Refine
Has Fulltext
- no (1645) (remove)
Year of publication
- 2024 (1)
- 2023 (8)
- 2022 (42)
- 2021 (42)
- 2020 (60)
- 2019 (54)
- 2018 (55)
- 2017 (52)
- 2016 (52)
- 2015 (47)
- 2014 (37)
- 2013 (44)
- 2012 (30)
- 2011 (35)
- 2010 (28)
- 2009 (31)
- 2008 (9)
- 2007 (12)
- 2006 (52)
- 2005 (71)
- 2004 (51)
- 2003 (49)
- 2002 (51)
- 2001 (73)
- 2000 (71)
- 1999 (95)
- 1998 (104)
- 1997 (104)
- 1996 (73)
- 1995 (100)
- 1994 (73)
- 1993 (16)
- 1992 (18)
- 1991 (4)
Document Type
- Article (1061)
- Monograph/Edited Volume (420)
- Doctoral Thesis (88)
- Other (46)
- Review (16)
- Conference Proceeding (7)
- Preprint (4)
- Part of a Book (3)
Is part of the Bibliography
- yes (1645)
Keywords
- data assimilation (8)
- Bayesian inference (7)
- ensemble Kalman filter (6)
- Navier-Stokes equations (5)
- discrepancy principle (5)
- linear term (5)
- Cauchy problem (4)
- Data assimilation (4)
- Earthquake interaction (4)
- Elliptic complexes (4)
- Fredholm property (4)
- Geomagnetic field (4)
- Neumann problem (4)
- Pseudo-differential operators (4)
- Statistical seismology (4)
- clone (4)
- linear hypersubstitution (4)
- optimal transport (4)
- partial clone (4)
- regularization (4)
- uncertainty quantification (4)
- Bayesian inverse problems (3)
- Bayesian inversion (3)
- DLR equations (3)
- Dyson-Schwinger equations (3)
- Hodge theory (3)
- Kalman filter (3)
- Probabilistic forecasting (3)
- Transformation semigroups (3)
- equi-singular connections (3)
- forecasting (3)
- gradient flow (3)
- graphs (3)
- index (3)
- localization (3)
- multiplicative noise (3)
- relative rank (3)
- statistical seismology (3)
- stochastic differential equations (3)
- transformations (3)
- Aerosols (2)
- Aluminium (2)
- Arctic haze (2)
- Asymptotics of solutions (2)
- Boolean model (2)
- Dirac operator (2)
- Dirichlet form (2)
- Dirichlet to Neumann operator (2)
- Edge calculus (2)
- Ellipticity of corner-degenerate operators (2)
- Ensemble Kalman filter (2)
- Finsler distance (2)
- Fokker-Planck equation (2)
- Fredholm complexes (2)
- Gamma-convergence (2)
- Gaussian process (2)
- Gibbs point process (2)
- Graphs (2)
- Iran (2)
- Laplacian (2)
- Left-ordered groups (2)
- Levenberg-Marquardt method (2)
- Lidar (2)
- MCMC (2)
- Machine learning (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)
- Multiple zeta values (2)
- Onsager-Machlup functional (2)
- Order-preserving transformations (2)
- Picard-Fuchs equations (2)
- Poincare inequality (2)
- Quasilinear equations (2)
- Removable sets (2)
- Royden boundary (2)
- Schrodinger operators (2)
- Scientific discovery learning (2)
- Seismicity and tectonics (2)
- Specific entropy (2)
- Time series (2)
- Toeplitz operators (2)
- Uncertainty quantification (2)
- WKB-expansion (2)
- Wavelet transform (2)
- Yamabe operator (2)
- Zaremba problem (2)
- adaptive estimation (2)
- alpha-stable Levy process (2)
- alternative variety (2)
- and prediction (2)
- asymptotic behavior (2)
- boundary value problems (2)
- classical solution (2)
- cluster expansion (2)
- cohomology (2)
- confidence sets (2)
- counterterms (2)
- de Rham complex (2)
- early stopping (2)
- estimation (2)
- filter (2)
- formula (2)
- generators (2)
- geomagnetic field (2)
- graph (2)
- ground state (2)
- hyperbolic tilings (2)
- inflammatory bowel disease (2)
- infliximab (2)
- inverse problem (2)
- isotopic tiling theory (2)
- iterative regularization (2)
- kernel methods (2)
- linear formula (2)
- linear tree language (2)
- local time (2)
- logarithmic source condition (2)
- manifolds with boundary (2)
- maximal subsemigroups (2)
- maximum a posteriori (2)
- methods (2)
- minimax convergence rates (2)
- models (2)
- nonlinear filtering (2)
- nonlinear operator (2)
- operator-valued symbols (2)
- orbifolds (2)
- orthogroup (2)
