srichan and Denecke, Klaus-Dieter}, title = {Tree Transformations defined by Hypersubstitutions}, issn = {1509 - 9415}, year = {2001}, language = {en} } @article{ArwornDenecke2002, author = {Arworn, Srichan and Denecke, Klaus-Dieter}, title = {Intervals and complete congruences defined by M-solid varieties}, year = {2002}, language = {en} } @article{ArwornDeneckeKoppitz2001, author = {Arworn, Srichan and Denecke, Klaus-Dieter and Koppitz, J{\"o}rg}, title = {Strongly luid and weakly unsolid varieties}, issn = {1346-0862}, year = {2001}, language = {en} } @article{AsariWardinski2015, author = {Asari, Seiki and Wardinski, Ingo}, title = {On magnetic estimation of Earth's core angular momentum variation}, series = {Journal of geophysical research : Solid earth}, volume = {120}, journal = {Journal of geophysical research : Solid earth}, number = {10}, publisher = {American Geophysical Union}, address = {Washington}, issn = {2169-9313}, doi = {10.1002/2014JB011458}, pages = {6740 -- 6757}, year = {2015}, abstract = {We study systematically the estimation of Earth's core angular momentum (CAM) variation between 1962.0 and 2008.0 by using core surface flow models derived from the recent geomagnetic field model C(3)FM2. Various flow models are derived by changing four parameters that control the least squares flow inversion. The parameters include the spherical harmonic (SH) truncation degree of the flow models and two Lagrange multipliers that control the weights of two additional constraints. The first constraint forces the energy spectrum of the flow solution to follow a power law l-p, where l is the SH degree and p is the fourth parameter. The second allows to modulate the solution continuously between the dynamical states of tangential geostrophy (TG) and tangential magnetostrophy (TM). The calculated CAM variations are examined in reference to two features of the observed length-of-day (LOD) variation, namely, its secular trend and 6year oscillation. We find flow models in either TG or TM state for which the estimated CAM trends agree with the LOD trend. It is necessary for TM models to have their flows dominate at planetary scales, whereas TG models should not be of this scale; otherwise, their CAM trends are too steep. These two distinct types of flow model appear to correspond to the separate regimes of previous numerical dynamos that are thought to be applicable to the Earth's core. The phase of the subdecadal CAM variation is coherently determined from flow models obtained with extensively varying inversion settings. Multiple sources of model ambiguity need to be allowed for in discussing whether these phase estimates properly represent that of Earth's CAM as an origin of the observed 6year LOD oscillation.}, language = {en} } @article{AyanbayevKlebanovLietal.2021, author = {Ayanbayev, Birzhan and Klebanov, Ilja and Li, Han Cheng and Sullivan, Tim J.}, title = {Gamma-convergence of Onsager-Machlup functionals}, series = {Inverse problems : an international journal of inverse problems, inverse methods and computerised inversion of data}, volume = {38}, journal = {Inverse problems : an international journal of inverse problems, inverse methods and computerised inversion of data}, number = {2}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {0266-5611}, doi = {10.1088/1361-6420/ac3f81}, pages = {32}, year = {2021}, abstract = {The Bayesian solution to a statistical inverse problem can be summarised by a mode of the posterior distribution, i.e. a maximum a posteriori (MAP) estimator. The MAP estimator essentially coincides with the (regularised) variational solution to the inverse problem, seen as minimisation of the Onsager-Machlup (OM) functional of the posterior measure. An open problem in the stability analysis of inverse problems is to establish a relationship between the convergence properties of solutions obtained by the variational approach and by the Bayesian approach. To address this problem, we propose a general convergence theory for modes that is based on the Gamma-convergence of OM functionals, and apply this theory to Bayesian inverse problems with Gaussian and edge-preserving Besov priors. Part II of this paper considers more general prior distributions.}, language = {en} } @article{AyanbayevKlebanovLieetal.2021, author = {Ayanbayev, Birzhan and Klebanov, Ilja and Lie, Han Cheng and Sullivan, Tim J.}, title = {Gamma-convergence of Onsager-Machlup functionals}, series = {Inverse problems : an international journal of inverse problems, inverse methods and computerised inversion of data}, volume = {38}, journal = {Inverse problems : an international journal of inverse problems, inverse methods and computerised inversion of data}, number = {2}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {0266-5611}, doi = {10.1088/1361-6420/ac3f82}, pages = {35}, year = {2021}, abstract = {We derive Onsager-Machlup functionals for countable product measures on weighted l(p) subspaces of the sequence space R-N. Each measure in the product is a shifted and scaled copy of a reference probability measure on R that admits a sufficiently regular Lebesgue density. We study the equicoercivity and Gamma-convergence of sequences of Onsager-Machlup functionals associated to convergent sequences of measures within this class. We use these results to establish analogous results for probability measures on separable Banach or Hilbert spaces, including Gaussian, Cauchy, and Besov measures with summability parameter 1 <= p <= 2. Together with part I of this paper, this provides a basis for analysis of the convergence of maximum a posteriori estimators in Bayesian inverse problems and most likely paths in transition path theory.}, language = {en} } @article{AzzaliGoetteSchick2015, author = {Azzali, Sara and Goette, Sebastian and Schick, Thomas}, title = {Large time limit and local L-2-index theorems for families}, series = {Journal of noncommutative geometry}, volume = {9}, journal = {Journal of noncommutative geometry}, number = {2}, publisher = {EMS Publ.}, address = {Z{\"u}rich}, issn = {1661-6952}, doi = {10.4171/JNCG/203}, pages = {621 -- 664}, year = {2015}, abstract = {We compute explicitly, and without any extra regularity assumptions, the large time limit of the fibrewise heat operator for Bismut-Lott type superconnections in the L-2-setting. This is motivated by index theory on certain non-compact spaces (families of manifolds with cocompact group action) where the convergence of the heat operator at large time implies refined L-2-index formulas. As applications, we prove a local L-2-index theorem for families of signature operators and an L-2-Bismut-Lott theorem, expressing the Becker-Gottlieb transfer of flat bundles in terms of Kamber-Tondeur classes. With slightly stronger regularity we obtain the respective refined versions: we construct L-2-eta forms and L-2-torsion forms as transgression forms.}, language = {en} } @article{AzzaliPaycha2020, author = {Azzali, Sara and Paycha, Sylvie}, title = {Spectral zeta-invariants lifted to coverings}, series = {Transactions of the American Mathematical Society}, volume = {373}, journal = {Transactions of the American Mathematical Society}, number = {9}, publisher = {American Mathematical Society}, address = {Providence, RI}, issn = {0002-9947}, doi = {10.1090/tran/8067}, pages = {6185 -- 6226}, year = {2020}, abstract = {The canonical trace and the Wodzicki residue on classical pseudo-differential operators on a closed manifold are characterised by their locality and shown to be preserved under lifting to the universal covering as a result of their local feature. As a consequence, we lift a class of spectral zeta-invariants using lifted defect formulae which express discrepancies of zeta-regularised traces in terms of Wodzicki residues. We derive Atiyah's L-2-index theorem as an instance of the Z(2)-graded generalisation of the canonical lift of spectral zeta-invariants and we show that certain lifted spectral zeta-invariants for geometric operators are integrals of Pontryagin and Chern forms.}, language = {en} } @article{AzzaliWahl2019, author = {Azzali, Sara and Wahl, Charlotte}, title = {Two-cocycle twists and Atiyah-Patodi-Singer index theory}, series = {Mathematical Proceedings of the Cambridge Philosophical Society}, volume = {167}, journal = {Mathematical Proceedings of the Cambridge Philosophical Society}, number = {3}, publisher = {Cambridge Univ. Press}, address = {New York}, issn = {0305-0041}, doi = {10.1017/S0305004118000427}, pages = {437 -- 487}, year = {2019}, abstract = {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.