Refine
Year of publication
- 2023 (8)
- 2022 (35)
- 2021 (48)
- 2020 (75)
- 2019 (60)
- 2018 (57)
- 2017 (63)
- 2016 (71)
- 2015 (65)
- 2014 (53)
- 2013 (53)
- 2012 (60)
- 2011 (37)
- 2010 (35)
- 2009 (33)
- 2008 (17)
- 2007 (15)
- 2006 (56)
- 2005 (76)
- 2004 (59)
- 2003 (50)
- 2002 (51)
- 2001 (74)
- 2000 (71)
- 1999 (96)
- 1998 (104)
- 1997 (104)
- 1996 (73)
- 1995 (100)
- 1994 (73)
- 1993 (16)
- 1992 (18)
- 1991 (4)
Document Type
- Article (1044)
- Monograph/Edited Volume (424)
- Doctoral Thesis (148)
- Preprint (95)
- Other (46)
- Postprint (16)
- Review (16)
- Conference Proceeding (9)
- Master's Thesis (7)
- Part of a Book (3)
Is part of the Bibliography
- yes (1811) (remove)
Keywords
- data assimilation (10)
- regularization (8)
- Cauchy problem (7)
- Fredholm property (7)
- cluster expansion (7)
- discrepancy principle (7)
- Bayesian inference (6)
- index (6)
- reciprocal class (6)
- Dirac operator (5)
- Elliptic complexes (5)
- Navier-Stokes equations (5)
- Neumann problem (5)
- Pseudo-differential operators (5)
- ensemble Kalman filter (5)
- linear term (5)
- stochastic differential equations (5)
- Bayesian inversion (4)
- Data assimilation (4)
- Earthquake interaction (4)
- Geomagnetic field (4)
- Hodge theory (4)
- Mathematikunterricht (4)
- Modellierung (4)
- Statistical seismology (4)
- Toeplitz operators (4)
- boundary value problems (4)
- clone (4)
- graphs (4)
- infinite-dimensional Brownian diffusion (4)
- linear hypersubstitution (4)
- local time (4)
- multiplicative noise (4)
- nonlinear operator (4)
- optimal transport (4)
- partial clone (4)
- random point processes (4)
- statistical mechanics (4)
- stochastic analysis (4)
- tunneling (4)
- Bayesian inverse problems (3)
- DLR equations (3)
- Dirichlet form (3)
- Dyson-Schwinger equations (3)
- Eigenvalues (3)
- Fredholm complexes (3)
- Gibbs measure (3)
- Kalman filter (3)
- Lefschetz number (3)
- Lidar (3)
- MCMC (3)
- Malliavin calculus (3)
- Markov processes (3)
- Probabilistic forecasting (3)
- Quasilinear equations (3)
- Riemannian manifold (3)
- Transformation semigroups (3)
- asymptotic expansion (3)
- classical solution (3)
- counting process (3)
- equi-singular connections (3)
- evolution equation (3)
- filter (3)
- forecasting (3)
- gradient flow (3)
- hyperbolic tilings (3)
- isotopic tiling theory (3)
- kernel methods (3)
- localization (3)
- logarithmic source condition (3)
- minimax convergence rates (3)
- parameter estimation (3)
- point process (3)
- relative rank (3)
- reproducing kernel Hilbert space (3)
- reversible measure (3)
- skew Brownian motion (3)
- star product (3)
- stochastic bridge (3)
- transformations (3)
- uncertainty quantification (3)
- 26D15 (2)
- 31C20 (2)
- 35B09 (2)
- 35R02 (2)
- 39A12 (primary) (2)
- 58E35 (secondary) (2)
- Aerosols (2)
- Alterung (2)
- Aluminium (2)
- Arctic haze (2)
- Asymptotics of solutions (2)
- Averaging principle (2)
- Boolean model (2)
- Boundary value methods (2)
- Boutet de Monvel's calculus (2)
- Brownian motion with discontinuous drift (2)
- Cauchy data spaces (2)
- Cluster expansion (2)
- Corona (2)
- Cox model (2)
- Diracoperator (2)
- Dirichlet problem (2)
- Dirichlet to Neumann operator (2)
- Duality formula (2)
- Edge calculus (2)
- Einstein-Hilbert action (2)
- Ellipticity of corner-degenerate operators (2)
- Ensemble Kalman filter (2)
- Euler-Lagrange equations (2)
- Finite difference method (2)
- Finsler distance (2)
- Fokker-Planck equation (2)
- Foucault (2)
- Fourth order Sturm-Liouville problem (2)
- Fredholm operator (2)
- Gamma-convergence (2)
- Geomagnetism (2)
- Geomagnetismus (2)
- Gibbs point process (2)
- Gibbs point processes (2)
- Graphs (2)
- Heat equation (2)
- Hughes-free (2)
- Index theory (2)
- Infinite-dimensional SDE (2)
- Inverse Sturm-Liouville problem (2)
- Inversion (2)
- Iran (2)
- Kunststofflichtwellenleiter (2)
- Lagrangian system (2)
- Langzeitverhalten (2)
- Laplace-Beltrami operator (2)
- Laplacian (2)
- Left-ordered groups (2)
- Levenberg-Marquardt method (2)
- Levy process (2)
- Lichtwellenleiter (2)
- Machine learning (2)
- Magnus expansion (2)
- Markov chain (2)
- Markov chains (2)
- Markovprozesse (2)
- Mathematikdidaktik (2)
- Mathematische Physik (2)
- Maximal subsemigroups (2)
- Maximum expected earthquake magnitude (2)
- Mellin symbols with values in the edge calculus (2)
- Meromorphic operator-valued symbols (2)
- Model order reduction (2)
- Morse-Smale property (2)
- Multiple zeta values (2)
- Numerov's method (2)
- Onsager-Machlup functional (2)
- Order-preserving transformations (2)
- PBPK (2)
- POF (2)
- Perturbed complexes (2)
- Picard-Fuchs equations (2)
- Poincare inequality (2)
- Randwertprobleme (2)
- Removable sets (2)
- Riemann-Hilbert problem (2)
- Royden boundary (2)
- Runge-Kutta methods (2)
- SPDEs (2)
- Schrodinger operators (2)
- Scientific discovery learning (2)
- Seismicity and tectonics (2)
- Specific entropy (2)
- Stochastic Differential Equation (2)
- Streuung (2)
- Sturm-Liouville problem (2)
- TIMSS (2)
- Temperatur (2)
- Time series (2)
- Tunneleffekt (2)
- Uncertainty quantification (2)
- Unterrichtsmethode (2)
- Verzweigungsprozess (2)
- Videostudie (2)
- Vietnam (2)
- WKB-expansion (2)
- Wahrscheinlichkeitstheorie (2)
- Wasserstein distance (2)
- Wavelet transform (2)
- Wellengleichung (2)
- Wiener measure (2)
- Yamabe operator (2)
- Zaremba problem (2)
- adaptive estimation (2)
- alpha-stable Levy process (2)
- and prediction (2)
- approximate differentiability (2)
- asymptotic behavior (2)
- asymptotic method (2)
- birth-death-mutation-competition point process (2)
- boundary layer (2)
- boundary regularity (2)
- branching process (2)
- bridge (2)
- coarea formula (2)
- cohomology (2)
- confidence sets (2)
- conjugate gradient (2)
- counterterms (2)
- coupling methods (2)
- curvature (2)
- de Rham complex (2)
- didactics of mathematics (2)
- difference operator (2)
- dimension independent bound (2)
- division of spaces (2)
- duality formula (2)
- early stopping (2)
- elliptic complexes (2)
- ellipticity (2)
- estimation (2)
- exact simulation (2)
- existence (2)
- first boundary value problem (2)
- formula (2)
- generators (2)
- geodesic distance (2)
- geometry (2)
- ground state (2)
- hard core potential (2)
- heat equation (2)
- heat kernel (2)
- high dimensional (2)
- higher-order Sturm–Liouville problems (2)
- ill-posed problems (2)
- infinite divisibility (2)
- infinitely divisible point processes (2)
- inflammatory bowel disease (2)
- infliximab (2)
- integration by parts formula (2)
- interacting particle systems (2)
- interaction matrix (2)
- inverse Sturm–Liouville problems (2)
- inverse problems (2)
- inversion (2)
- iterative regularization (2)
- jump process (2)
- knots (2)
- lattice packing and covering (2)
- lidar (2)
- linear formula (2)
- linear tree language (2)
- localisation (2)
- long-time behaviour (2)
- mapping degree (2)
- maps on surfaces (2)
- mathematics education (2)
- mathematische Modellierung (2)
- maximal subsemigroups (2)
- maximum a posteriori (2)
- metastability (2)
- methods (2)
- mild solution (2)
- minimax optimality (2)
- modeling (2)
- modelling optical fibres waveguides pof scattering temperature aging ageing (2)
- models (2)
- modified Landweber method (2)
- molecular weaving (2)
- networks (2)
- non-Markov drift (2)
- nonlinear (2)
- nonlinear equations (2)
- nonlinear filtering (2)
- nonparametric regression (2)
- operator-valued symbols (2)
- optimal rate (2)
- optische Fasern (2)
- orbifolds (2)
- p-Laplace operator (2)
- parametrices (2)
- partial least squares (2)
- particle filter (2)
- path integral (2)
- periodic entanglement (2)
- pharmacokinetics (2)
- pharmacometrics (2)
- polyhedra and polytopes (2)
- positive solutions (2)
- prediction (2)
- random walk on Abelian group (2)
- random walks on graphs (2)
- reciprocal characteristics (2)
- reciprocal processes (2)
- regular figures (2)
- regularisation (2)
- regularization methods (2)
- renormalization Hopf algebra (2)
- restricted range (2)
- reziproke Klassen (2)
- sampling (2)
- sequential data assimilation (2)
- singular manifolds (2)
- singular perturbation (2)
- skew diffusions (2)
- small noise asymptotic (2)
- stability and accuracy (2)
- stable limit cycle (2)
- statistical model selection (2)
- statistical seismology (2)
- stopping rules (2)