- particle filter (2)
- pediatrics (2)
- point process (2)
- population pharmacokinetics (2)
- positive solutions (2)
- prediction (2)
- reciprocal class (2)
- renormalization Hopf algebra (2)
- reproducing kernel Hilbert space (2)
- restricted range (2)
- reversible measure (2)
- secular variation (2)
- sequential data assimilation (2)
- strong semilattice of semigroups (2)
- term (2)
- trace (2)
- transfer operator (2)
- transition path theory (2)
- tunneling (2)
- uniqueness (2)
- (2+1)-dimensional gravity (1)
- (generalised) wealdy differentiable function (1)
- 26D15 (1)
- 31A25 (1)
- 31C20 (1)
- 35B09 (1)
- 35J70 (1)
- 35K65 (1)
- 35R02 (1)
- 39A12 (primary) (1)
- 47A52 (1)
- 47G30 (1)
- 58E35 (secondary) (1)
- 58J40 (1)
- 65F18 (1)
- 65R20 (1)
- 65R32 (1)
- 78A46 (1)
- AERONET (1)
- AFM (1)
- ALOS-2 PALSAR-2 (1)
- AMS (1)
- APC concentration gradient (1)
- Absorption kinetics (1)
- Achievement goal orientation (1)
- Aerosol (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)
- Angiogenesis (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)
- Atiyah-Bott obstruction (1)
- Atmosphere (1)
- Audience Response System (1)
- Automotive (1)
- Averaging principle (1)
- BTZ black hole (1)
- Banach-valued process (1)
- Bayesian (1)
- Bayesian method (1)
- Beltrami equation (1)
- Bernstein inequality (1)
- Biodiversity (1)
- Birkhoff theorem (1)
- Birman–Krein formula (1)
- Birth-and-death process (1)
- Bisectorial operator (1)
- Bivariant K-theory (1)
- Blood coagulation network (1)
- Boundary value method (1)
- Boundary value methods (1)
- Boundary value problem (1)
- Boundary value problems (1)
- Boutet de Monvel's calculus (1)
- Brownian motion with discontinuous drift (1)
- Broyden's method (1)
- Bruck-Reilly extension (1)
- CFD (1)
- CHAMP satellite (1)
- COCOMO (1)
- COVID-19 (1)
- CRPS (1)
- Caccioppoli inequality (1)
- Calculation (1)
- Canonical (Marcus) SDE (1)
- Cartan's development (1)
- Cartesian product of varifolds (1)
- Casimir energy (1)
- Cauchy data spaces (1)
- Cell-level kinetics (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 semigroup (1)
- Clifford-Halbgruppen (1)
- Cloud Computing (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)
- Constant scalar curvature (1)
- Continuum (1)
- Continuum random cluster model (1)
- Control theory (1)
- Convergence rates (1)
- Convex cones (1)
- Core (1)
- Core dynamics (1)
- Core field (1)
- Corner pseudo-differential operators (1)
- Correlation based modelling (1)
- Counting process (1)
- Cox model (1)
- Critical mathematics education (1)
- Critique (1)
- Curvature varifold (1)
- C‐ reactive protein remission (1)
- DFN (1)
- DLR equation (1)
- DMSP (1)
- Daily gravity field (1)
- Data augmentation (1)
- Data-driven modelling (1)
- De Rham complex (1)
- Decay of eigenfunctions (1)
- Decorated cones (1)
- Definitions (1)
- Delaney--Dress (1)
- Dependent thinning (1)
- Derivation (1)
- Detailed balance (1)
- Determinant (1)
- Deterministic finite state automata (1)
- Diagrams (1)
- Dickkopf diffusion and feedback regulation (1)
- Differential invariant (1)
- Digital technology (1)
- Direct method (1)
- Dirichlet mixture (1)
- Dirichlet problem (1)
- Dirichlet-form (1)
- Disagreement percolation (1)
- Discontinuous Robin condition (1)
- Discovery learning (1)
- Discrete Dirichlet forms (1)
- Discrete-element method (1)
- Distributed Learning (1)
- Dobrushin criterion; (1)
- Duality formula (1)
- DySEM (1)
- Dynamical systems (1)
- Dynamo (1)
- Dynamo: theories and simulations (1)
- E-band (1)
- EGFR (1)
- Earth rotation (1)
- Earth's magnetic field (1)
- Earthquake dynamics (1)
- Earthquake modeling (1)
- Ecosystem (1)
- Edge and corner pseudo-differential operators (1)
- Edge degenerate operators (1)
- Edge symbols (1)
- Efficient solutions (1)