}, language = {en} } @article{BaakeBaakeBovieretal.2005, author = {Baake, Ellen and Baake, Michael and Bovier, Anton and Klein, Markus}, title = {An asymptotic maximum principle for essentially linear evolution models}, issn = {0303-6812}, year = {2005}, abstract = {Recent work on mutation-selection models has revealed that, under specific assumptions on the fitness function and the mutation rates, asymptotic estimates for the leading eigenvalue of the mutation-reproduction matrix may be obtained through a low-dimensional maximum principle in the limit N --> infinity (where N, or N-d with d greater than or equal to 1, is proportional to the number of types). In order to extend this variational principle to a larger class of models, we consider here a family of reversible matrices of asymptotic dimension N-d and identify conditions under which the high-dimensional Rayleigh-Ritz variational problem may be reduced to a low-dimensional one that yields the leading eigenvalue up to an error term of order 1/N. For a large class of mutation-selection models, this implies estimates for the mean fitness, as well as a concentration result for the ancestral distribution of types}, language = {en} } @article{BachmannSchmidt2000, author = {Bachmann, Michael and Schmidt, Hans-J{\"u}rgen}, title = {Period-doubling bifurcation in strongly anisotropic Bianchi I quantum cosmology}, year = {2000}, language = {en} } @article{BachmannSchmidt1999, author = {Bachmann, Michael and Schmidt, Hans-J{\"u}rgen}, title = {Period-doubling bifurcation in strongly anisotropic Bianchi I quantum cosmology}, series = {General relativity and quantum cosmology : preprints gr-qc}, volume = {9912068}, journal = {General relativity and quantum cosmology : preprints gr-qc}, year = {1999}, language = {en} } @article{BachocBlanchardNeuvial2018, author = {Bachoc, Francois and Blanchard, Gilles and Neuvial, Pierre}, title = {On the post selection inference constant under restricted isometry properties}, series = {Electronic journal of statistics}, volume = {12}, journal = {Electronic journal of statistics}, number = {2}, publisher = {Institute of Mathematical Statistics}, address = {Cleveland}, issn = {1935-7524}, doi = {10.1214/18-EJS1490}, pages = {3736 -- 3757}, year = {2018}, abstract = {Uniformly valid confidence intervals post model selection in regression can be constructed based on Post-Selection Inference (PoSI) constants. PoSI constants are minimal for orthogonal design matrices, and can be upper bounded in function of the sparsity of the set of models under consideration, for generic design matrices. In order to improve on these generic sparse upper bounds, we consider design matrices satisfying a Restricted Isometry Property (RIP) condition. We provide a new upper bound on the PoSI constant in this setting. This upper bound is an explicit function of the RIP constant of the design matrix, thereby giving an interpolation between the orthogonal setting and the generic sparse setting. We show that this upper bound is asymptotically optimal in many settings by constructing a matching lower bound.}, language = {en} } @article{BaerenzungHolschneiderLesur2014, author = {Baerenzung, Julien and Holschneider, Matthias and Lesur, Vincent}, title = {Bayesian inversion for the filtered flow at the Earth's core-mantle boundary}, series = {Journal of geophysical research : Solid earth}, volume = {119}, journal = {Journal of geophysical research : Solid earth}, number = {4}, publisher = {American Geophysical Union}, address = {Washington}, issn = {2169-9313}, doi = {10.1002/2013JB010358}, pages = {2695 -- 2720}, year = {2014}, abstract = {The inverse problem of determining the flow at the Earth's core-mantle boundary according to an outer core magnetic field and secular variation model has been investigated through a Bayesian formalism. To circumvent the issue arising from the truncated nature of the available fields, we combined two modeling methods. In the first step, we applied a filter on the magnetic field to isolate its large scales by reducing the energy contained in its small scales, we then derived the dynamical equation, referred as filtered frozen flux equation, describing the spatiotemporal evolution of the filtered part of the field. In the second step, we proposed a statistical parametrization of the filtered magnetic field in order to account for both its remaining unresolved scales and its large-scale uncertainties. These two modeling techniques were then included in the Bayesian formulation of the inverse problem. To explore the complex posterior distribution of the velocity field resulting from this development, we numerically implemented an algorithm based on Markov chain Monte Carlo methods. After evaluating our approach on synthetic data and comparing it to previously introduced methods, we applied it to a magnetic field model derived from satellite data for the single epoch 2005.0. We could confirm the existence of specific features already observed in previous studies. In particular, we retrieved the planetary scale eccentric gyre characteristic of flow evaluated under the compressible quasi-geostrophy assumption although this hypothesis was not considered in our study. In addition, through the sampling of the velocity field posterior distribution, we could evaluate the reliability, at any spatial location and at any scale, of the flow we calculated. The flow uncertainties we determined are nevertheless conditioned by the choice of the prior constraints we applied to the velocity field.}, language = {en} } @article{BaerenzungHolschneiderWichtetal.2020, author = {Baerenzung, Julien and Holschneider, Matthias and Wicht, Johannes and Lesur, Vincent and Sanchez, Sabrina}, title = {The Kalmag model as a candidate for IGRF-13}, series = {Earth, planets and space}, volume = {72}, journal = {Earth, planets and space}, number = {1}, publisher = {Springer}, address = {New York}, issn = {1880-5981}, doi = {10.1186/s40623-020-01295-y}, pages = {13}, year = {2020}, abstract = {We present a new model of the geomagnetic field spanning the last 20 years and called Kalmag. Deriving from the assimilation of CHAMP and Swarm vector field measurements, it separates the different contributions to the observable field through parameterized prior covariance matrices. To make the inverse problem numerically feasible, it has been sequentialized in time through the combination of a Kalman filter and a smoothing algorithm. The model provides reliable estimates of past, present and future mean fields and associated uncertainties. The version presented here is an update of our IGRF candidates; the amount of assimilated data has been doubled and the considered time window has been extended from [2000.5, 2019.74] to [2000.5, 2020.33].}, language = {en} } @article{BagderinaTarkhanov2014, author = {Bagderina, Yulia Yu. and Tarkhanov, Nikolai Nikolaevich}, title = {Differential invariants of a class of Lagrangian systems with two degrees of freedom}, series = {Journal of mathematical analysis and applications}, volume = {410}, journal = {Journal of mathematical analysis and applications}, number = {2}, publisher = {Elsevier}, address = {San Diego}, issn = {0022-247X}, doi = {10.1016/j.jmaa.2013.08.015}, pages = {733 -- 749}, year = {2014}, language = {en} } @article{BagderinaTarkhanov2015, author = {Bagderina, Yulia Yu. and Tarkhanov, Nikolai Nikolaevich}, title = {Solution of the equivalence problem for the third Painleve equation}, series = {Journal of mathematical physics}, volume = {56}, journal = {Journal of mathematical physics}, number = {1}, publisher = {American Institute of Physics}, address = {Melville}, issn = {0022-2488}, doi = {10.1063/1.4905383}, pages = {15}, year = {2015}, abstract = {We find necessary conditions for a second order ordinary differential equation to be equivalent to the Painleve III equation under a general point transformation. Their sufficiency is established by reduction to known results for the equations of the form y ' = f (x, y). We consider separately the generic case and the case of reducibility to an autonomous equation. The results are illustrated by the primary resonance equation.}, language = {en} } @article{BaileyBenZionBeckeretal.2010, author = {Bailey, Iain W. and Ben-Zion, Yehuda and Becker, Thorsten W. and Holschneider, Matthias}, title = {Quantifying focal mechanism heterogeneity for fault zones in central and southern California}, issn = {0956-540X}, doi = {10.1111/j.1365-246X.2010.04745.x}, year = {2010}, abstract = {P>We present a statistical analysis of focal mechanism orientations for nine California fault zones with the goal of quantifying variations of fault zone heterogeneity at seismogenic depths. The focal mechanism data are generated from first motion polarities for earthquakes in the time period 1983-2004, magnitude range 0-5, and depth range 0-15 km. Only mechanisms with good quality solutions are used. We define fault zones using 20 km wide rectangles and use summations of normalized potency tensors to describe the distribution of double-couple orientations for each fault zone. Focal mechanism heterogeneity is quantified using two measures computed from the tensors that relate to the scatter in orientations and rotational asymmetry or skewness of the distribution. We illustrate the use of these quantities by showing relative differences in the focal mechanism heterogeneity characteristics for different fault zones. These differences are shown to relate to properties of the fault zone surface traces such that increased scatter correlates with fault trace complexity and rotational asymmetry correlates with the dominant fault trace azimuth. These correlations indicate a link between the long-term evolution of a fault zone over many earthquake cycles and its seismic behaviour over a 20 yr time period. Analysis of the partitioning of San Jacinto fault zone focal mechanisms into different faulting styles further indicates that heterogeneity is dominantly controlled by structural properties of the fault zone, rather than time or magnitude related properties of the seismicity.