- tangles (2)
- teaching methods (2)
- term (2)
- trace (2)
- transfer operator (2)
- transition path theory (2)
- variational stability (2)
- wave equation (2)
- weak boundary values (2)
- (2+1)-dimensional gravity (1)
- (generalised) wealdy differentiable function (1)
- (sub-) tropical Africa (1)
- (sub-) tropisches Afrika (1)
- 31A25 (1)
- 35J70 (1)
- 35K65 (1)
- 4-Mannigfaltigkeiten (1)
- 47A52 (1)
- 47G30 (1)
- 58J40 (1)
- 65F18 (1)
- 65R20 (1)
- 65R32 (1)
- 78A46 (1)
- ACAT (1)
- AERONET (1)
- AFM (1)
- ALOS-2 PALSAR-2 (1)
- AMS (1)
- APC concentration gradient (1)
- Absorption kinetics (1)
- Achievement goal orientation (1)
- Activity Theory (1)
- Aerosol (1)
- Aerosole (1)
- Agmon estimates (1)
- Al-26 (1)
- Alfred Schütz (1)
- Algebraic Birkhoff factorisation (1)
- Algebraic quantum field theory (1)
- Algorithmic (1)
- Alternatividentitäten (1)
- Alternativvarietäten (1)
- Aluminium adjuvants (1)
- Analytic continuation (1)
- Analytic extension (1)
- Anfangsrandwertproblem (1)
- Angiogenesis (1)
- Angle (1)
- Angular derivatives (1)
- Animal movement modeling (1)
- Anisotropic pseudo-differential operators (1)
- Approximate approximations (1)
- Arctic (1)
- Arnoldi process (1)
- Artof (1)
- Assimilation (1)
- Asymptotic variance of maximum partial likelihood estimate (1)
- Asymptotische Entwicklung (1)
- Atiyah-Bott obstruction (1)
- Atmosphere (1)
- Audience Response System (1)
- Aufgabensammlung (1)
- Aussterbewahrscheinlichkeit (1)
- Automotive (1)
- BTZ black hole (1)
- Banach-valued process (1)
- Bayesian (1)
- Bayesian Inference (1)
- Bayesian method (1)
- Bayessche Inferenz (1)
- Beltrami equation (1)
- Bernstein inequality (1)
- Bewegungsgleichung (1)
- Bienaymé-Galton-Watson Prozess (1)
- Bienaymé-Galton-Watson process (1)
- Biodiversity (1)
- Birkhoff theorem (1)
- Birth-and-death process (1)
- Bisectorial operator (1)
- Bivariant K-theory (1)
- Blood coagulation network (1)
- Borel Funktionen (1)
- Borel functions (1)
- Bose-Einstein condensation (1)
- Boundary Value Problems (1)
- Boundary value method (1)
- Boundary value problem (1)
- Boundary value problems (1)
- Boundary value problems for first order systems (1)
- Boutet de Monvels Kalkül (1)
- Brownian bridge (1)
- Brownian motion (1)
- Broyden's method (1)
- Bruchzahlen (1)
- Bruck-Reilly extension (1)
- CCR-algebra (1)
- CFD (1)
- CHAMP satellite (1)
- COCOMO (1)
- COVID-19 (1)
- CRPS (1)
- Caccioppoli inequality (1)
- Calculation (1)
- Calculus of Variation (1)
- Canonical (Marcus) SDE (1)
- Canonical Gibbs measure (1)
- Carleman formulas (1)
- Cartan's development (1)
- Cartesian product of varifolds (1)
- Case-Cohort-Design (1)
- Cauchy horizon (1)
- Cauchyhorizont (1)
- Cell-level kinetics (1)
- Censoring (1)
- Central extensions of groups (1)
- Chamseddine-Connes spectral action (1)
- Characteristic polynomial (1)
- Cheeger inequalities (1)
- Cheeger inequality (1)
- Chicken chorioallantoic membrane (CAM) (1)
- Classification (1)
- Classroom Response System (1)
- Clearance induction (1)
- Clicker (1)
- Clifford algebra (1)
- Clifford semigroup (1)
- Clifford-Halbgruppen (1)
- Cloud Computing (1)
- Cluster Entwicklung (1)
- Cluster-Expansion (1)
- Clusteranalyse (1)
- Coarea Formel (1)
- Collapse (1)
- Commutative geometries (1)
- Complete asymptotics (1)
- Composition operators (1)
- Compound Poisson processes (1)
- Computer simulations (1)
- Conceptual change (1)
- Condition number (1)
- Cone (1)
- Cone and edge pseudo-differential operators (1)
- Confidence intervals (1)
- Conical zeta values (1)
- Connectivity (1)
- Connes-Kreimer Hopf algebra (1)
- Conradian left-order (1)
- Conradian ordered groups (1)
- Constant scalar curvature (1)
- Continuum (1)
- Continuum random cluster model (1)
- Control theory (1)
- Convergence rates (1)
- Convex cones (1)
- Core (1)
- Core Field Modeling (1)
- Core dynamics (1)
- Core field (1)
- Corner pseudo-differential operators (1)
- Correlation based modelling (1)
- Counting process (1)
- Covid-19 (1)
- Cox-Modell (1)
- Critical mathematics education (1)
- Critique (1)
- Cross-effects (1)
- Curie-Weiss Potts Model (1)
- Curie-Weiss Potts Modell (1)
- Curvature varifold (1)
- C‐ reactive protein remission (1)
- DFN (1)
- DLR equation (1)
- DLR-Gleichungen (1)
- DMSP (1)
- Daily gravity field (1)
- Data Assimilation (1)
- Data-Driven Methods (1)
- Data-driven modelling (1)
- Daten Assimilation (1)
- Datenassimilation (1)
- Datengetriebene Methoden (1)
- De Rham complex (1)
- Decay of eigenfunctions (1)
- Decorated cones (1)
- Definitions (1)
- Delaney--Dress (1)
- Delaney–Dress tiling theory (1)
- Deligne Cohomology (1)
- Deligne Kohomologie (1)
- Dependent thinning (1)
- Derivation (1)
- Design Research (1)
- Detailed balance (1)
- Detektion multipler Übergänge (1)
- Determinant (1)
- Determinantal point processes (1)
- Determinante (1)
- Deterministic finite state automata (1)
- Diagrams (1)
- Dichte eines Maßes (1)
- Dickkopf diffusion and feedback regulation (1)
- Didaktik der Mathematik (1)
- Differential Geometrie (1)
- Differential Geometry (1)
- Differential invariant (1)
- Differentialgeometrie (1)
- Differentialoperatoren (1)
- Differenzenoperator (1)
- Digital Tools (1)
- Digital technology (1)
- Digitale Werkzeuge (1)
- Dirac Operator (1)
- Dirac-harmonic maps (1)
- Dirac-harmonische Abbildungen (1)
- Dirac-type operator (1)
- Direct method (1)
- Dirichlet mixture (1)
- Dirichlet-form (1)
- Dirichlet-to-Neumann operator (1)
- Disagreement percolation (1)
- Discontinuous Robin condition (1)
- Discovery learning (1)
- Discrete Dirichlet forms (1)
- Discrete-element method (1)
- Distributed Learning (1)
- Disziplinierung (1)
- Divisionsbäume (1)
- Dobrushin criterion (1)
- Dobrushin criterion; (1)
- Dobrushin-Kriterium (1)
- Dualitätsformeln (1)
- Dubrovinring (1)
- DySEM (1)
- Dynamical systems (1)
- Dynamo (1)
- Dynamo: theories and simulations (1)
- E-band (1)
- EGFR (1)
- EM (1)
- Earth rotation (1)
- Earth's magnetic field (1)
- Earthquake dynamics (1)
- Ecosystem (1)
- Edge and corner pseudo-differential operators (1)
- Edge degenerate operators (1)
- Edge symbols (1)
- Efficient solutions (1)
- Effort (1)
- Eichtheorie (1)
- Eigenvalue problem (1)
- Einstein manifolds (1)
- Einstein space (1)
- Einstein-Hilbert-Wirkung (1)
- Einstein-Mannigfaltigkeiten (1)
- Elastizität (1)
- Electromagnetic induction (1)
- Electron spectroscopy (1)
- Elektrodynamik (1)
- Elliptic boundary (1)
- Elliptic operators (1)
- Ellipticity and parametrices (1)
- Ellipticity of edge-degenerate operators (1)
- Elliptische Komplexe (1)
- Elliptizität (1)
- Endothelin (ET) (1)
- Energy resolution (1)
- Ensemble Kalman (1)
- Ensemble Kalman Filter (1)
- Entdeckendes Lernen (1)
- Entropiemethode (1)
- Entropy method (1)
- Entstehungsfragestellung (1)
- Environmental DNA (1)
- Epidemiologie (1)
- Epidemiology (1)
- Epistemologie (1)
- Epistemology (1)
- Equivalence (1)
- Error analysis (1)
- Error control/adaptivity (1)
- Error covariance (1)
- Essential spectrum (1)
- Estimability (1)
- Estimation for branching processes (1)
- Euclidean fields (1)
- Euler equations (1)
- Evolution Strategies (1)
- Evolutionsgleichung (1)
- Evolutionsstrategien (1)
- Exact solution (1)
- Exponential decay of pair correlation (1)
- Extensive transformation (1)
- Extremal problem (1)
- Eyring-Kramers Formel (1)
- FIB patterning (1)
- False discovery rate (1)
- Fast win (1)
- Fault slip (1)
- Feedback (1)
- Feller Diffusionsprozesse (1)
- Feller diffusion processes (1)
- Fence (1)
- Fermi golden rule (1)
- Feynman-Kac formula (1)
- Fibroblasten (1)
- Filterung (1)
- Finite energy sections (1)
- Finite transformation semigroup (1)
- Finsler-Abstand (1)
- Finsler-distance (1)
- First exit location (1)
- First exit time (1)
- First order PDE (1)
- First passage time (1)
- First variation (1)
- Fischer-Riesz equations (1)
- Fitness (1)
- Fixationsbewegungen der Augen (1)
- Flocking (1)
- Fluvial (1)
- Foliated spaces (1)
- Force splitting (1)
- Forecasting and prediction (1)
- Fortuin-Kasteleyn representation (1)
- Fourier Integraloperatoren (1)
- Fourier and Mellin transform (1)
- Fourier and Mellin transforms (1)
- Fourier transform (1)
- Fourier-Laplace transform (1)
- Fractal (1)
- Fractions with linear poles (1)
- Fredholm Komplexe (1)
- Fredholm alternative (1)
- Fredholm operators (1)