- Effort (1)
- Eigenvalue problem (1)
- Eigenvalues (1)
- Einstein space (1)
- Einstein-Hilbert action (1)
- Electromagnetic induction (1)
- Electron spectroscopy (1)
- Elliptic boundary (1)
- Ellipticity and parametrices (1)
- Ellipticity of edge-degenerate operators (1)
- Endothelin (ET) (1)
- Energy resolution (1)
- Ensemble Kalman (1)
- Ensemble Kalman Filter (1)
- Entdeckendes Lernen (1)
- Environmental DNA (1)
- Epistemologie (1)
- Epistemology (1)
- Equivalence (1)
- Error analysis (1)
- Error control/adaptivity (1)
- Error covariance (1)
- Essential spectrum (1)
- Estimability (1)
- Euclidean fields (1)
- Euler-Lagrange equations (1)
- Europe (1)
- Exact solution (1)
- Exponential decay of pair correlation (1)
- Extensive transformation (1)
- FIB patterning (1)
- False discovery rate (1)
- Fast win (1)
- Fault slip (1)
- Fence (1)
- Fermi golden rule (1)
- Finite difference method (1)
- Finite energy sections (1)
- Finite transformation semigroup (1)
- First exit location (1)
- First exit time (1)
- First order PDE (1)
- First passage time (1)
- First variation (1)
- Fluvial (1)
- Foliated spaces (1)
- Force splitting (1)
- Forecasting and prediction (1)
- Fortuin-Kasteleyn representation (1)
- Foucault (1)
- Fourier and Mellin transform (1)
- Fourier and Mellin transforms (1)
- Fourier transform (1)
- Fourier-Laplace transform (1)
- Fourth order Sturm-Liouville problem (1)
- Fractal (1)
- Fractions with linear poles (1)
- Fredholm alternative (1)
- Fredholm operator (1)
- Freidlin-Wentzell theory (1)
- Fremdverstehen (1)
- Full rank matrix filters (1)
- Functional calculus (1)
- Future time interval (1)
- Fuzzy logic (1)
- G-Wishart distribution (1)
- GPS (1)
- GRACE (1)
- Gas and hydrate systems (1)
- Gauss-Bonnet-Chern (1)
- Gaussian graphical models (1)
- Gaussian kernel estimators (1)
- Gaussian mixtures (1)
- Gaussian sequence model (1)
- Gender (1)
- Generalised mean curvature vector (1)
- Generalized hybrid Monte Carlo (1)
- Geodetic measurements (1)
- Geodynamo (1)
- Geomagnetic jerks (1)
- Geomagnetic models (1)
- Geomagnetic secular variation (1)
- Geomagnetic storm (1)
- Geomagnetism (1)
- Geometry (1)
- Geopotential theory (1)
- Gestagenic drug (1)
- Gestures (1)
- Gibbs measure (1)
- Gibbs processes (1)
- Gigli-Mantegazza flow (1)
- Girsanov formula (1)
- Global attractor (1)
- Global sensitivity analysis (1)
- Globally hyperbolic Lorentz manifold (1)
- Goal specificity (1)
- Goursat problem (1)
- Granular matter (1)
- Graph Laplacians (1)
- Gravity anomalies and Earth structure (1)
- Greatest harmonic minorant (1)
- Green's function (1)
- Green´s Relations (1)
- H-infinity-functional calculus (1)
- Haar system (1)
- Halbgruppentheorie (1)
- Hamiltonian dynamics (1)
- Hamiltonicity (1)
- Harmonic measure (1)
- Hawkes process (1)
- Heat kernel coefficients (1)
- Heavy-tailed distributions (1)
- Helmholtz problem (1)
- Heuristics (1)
- High dimensional statistical inference (1)
- Hilbert Scales (1)
- Hochschule (1)
- Holder-type source condition (1)
- Holomorphic map (1)
- Holomorphic mappings (1)
- Hopf algebra (1)
- Hopf algebra of Feynman diagrams (1)
- Hughes-free (1)
- Hyperbolic dynamical system (1)
- IGRF (1)
- ITG-Grace2010 (1)
- Idempotents (1)
- Identities (1)
- Ill-conditioning (1)
- In vitro dissolution (1)
- Indefinite (1)
- Index theory (1)
- Induced (1)
- Inference post model-selection (1)
- Infinite chain (1)
- Infinite divisibility (1)
- Infinite graph (1)
- Infinite-dimensional SDE (1)
- Infinite-dimensional interacting diffusion (1)
- Infinitely divisible point processes (1)
- Inquiry-based learning (1)
- Instruction (1)
- Integrability (1)
- Integral varifold (1)
- Integration by parts formula (1)
- Interpolation (1)
- Intrinsic metrics for Dirichlet forms (1)