}, language = {en} } @article{Bandara2021, author = {Bandara, Lashi}, title = {Functional calculus and harmonic analysis in geometry}, series = {S{\~a}o Paulo journal of mathematical sciences / Instituto de Matem{\´a}tica e Estat{\´i}stica da Universidade de S{\~a}o Paulo}, volume = {15}, journal = {S{\~a}o Paulo journal of mathematical sciences / Instituto de Matem{\´a}tica e Estat{\´i}stica da Universidade de S{\~a}o Paulo}, number = {1}, publisher = {Springer}, address = {Cham}, issn = {1982-6907}, doi = {10.1007/s40863-019-00149-0}, pages = {20 -- 53}, year = {2021}, abstract = {In this short survey article, we showcase a number of non-trivial geometric problems that have recently been resolved by marrying methods from functional calculus and real-variable harmonic analysis. We give a brief description of these methods as well as their interplay. This is a succinct survey that hopes to inspire geometers and analysts alike to study these methods so that they can be further developed to be potentially applied to a broader range of questions.}, language = {en} } @article{BandaraBryan2020, author = {Bandara, Lashi and Bryan, Paul}, title = {Heat kernels and regularity for rough metrics on smooth manifolds}, series = {Mathematische Nachrichten}, volume = {293}, journal = {Mathematische Nachrichten}, number = {12}, publisher = {Wiley-VCH}, address = {Weinheim}, issn = {0025-584X}, doi = {10.1002/mana.201800459}, pages = {2255 -- 2270}, year = {2020}, abstract = {We consider rough metrics on smooth manifolds and corresponding Laplacians induced by such metrics. We demonstrate that globally continuous heat kernels exist and are Holder continuous locally in space and time. This is done via local parabolic Harnack estimates for weak solutions of operators in divergence form with bounded measurable coefficients in weighted Sobolev spaces.}, language = {en} } @article{BandaraMcIntoshRosen2017, author = {Bandara, Lashi and McIntosh, Alan and Rosen, Andreas}, title = {Riesz continuity of the Atiyah}, series = {Mathematische Annalen}, volume = {370}, journal = {Mathematische Annalen}, number = {1-2}, publisher = {Springer}, address = {Heidelberg}, issn = {0025-5831}, doi = {10.1007/s00208-017-1610-7}, pages = {863 -- 915}, year = {2017}, abstract = {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 Calder{\´o}n'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.}, language = {en} } @article{BandaraRosen2019, author = {Bandara, Menaka Lashitha and Rosen, Andreas}, title = {Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of local boundary conditions}, series = {Communications in partial differential equations}, volume = {44}, journal = {Communications in partial differential equations}, number = {12}, publisher = {Taylor \& Francis Group}, address = {Philadelphia}, issn = {0360-5302}, doi = {10.1080/03605302.2019.1611847}, pages = {1253 -- 1284}, year = {2019}, abstract = {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.}, language = {en} } @article{Baumgaertel2009, author = {Baumgaertel, Hellmut}, title = {Spectral and scattering theory of Friedrichs Models on the positive half line with Hilbert-Schmidt perturbations}, issn = {1424-0637}, doi = {10.1007/s00023-009-0398-8}, year = {2009}, abstract = {The spectral theory of the Friedrichs model on the positive half line with Hilbert-Schmidt perturbations, equipped with distinguished analytic properties, is presented. In general, the (separable) multiplicity Hilbert space is assumed to be infinite-dimensional. The results include a spectral characterization of its resonances and the association of so-called Gamov vectors. Sufficient conditions are presented such that all resonances are simple poles of the scattering matrix. The connection between their residual terms and the associated Gamov vectors is pointed out.}, language = {en} } @article{BaumgaertelGrundling2005, author = {Baumgaertel, Hellmut and Grundling, H.}, title = {Superselection in the presence of constraints}, issn = {0022-2488}, year = {2005}, abstract = {Superselection and constraints occur together in many gauge theories, and here we begin a study of such systems. Our main focus will be to analyze compatibility questions between constraining and superselection, and we will develop an example modelled on QED in which our framework is realized. We proceed from a generalization of Doplicher- Roberts superselection theory to the case of the nontrivial center, and a set of Dirac quantum constraints and find conditions under which the superselection structures will survive constraining in some form. This involves an analysis of the restriction and factorization of superselection structures. (c) 2005 American Institute of Physics}, language = {en} } @article{BaumgaertelKaldassKomy2009, author = {Baumgaertel, Hellmut and Kaldass, Hani and Komy, Soliman}, title = {On spectral properties of the resonances for selected potential scattering systems}, issn = {0022-2488}, doi = {10.1063/1.3072675}, year = {2009}, abstract = {The resonances (poles of the scattering matrix) of quantum mechanical scattering by central-symmetric potentials with compact support and zero angular momentum are spectrally characterized directly in terms of the Hamiltonian by a (generalized) eigenvalue problem distinguished by an additional condition (called boundary condition). The connection between the (generalized) eigenspace of a resonance and corresponding Gamov vectors is pointed out. A condition is presented such that a relation between special transition probabilities and infinite sums of residual terms for all complex-conjugated pairs of resonances can be proved. In the case of the square well potential the condition is satisfied.}, language = {en} } @article{Baumgaertel2006, author = {Baumg{\"a}rtel, Hellmut}, title = {Generalized eigenvectors for resonances in the Friedrichs model and their associated Gamov vectors}, issn = {0129-055X}, doi = {10.1142/S0129055X06002589}, year = {2006}, abstract = {A Gelfand triplet for the Hamiltonian H of the Priedrichs model on R with multiplicity space K, dim K < infinity, is constructed such that exactly the resonances (poles of the inverse of the Livsic-matrix) are (generalized) eigenvalues of H. The corresponding eigen(anti)linear forms are calculated explicitly. Using the wave matrices for the wave (Moller) operators the corresponding eigen(anti)linear forms on the Schwartz space S for the unperturbed Hamiltonian Ho are also calculated. It turns out that they are of pure Dirac type and can be characterized by their corresponding Gamov vector lambda -> k/(zeta(0)-lambda)(-1), zeta(0) resonance, k epsilon K, which is uniquely determined by restriction of S to S boolean AND H-+(2), where H-+(2) denotes the Hardy space of the upper half-plane. Simultaneously this restriction yields a truncation of the generalized evolution to the well-known decay semigroup for t >= 0 of the Toeplitz type on H-+(2). That is: Exactly those pre-Gamov vectors a lambda -> k/(zeta-lambda)(-1), ( from the lower half-plane, k epsilon K., have an extension to a generalized eigenvector of H if zeta is a resonance and if k is from that subspace of K which is uniquely determined by its corresponding Dirac type antilinear form}, language = {en} } @article{Baumgaertel1995, author = {Baumg{\"a}rtel, Hellmut}, title = {Fourier transformation of Hilbert C*-systems, with compact groups, by their regular representation}, year = {1995}, language = {en} } @article{Baumgaertel1995, author = {Baumg{\"a}rtel, Hellmut}, title = {On Haag dual nets over compact spaces}, year = {1995}, language = {en} } @article{Baumgaertel1997, author = {Baumg{\"a}rtel, Hellmut}, title = {A modified approach to the Doplicher-Roberts theorem on the construction of the field algebra and the symmetry group in superselection theory}, year = {1997}, language = {en} } @article{Baumgaertel2012, author = {Baumg{\"a}rtel, Hellmut}, title = {On a critical radiation density in the Friedmann equation}, series = {Journal of mathematical physics}, volume = {53}, journal = {Journal of mathematical physics}, number = {12}, publisher = {American Institute of Physics}, address = {Melville}, issn = {0022-2488}, doi = {10.1063/1.4771668}, pages = {9}, year = {2012}, abstract = {The paper presents a classification of the basic types of admissible solutions of the general Friedmann equation with non-vanishing cosmological constant and for the case that radiation and matter do not couple. There are four distinct types. The classification uses first the discriminant of a polynomial of the third degree, closely related to the right hand side of the Friedmann equation. The decisive term is then a critical radiation density which can be calculated explicitly.