- Freidlin-Wentzell theory (1)
- Fremdverstehen (1)
- Frühförderung (1)
- Full rank matrix filters (1)
- Functional calculus (1)
- Fundamentale Ideen (1)
- Funktorgeometrie (1)
- Future time interval (1)
- Fuzzy logic (1)
- G-Wishart distribution (1)
- GPS (1)
- GRACE (1)
- Gamification (1)
- Gauge theory (1)
- Gauss-Bonnet-Chern (1)
- Gaussian Loop Processes (1)
- Gaussian graphical models (1)
- Gaussian kernel estimators (1)
- Gaussian mixtures (1)
- Gaussian process (1)
- Gaussian processes (1)
- Gaussian sequence model (1)
- Gauß-Prozesse (1)
- Gaußsche Loopprozess (1)
- Gender (1)
- Generalised mean curvature vector (1)
- Generalized hybrid Monte Carlo (1)
- Generalized translation operator (1)
- Geodetic measurements (1)
- Geodynamo (1)
- Geodäten (1)
- Geomagnetic jerks (1)
- Geomagnetic models (1)
- Geomagnetic secular variation (1)
- Geomagnetic storm (1)
- Geometric Analysis (1)
- Geometrie (1)
- Geometrieunterricht (1)
- Geometrische Analysis (1)
- Geometrische Reproduktionsverteilung (1)
- Geometry (1)
- Geopotential theory (1)
- Gerben (1)
- Gerbes (1)
- Gestagenic drug (1)
- Gestaltungsprinzipien (1)
- Gestures (1)
- Gibbs field (1)
- Gibbs processes (1)
- Gibbs state (1)
- Gibbssche Punktprozesse (1)
- Gigli-Mantegazza flow (1)
- Girsanov formula (1)
- Glauber Dynamics (1)
- Glauber Dynamik (1)
- Global Differentialgeometry (1)
- Global attractor (1)
- Global sensitivity analysis (1)
- Globale Differentialgeometrie (1)
- Globally hyperbolic Lorentz manifold (1)
- Goal specificity (1)
- Goursat problem (1)
- Gradient flow (1)
- Gradientenfluss (1)
- Granular matter (1)
- Graph Laplacians (1)
- Graphentheorie (1)
- Gravitation (1)
- Gravitationswelle (1)
- Gravity anomalies and Earth structure (1)
- Greatest harmonic minorant (1)
- Green formula (1)
- Green's function (1)
- Green's operator (1)
- Green´s Relations (1)
- Grenzwertsatz (1)
- Grundvorstellungen (1)
- H-infinity-functional calculus (1)
- HIV (1)
- HIV Erkrankung (1)
- Haar system (1)
- Halbgruppentheorie (1)
- Hamiltonian dynamics (1)
- Hamiltonicity (1)
- Harmonic measure (1)
- Hauptfaserbündel (1)
- Heat Flow (1)
- Heat kernel coefficients (1)
- Heavy-tailed distributions (1)
- Helmholtz problem (1)
- Hermeneutik (1)
- Heuristics (1)
- High dimensional statistical inference (1)
- Higher-order Sturm-Liouville problem (1)
- Hilbert Scales (1)
- Historie der Verzweigungsprozesse (1)
- Hochschule (1)
- Holder-type source condition (1)
- Holomorphic map (1)
- Holomorphic mappings (1)
- Holonomie (1)
- Holonomy (1)
- Hopf algebra (1)
- Hopf algebra of Feynman diagrams (1)
- Hughes-frei (1)
- Hyperbolic dynamical system (1)
- Hypoelliptic operators (1)
- Hölder-type source condition (1)
- IGRF (1)
- ITG-Grace2010 (1)
- Idempotents (1)
- Identities (1)
- Ill-conditioning (1)
- In vitro dissolution (1)
- Indefinite (1)
- Index Theorie (1)
- Inference post model-selection (1)
- Infinite chain (1)
- Infinite dimensional manifolds (1)
- Infinite divisibility (1)
- Infinite graph (1)
- Infinite-dimensional interacting diffusion (1)
- Infinitely divisible point processes (1)
- Innovation (1)
- Inquiry-based learning (1)
- Instabilität des Prozesses (1)
- Instruction (1)
- Integrability (1)
- Integral varifold (1)
- Integration by parts formula (1)
- Interacting Diffusion Processes (1)
- Interpolation (1)
- Intrinsic metrics for Dirichlet forms (1)
- Intrinsicmotivation (1)
- Inverse Probleme (1)
- Inverse Problems (1)
- Inverse ill-posed problem (1)
- Inverse problem (1)
- Inverse theory (1)
- Inverses Sturm-Liouville-Problem (1)
- Ionospheric current (1)
- Irrfahrten auf Graphen (1)
- Isometry group (1)
- Iterated corner asymptotics of solutions (1)
- Ito SDE (1)
- Ito integral (1)
- Jump processes (1)
- K-Means Verfahren (1)
- KB-space (1)
- Kalman Bucy filter (1)
- Kalman Filter (1)
- Kalman smoother (1)
- Kalman-Bucy Filter (1)
- Kanten-Randwertprobleme (1)
- Kato square root problem (1)
- Kegel space (1)
- Kern Methoden (1)
- Kernel regression (1)
- Kernfeldmodellierung (1)
- Kette von Halbgruppen (1)
- Kinesin V (1)
- Kirkwood--Salsburg equations (1)
- Kirkwood-Salsburg-Gleichungen (1)
- Kolmogorov-Smirnov type tests (1)
- Kombinationstherapie (1)
- Konfidenzintervall (1)
- Kontinuumsgrenzwert (1)
- Kontrolltheorie (1)
- Konvergenzrate (1)
- Koopman operator (1)
- Koopman semigroup (1)
- Kopplung (1)
- Kritikalitätstheorem (1)
- Kulturelle Aktivität (1)
- Kähler-Mannigfaltigkeit (1)
- L-2-invariants (1)
- L2 metrics (1)
- L2-Metrik (1)
- LETKF (1)
- Lagrange Distributionen (1)
- Lagrangian modeling (1)
- Lagrangian modelling (1)
- Lagrangian submanifolds (1)
- Lagrangian-averaged equations (1)
- Lame system (1)
- Lamé system (1)
- Landing site selection (1)
- Landweber iteration (1)
- Langevin Dynamics (1)
- Langevin diffusions (1)
- Langevin dynamics (1)
- Langevin-Diffusions (1)
- Laplace expansion (1)
- Laplace-type operator (1)
- Lattice cones (1)
- Laufzeittomographie (1)
- Learning theory (1)
- Lehrkräftebildung Mathematik (1)
- Lehrpotential (1)
- Lehrtext (1)
- Leistungstests (1)
- Leitidee „Daten und Zufall“ (1)
- Lernen (1)
- Lernspiele (1)
- Lerntheorie (1)
- Level of confidence (1)
- Levy Maß (1)
- Levy diffusion approximation (1)
- Levy diffusions on manifolds (1)
- Levy measure (1)
- Levy processes (1)
- Levy type processes (1)
- Lidar remote sensing (1)
- Lie groupoid (1)
- Linear inverse problems (1)
- Linearized equation (1)
- Liouville theorem (1)
- Lipopolysaccharides (LPS) (1)
- Lipschitz domain (1)
- Lipschitz domains (1)
- Lithology (1)
- Local index theory (1)
- Locality (1)
- Logik (1)
- Logrank test (1)
- Lokalitätsprinzip (1)
- Loop space (1)
- Lorentzgeometrie (1)
- Lorentzian Geometry (1)
- Lorenz 96 (1)
- Low rank matrices (1)
- Lower bound (1)
- Lumping (1)
- Lyapunov equation (1)
- Lyapunov function (1)
- Lévy diffusion approximation (1)
- Lévy diffusions on manifolds (1)
- Lévy measure (1)
- Lévy type processes (1)
- MASCOT (1)
- MCMC modelling (1)
- MCMC-Verfahren (1)
- MOSAiC (1)
- Magnetfeldmodellierung (1)
- Magnetic anomalies: modelling and interpretation (1)
- Magnetic field variations through time (1)
- Magnetosphere (1)
- Manifolds with boundary (1)
- Mannigfaltigkeit (1)
- Mannigfaltigkeiten mit Kante (1)
- Mannigfaltigkeiten mit Singularitäten (1)
- Marcus canonical equation (1)
- Marked Gibbs process (1)
- Markierte Gibbs-Punkt-Prozesse (1)
- Markov Chain (1)
- Markov semigroups (1)
- Markov-Ketten (1)
- Markov-field property (1)
- Markovketten (1)
- Martin-Dynkin boundary (1)
- Marx (1)
- Mathematical Physics (1)
- Mathematical model (1)
- Mathematical modeling (1)
- Mathematics classrooms (1)
- Mathematics textbooks (1)
- Matrix function approximation (1)
- Maximal subsemibands (1)
- McKean-Vlasov (1)
- Measure-preserving semiflow (1)
- Mehrtyp-Verzweigungsprozesse (1)
- Mellin (1)
- Mellin and Green operators edge symbols (1)
- Mellin operators (1)
- Mellin oscillatory integrals (1)
- Mellin quantization (1)
- Mellin quantizations (1)
- Mellin transform (1)
- Mellin-Symbole (1)
- Mellin-Symbols (1)
- Menger algebra of rank n (1)
- Metastabilität (1)
- Metastasis (1)
- Methode (1)
- Microdialyse (1)
- Microphysical particle properties (1)
- Microphysical properties (1)
- Mikrophysik (1)
- Mikrosakkaden (1)
- Mikrosakkadensequenzen (1)
- Milnor Moore theorem (1)
- Minimax Optimality (1)
- Minimax Optimalität (1)
- Minimax convergence rates (1)
- Minimax hypothesis testing (1)
- Minimization (1)
- Minimizers (1)
- Mischzeiten (1)
- Misconceptions (1)
- Mittag-Leffler function (1)
- Mixing Times (1)
- Model comparison (1)
- Model selection (1)
- Modellreduktion (1)
- Modified Hamiltonians (1)
- Moduli space (1)
- Moduli spaces (1)
- Modulraum (1)
- Molecular dynamics (1)
- Molecular motor (1)
- Mollification (1)
- Monte Carlo (1)
- Monte Carlo method (1)
- Montel theorem (1)
- Motivation (1)
- Multi objective function (1)
- Multichannel wavelets (1)
- Multigrid (1)
- Multiple problem spaces (1)
- Multiple time stepping (1)
- Multiplicative Levy noise (1)
- Multiplicative noise (1)
- Multiscale analysis (1)
- Multitype branching processes (1)
- Multivariate meromorphic functions (1)
- Multizeta-Abbildungen (1)
- NLME (1)
- NWP (1)
- Navier-Stokes-Gleichungen (1)
- Navier-Stoks equations (1)
- Newton Polytope (1)
- Newton method (1)
- Newton polytopes (1)