- Intrinsicmotivation (1)
- Inverse Sturm-Liouville problem (1)
- Inverse ill-posed problem (1)
- Inverse problem (1)
- Inverse problems (1)
- Inverse theory (1)
- Inversion (1)
- Ionospheric current (1)
- Isometry group (1)
- Iterated corner asymptotics of solutions (1)
- Ito SDE (1)
- Ito integral (1)
- Jump processes (1)
- KB-space (1)
- Kalman Bucy filter (1)
- Kalman smoother (1)
- Kalman-Bucy Filter (1)
- Kato condition (1)
- Kato square root problem (1)
- Kegel space (1)
- Kernel regression (1)
- Kette von Halbgruppen (1)
- Kinesin V (1)
- Koopman operator (1)
- Koopman semigroup (1)
- L-2-invariants (1)
- LETKF (1)
- Lagrangian modeling (1)
- Lagrangian modelling (1)
- Lagrangian system (1)
- Lagrangian-averaged equations (1)
- Lame system (1)
- Landing site selection (1)
- Landweber iteration (1)
- Langevin dynamics (1)
- Laplace-Beltrami operator (1)
- Laplace-type operator (1)
- Lattice cones (1)
- Learning theory (1)
- Lefschetz number (1)
- Lerntheorie (1)
- Level of confidence (1)
- Levy diffusion approximation (1)
- Levy diffusions on manifolds (1)
- Levy process (1)
- Levy processes (1)
- Levy type processes (1)
- Lidar remote sensing (1)
- Lie groupoid (1)
- Linear inverse problems (1)
- Linearized equation (1)
- Lipopolysaccharides (LPS) (1)
- Lipschitz domain (1)
- Lithology (1)
- Local index theory (1)
- Locality (1)
- Lorenz 96 (1)
- Low rank matrices (1)
- Lower bound (1)
- Lyapunov equation (1)
- Lyapunov function (1)
- MASCOT (1)
- MCMC modelling (1)
- MOSAiC (1)
- Magnetic anomalies: modelling and interpretation (1)
- Magnetic field variations through time (1)
- Magnetosphere (1)
- Magnus expansion (1)
- Malliavin calculus (1)
- Manifolds with boundary (1)
- Marcus canonical equation (1)
- Marked Gibbs process (1)
- Markov Chain (1)
- Markov chain (1)
- Markov semigroups (1)
- Marx (1)
- Mathematical model (1)
- Mathematical modeling (1)
- Mathematics classrooms (1)
- Mathematikunterricht (1)
- Matrix function approximation (1)
- Maximal subsemibands (1)
- McKean-Vlasov (1)
- Measure-preserving semiflow (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)
- Menger algebra of rank n (1)
- Metastasis (1)
- Microphysical particle properties (1)
- Microphysical properties (1)
- Minimax Optimality (1)
- Minimax convergence rates (1)
- Minimax hypothesis testing (1)
- Minimization (1)
- Minimizers (1)
- Misconceptions (1)
- Mittag-Leffler function (1)
- Model comparison (1)
- Model selection (1)
- Modified Hamiltonians (1)
- Moduli space (1)
- Molecular dynamics (1)
- Molecular motor (1)
- Mollification (1)
- Monte Carlo (1)
- Monte Carlo method (1)
- Morse-Smale property (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)
- Multivariate meromorphic functions (1)
- NWP (1)
- Nodal domain (1)
- Non-Markov drift (1)
- Non-coercive problem (1)
- Non-linear semigroups (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)
- Numerical simulation (1)
- Numerical weather prediction (1)
- Numerov's method (1)
- Ny-Alesund (1)
- ODE with random initial conditions (1)
- OSSS inequality (1)
- Ollivier-Ricci (1)
- Operation (1)
- Operator algebras (1)
- Operator differential equations (1)
- Operator-valued symbols (1)
- Operator-valued symbols of Mellin type (1)
- Operators on singular cones (1)
- Operators on singular manifolds (1)
- Optimal transportation (1)
- Optimality conditions (1)
- Order-preserving (1)
- Order-preserving bijections (1)
- Order-preserving maps (1)
- Order-reversing transformations (1)
- Ordered fields (1)
- Ordinary differential equations (1)
- Orlicz space height-excess (1)
- Ornstein-Uhlenbeck (1)
- Orthogonal connections with torsion (1)
- Orthogruppen (1)
- PBPK (1)
- PBTK (1)
- PC-MRI (1)
- PROP (1)
- Pacific Ocean (1)
- Pade approximants (1)
- Paleoclimate reconstruction (1)