}, language = {en} } @article{Baumgaertel2001, author = {Baumg{\"a}rtel, Hellmut}, title = {An Application of the DR-Duality Theory for Compact Groups to Endomorphism Categories of C*-Algebras with Nontrivial Center}, year = {2001}, language = {en} } @article{Baumgaertel2000, author = {Baumg{\"a}rtel, Hellmut}, title = {Dual actions on C*-algebras and Hilbert extensions}, year = {2000}, language = {en} } @article{Baumgaertel2000, author = {Baumg{\"a}rtel, Hellmut}, title = {On a theorem of Ashtekar and Lewandowski in the mathematical framework of canonical quantization in quantum gravity}, year = {2000}, language = {en} } @article{Baumgaertel1999, author = {Baumg{\"a}rtel, Hellmut}, title = {On a theorem of Ashtekar and Lewandowski}, isbn = {981-023627-1}, year = {1999}, language = {en} } @article{Baumgaertel1999, author = {Baumg{\"a}rtel, Hellmut}, title = {An inverse problem for superselection structures on C*-algebras with nontrivial center}, year = {1999}, language = {en} } @article{BaumgaertelCarey2001, author = {Baumg{\"a}rtel, Hellmut and Carey, A.}, title = {Hilbert systems for actions of the circle group}, year = {2001}, language = {en} } @article{BaumgaertelJurkeLledo2002, author = {Baumg{\"a}rtel, Hellmut and Jurke, Matthias and Lled{\´o}, Fernando}, title = {Twisted duality for the CAR-algebra}, year = {2002}, language = {en} } @article{BaumgaertelJurkeLledo1995, author = {Baumg{\"a}rtel, Hellmut and Jurke, Matthias and Lled{\´o}, Fernando}, title = {On free nets over Minkowski space}, year = {1995}, language = {en} } @article{BaumgaertelLledo2004, author = {Baumg{\"a}rtel, Hellmut and Lledo, Fernando}, title = {Duality of compact groups and Hilbert C*-systems for C*-algebras with a nontrivial center}, issn = {0129-167X}, year = {2004}, abstract = {In this paper we present duality theory for compact groups in the case when the C*-algebra A, the fixed point algebra of the corresponding Hilbert C*-system (F, 9), has a nontrivial center Z superset of C1 and the relative commutant satisfies the minimality condition A' boolean AND F = Z, as well as a technical condition called regularity. The abstract characterization of the mentioned Hilbert C*-system is expressed by means of an inclusion of C*- categories T-c < T, where T-c is a suitable DR-category and T a full subcategory of the category of endomorphisms of A. Both categories have the same objects and the arrows of T can be generated from the arrows of T-c and the center Z. A crucial new element that appears in the present analysis is an abelian group C(G), which we call the chain group of G, and that can be constructed from certain equivalence relation defined on (G) over cap, the dual object of G. The chain group, which is isomorphic to the character group of the center of g, determines the action of irreducible endomorphisms of A when restricted to Z. Moreover, C(g) encodes the possibility of defining a symmetry epsilon also for the larger category T of the previous inclusion}, language = {en} } @article{BaumgaertelLledo1997, author = {Baumg{\"a}rtel, Hellmut and Lled{\´o}, Fernando}, title = {Some results on superselection structures for C*-algebras with nontrivial center}, isbn = {981-02-3984-X}, year = {1997}, language = {en} } @article{BaumgaertelLledo1997, author = {Baumg{\"a}rtel, Hellmut and Lled{\´o}, Fernando}, title = {Superselection structures for C*-algebras with nontrivial center}, year = {1997}, language = {en} } @article{Becker2014, author = {Becker, Christian}, title = {Relative differential cohomology}, series = {Lecture notes in mathematics : a collection of informal reports and seminars}, volume = {2112}, journal = {Lecture notes in mathematics : a collection of informal reports and seminars}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-319-07034-6; 978-3-319-07033-9}, issn = {0075-8434}, doi = {10.1007/978-3-319-07034-6_2}, pages = {91 -- 180}, year = {2014}, abstract = {We study two notions of relative differential cohomology, using the model of differential characters. The two notions arise from the two options to construct relative homology, either by cycles of a quotient complex or of a mapping cone complex. We discuss the relation of the two notions of relative differential cohomology to each other. We discuss long exact sequences for both notions, thereby clarifying their relation to absolute differential cohomology. We construct the external and internal product of relative and absolute characters and show that relative differential cohomology is a right module over the absolute differential cohomology ring. Finally we construct fiber integration and transgression for relative differential characters.}, language = {en} } @article{Becker2016, author = {Becker, Christian}, title = {Cheeger-Chern-Simons Theory and Differential String Classes}, series = {Annales de l'Institut Henri Poincar{\~A}©}, volume = {17}, journal = {Annales de l'Institut Henri Poincar{\~A}©}, publisher = {Springer}, address = {Basel}, issn = {1424-0637}, doi = {10.1007/s00023-016-0485-6}, pages = {1529 -- 1594}, year = {2016}, abstract = {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.}, language = {en} } @article{BeckerBeniniSchenkeletal.2019, author = {Becker, Christian and Benini, Marco and Schenkel, Alexander and Szabo, Richard J.}, title = {Cheeger-Simons differential characters with compact support and Pontryagin duality}, series = {Communications in analysis and geometry}, volume = {27}, journal = {Communications in analysis and geometry}, number = {7}, publisher = {International Press of Boston}, address = {Somerville}, issn = {1019-8385}, doi = {10.4310/CAG.2019.v27.n7.a2}, pages = {1473 -- 1522}, year = {2019}, abstract = {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.}, language = {en} } @article{BeckusBellissardCornean2019, author = {Beckus, Siegfried and Bellissard, Jean and Cornean, Horia}, title = {Holder Continuity of the Spectra for Aperiodic Hamiltonians}, series = {Annales de l'Institut Henri Poincar{\´e}}, volume = {20}, journal = {Annales de l'Institut Henri Poincar{\´e}}, number = {11}, publisher = {Springer}, address = {Cham}, issn = {1424-0637}, doi = {10.1007/s00023-019-00848-6}, pages = {3603 -- 3631}, year = {2019}, abstract = {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.}, language = {en} } @article{BeckusBellissardDeNittis2020, author = {Beckus, Siegfried and Bellissard, Jean and De Nittis, Giuseppe}, title = {Spectral continuity for aperiodic quantum systems}, series = {Journal of mathematical physics}, volume = {61}, journal = {Journal of mathematical physics}, number = {12}, publisher = {American Institute of Physics}, address = {Melville, NY}, issn = {0022-2488}, doi = {10.1063/5.0011488}, pages = {19}, year = {2020}, abstract = {This work provides a necessary and sufficient condition for a symbolic dynamical system to admit a sequence of periodic approximations in the Hausdorff topology. The key result proved and applied here uses graphs that are called De Bruijn graphs, Rauzy graphs, or Anderson-Putnam complex, depending on the community. Combining this with a previous result, the present work justifies rigorously the accuracy and reliability of algorithmic methods used to compute numerically the spectra of a large class of self-adjoint operators. The so-called Hamiltonians describe the effective dynamic of a quantum particle in aperiodic media. No restrictions on the structure of these operators other than general regularity assumptions are imposed. In particular, nearest-neighbor correlation is not necessary. Examples for the Fibonacci and the Golay-Rudin-Shapiro sequences are explicitly provided illustrating this discussion. While the first sequence has been thoroughly studied by physicists and mathematicians alike, a shroud of mystery still surrounds the latter when it comes to spectral properties. In light of this, the present paper gives a new result here that might help uncovering a solution.}, language = {en} } @article{BeckusEliaz2021, author = {Beckus, Siegfried and Eliaz, Latif}, title = {Eigenfunctions growth of R-limits on graphs}, series = {Journal of spectral theory / European Mathematical Society}, volume = {11}, journal = {Journal of spectral theory / European Mathematical Society}, number = {4}, publisher = {EMS Press, an imprint of the European Mathematical Society - EMS - Publishing House GmbH, Institut f{\"u}r Mathematik, Technische Universit{\"a}t}, address = {Berlin}, issn = {1664-039X}, doi = {10.4171/JST/389}, pages = {1895 -- 1933}, year = {2021}, abstract = {A characterization of the essential spectrum of Schrodinger operators on infinite graphs is derived involving the concept of R-limits. This concept, which was introduced previously for operators on N and Z(d) as "right-limits," captures the behaviour of the operator at infinity. For graphs with sub-exponential growth rate, we show that each point in sigma(ss)(H) corresponds to a bounded generalized eigenfunction of a corresponding R-limit of H. If, additionally, the graph is of uniform sub-exponential growth, also the converse inclusion holds.