- Nodal domain (1)
- Non-Markov drift (1)
- Non-coercive problem (1)
- Non-linear semigroups (1)
- Non-proportional hazards (1)
- Non-regular drift (1)
- Non-symmetric potential (1)
- Nonlinear Laplace operator (1)
- Nonlinear filters (1)
- Nonlinear ill-posed problems (1)
- Nonlinear systems (1)
- Nonparametric regression (1)
- Normalenbündel (1)
- Numerical simulation (1)
- Numerical weather prediction (1)
- Ny-Alesund (1)
- ODE with random initial conditions (1)
- OSSS inequality (1)
- Ollivier-Ricci (1)
- Onkologie (1)
- Operation (1)
- Operator algebras (1)
- Operator differential equations (1)
- Operator-valued symbols (1)
- Operator-valued symbols of Mellin type (1)
- Operators on manifolds with second order singularities (1)
- Operators on singular cones (1)
- Operators on singular manifolds (1)
- Operatortheorie (1)
- Optimal transportation (1)
- Optimality conditions (1)
- Optimierung (1)
- Optimization (1)
- Orbifolds (1)
- Order-preserving (1)
- Order-preserving bijections (1)
- Order-preserving maps (1)
- Order-reversing transformations (1)
- Ordered fields (1)
- Ordinary differential equations (1)
- Ordnungs-Filtrierung (1)
- Orlicz space height-excess (1)
- Ornstein-Uhlenbeck (1)
- Orthogonal connections with torsion (1)
- Orthogruppen (1)
- PBTK (1)
- PC-MRI (1)
- Pacific Ocean (1)
- Pade approximants (1)
- Paleoclimate reconstruction (1)
- Paleoecology (1)
- Paleogeography (1)
- Papangelou Process (1)
- Papangelou process (1)
- Papangelou processes (1)
- Papangelou-Prozess (1)
- Paracrine and autocrine regulation (1)
- Parameter Schätzung (1)
- Parametrices (1)
- Parametrices of elliptic operators (1)
- Partial Differential Equations (1)
- Partial Integration (1)
- Partial algebra (1)
- Partielle Differential Gleichungen (1)
- Peano phenomena (1)
- Penalized likelihood (1)
- Perfect groups (1)
- Permuted balance (1)
- Perron-Frobenius operator (1)
- Personal Response System (1)
- Perturbation theory (1)
- Perturbative renormalization (1)
- Pfadintegrale (1)
- Pfaffian (1)
- Pharmacokinetic models (1)
- Pharmakokinetik (1)
- Pharmakometrie (1)
- Phase transition (1)
- Physics concepts (1)
- Plio-Pleistocene (1)
- Plio-Pleistozän (1)
- PoSI constants (1)
- Poincaré Birkhoff Witt theorem (1)
- Point Processes (1)
- Point process (1)
- Poisson process (1)
- Polya Process (1)
- Polya difference process (1)
- Polya sum (1)
- Polyascher Prozess (1)
- Polymere (1)
- Populationen (1)
- Populations Analyse (1)
- Porous medium equation (1)
- Positional games (1)
- Positive mass theorem (1)
- Positive scalar curvature (1)
- Positive semigroups (1)
- Potential theory (1)
- Pregnancy (1)
- Primary 26D15 (1)
- Primary: 47B35 (1)
- Prinicipal Fibre Bundles (1)
- Probabilistic Cellular Automata (1)
- Probabilistic numerical methods (1)
- Problem solving (1)
- Professionswissen (1)
- Proportional hazards (1)
- Protein binding (1)
- Proving (1)
- Proxy forward modeling (1)
- Pseudo-Differentialoperatoren (1)
- Pseudo-differential algebras (1)
- Pseudodifferentialoperatoren auf dem Torus (1)
- Punktprozess (1)
- Punktprozesse (1)
- Quadratic tilt-excess (1)
- Quadrature mirror filters (1)
- Quadrature rule (1)
- Quantenfeldtheorie (1)
- Quantifizierung von Unsicherheit (1)
- Quantizations (1)
- Quantizer (1)
- Quasi Random Walk (1)
- Quasi-shuffles (1)
- Quasimodes (1)
- Quotientenschiefkörper (1)
- RMSE (1)
- Radar backscatter (1)
- Rahmenlehrplan (1)
- Raman lidar (1)
- Randbedingungen (1)
- Random Field Ising Model (1)
- Random cluster model (1)
- Random feature maps (1)
- Random measures (1)
- Randomisation (1)
- Randomised tree algorithm (1)
- Randomized strategy (1)
- Rank (1)
- Rank of semigroup (1)
- Rarita-Schwinger (1)
- Raumzeiten mit zeitartigen Rand (1)
- Reaction-diffusion system (1)
- Real-variable harmonic analysis (1)
- Realistic Mathematics Education (1)
- Rechnen (1)
- Reciprocal processes (1)
- Reclassification (1)
- Rectifiable varifold (1)
- Recursive transport equations (1)
- Regular semigroups (1)
- Regular variation (1)
- Regularisierung (1)
- Regularity analysis (1)
- Regularization (1)
- Reihendarstellungen (1)
- Reinforcement Learning (1)
- Rektifizierbarkeit höherer Ordnung (1)
- Renormalisation (1)
- Renormalization (1)
- Renormalized integral (1)
- Reproducing kernel Hilbert space (1)
- Reproduktionsrate (1)
- Resampling (1)
- Retrieval (1)
- Reversibility (1)
- Rho invariants (1)
- Ricci flow (1)
- Ricci solitons (1)
- Ricci-Fluss (1)
- Riemannsche Geometrie (1)
- Riesz continuity (1)
- Riesz topology (1)
- Risikoanalyse (1)
- Risk analysis (1)
- Risk assessment (1)
- Risk model (1)
- Root function (1)
- Rooted trees (1)
- Rota-Baxter (1)
- Rota-Baxter algebra (1)
- Rothe method (1)
- Rough paths (1)
- SAR amplitude (1)
- SHBG (1)
- Sakkadendetektion (1)
- Sand pile (1)
- Satellite geodesy (1)
- Satellite magnetics (1)
- Satellite magnetometer observations (1)
- Satz von Milnor Moore (1)
- Satz von Poincaré Birkhoff Witt (1)
- Scattering theory (1)
- Schrodinger equation (1)
- Schrödinger Problem (1)
- Schrödinger operator (1)
- Schrödinger operators (1)
- Schrödinger problem (1)
- Schulbuch (1)
- Schwarzes Loch (1)
- Schätzung von Verzweigungsprozessen (1)
- Second fundamental form (1)
- Secondary: 47L80 (1)
- Secular variation (1)
- Secular variation rate of change (1)
- Sedimentary ancient DNA (sedaDNA) (1)
- Seiberg-Witten theory (1)
- Seiberg-Witten-Invariante (1)
- Sekundarstufe I (1)
- Selbstassemblierung (1)
- Self-interacting scalar field (1)
- Semi-classical analysis (1)
- Semi-klasische Abschätzung (1)
- Semiclassical analysis (1)
- Semiclassical difference operator (1)
- Semigroup (1)
- Semiklassische Spektralasymptotik (1)
- Sentinel-1 (1)
- Sequential data assimilation (1)
- Sharp threshold (1)
- Shintani zeta values (1)
- Shnol theorem (1)
- Shuffle products (1)
- Shuffles (1)
- Signatures (1)
- Simulation (1)
- Simulation of Gaussian processes (1)
- Simulationsstudien (1)
- Singular analysis (1)
- Singular cones (1)
- Sinkhorn approximation (1)
- Sinkhorn problem (1)
- Skew Diffusionen (1)
- Skorokhod' s invariance principle (1)
- Small (1)
- Smooth cones (1)
- Smoothing (1)
- Sobolev Poincare inequality (1)
- Sobolev spaces (1)
- Sociolinguistics (1)
- Soziolinguistik (1)
- Space-Time Cluster Expansions (1)
- Spectral Regularization (1)
- Spectral analysis (1)
- Spectral exponent (1)
- Spectral flow (1)
- Spectral gap (1)
- Spectral regularization (1)
- Spectral theory of graphs (1)
- Spectral triples (1)
- Spektraltheorie (1)
- Spezifikationstests (1)
- Spiel (1)
- Spin Geometrie (1)
- Spin Geometry (1)
- Spin Hall effekte (1)
- Spin geometry (1)
- Stability selection (1)
- Statistical inverse problem (1)
- Statistical learning (1)
- Statistical methods (1)
- Stichprobenentnahme aus einem statistischen Modell (1)
- Stochastic Burgers equations (1)
- Stochastic Hamiltonian (1)
- Stochastic bridges (1)
- Stochastic differential equations (1)
- Stochastic domination (1)
- Stochastic epidemic model (1)
- Stochastic geometry (1)
- Stochastic systems (1)
- Stochastik (1)
- Stormer-Verlet method (1)
- Strain (1)
- Stratified spaces (1)
- Stratonovich SDE (1)
- Stratonovich integral (1)
- Stress (1)
- Stress drop (1)
- Strike-slip fault model (1)
- Strings (1)
- Structured population equation (1)
- Strukturbildung (1)
- Studium (1)
- Sturm-Liouville problems (1)
- Sturm-Liouville problems of higher order (1)
- Sturm-Liouville-Problem (1)
- Sturm-Liouville-Problem höherer Ordnung (1)
- Subcritical (1)
- Subdivision schemes (1)
- Subdivisions (1)
- Subsampling (1)
- Super-quadratic tilt-excess (1)
- Supergeometrie (1)
- Surface roughness (1)
- Surgery (1)
- Svalbard (1)
- Sylvester equations (1)
- Symplectic manifold (1)
- Synchrotron (1)
- Systeme interagierender Partikel (1)
- Systempharmakologie (1)
- TEC (1)
- Taphonomy (1)
- Technology (1)
- TerraSAR-X/TanDEM-X (1)
- Testfähigkeit (1)
- Tetration (1)
- Textbook analysis (1)
- Textbook research (1)
- The Yamabe (1)
- Therapeutic proteins (1)
- Thermal mathematical model (1)
- Three-space theory (1)
- Tibetan Plateau (1)
- Tides (1)
- Tikhonov regularization (1)
- Time duality (1)
- Time integration (1)
- Time of flight (1)
- Toeplitz-type pseudodifferential operators (1)
- Topological model (1)
- Toxicokinetic modelling (1)
- Toxicokinetics (1)
- Trace Dirichlet form (1)