- Paleoecology (1)
- Paleogeography (1)
- Papangelou process (1)
- Papangelou processes (1)
- Paracrine and autocrine regulation (1)
- Parametrices of elliptic operators (1)
- Partial algebra (1)
- Penalized likelihood (1)
- Perfect groups (1)
- Permeability and porosity (1)
- Permuted balance (1)
- Perron-Frobenius operator (1)
- Personal Response System (1)
- Perturbation theory (1)
- Perturbative renormalization (1)
- Pfaffian (1)
- Pharmacokinetic models (1)
- Phase transition (1)
- Physics concepts (1)
- Physics-based machine learning (1)
- PoSI constants (1)
- Poisson process (1)
- Polya difference process (1)
- Polya sum (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)
- Probabilistic numerical methods (1)
- Problem solving (1)
- Proper orthogonal decomposition (1)
- Protein binding (1)
- Proving (1)
- Proxy forward modeling (1)
- Pseudo-differential algebras (1)
- Quadratic tilt-excess (1)
- Quadrature mirror filters (1)
- Quadrature rule (1)
- Quantizations (1)
- Quasi Random Walk (1)
- Quasi-shuffles (1)
- Quasimodes (1)
- RMSE (1)
- Radar backscatter (1)
- Raman lidar (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)
- Reaction-diffusion system (1)
- Real-variable harmonic analysis (1)
- Reciprocal processes (1)
- Reclassification (1)
- Rectifiable varifold (1)
- Recursive transport equations (1)
- Regular semigroups (1)
- Regular variation (1)
- Regularity analysis (1)
- Regularization (1)
- Renormalisation (1)
- Renormalization (1)
- Reproducing kernel Hilbert space (1)
- Reversibility (1)
- Rho invariants (1)
- Ricci solitons (1)
- Riemannian manifold (1)
- Riesz continuity (1)
- Riesz topology (1)
- Risk assessment (1)
- Risk model (1)
- Roe algebras (1)
- Root function (1)
- Rooted trees (1)
- Rota-Baxter (1)
- Rota-Baxter algebra (1)
- Rothe method (1)
- Rough paths (1)
- Runge-Kutta methods (1)
- SAR amplitude (1)
- SHBG (1)
- SPDEs (1)
- Sampling (1)
- Sand pile (1)
- Satellite geodesy (1)
- Satellite magnetics (1)
- Satellite magnetometer observations (1)
- Scattering theory (1)
- Schrodinger equation (1)
- Schrödinger operator (1)
- Schrödinger operators (1)
- Second fundamental form (1)
- Secondary: 47L80 (1)
- Secular variation (1)
- Secular variation rate of change (1)
- Sedimentary ancient DNA (sedaDNA) (1)
- Self-exciting point process (1)
- Self-interacting scalar field (1)
- Semi-classical analysis (1)
- Semiclassical analysis (1)
- Semiclassical difference operator (1)
- Semigroup (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 of Gaussian processes (1)
- Singular analysis (1)
- Singular cones (1)
- Sinkhorn approximation (1)
- Sinkhorn problem (1)
- Small (1)
- Smooth cones (1)
- Smoothing (1)
- Sobolev Poincare inequality (1)
- Sobolev spaces (1)
- Sociolinguistics (1)
- Soziolinguistik (1)
- Spatio-temporal ETAS model (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)
- Spin geometry (1)
- Stability selection (1)
- Statistical inverse problem (1)
- Statistical learning (1)
- Statistical methods (1)
- Stochastic Burgers equations (1)
- Stochastic Differential Equation (1)
- Stochastic Hamiltonian (1)
- Stochastic bridges (1)
- Stochastic differential equations (1)
- Stochastic domination (1)
- Stochastic epidemic model (1)
- Stochastic geometry (1)
- Stochastic systems (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)
- Structured population equation (1)
- Studium (1)
- Sturm-Liouville problem (1)
- Sturm-Liouville problems of higher order (1)
- Subcritical (1)
- Subdivision schemes (1)
- Subdivisions (1)
- Subsampling (1)
- Super-quadratic tilt-excess (1)
- Surface roughness (1)
- Surgery (1)
- Svalbard (1)
- Sylvester equations (1)
- Symplectic manifold (1)
- Synchrotron (1)
- TEC (1)
- Taphonomy (1)
- Technology (1)