}, language = {en} } @article{BeckusPinchover2020, author = {Beckus, Siegfried and Pinchover, Yehuda}, title = {Shnol-type theorem for the Agmon ground state}, series = {Journal of spectral theory}, volume = {10}, journal = {Journal of spectral theory}, number = {2}, publisher = {EMS Publishing House}, address = {Z{\"u}rich}, issn = {1664-039X}, doi = {10.4171/JST/296}, pages = {355 -- 377}, year = {2020}, abstract = {LetH be a Schrodinger operator defined on a noncompact Riemannianmanifold Omega, and let W is an element of L-infinity (Omega; R). Suppose that the operator H + W is critical in Omega, and let phi be the corresponding Agmon ground state. We prove that if u is a generalized eigenfunction ofH satisfying vertical bar u vertical bar <= C-phi in Omega for some constant C > 0, then the corresponding eigenvalue is in the spectrum of H. The conclusion also holds true if for some K is an element of Omega the operator H admits a positive solution in (Omega) over bar = Omega \ K, and vertical bar u vertical bar <= C psi in (Omega) over bar for some constant C > 0, where psi is a positive solution of minimal growth in a neighborhood of infinity in Omega. Under natural assumptions, this result holds also in the context of infinite graphs, and Dirichlet forms.}, language = {en} } @article{BeinruckerDoganBlanchard2016, author = {Beinrucker, Andre and Dogan, Urun and Blanchard, Gilles}, title = {Extensions of stability selection using subsamples of observations and covariates}, series = {Statistics and Computing}, volume = {26}, journal = {Statistics and Computing}, publisher = {Springer}, address = {Dordrecht}, issn = {0960-3174}, doi = {10.1007/s11222-015-9589-y}, pages = {1059 -- 1077}, year = {2016}, abstract = {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.}, language = {en} } @article{BellingeriFrizPaychaetal.2022, author = {Bellingeri, Carlo and Friz, Peter and Paycha, Sylvie and Preiß, Rosa Lili Dora}, title = {Smooth rough paths, their geometry and algebraic renormalization}, series = {Vietnam journal of mathematics}, volume = {50}, journal = {Vietnam journal of mathematics}, number = {3}, publisher = {Springer}, address = {Singapore}, issn = {2305-221X}, doi = {10.1007/s10013-022-00570-7}, pages = {719 -- 761}, year = {2022}, abstract = {We introduce the class of "smooth rough paths" and study their main properties. Working in a smooth setting allows us to discard sewing arguments and focus on algebraic and geometric aspects. Specifically, a Maurer-Cartan perspective is the key to a purely algebraic form of Lyons' extension theorem, the renormalization of rough paths following up on [Bruned et al.: A rough path perspective on renormalization, J. Funct. Anal. 277(11), 2019], as well as a related notion of "sum of rough paths". We first develop our ideas in a geometric rough path setting, as this best resonates with recent works on signature varieties, as well as with the renormalization of geometric rough paths. We then explore extensions to the quasi-geometric and the more general Hopf algebraic setting.}, language = {en} } @article{Benini2016, author = {Benini, Marco}, title = {Optimal space of linear classical observables for Maxwell k-forms via spacelike and timelike compact de Rham cohomologies}, series = {Journal of mathematical physics}, volume = {57}, journal = {Journal of mathematical physics}, publisher = {American Institute of Physics}, address = {Melville}, issn = {0022-2488}, doi = {10.1063/1.4947563}, pages = {1249 -- 1279}, year = {2016}, abstract = {Being motivated by open questions in gauge field theories, we consider non-standard de Rham cohomology groups for timelike compact and spacelike compact support systems. These cohomology groups are shown to be isomorphic respectively to the usual de Rham cohomology of a spacelike Cauchy surface and its counterpart with compact support. Furthermore, an analog of the usual Poincare duality for de Rham cohomology is shown to hold for the case with non-standard supports as well. We apply these results to find optimal spaces of linear observables for analogs of arbitrary degree k of both the vector potential and the Faraday tensor. The term optimal has to be intended in the following sense: The spaces of linear observables we consider distinguish between different configurations; in addition to that, there are no redundant observables. This last point in particular heavily relies on the analog of Poincare duality for the new cohomology groups. Published by AIP Publishing.}, language = {en} } @article{BeniniCapoferriDappiaggi2017, author = {Benini, Marco and Capoferri, Matteo and Dappiaggi, Claudio}, title = {Hadamard States for Quantum Abelian Duality}, series = {Annales de l'Institut Henri Poincar{\´e}}, volume = {18}, journal = {Annales de l'Institut Henri Poincar{\´e}}, publisher = {Springer}, address = {Basel}, issn = {1424-0637}, doi = {10.1007/s00023-017-0593-y}, pages = {3325 -- 3370}, year = {2017}, abstract = {Abelian duality is realized naturally by combining differential cohomology and locally covariant quantum field theory. This leads to a -algebra of observables, which encompasses the simultaneous discretization of both magnetic and electric fluxes. We discuss the assignment of physically well-behaved states on this algebra and the properties of the associated GNS triple. We show that the algebra of observables factorizes as a suitable tensor product of three -algebras: the first factor encodes dynamical information, while the other two capture topological data corresponding to electric and magnetic fluxes. On the former factor and in the case of ultra-static globally hyperbolic spacetimes with compact Cauchy surfaces, we exhibit a state whose two-point correlation function has the same singular structure of a Hadamard state. Specifying suitable counterparts also on the topological factors, we obtain a state for the full theory, ultimately implementing Abelian duality transformations as Hilbert space isomorphisms.}, language = {en} } @article{BeniniSchenkel2017, author = {Benini, Marco and Schenkel, Alexander}, title = {Quantum Field Theories on Categories Fibered in Groupoids}, series = {Communications in mathematical physics}, volume = {356}, journal = {Communications in mathematical physics}, publisher = {Springer}, address = {New York}, issn = {0010-3616}, doi = {10.1007/s00220-017-2986-7}, pages = {19 -- 64}, year = {2017}, abstract = {We introduce an abstract concept of quantum field theory on categories fibered in groupoids over the category of spacetimes. This provides us with a general and flexible framework to study quantum field theories defined on spacetimes with extra geometric structures such as bundles, connections and spin structures. Using right Kan extensions, we can assign to any such theory an ordinary quantum field theory defined on the category of spacetimes and we shall clarify under which conditions it satisfies the axioms of locally covariant quantum field theory. The same constructions can be performed in a homotopy theoretic framework by using homotopy right Kan extensions, which allows us to obtain first toy-models of homotopical quantum field theories resembling some aspects of gauge theories.}, language = {en} } @article{BeniniSchenkel2017, author = {Benini, Marco and Schenkel, Alexander}, title = {Poisson Algebras for Non-Linear Field Theories in the Cahiers Topos}, series = {Annales de l'Institut Henri Poincar{\´e}}, volume = {18}, journal = {Annales de l'Institut Henri Poincar{\´e}}, publisher = {Springer}, address = {Basel}, issn = {1424-0637}, doi = {10.1007/s00023-016-0533-2}, pages = {1435 -- 1464}, year = {2017}, language = {en} } @article{BergemannGottwaldReich2009, author = {Bergemann, Kay and Gottwald, Georg and Reich, Sebastian}, title = {Ensemble propagation and continuous matrix factorization algorithms}, issn = {0035-9009}, doi = {10.1002/qj.457}, year = {2009}, abstract = {We consider the problem of propagating an ensemble of solutions and its characterization in terms of its mean and covariance matrix. We propose differential equations that lead to a continuous matrix factorization of the ensemble into a generalized singular value decomposition (SVD). The continuous factorization is applied to ensemble propagation under periodic rescaling (ensemble breeding) and under periodic Kalman analysis steps (ensemble Kalman filter). We also use the continuous matrix factorization to perform a re-orthogonalization of the ensemble after each time-step and apply the resulting modified ensemble propagation algorithm to the ensemble Kalman filter. Results from the Lorenz-96 model indicate that the re-orthogonalization of the ensembles leads to improved filter performance.}, language = {en} } @article{BergemannReich2010, author = {Bergemann, Kay and Reich, Sebastian}, title = {A localization technique for ensemble Kalman filters}, issn = {0035-9009}, doi = {10.1002/Qj.591}, year = {2010}, abstract = {Ensemble Kalman filter techniques are widely used to assimilate observations into dynamical models. The phase- space dimension is typically much larger than the number of ensemble members, which leads to inaccurate results in the computed covariance matrices. These inaccuracies can lead, among other things, to spurious long-range correlations, which can be eliminated by Schur-product-based localization techniques. In this article, we propose a new technique for implementing such localization techniques within the class of ensemble transform/square-root Kalman filters. Our approach relies on a continuous embedding of the Kalman filter update for the ensemble members, i.e. we state an ordinary differential equation (ODE) with solutions that, over a unit time interval, are equivalent to the Kalman filter update. The ODE formulation forms a gradient system with the observations as a cost functional. Besides localization, the new ODE ensemble formulation should also find useful application in the context of nonlinear observation operators and observations that arrive continuously in time.