- Transformation semigroup (1)
- Transformation semigroups on infinite chains (1)
- Tunneling (1)
- Turbulence (1)
- Twisted product (1)
- Twisted symbolic estimates (1)
- Two-level interacting process (1)
- Two-sample tests (1)
- Tätigkeitstheorie (1)
- Umbilic product (1)
- Uncertainty Quantification (1)
- Unendlichdimensionale Mannigfaltigkeit (1)
- Unique Gibbs state (1)
- Unit disk (1)
- Universal covering group (1)
- Van der Pol oscillator (1)
- Variable selection (1)
- Variational principle (1)
- Variationsrechnung (1)
- Variationsrechung (1)
- Variationsstabilität (1)
- Varifaltigkeit (1)
- Vector bundle (1)
- Vector subdivision schemes (1)
- Verknüpfung Fachwissenschaft und Fachdidaktik (1)
- Verzweigungsprozesse (1)
- Visuospatial reasoning (1)
- Vitali theorem (1)
- Volterra operator (1)
- WKB ansatz (1)
- WKB approximation (1)
- WKB expansion (1)
- WKB method (1)
- Wahrscheinlichkeitsverteilung (1)
- Warped product (1)
- Wave equation (1)
- Wave operator (1)
- Waveletanalyse (1)
- Weighted (1)
- Weighted edge spaces (1)
- Well log (1)
- Weyl tensor (1)
- Wide angle (1)
- Willmore functional (1)
- Winkel (1)
- Wnt/beta-catenin signalling pathway (1)
- Wärmefluss (1)
- Wärmekern (1)
- Wärmeleitungsgleichung (1)
- Yamabe invariant (1)
- Yamabe problem (1)
- Yamabe-Problem (1)
- Zahlbereichserweiterung (1)
- Zahlerwerb (1)
- Zellmotilität (1)
- Zeta-function (1)
- Zig-zag order (1)
- Zufallsvariable (1)
- Zustandsschätzung (1)
- Zählprozesse (1)
- a posteriori stopping rule (1)
- absorbing boundary (1)
- accelerated small (1)
- accuracy (1)
- acute severe (1)
- adaptive (1)
- adaptivity (1)
- adrenal insufficiency (1)
- aerosol (1)
- aerosol size distribution (1)
- aerosol-boundary layer interactions (1)
- aerosols (1)
- affine (1)
- affine invariance (1)
- algebra (1)
- algebra of rank n (1)
- algebraic systems (1)
- algebras (1)
- alignment (1)
- alternating direction implicit (1)
- alternative variety (1)
- amoeboid motion (1)
- amöboide Bewegung (1)
- analytic continuation (1)
- analytic functional (1)
- analytic perturbation theory (1)
- angewandte Mathematik (1)
- animal behavior (1)
- antigen processing (1)
- applied mathematics (1)
- approximation (1)
- approximative Differenzierbarkeit (1)
- aptitude tests (1)
- archaeomagnetism (1)
- articulation (1)
- association (1)
- asteroseismology (1)
- asymptotic approximation (1)
- asymptotic expansions (1)
- asymptotic methods (1)
- asymptotic properties of eigenfunctions (1)
- asymptotical normal distribution (1)
- asymptotics (1)
- asymptotische Entwicklung (1)
- asymptotische Normalverteilung (1)
- aurora (1)
- autonomic nervous system (1)
- backtrajectories; (1)
- backward heat problem (1)
- balanced dynamics (1)
- basic ideas ('Grundvorstellungen') (1)
- bayessche Inferenz (1)
- bedingter Erwartungswert (1)
- beta-functions (1)
- binding (1)
- bioinformatics (1)
- biological population equations (1)
- birhythmic behavior (1)
- black hole (1)
- black holes (1)
- body mass index procedure (1)
- body surface area (1)
- boundary conditions (1)
- boundary element method (1)
- bounds (1)
- branching processes (1)
- bridges of random walks (1)
- calculation (1)
- calculus of variations (1)
- canonical Marcus integration (1)
- category equivalence of clones (1)
- cell motility (1)
- certolizumab pegol (1)
- chain of semigroups (1)
- characteristic boundary point (1)
- characteristic points (1)
- characterization of point processes (1)
- chemical master equation (1)
- chemistry (1)
- classification with partial labels (1)
- clathrin (1)
- clone of operations (1)
- cluster analysis (1)
- clustering (1)
- coercivity (1)
- coherent set (1)
- collegial supervision (1)
- coloration of terms (1)
- colored solid varieties (1)
- compact resolvent (1)
- companies (1)
- completeness (1)
- completeness levels (1)
- complex systems (1)
- composition of terms (1)
- composition operator (1)
- compound Poisson processes (1)
- compound polyhedra (1)
- computational biology (1)
- concentration (1)
- concentration inequalities (1)
- condition number (1)
- conditional Bayes factors (1)
- conditional Wiener measure (1)
- conditional expectation value (1)
- conditions (1)
- conditions of success (1)
- confidence interval (1)
- confidence intervals (1)
- congruence (1)
- conservative discretization (1)
- consistency (1)
- constitutive relations (1)
- continuity in Sobolev spaces with double weights (1)
- continuous testing (1)
- continuous time Markov chain (1)
- continuous-time data assimilation (1)
- control theory (1)
- convergence assessment (1)
- convergence rate (1)
- corner Sobolev spaces with double weights (1)
- corner parametrices (1)
- corona virus (1)
- correlated noise (1)
- cortisol (1)
- coupling (1)
- criticality theorem (1)
- crohn's disease (1)
- crossed product (1)
- curvature varifold (1)
- cusp (1)
- das Cauchyproblem (1)
- das Goursatproblem (1)
- das charakteristische Cauchyproblem (1)
- data-driven (1)
- dbar-Neumann problem (1)
- decay of eigenfunctions (1)
- decomposition (1)
- delaney-dress tiling theory (1)
- density estimation (1)
- density of a measure (1)
- design elements (1)
- design research (1)
- detailed balance equation (1)
- determinant (1)
- determinantal point processes (1)
- determinantische Punktprozesse (1)
- dht-symmetric category (1)
- die linearisierte Einsteingleichung (1)
- differential cohomology (1)
- differential geometry (1)
- differential operators (1)
- diffusion maps (1)
- dimension reduction (1)
- direct and indirect climate observations (1)
- direkte und indirekte Klimaobservablen (1)
- disagreement percolation (1)
- discontinuous Robin condition (1)
- discontinuous drift (1)
- discrete Schrodinger (1)
- discrete Witten complex (1)
- discrete spectrum (1)
- disease activity (1)
- disjunction of identities (1)
- diskontinuierliche Drift (1)
- diskreter Witten-Laplace-Operator (1)
- distorted Brownian motion (1)
- distribution (1)
- distribution with asymptotics (1)
- distributional boundary (1)
- distributions with one-sided support (1)
- division ring of fractions (1)
- division rings (1)
- division trees (1)
- doppelsemigroup (1)
- dried blood spots (1)
- drug monitoring (1)
- duality formulae (1)
- dynamical models (1)
- dynamical system (1)
- dynamical system representation (1)
- early mathematical education (1)
- earthquake precursor (1)
- edge boundary value problems (1)
- edge quantizations (1)
- edge- and corner-degenerate symbols (1)
- eigenfunction (1)
- eigenvalue asymptotics (1)
- eigenvalue decay (1)
- eigenvalues (1)
- elasticity (1)
- electrodynamics (1)
- elliptic boundary (1)
- elliptic boundary conditions (1)
- elliptic complex (1)
- elliptic differential operators of firstorder (1)
- elliptic equation (1)
- elliptic problems (1)
- elliptic quasicomplexes (1)
- ellipticity with parameter (1)
- elliptische Gleichungen (1)
- elliptische Quasi-Komplexe (1)
- embedded Markov chain (1)
- embeddings (1)
- empirical Wasserstein distance (1)
- endomorphism semigroup (1)
- enlargement of filtration (1)
- ensembles (1)
- entropy (1)
- equation of motion (1)
- equatorial ionization anomaly (1)
- equatorial ionosphere (1)
- equatorial plasma bubbles (1)
- equivalence (1)
- ergodic diffusion processes (1)
- ergodic rates (1)
- error diagram (1)
- erste Variation (1)
- essential position in terms (1)
- eta forms (1)
- exact simulation method (1)
- exact simulation methods (1)
- exact solution (1)
- exakte Simulation (1)
- exchange algorithms (1)
- exercise collection (1)
- exit calculus (1)
- exponential decay (1)
- extinction probability (1)
- eye movements (1)
- false discovery rate (1)
- fat-free mass (1)
- feedback (1)
- feedback particle filter (1)
- fence-preserving transformations (1)
- fibration (1)
- fibroblasts (1)
- field-aligned currents (1)
- filtering (1)
- finite transformation semigroup (1)
- finsler distance (1)
- first exit location (1)
- first exit times (1)
- first passage times (1)
- first variation (1)
- fixational eye movements (1)
- fixed point formula (1)
- flocking (1)
- flood loss estimation (1)
- fluid mechanics (1)
- fluid-structure interaction (1)
- foliated diffusion (1)
- forcing from below (1)
- fore-casting (1)
- formal (1)
- formal power series (1)
- formulas (1)
- fractional calculus (1)
- fractions (1)
- fracture (1)
- fracture network (1)