- TerraSAR-X/TanDEM-X (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)
- Transition probabilities (1)
- Tunneling (1)
- Turbulence (1)
- Twisted product (1)
- Twisted symbolic estimates (1)
- Umbilic product (1)
- Unique Gibbs state (1)
- Unit disk (1)
- Universal covering group (1)
- Van der Pol oscillator (1)
- Variable selection (1)
- Variational principle (1)
- Vector bundle (1)
- Vector subdivision schemes (1)
- Visuospatial reasoning (1)
- Volterra operator (1)
- WKB ansatz (1)
- WKB approximation (1)
- WKB expansion (1)
- Warped product (1)
- Wasserstein distance (1)
- Wave equation (1)
- Weighted (1)
- Weighted edge spaces (1)
- Well log (1)
- Weyl tensor (1)
- Wide angle (1)
- Willmore functional (1)
- Wnt/beta-catenin signalling pathway (1)
- Yamabe invariant (1)
- Zeta-function (1)
- Zig-zag order (1)
- a posteriori stopping rule (1)
- accelerated small (1)
- accuracy (1)
- acute severe (1)
- adaptive (1)
- adaptivity (1)
- adipose tissue (1)
- adrenal insufficiency (1)
- aerosol (1)
- aerosol size distribution (1)
- aerosol-boundary layer interactions (1)
- affine (1)
- affine invariance (1)
- algebra (1)
- algebra of rank n (1)
- algebraic systems (1)
- algebras (1)
- alignment (1)
- alternating direction implicit (1)
- analytic functional (1)
- analytic perturbation theory (1)
- animal behavior (1)
- anti-infective (1)
- antibiotics (1)
- antigen processing (1)
- antimicrobial stewardship (1)
- approximate differentiability (1)
- approximation (1)
- archaeomagnetism (1)
- articulation (1)
- assimilation (1)
- association (1)
- asteroseismology (1)
- asymptotic (1)
- asymptotic approximation (1)
- asymptotic expansion (1)
- asymptotic expansions (1)
- asymptotic method (1)
- asymptotic properties of eigenfunctions (1)
- aurora (1)
- autonomic nervous system (1)
- b-value (1)
- backtrajectories; (1)
- backward heat problem (1)
- balanced dynamics (1)
- behavior (1)
- beta-functions (1)
- binding (1)
- bioinformatics (1)
- biological population equations (1)
- birhythmic behavior (1)
- black holes (1)
- body mass index procedure (1)
- body surface area (1)
- boundary element method (1)
- boundary regularity (1)
- bridge (1)
- category equivalence of clones (1)
- certolizumab pegol (1)
- chain of semigroups (1)
- characterization of point processes (1)
- chemical master equation (1)
- chemistry (1)
- classification with partial labels (1)
- clathrin (1)
- clifford semigroup (1)
- clone of operations (1)
- cluster (1)
- clustering (1)
- coarea formula (1)
- coherent set (1)
- coloration of terms (1)
- colored solid varieties (1)
- compact resolvent (1)
- companies (1)
- completeness levels (1)
- composition of terms (1)
- compound polyhedra (1)
- computational biology (1)
- concentration (1)
- concentration inequalities (1)
- condition number (1)
- conditional Bayes factors (1)
- conditions (1)
- conditions of success (1)
- confidence intervals (1)
- congenital adrenal hyperplasia (1)
- conjugate gradient (1)
- conservative discretization (1)
- consistency (1)
- continuous testing (1)
- continuous-time data assimilation (1)
- convergence assessment (1)
- convergence rate (1)
- convolution (1)
- corner Sobolev spaces with double weights (1)
- corner parametrices (1)
- correlated noise (1)
- cortisol (1)
- coupling methods (1)
- critically ill (1)
- crohn's disease (1)
- crossed product (1)
- curvature varifold (1)
- data-driven (1)
- decomposition (1)
- delaney-dress tiling theory (1)
- density estimation (1)
- derivative-free optimization (1)
- dht-symmetric category (1)
- difference operator (1)
- differential cohomology (1)
- diffusion maps (1)
- dimension independent bound (1)
- dimension reduction (1)
- disagreement percolation (1)
- discrete Schrodinger (1)
- discrete spectrum (1)
- disease activity (1)