}, language = {en} } @article{BergemannReich2010, author = {Bergemann, Kay and Reich, Sebastian}, title = {A mollified ensemble Kalman filter}, issn = {0035-9009}, doi = {10.1002/Qj.672}, year = {2010}, abstract = {It is well recognized that discontinuous analysis increments of sequential data assimilation systems, such as ensemble Kalman filters, might lead to spurious high-frequency adjustment processes in the model dynamics. Various methods have been devised to spread out the analysis increments continuously over a fixed time interval centred about the analysis time. Among these techniques are nudging and incremental analysis updates (IAU). Here we propose another alternative, which may be viewed as a hybrid of nudging and IAU and which arises naturally from a recently proposed continuous formulation of the ensemble Kalman analysis step. A new slow-fast extension of the popular Lorenz-96 model is introduced to demonstrate the properties of the proposed mollified ensemble Kalman filter.}, language = {en} } @article{BergemannReich2012, author = {Bergemann, Kay and Reich, Sebastian}, title = {An ensemble Kalman-Bucy filter for continuous data assimilation}, series = {Meteorologische Zeitschrift}, volume = {21}, journal = {Meteorologische Zeitschrift}, number = {3}, publisher = {Schweizerbart}, address = {Stuttgart}, issn = {0941-2948}, doi = {10.1127/0941-2948/2012/0307}, pages = {213 -- 219}, year = {2012}, abstract = {The ensemble Kalman filter has emerged as a promising filter algorithm for nonlinear differential equations subject to intermittent observations. In this paper, we extend the well-known Kalman-Bucy filter for linear differential equations subject to continous observations to the ensemble setting and nonlinear differential equations. The proposed filter is called the ensemble Kalman-Bucy filter and its performance is demonstrated for a simple mechanical model (Langevin dynamics) subject to incremental observations of its velocity.}, language = {en} } @article{BernutatBoeckmannRamlau1998, author = {Bernutat, Claudia and B{\"o}ckmann, Christine and Ramlau, Ronny}, title = {Examination of the Nonlinear LIDAR-Operator : an Inverse Ill-posed Problem}, year = {1998}, language = {en} } @article{BettenbuehlRusconiEngbertetal.2012, author = {Bettenb{\"u}hl, Mario and Rusconi, Marco and Engbert, Ralf and Holschneider, Matthias}, title = {Bayesian selection of Markov Models for symbol sequences application to microsaccadic eye movements}, series = {PLoS one}, volume = {7}, journal = {PLoS one}, number = {9}, publisher = {PLoS}, address = {San Fransisco}, issn = {1932-6203}, doi = {10.1371/journal.pone.0043388}, pages = {10}, year = {2012}, abstract = {Complex biological dynamics often generate sequences of discrete events which can be described as a Markov process. The order of the underlying Markovian stochastic process is fundamental for characterizing statistical dependencies within sequences. As an example for this class of biological systems, we investigate the Markov order of sequences of microsaccadic eye movements from human observers. We calculate the integrated likelihood of a given sequence for various orders of the Markov process and use this in a Bayesian framework for statistical inference on the Markov order. Our analysis shows that data from most participants are best explained by a first-order Markov process. This is compatible with recent findings of a statistical coupling of subsequent microsaccade orientations. Our method might prove to be useful for a broad class of biological systems.}, language = {en} } @article{BiskabornSmithNoetzlietal.2019, author = {Biskaborn, Boris and Smith, Sharon L. and Noetzli, Jeannette and Matthes, Heidrun and Vieira, Goncalo and Streletskiy, Dmitry A. and Schoeneich, Philippe and Romanovsky, Vladimir E. and Lewkowicz, Antoni G. and Abramov, Andrey and Allard, Michel and Boike, Julia and Cable, William L. and Christiansen, Hanne H. and Delaloye, Reynald and Diekmann, Bernhard and Drozdov, Dmitry and Etzelmueller, Bernd and Grosse, Guido and Guglielmin, Mauro and Ingeman-Nielsen, Thomas and Isaksen, Ketil and Ishikawa, Mamoru and Johansson, Margareta and Johannsson, Halldor and Joo, Anseok and Kaverin, Dmitry and Kholodov, Alexander and Konstantinov, Pavel and Kroeger, Tim and Lambiel, Christophe and Lanckman, Jean-Pierre and Luo, Dongliang and Malkova, Galina and Meiklejohn, Ian and Moskalenko, Natalia and Oliva, Marc and Phillips, Marcia and Ramos, Miguel and Sannel, A. Britta K. and Sergeev, Dmitrii and Seybold, Cathy and Skryabin, Pavel and Vasiliev, Alexander and Wu, Qingbai and Yoshikawa, Kenji and Zheleznyak, Mikhail and Lantuit, Hugues}, title = {Permafrost is warming at a global scale}, series = {Nature Communications}, volume = {10}, journal = {Nature Communications}, publisher = {Nature Publ. Group}, address = {London}, issn = {2041-1723}, doi = {10.1038/s41467-018-08240-4}, pages = {11}, year = {2019}, abstract = {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.}, language = {en} } @article{BlanchardCarpentierGutzeit2018, author = {Blanchard, Gilles and Carpentier, Alexandra and Gutzeit, Maurilio}, title = {Minimax Euclidean separation rates for testing convex hypotheses in R-d}, series = {Electronic journal of statistics}, volume = {12}, journal = {Electronic journal of statistics}, number = {2}, publisher = {Institute of Mathematical Statistics}, address = {Cleveland}, issn = {1935-7524}, doi = {10.1214/18-EJS1472}, pages = {3713 -- 3735}, year = {2018}, abstract = {We consider composite-composite testing problems for the expectation in the Gaussian sequence model where the null hypothesis corresponds to a closed convex subset C of R-d. We adopt a minimax point of view and our primary objective is to describe the smallest Euclidean distance between the null and alternative hypotheses such that there is a test with small total error probability. In particular, we focus on the dependence of this distance on the dimension d and variance 1/n giving rise to the minimax separation rate. In this paper we discuss lower and upper bounds on this rate for different smooth and non-smooth choices for C.}, language = {en} } @article{BlanchardDelattreRoquain2014, author = {Blanchard, Gilles and Delattre, Sylvain and Roquain, Etienne}, title = {Testing over a continuum of null hypotheses with False Discovery Rate control}, series = {Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability}, volume = {20}, journal = {Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability}, number = {1}, publisher = {International Statistical Institute}, address = {Voorburg}, issn = {1350-7265}, doi = {10.3150/12-BEJ488}, pages = {304 -- 333}, year = {2014}, abstract = {We consider statistical hypothesis testing simultaneously over a fairly general, possibly uncountably infinite, set of null hypotheses, under the assumption that a suitable single test (and corresponding p-value) is known for each individual hypothesis. We extend to this setting the notion of false discovery rate (FDR) as a measure of type I error. Our main result studies specific procedures based on the observation of the p-value process. Control of the FDR at a nominal level is ensured either under arbitrary dependence of p-values, or under the assumption that the finite dimensional distributions of the p-value process have positive correlations of a specific type (weak PRDS). Both cases generalize existing results established in the finite setting. Its interest is demonstrated in several non-parametric examples: testing the mean/signal in a Gaussian white noise model, testing the intensity of a Poisson process and testing the c.d.f. of i.i.d. random variables.