- frameworks (1)
- free algebra (1)
- frequency-modulated continuous-wave (FMCW) (1)
- functional calculus (1)
- functor geometry (1)
- fundamental ideas (1)
- game (1)
- game-based (1)
- gamification (1)
- generalized Abelian gauge theory (1)
- generalized Bruck-Reilly *-extension (1)
- generalized Laplace operator (1)
- generalized eigenfunction (1)
- generalized eigenfunctions (1)
- generating sets (1)
- geodesics (1)
- geodätischer Abstand (1)
- geomagnetic field (1)
- geomagnetism (1)
- geometric reproduction distribution (1)
- geomorphology (1)
- geophysics (1)
- geopotential theory (1)
- geordnete Gruppen von Conrad-Typ (1)
- global-hyperbolisch (1)
- globally hyperbolic (1)
- globally hyperbolic spacetime (1)
- goodness-of-fit (1)
- gradient-free (1)
- gradient-free sampling methods (1)
- graph (1)
- graph Laplacian (1)
- graph theory (1)
- gravitation (1)
- gravitational wave (1)
- green function (1)
- group (1)
- group ring (1)
- groups (1)
- guiding idea “Daten und Zufall” (1)
- hard core interaction (1)
- heat asymptotics (1)
- heavy-tailed distributions (1)
- helicates (1)
- hemodynamics (1)
- hermeneutics (1)
- heterogeneity (1)
- high-dimensional inference (1)
- higher operations (1)
- higher order rectifiability (1)
- higher singularities (1)
- highly (1)
- history of branching processes (1)
- hitting times (1)
- holomorphic function (1)
- holonomic constraints (1)
- host-parasite stochastic particle system (1)
- hybrid model (1)
- hybrids (1)
- hydraulic tomography (1)
- hydrogeophysics (1)
- hydrostatic atmosphere (1)
- hyperbolic dynamical system (1)
- hyperequational theory (1)
- hypoelliptic estimate (1)
- höhere Operationen (1)
- höhere Singularitäten (1)
- idealised turbulence (1)
- idleness (1)
- ill-posed (1)
- ill-posed problem (1)
- indecomposable varifold (1)
- independent splittings (1)
- index of stability (1)
- inegral formulas (1)
- infinite-dimensional diffusion (1)
- infinitesimal generator (1)
- infliximab dosing (1)
- initial boundary value problem (1)
- instability of the process (1)
- integral Fourier operators (1)
- integral equation (1)
- integral formulas (1)
- integral representation method (1)
- integration by parts on path space (1)
- interacting particles (1)
- interassociativity (1)
- interindividual differences (1)
- intrinsic diameter (1)
- intrinsischer Diameter (1)
- invariance (1)
- invariant (1)
- inverse Probleme (1)
- inverse Sturm-Liouville problems (1)
- inverse correlation estimation (1)
- inverse ill-posed problem (1)
- inverse potential problems (1)
- inverse problem (1)
- inverse scattering (1)
- inverse semigroup (1)
- inverse theory (1)
- ionospheric convection (1)
- ionospheric precursors of earthquakes (1)
- isoperimetric estimates (1)
- isoperimetric inequality (1)
- isoperimetrische Ungleichung (1)
- iterated asymptotics (1)
- jump processes (1)
- k-means clustering (1)
- kanten- und ecken-entartete Symbole (1)
- kernel method (1)
- kernel operator (1)
- kernel-based Bayesian inference (1)
- kernel-basierte Bayes'sche Inferenz (1)
- kleine Parameter (1)
- kollegiale Supervision (1)
- komplexe Systeme (1)
- komplexe mechanistische Systeme (1)
- konstitutive Gleichungen (1)
- label noise (1)
- large deviations principle (1)
- large-scale mechanistic systems (1)
- laser remote sensing (1)
- lattice point (1)
- learning (1)
- learning rates (1)
- least favorable configuration (1)
- left ordered groups (1)
- left-right asymmetry (1)
- likelihood function (1)
- limit theorem (1)
- limiting distribution (1)
- linear fractional case (1)
- linear hyperidentity (1)
- linear identity (1)
- linear inverse problems (1)
- linear programming (1)
- linear regression (1)
- linear response (1)
- linearly implicit time stepping methods (1)
- linical databases (1)
- linking of subject science and didactic (1)
- linksgeordnete Gruppen (1)
- locality principle (1)
- locally indicable (1)
- locally indicable group (1)
- log-concavity (1)
- logarithmic convergence rate (1)
- logarithmic residue (1)
- logic (1)
- logistic regression analysis (1)
- logistische Regression (1)
- lokal indizierbar (1)
- long-time corrections (1)
- low rank matrix recovery (1)
- low rank recovery (1)
- low-lying eignvalues (1)
- low-rank approximations (1)
- lumping (1)
- macromolecular decay (1)
- magnetic (1)
- magnetic field modeling (1)
- magnetic field variations through (1)
- magnetisch (1)
- magnitude errors (1)
- makromolekularer Zerfall (1)
- manifold (1)
- manifold with boundary (1)
- manifolds with boundary (1)
- manifolds with conical singularities (1)
- manifolds with corners (1)
- manifolds with edge (1)
- manifolds with edge and boundary (1)
- manifolds with singularities (1)
- many-electron systems (1)
- mapping class (1)
- mapping class group (1)
- mapping class groups (1)
- marked Gibbs point processes (1)
- mathematical modeling (1)
- mathematical modelling (1)
- mathematical physics (1)
- mathematische Physik (1)
- matrices (1)
- matrix completion (1)
- maximal regularity (1)
- maximal subsemigroup (1)
- mean curvature (1)
- mean ergodic (1)
- mean-field equations (1)
- mechanistic modeling (1)
- mechanistische Modellierung (1)
- mental arithmetic (1)
- mental number line (1)
- meromorphe Fortsetzung (1)
- meromorphic continuation (1)
- mesoscale forecasting (1)
- metal-organic (1)
- method (1)
- methods: data analysis (1)
- microdialysis (1)
- microlocal analysis (1)
- microlokale Analysis (1)
- microphysical properties (1)
- microphysics (1)
- microsaccades (1)
- middle school (1)
- minimax hypothesis testing (1)
- minimax rate (1)
- minor planets, asteroids: individual: (162173) Ryugu (1)
- mit Anwendungen in der Laufzeittomographie, Seismischer Quellinversion und Magnetfeldmodellierung (1)
- mittlere Krümmung (1)
- mixed membership models (1)
- mixed problems (1)
- mixing (1)
- mixing optimization (1)
- mixture of bridges (1)
- mixture proportion estimation (1)
- modal analysis (1)
- model error (1)
- model order reduction (1)
- model selection (1)
- model uncertainty (1)
- model-informed precision dosing (1)
- modellinformierte Präzisionsdosierung (1)
- molecular motor (1)
- monoclonal antibodies (1)
- monotone coupling (1)
- monotone random (1)
- monotonicity conditions (1)
- morphology (1)
- motion correction (1)
- motivation (1)
- motivic Feynman rules (1)
- multi-armed bandits (1)
- multi-change point detection (1)
- multi-hypersubstitutions (1)
- multi-modular morphology (1)
- multi-scale diffusion processes (1)
- multi-well potential (1)
- multiclass classification with label noise (1)
- multilevel Monte Carlo (1)
- multiple testing (1)
- multiple testing; (1)
- multiplicative Lévy noise (1)
- multiscale analysis (1)
- multiscale dynamics (1)
- multivariable (1)
- multizeta functions (1)
- mutual contamination models (1)
- n-ary operation (1)
- n-ary term (1)
- negative Zahlen (1)
- negative curvature (1)
- negative numbers (1)
- nicht-lineare gemischte Modelle (NLME) (1)
- nichtlineare Modelle (1)
- nichtlineare partielle Differentialgleichung (1)
- nodal flow (1)
- noise Levy diffusions (1)
- non-Gaussian (1)
- non-dissipative regularisations (1)
- non-linear integro-differential equations (1)
- non-regular drift (1)
- non-uniqueness (1)
- nonasymptotic minimax separation rate (1)
- nondeterministic linear hypersubstitution (1)
- nonlinear PDI (1)
- nonlinear data assimilation (1)
- nonlinear partial differential equations (1)
- nonlinear semigroup (1)
- nonparametric hypothesis testing (1)
- nonparametric statistics (1)
- nonsmooth curves (1)
- normal bundle (1)
- normal reflection (1)
- nuclear norm (1)
- number (1)
- numerical (1)
- numerical analysis/modeling (1)
- numerical approximation (1)
- numerical extension (1)
- numerical methods (1)
- numerical relativity (1)
- numerical weather prediction (1)
- numerical weather prediction/forecasting (1)
- offene Wissenschaft (1)
- oncology (1)
- open mapping theorem (1)
- open science (1)
- operational momentum (1)
- operator (1)
- operator calculus (1)
- operator valued symbols (1)
- operators (1)
- operators with corner symbols (1)
- optimal order (1)
- oracle inequalities (1)
- oracle inequality (1)
- oral anticancer drugs (1)
- order continuous norm (1)
- order filtration (1)
- order-preserving (1)
- order-preserving mappings (1)
- ordered group (1)