- disjunction of identities (1)
- distribution (1)
- distribution kernel (1)
- distribution with asymptotics (1)
- distributional boundary (1)
- distributions with one-sided support (1)
- division of spaces (1)
- division ring of fractions (1)
- division rings (1)
- dried blood spots (1)
- drug monitoring (1)
- duality formula (1)
- dynamical models (1)
- early mathematical education (1)
- earthquake hazards (1)
- earthquake interaction (1)
- earthquake precursor (1)
- eigenfunction (1)
- eigenvalue asymptotics (1)
- eigenvalue decay (1)
- eigenvalue estimate (1)
- eigenvalues (1)
- elliptic boundary (1)
- elliptic complexes (1)
- elliptic differential operators of firstorder (1)
- elliptic equation (1)
- ellipticity (1)
- embedded Markov chain (1)
- embeddings (1)
- endomorphism semigroup (1)
- ensembles (1)
- equation (1)
- equatorial ionization anomaly (1)
- equatorial ionosphere (1)
- equatorial plasma bubbles (1)
- ergodic diffusion processes (1)
- error diagram (1)
- essential position in terms (1)
- eta forms (1)
- evolution equation (1)
- exact simulation methods (1)
- exact solution (1)
- exchange algorithms (1)
- existence (1)
- exit calculus (1)
- expansion (1)
- exponential decay (1)
- eye movements (1)
- false discovery rate (1)
- fat-free mass (1)
- feedback particle filter (1)
- fence-preserving transformations (1)
- fibration (1)
- field-aligned currents (1)
- finite transformation semigroup (1)
- first boundary value problem (1)
- first exit location (1)
- first exit times (1)
- first passage times (1)
- flood loss estimation (1)
- fluid mechanics (1)
- fluid-structure interaction (1)
- forcing from below (1)
- fore-casting (1)
- forecasting and prediction (1)
- formal (1)
- formal power series (1)
- formulas (1)
- fosfomycin (1)
- fractional calculus (1)
- fracture (1)
- fracture network (1)
- frameworks (1)
- frequency-modulated continuous-wave (FMCW) (1)
- functional calculus (1)
- generalized Abelian gauge theory (1)
- generalized Bruck-Reilly *-extension (1)
- generalized eigenfunction (1)
- generalized eigenfunctions (1)
- generating sets (1)
- geodesic distance (1)
- geomorphology (1)
- geophysics (1)
- geopotential theory (1)
- gradient-free (1)
- gradient-free sampling methods (1)
- graph Laplacian (1)
- green function (1)
- group (1)
- group ring (1)
- groups (1)
- hard core interaction (1)
- hard core potential (1)
- heat (1)
- heat kernel (1)
- helicates (1)
- hemodynamics (1)
- heterogeneity (1)
- high dimensional (1)
- high-dimensional inference (1)
- higher index theory (1)
- higher-order Sturm–Liouville problems (1)
- highly (1)
- holomorphic function (1)
- holonomic constraints (1)
- hybrid model (1)
- hybrids (1)
- hydraulic tomography (1)
- hydrocortisone (1)
- hydrogeophysics (1)
- hydrostatic atmosphere (1)
- idealised turbulence (1)
- idleness (1)
- ill-posed problem (1)
- ill-posed problems (1)
- independent splittings (1)
- induced field (1)
- inegral formulas (1)
- infinite-dimensional diffusion (1)
- infinite-dimensional diffusions (1)
- infinitesimal generator (1)
- infliximab dosing (1)
- integral equation (1)
- integration by parts formula (1)
- interacting particle system (1)
- interacting particle systems (1)
- interacting particles (1)
- interaction matrix (1)
- interindividual differences (1)
- interstitial space fluid (1)
- invariance (1)
- invariant measure (1)
- inverse Sturm-Liouville problems (1)
- inverse Sturm–Liouville problems (1)
- inverse correlation estimation (1)
- inverse ill-posed problem (1)
- inverse potential problems (1)
- inverse problems (1)
- inverse scattering (1)
- inverse semigroup (1)
- inverse theory (1)
- inversion (1)
- ionospheric convection (1)
- ionospheric precursors of earthquakes (1)
- isoperimetric estimates (1)