}, language = {en} } @article{BlanchardDickhausRoquainetal.2014, author = {Blanchard, Gilles and Dickhaus, Thorsten and Roquain, Etienne and Villers, Fanny}, title = {On least favorable configurations for step-up-down tests}, series = {Statistica Sinica}, volume = {24}, journal = {Statistica Sinica}, number = {1}, publisher = {Statistica Sinica, Institute of Statistical Science, Academia Sinica}, address = {Taipei}, issn = {1017-0405}, doi = {10.5705/ss.2011.205}, pages = {1 -- U31}, year = {2014}, language = {en} } @article{BlanchardFlaskaHandyetal.2016, author = {Blanchard, Gilles and Flaska, Marek and Handy, Gregory and Pozzi, Sara and Scott, Clayton}, title = {Classification with asymmetric label noise: Consistency and maximal denoising}, series = {Electronic journal of statistics}, volume = {10}, journal = {Electronic journal of statistics}, publisher = {Institute of Mathematical Statistics}, address = {Cleveland}, issn = {1935-7524}, doi = {10.1214/16-EJS1193}, pages = {2780 -- 2824}, year = {2016}, abstract = {In many real-world classification problems, the labels of training examples are randomly corrupted. Most previous theoretical work on classification with label noise assumes that the two classes are separable, that the label noise is independent of the true class label, or that the noise proportions for each class are known. In this work, we give conditions that are necessary and sufficient for the true class-conditional distributions to be identifiable. These conditions are weaker than those analyzed previously, and allow for the classes to be nonseparable and the noise levels to be asymmetric and unknown. The conditions essentially state that a majority of the observed labels are correct and that the true class-conditional distributions are "mutually irreducible," a concept we introduce that limits the similarity of the two distributions. For any label noise problem, there is a unique pair of true class-conditional distributions satisfying the proposed conditions, and we argue that this pair corresponds in a certain sense to maximal denoising of the observed distributions. Our results are facilitated by a connection to "mixture proportion estimation," which is the problem of estimating the maximal proportion of one distribution that is present in another. We establish a novel rate of convergence result for mixture proportion estimation, and apply this to obtain consistency of a discrimination rule based on surrogate loss minimization. Experimental results on benchmark data and a nuclear particle classification problem demonstrate the efficacy of our approach.}, language = {en} } @article{BlanchardHoffmannReiss2018, author = {Blanchard, Gilles and Hoffmann, Marc and Reiss, Markus}, title = {Optimal adaptation for early stopping in statistical inverse problems}, series = {SIAM/ASA Journal on Uncertainty Quantification}, volume = {6}, journal = {SIAM/ASA Journal on Uncertainty Quantification}, number = {3}, publisher = {Society for Industrial and Applied Mathematics}, address = {Philadelphia}, issn = {2166-2525}, doi = {10.1137/17M1154096}, pages = {1043 -- 1075}, year = {2018}, abstract = {For linear inverse problems Y = A mu + zeta, it is classical to recover the unknown signal mu by iterative regularization methods ((mu) over cap,(m) = 0,1, . . .) and halt at a data-dependent iteration tau using some stopping rule, typically based on a discrepancy principle, so that the weak (or prediction) squared-error parallel to A((mu) over cap (()(tau)) - mu)parallel to(2) is controlled. In the context of statistical estimation with stochastic noise zeta, we study oracle adaptation (that is, compared to the best possible stopping iteration) in strong squared- error E[parallel to((mu) over cap (()(tau)) - mu)parallel to(2)]. For a residual-based stopping rule oracle adaptation bounds are established for general spectral regularization methods. The proofs use bias and variance transfer techniques from weak prediction error to strong L-2-error, as well as convexity arguments and concentration bounds for the stochastic part. Adaptive early stopping for the Landweber method is studied in further detail and illustrated numerically.}, language = {en} } @article{BlanchardHoffmannReiss2018, author = {Blanchard, Gilles and Hoffmann, Marc and Reiss, Markus}, title = {Early stopping for statistical inverse problems via truncated SVD estimation}, series = {Electronic journal of statistics}, volume = {12}, journal = {Electronic journal of statistics}, number = {2}, publisher = {Institute of Mathematical Statistics}, address = {Cleveland}, issn = {1935-7524}, doi = {10.1214/18-EJS1482}, pages = {3204 -- 3231}, year = {2018}, abstract = {We consider truncated SVD (or spectral cut-off, projection) estimators for a prototypical statistical inverse problem in dimension D. Since calculating the singular value decomposition (SVD) only for the largest singular values is much less costly than the full SVD, our aim is to select a data-driven truncation level (m) over cap is an element of {1, . . . , D} only based on the knowledge of the first (m) over cap singular values and vectors. We analyse in detail whether sequential early stopping rules of this type can preserve statistical optimality. Information-constrained lower bounds and matching upper bounds for a residual based stopping rule are provided, which give a clear picture in which situation optimal sequential adaptation is feasible. Finally, a hybrid two-step approach is proposed which allows for classical oracle inequalities while considerably reducing numerical complexity.}, language = {en} } @article{BlanchardKawanabeSugiyamaetal.2006, author = {Blanchard, Gilles and Kawanabe, Motoaki and Sugiyama, Masashi and Spokoiny, Vladimir G. and M{\"u}ller, Klaus-Robert}, title = {In search of non-Gaussian components of a high-dimensional distribution}, issn = {1532-4435}, year = {2006}, abstract = {Finding non-Gaussian components of high-dimensional data is an important preprocessing step for efficient information processing. This article proposes a new linear method to identify the '' non-Gaussian subspace '' within a very general semi-parametric framework. Our proposed method, called NGCA (non-Gaussian component analysis), is based on a linear operator which, to any arbitrary nonlinear (smooth) function, associates a vector belonging to the low dimensional non-Gaussian target subspace, up to an estimation error. By applying this operator to a family of different nonlinear functions, one obtains a family of different vectors lying in a vicinity of the target space. As a final step, the target space itself is estimated by applying PCA to this family of vectors. We show that this procedure is consistent in the sense that the estimaton error tends to zero at a parametric rate, uniformly over the family, Numerical examples demonstrate the usefulness of our method}, language = {en} } @article{BlanchardKraemer2016, author = {Blanchard, Gilles and Kraemer, Nicole}, title = {Convergence rates of Kernel Conjugate Gradient for random design regression}, series = {Analysis and applications}, volume = {14}, journal = {Analysis and applications}, publisher = {World Scientific}, address = {Singapore}, issn = {0219-5305}, doi = {10.1142/S0219530516400017}, pages = {763 -- 794}, year = {2016}, abstract = {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.}, language = {en} } @article{BlanchardMathe2012, author = {Blanchard, Gilles and Mathe, Peter}, title = {Discrepancy principle for statistical inverse problems with application to conjugate gradient iteration}, series = {Inverse problems : an international journal of inverse problems, inverse methods and computerised inversion of data}, volume = {28}, journal = {Inverse problems : an international journal of inverse problems, inverse methods and computerised inversion of data}, number = {11}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {0266-5611}, doi = {10.1088/0266-5611/28/11/115011}, pages = {23}, year = {2012}, abstract = {The authors discuss the use of the discrepancy principle for statistical inverse problems, when the underlying operator is of trace class. Under this assumption the discrepancy principle is well defined, however a plain use of it may occasionally fail and it will yield sub-optimal rates. Therefore, a modification of the discrepancy is introduced, which corrects both of the above deficiencies. For a variety of linear regularization schemes as well as for conjugate gradient iteration it is shown to yield order optimal a priori error bounds under general smoothness assumptions. A posteriori error control is also possible, however at a sub-optimal rate, in general. This study uses and complements previous results for bounded deterministic noise.}, language = {en} } @article{BlanchardMuecke2018, author = {Blanchard, Gilles and M{\"u}cke, Nicole}, title = {Optimal rates for regularization of statistical inverse learning problems}, series = {Foundations of Computational Mathematics}, volume = {18}, journal = {Foundations of Computational Mathematics}, number = {4}, publisher = {Springer}, address = {New York}, issn = {1615-3375}, doi = {10.1007/s10208-017-9359-7}, pages = {971 -- 1013}, year = {2018}, abstract = {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.}, language = {en} } @article{BlanchardMuecke2020, author = {Blanchard, Gilles and M{\"u}cke, Nicole}, title = {Kernel regression, minimax rates and effective dimensionality}, series = {Analysis and applications}, volume = {18}, journal = {Analysis and applications}, number = {4}, publisher = {World Scientific}, address = {New Jersey}, issn = {0219-5305}, doi = {10.1142/S0219530519500258}, pages = {683 -- 696}, year = {2020}, abstract = {We investigate if kernel regularization methods can achieve minimax convergence rates over a source condition regularity assumption for the target function. These questions have been considered in past literature, but only under specific assumptions about the decay, typically polynomial, of the spectrum of the the kernel mapping covariance operator. In the perspective of distribution-free results, we investigate this issue under much weaker assumption on the eigenvalue decay, allowing for more complex behavior that can reflect different structure of the data at different scales.