- orientation-preserving (1)
- orientation-preserving and orientation-reversing transformations (1)
- orientation-preserving transformations (1)
- orthogroup (1)
- oscillatory systems (1)
- p-Branen (1)
- p-Laplace Operator (1)
- p-Laplace equation (1)
- p-branes (1)
- palaeomagnetism (1)
- paleoearthquakes (1)
- parabolic Harnack estimate (1)
- parametrices of elliptic operators (1)
- part-whole concept (1)
- partial (1)
- partial Menger (1)
- partial algebras (1)
- partial averaging (1)
- partial ordering (1)
- particle filters (1)
- particle methods (1)
- particle microphysics (1)
- particle precipitation (1)
- partielle Integration (1)
- partielle Integration auf dem Pfadraum (1)
- patch antenna (1)
- pathwise expectations (1)
- pediatrics (1)
- percolation (1)
- periodic Gaussian process (1)
- periodic Ornstein-Uhlenbeck process (1)
- permanental and determinantal point processes (MSC 2010) 35K55 (1)
- permanental- (1)
- personalised medicine (1)
- pharmacokinetic (1)
- phase dynamics (1)
- phase-locked loop (PLL) (1)
- photometer (1)
- physical SRB measures (1)
- physiologie-basierte Pharmacokinetic (PBPK) (1)
- pi-inverse monoid (1)
- planar rotors (1)
- polymer (1)
- popPBPK (1)
- popPK (1)
- population analysis (1)
- populations (1)
- porous medium equation (1)
- positive correlation (1)
- positive mass theorem (1)
- positive operators (1)
- posterior distribution (1)
- power amplifier (PA) (1)
- power series (1)
- presentations (1)
- principle (1)
- probabilistic modeling (1)
- probability distribution (1)
- probability generating function (1)
- probability theory (1)
- problem (1)
- problem-solving (1)
- problems (1)
- professional knowledge (1)
- proposal densities (1)
- proteasome (1)
- protein degradation (1)
- proteolysis (1)
- pseudo-differential boundary value problems (1)
- pseudo-differential equation (1)
- pseudo-differential operators (1)
- pseudo-differentielle Gleichungen (1)
- pseudodifferential operator (1)
- pseudodifferential operators (1)
- pseudodifferentiale Operatoren (1)
- pseudospectral method (1)
- quantification (1)
- quantizer (1)
- quantum field theory (1)
- quasiconformal mapping (1)
- quasilinear Fredholm operator (1)
- quasilinear Fredholm operators (1)
- quasilinear equation (1)
- quasimodes (1)
- question of origin (1)
- r-hypersubstitution (1)
- r-term (1)
- radar (1)
- radiation mechanisms: thermal (1)
- random KMM-measure (1)
- random matrix theory (1)
- random sum (1)
- random variable (1)
- random walk (1)
- randomly forced Duffing equation (1)
- randomness (1)
- rank (1)
- rapid variations (1)
- rare events (1)
- rational Krylov (1)
- reading (1)
- real-variable harmonic analysis (1)
- rectifiable varifold (1)
- red blood cells (1)
- regimen (1)
- regular and singular inverse Sturm-Liouville problems (1)
- regular monoid (1)
- regular polyhedra (1)
- regularization method (1)
- regularly varying Levy process (1)
- reinforcement learning (1)
- rejection sampling (1)
- rekonstruktive Fallanalyse (1)
- rektifizierbare Varifaltigkeit (1)
- relative isoperimetric inequality (1)
- relative ranks (1)
- removable set (1)
- removable sets (1)
- representations of groups as automorphism groups of (1)
- reproduction rate (1)
- resampling (1)
- rescaled lattice (1)
- resolvents (1)
- resonances (1)
- restricted isometry property (1)
- retrieval (1)
- reziproke Invarianten (1)
- right limits (1)
- rock mechanics (1)
- root functions (1)
- rooted trees (1)
- rough metrics (1)
- saccade detection (1)
- saccades (1)
- scalable (1)
- scaled lattice (1)
- schlecht gestellt (1)
- secular variation (1)
- seismic hazard (1)
- seismic source inversion (1)
- seismische Quellinversion (1)
- self-assembly (1)
- semi-Lagrangian method (1)
- semi-classical difference operator (1)
- semi-classical limit (1)
- semi-classical spectral estimates (1)
- semiclassical Agmon estimate (1)
- semiclassical spectral asymptotics (1)
- semigroup (1)
- semigroup representations (1)
- semigroup theory (1)
- semigroups on infinite chain (1)
- semipermeable barriers (1)
- sequences of microsaccades (1)
- sequential learning (1)
- series representation (1)
- shallow-water equations (1)
- short-range prediction (1)
- signal detection (1)
- simulation (1)
- simulations (1)
- singular Sturm-Liouville (1)
- singular drifts (1)
- singular foliation (1)
- singular integral equations (1)
- singular point (1)
- singular points (1)
- singuläre Mannigfaltigkeiten (1)
- skew diffusion (1)
- skew field of fraction (1)
- small ball probabilities (1)
- small ball probabilities; (1)
- small noise asymptotics (1)
- small parameter (1)
- smooth drift dependence (1)
- smoother (1)
- socialisation (1)
- soft matter (1)
- space-time Gibbs field (1)
- spacecraft operations (1)
- spacetimes with timelike boundary (1)
- sparsity (1)
- specific entropy (1)
- spectral cut-off (1)
- spectral flow (1)
- spectral kernel function (1)
- spectral regularization (1)
- spectral theorem (1)
- spectral theory (1)
- spin Hall effect (1)
- spirallike function (1)
- spread correction (1)
- stability (1)
- stable variety (1)
- stark Hughes-frei (1)
- starker Halbverband von Halbgruppen (1)
- stars: early-type (1)
- stars: individual: Vega (1)
- stars: oscillations (1)
- stars: rotation (1)
- starspots (1)
- state estimation (1)
- statistical (1)
- statistical inference (1)
- statistical inverse problem (1)
- statistical machine learning (1)
- statistical methods (1)
- statistics (1)
- statistische Inferenz (1)
- statistisches maschinelles Lernen (1)
- step process (1)
- step-up (1)
- stiff ODE (1)
- stochastic Burgers equations (1)
- stochastic Marcus (canonical) differential equation (1)
- stochastic bridges (1)
- stochastic completeness (1)
- stochastic interacting particles (1)
- stochastic mechanics (1)
- stochastic models (1)
- stochastic ordering (1)
- stochastic process (1)
- stochastic reaction diffusion equation with heavy-tailed Levy noise (1)
- stochastic systems (1)
- stochastics (1)
- stochastische Anordnung (1)
- stochastische Mechanik (1)
- stochastische Zellulare Automaten (1)
- stochastisches interagierendes System (1)
- stress variability (1)
- strong semilattice of semigroups (1)
- strongly Hughes-free (1)
- strongly pseudoconvex domains (1)
- strongly tempered stable Levy measure (1)
- structure formation (1)
- structured cantilever (1)
- structured numbers (1)
- strukturierte Zahlen (1)
- sub-grid scale (1)
- subspaces (1)
- supergeometry (1)
- superposition (1)
- superposition of n-ary operations and n-ary (1)
- superposition of operations (1)
- surgery (1)
- surrogate loss (1)
- survival analysis (1)
- symbols (1)
- symplectic manifold (1)
- systems pharmacology (1)
- target dimensions (1)
- targeted antineoplastic drugs (1)
- teacher training mathematics (1)
- teaching (1)
- temporal discretization (1)
- terms (1)
- terms and (1)
- terrigener Staub (1)
- terrigenous dust (1)
- test ability (1)
- tetration (1)
- the Cauchy problem (1)
- the Dirichlet problem (1)
- the Goursat problem (1)
- the characteristic Cauchy problem (1)
- the first boundary value problem (1)
- the linearised Einstein equation (1)
- theorem (1)
- theory (1)
- therapeutic (1)
- thermospheric wind (1)
- thymoproteasome (1)
- thymus (1)
- tiling theory (1)
- time (1)
- time duality (1)
- time reversal (1)
- time series (1)
- time series with heavy tails (1)
- time-fractional derivative (1)
- topic modeling (1)
- torsion forms (1)
- tracer tomography (1)
- transceiver (TRX) (1)
- transdimensional inversion (1)
- transformation (1)
- transformation semigroups (1)
- transformations on infinite set (1)
- transition paths (1)
- trapped surfaces (1)
- travel time tomography (1)
- triply periodic minimal surface (1)
- truncated SVD (1)
- two-dimensional topology (1)
- two-level interacting processes (1)
- tyrosine kinase inhibitors (1)
- ulcerative colitis (1)
- ultracontractivity (1)
- uncertainty (1)
- unendlich teilbare Punktprozesse (1)
- unendliche Teilbarkeit (1)
- uniqueness (1)
- universal Hopf algebra of renormalization (1)
- unknown variance (1)
- unsteady flow (1)
- unzerlegbare Varifaltigkeit (1)
- upper atmosphere model (1)
- vagal sympathetic activity (1)
- value problems (1)
- variational calculus (1)
- variational iteration method (1)
- variational principle (1)
- varifold (1)
- verification (1)
- video study (1)
- viral fitness (1)
- wahrscheinlichkeitserzeugende Funktion (1)
- wave structure (1)
- wavelet analysis (1)
- weak dependence (1)
- weakly almost periodic (1)
- weiche Materie (1)
- weight-based formulations (1)
- weighted (1)
- weighted Hölder spaces (1)
- weighted Sobolev spaces (1)
- weighted edge and corner spaces (1)
- weighted graphs (1)
- well-posedness (1)
- zero-noise limit (1)
- zufällige Summe (1)
- когомологии (1)
- комплекс де Рама (1)
- проблема Неймана (1)
- теория Ходжа (1)
Institute
- Institut für Mathematik (1811) (remove)
We establish elements of a new approach to ellipticity and parametrices within operator algebras on manifolds with higher singularities, only based on some general axiomatic requirements on parameter-dependent operators in suitable scales of spaes. The idea is to model an iterative process with new generations of parameter-dependent operator theories, together with new scales of spaces that satisfy analogous requirements as the original ones, now on a corresponding higher level. The "full" calculus involves two separate theories, one near the tip of the corner and another one at the conical exit to infinity. However, concerning the conical exit to infinity, we establish here a new concrete calculus of edge-degenerate operators which can be iterated to higher singularities.
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.
Assimilation of pseudo-tree-ring-width observations into an atmospheric general circulation model
(2017)
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.
Towards the assimilation of tree-ring-width records using ensemble Kalman filtering techniques
(2016)
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.
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.
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.
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.
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.
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.
We develop the method of Fischer-Riesz equations for general boundary value problems elliptic in the sense of Douglis-Nirenberg. To this end we reduce them to a boundary problem for a (possibly overdetermined) first order system whose classical symbol has a left inverse. For such a problem there is a uniquely determined boundary value problem which is adjoint to the given one with respect to the Green formula. On using a well elaborated theory of approximation by solutions of the adjoint problem, we find the Cauchy data of solutions of our problem.
We define weak boundary values of solutions to those nonlinear differential equations which appear as Euler-Lagrange equations of variational problems. As a result 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 the study of Lagrangian problems.
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.
We elaborate a boundary Fourier method for studying an analogue of the Hilbert problem for analytic functions within the framework of generalised Cauchy-Riemann equations. The boundary value problem need not satisfy the Shapiro-Lopatinskij condition and so it fails to be Fredholm in Sobolev spaces. We show a solvability condition of the Hilbert problem, which looks like those for ill-posed
problems, and construct an explicit formula for approximate solutions.
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.
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.
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.
Data assimilation has been an active area of research in recent years, owing to its wide utility. At the core of data assimilation are filtering, prediction, and smoothing procedures. Filtering entails incorporation of measurements' information into the model to gain more insight into a given state governed by a noisy state space model. Most natural laws are governed by time-continuous nonlinear models. For the most part, the knowledge available about a model is incomplete; and hence uncertainties are approximated by means of probabilities. Time-continuous filtering, therefore, holds promise for wider usefulness, for it offers a means of combining noisy measurements with imperfect model to provide more insight on a given state.
The solution to time-continuous nonlinear Gaussian filtering problem is provided for by the Kushner-Stratonovich equation. Unfortunately, the Kushner-Stratonovich equation lacks a closed-form solution. Moreover, the numerical approximations based on Taylor expansion above third order are fraught with computational complications. For this reason, numerical methods based on Monte Carlo methods have been resorted to. Chief among these methods are sequential Monte-Carlo methods (or particle filters), for they allow for online assimilation of data. Particle filters are not without challenges: they suffer from particle degeneracy, sample impoverishment, and computational costs arising from resampling.
The goal of this thesis is to:— i) Review the derivation of Kushner-Stratonovich equation from first principles and its extant numerical approximation methods, ii) Study the feedback particle filters as a way of avoiding resampling in particle filters, iii) Study joint state and parameter estimation in time-continuous settings, iv) Apply the notions studied to linear hyperbolic stochastic differential equations.
The interconnection between Itô integrals and stochastic partial differential equations and those of Stratonovich is introduced in anticipation of feedback particle filters. With these ideas and motivated by the variants of ensemble Kalman-Bucy filters founded on the structure of the innovation process, a feedback particle filter with randomly perturbed innovation is proposed. Moreover, feedback particle filters based on coupling of prediction and analysis measures are proposed. They register a better performance than the bootstrap particle filter at lower ensemble sizes.
We study joint state and parameter estimation, both by means of extended state spaces and by use of dual filters. Feedback particle filters seem to perform well in both cases. Finally, we apply joint state and parameter estimation in the advection and wave equation, whose velocity is spatially varying. Two methods are employed: Metropolis Hastings with filter likelihood and a dual filter comprising of Kalman-Bucy filter and ensemble Kalman-Bucy filter. The former performs better than the latter.
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.
Asymptotic Solutions of the Dirichlet Problem for the Heat Equation at a Characteristic Point
(2015)
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.
Asymptotic solutions of the Dirichlet problem for the heat equation at a characteristic point
(2012)
The Dirichlet problem for the heat equation in a bounded domain is characteristic, for there are boundary points at which the boundary touches a characteristic hyperplane t = c, c being a constant. It was I.G. Petrovskii (1934) who first found necessary and sufficient conditions on the boundary which guarantee that the solution is continuous up to the characteristic point, provided that the Dirichlet data are continuous. This paper initiated standing interest in studying general boundary value problems for parabolic equations in bounded domains. We contribute to the study by constructing a formal solution of the Dirichlet problem for the heat equation in a neighbourhood of a characteristic boundary point and showing its asymptotic character.
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.
Integral Fourier operators
(2017)
This volume of contributions based on lectures delivered at a school on Fourier Integral Operators
held in Ouagadougou, Burkina Faso, 14–26 September 2015, provides an introduction to Fourier Integral Operators (FIO) for a readership of Master and PhD students as well as any interested layperson. Considering the wide
spectrum of their applications and the richness of the mathematical tools they involve, FIOs lie the cross-road of many a field. This volume offers
the necessary background, whether analytic or geometric, to get acquainted with FIOs, complemented by more advanced material presenting various aspects of active research in that area.
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.
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.