}, language = {en} } @article{BlanchardZadorozhnyi2019, author = {Blanchard, Gilles and Zadorozhnyi, Oleksandr}, title = {Concentration of weakly dependent Banach-valued sums and applications to statistical learning methods}, series = {Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability}, volume = {25}, journal = {Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability}, number = {4B}, publisher = {International Statistical Institute}, address = {Voorburg}, issn = {1350-7265}, doi = {10.3150/18-BEJ1095}, pages = {3421 -- 3458}, year = {2019}, abstract = {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.}, language = {en} } @article{BoehmHolschneiderLignieresetal.2015, author = {Boehm, Thorsten and Holschneider, Matthias and Lignieres, Frederic and Petit, Pascal and Rainer, Monica and Paletou, Francois and Wade, Gregg and Alecian, Evelyne and Carfantan, Herve and Blazere, Aurore and Mirouh, Giovanni M.}, title = {Discovery of starspots on Vega First spectroscopic detection of surface structures on a normal A-type star}, series = {Astronomy and astrophysics : an international weekly journal}, volume = {577}, journal = {Astronomy and astrophysics : an international weekly journal}, publisher = {EDP Sciences}, address = {Les Ulis}, issn = {0004-6361}, doi = {10.1051/0004-6361/201425425}, pages = {12}, year = {2015}, abstract = {Context. The theoretically studied impact of rapid rotation on stellar evolution needs to be compared with these results of high-resolution spectroscopy-velocimetry observations. Early-type stars present a perfect laboratory for these studies. The prototype A0 star Vega has been extensively monitored in recent years in spectropolarimetry. A weak surface magnetic field was detected, implying that there might be a (still undetected) structured surface. First indications of the presence of small amplitude stellar radial velocity variations have been reported recently, but the confirmation and in-depth study with the highly stabilized spectrograph SOPHIE/OHP was required. Aims. The goal of this article is to present a thorough analysis of the line profile variations and associated estimators in the early-type standard star Vega (A0) in order to reveal potential activity tracers, exoplanet companions, and stellar oscillations. Methods. Vega was monitored in quasi-continuous high-resolution echelle spectroscopy with the highly stabilized velocimeter SOPHIE/OHP. A total of 2588 high signal-to-noise spectra was obtained during 34.7 h on five nights (2 to 6 of August 2012) in high-resolution mode at R = 75 000 and covering the visible domain from 3895 6270 angstrom. For each reduced spectrum, least square deconvolved equivalent photospheric profiles were calculated with a T-eff = 9500 and log g = 4.0 spectral line mask. Several methods were applied to study the dynamic behaviour of the profile variations (evolution of radial velocity, bisectors, vspan, 2D profiles, amongst others). Results. We present the discovery of a spotted stellar surface on an A-type standard star (Vega) with very faint spot amplitudes Delta F/Fc similar to 5 x 10(-4). A rotational modulation of spectral lines with a period of rotation P = 0.68 d has clearly been exhibited, unambiguously confirming the results of previous spectropolarimetric studies. Most of these brightness inhomogeneities seem to be located in lower equatorial latitudes. Either a very thin convective layer can be responsible for magnetic field generation at small amplitudes, or a new mechanism has to be invoked to explain the existence of activity tracing starspots. At this stage it is difficult to disentangle a rotational from a stellar pulsational origin for the existing higher frequency periodic variations. Conclusions. This first strong evidence that standard A-type stars can show surface structures opens a new field of research and ask about a potential link with the recently discovered weak magnetic field discoveries in this category of stars.}, language = {en} } @article{BoldrighiniFrigioMaponietal.2020, author = {Boldrighini, Carlo and Frigio, Sandro and Maponi, Pierluigi and Pellegrinotti, Alessandro and Sinai, Yakov G.}, title = {3-D incompressible Navier-Stokes equations: Complex blow-up and related real flows}, series = {Lectures in pure and applied mathematics}, journal = {Lectures in pure and applied mathematics}, number = {6}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-485-2}, issn = {2199-4951}, doi = {10.25932/publishup-47220}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-472201}, pages = {185 -- 194}, year = {2020}, language = {en} } @article{BomansonJanhunenSchaubetal.2016, author = {Bomanson, Jori and Janhunen, Tomi and Schaub, Torsten and Gebser, Martin and Kaufmann, Benjamin}, title = {Answer Set Programming Modulo Acyclicity}, series = {Fundamenta informaticae}, volume = {147}, journal = {Fundamenta informaticae}, publisher = {IOS Press}, address = {Amsterdam}, issn = {0169-2968}, doi = {10.3233/FI-2016-1398}, pages = {63 -- 91}, year = {2016}, abstract = {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.}, language = {en} } @article{BourneCushingLiuetal.2018, author = {Bourne, D. P. and Cushing, D. and Liu, S. and M{\"u}nch, Florentin and Peyerimhoff, Norbert}, title = {Ollivier-Ricci idleness functions of graphs}, series = {SIAM Journal on Discrete Mathematics}, volume = {32}, journal = {SIAM Journal on Discrete Mathematics}, number = {2}, publisher = {Society for Industrial and Applied Mathematics}, address = {Philadelphia}, issn = {0895-4801}, doi = {10.1137/17M1134469}, pages = {1408 -- 1424}, year = {2018}, abstract = {We study the Ollivier-Ricci curvature of graphs as a function of the chosen idleness. We show that this idleness function is concave and piecewise linear with at most three linear parts, and at most two linear parts in the case of a regular graph. We then apply our result to show that the idleness function of the Cartesian product of two regular graphs is completely determined by the idleness functions of the factors.}, language = {en} } @article{BovierEckhoffGayrardetal.2004, author = {Bovier, Anton and Eckhoff, Michael and Gayrard, Veronique and Klein, Markus}, title = {Metastability in reversible diffusion processes : I. Sharp asymptotics for capacities and exit times}, issn = {1435-9855}, year = {2004}, abstract = {We develop a potential theoretic approach to the problem of metastability for reversible diffusion processes with generators of the form -epsilonDelta+ delF(.) del on R-d or subsets of R-d, where F is a smooth function with finitely many local minima. In analogy to previous work on discrete Markov chains, we show that metastable exit times from the attractive domains of the minima of F can be related, up to multiplicative errors that tend to one as epsilon down arrow 0, to the capacities of suitably constructed sets. We show that these capacities can be computed, again up to multiplicative errors that tend to one, in terms of local characteristics of F at the starting minimum and the relevant saddle points. As a result, we are able to give the first rigorous proof of the classical Eyring - Kramers formula in dimension larger than 1. The estimates on capacities make use of their variational representation and monotonicity properties of Dirichlet forms. The methods developed here are extensions of our earlier work on discrete Markov chains to continuous diffusion processes}, language = {en} } @article{BovierEckhoffGayrardetal.2002, author = {Bovier, Anton and Eckhoff, Michael and Gayrard, Veronique and Klein, Markus}, title = {Metastability and low-Lying spectra in reversible Markov chains}, year = {2002}, language = {en} } @article{BovierEckhoffGayrardetal.2001, author = {Bovier, Anton and Eckhoff, Michael and Gayrard, Veronique and Klein, Markus}, title = {Metastability in stochastic dynamics of disordered mean-field models}, issn = {0178-8051}, year = {2001}, language = {en} } @article{BovierGayrardKlein2005, author = {Bovier, Anton and Gayrard, Veronique and Klein, Markus}, title = {Metastability in reversible diffusion processes : II. Precise asymptotics for small eigenvalues}, issn = {1435-9855}, year = {2005}, abstract = {We continue the analysis of the problem of metastability for reversible diffusion processes, initiated in [BEGK3], with a precise analysis of the low-lying spectrum of the generator. Recall that we are considering processes with generators of the form -epsilonDelta + delF(.) del on R-d or subsets of Rd, where F is a smooth function with finitely many local minima. Here we consider only the generic situation where the depths of all local minima are different. We show that in general the exponentially small part of the spectrum is given, up to multiplicative errors tending to one, by the eigenvalues of the classical capacity matrix of the array of capacitors made of balls of radius epsilon centered at the positions of the local minima of F. We also get very precise uniform control on the corresponding eigenfunctions. Moreover, these eigenvalues can be identified with the same precision with the inverse mean metastable exit times from each minimum. In [BEGK3] it was proven that these mean times are given, again up to multiplicative errors that tend to one, by the classical Eyring- Kramers formula}, language = {en} }