- iterated asymptotics (1)
- jump process (1)
- kernel operator (1)
- knots (1)
- label noise (1)
- large deviations principle (1)
- laser remote sensing (1)
- lattice packing and covering (1)
- learning rates (1)
- least favorable configuration (1)
- left-right asymmetry (1)
- lidar (1)
- likelihood function (1)
- limiting distribution (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)
- lithospheric field (1)
- localisation (1)
- locally indicable group (1)
- log-concavity (1)
- logarithmic convergence rate (1)
- long-time corrections (1)
- low rank matrix recovery (1)
- low rank recovery (1)
- low-rank approximations (1)
- machine learning (1)
- magnetic field variations through (1)
- magnetospheric field (1)
- magnitude errors (1)
- manifolds with conical singularities (1)
- manifolds with corners (1)
- manifolds with cylindrical ends (1)
- manifolds with edge and boundary (1)
- many-electron systems (1)
- mapping class (1)
- mapping class group (1)
- mapping degree (1)
- maps on surfaces (1)
- marked Gibbs point processes (1)
- matrices (1)
- matrix completion (1)
- maturation (1)
- maximal regularity (1)
- maximal subsemigroup (1)
- mean ergodic (1)
- mean-field dynamical system (1)
- mean-field equations (1)
- mental arithmetic (1)
- mental number line (1)
- meropenem (1)
- mesoscale forecasting (1)
- metal-organic (1)
- metastability (1)
- methods: data analysis (1)
- microdialysis (1)
- microphysical properties (1)
- middle-out approach (1)
- mild solution (1)
- minimax hypothesis testing (1)
- minimax optimality (1)
- minor planets, asteroids: individual: (162173) Ryugu (1)
- mixed membership models (1)
- mixing (1)
- mixing optimization (1)
- mixture proportion estimation (1)
- modal analysis (1)
- model error (1)
- model uncertainty (1)
- modified Landweber method (1)
- molecular weaving (1)
- monoclonal antibodies (1)
- morphology (1)
- motion correction (1)
- motivic Feynman rules (1)
- multi-armed bandits (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)
- multiscale analysis (1)
- multiscale dynamics (1)
- multivariable (1)
- mutual contamination models (1)
- n-ary operation (1)
- n-ary term (1)
- negative curvature (1)
- networks (1)
- nodal flow (1)
- noise Levy diffusions (1)
- non-Gaussian (1)
- non-Markov drift (1)
- non-dissipative regularisations (1)
- non-linear mixed effects modelling (NLME); (1)
- nonasymptotic minimax separation rate (1)
- nondeterministic linear hypersubstitution (1)
- nonlinear (1)
- nonlinear PDI (1)
- nonlinear data assimilation (1)
- nonlinear equations (1)
- nonparametric hypothesis testing (1)
- nonparametric regression (1)
- nonparametric statistics (1)
- normal band (1)
- normal reflection (1)
- nuclear norm (1)
- numerical (1)
- numerical analysis/modeling (1)
- numerical methods (1)
- numerical relativity (1)
- numerical weather prediction (1)
- numerical weather prediction/forecasting (1)
- obesity (1)
- obstacle scattering (1)
- open mapping theorem (1)
- operational momentum (1)
- operator (1)
- operator calculus (1)
- operator valued symbols (1)
- operators (1)
- operators with corner symbols (1)
- optimal order (1)
- optimal rate (1)
- oracle inequalities (1)
- oracle inequality (1)
- oral anticancer drugs (1)
- order continuous norm (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)
- oscillatory systems (1)
- p-Laplace equation (1)
- palaeomagnetism (1)
- paleoearthquakes (1)
- parabolic Harnack estimate (1)
- parabolic equations (1)
- parameter estimation (1)
- parametrices (1)
- parametrices of elliptic operators (1)
- partial (1)
- partial Menger (1)
- partial averaging (1)
- partial least squares (1)
- particle filters (1)
- particle methods (1)
- particle microphysics (1)
- particle precipitation (1)
- patch antenna (1)
- pathwise expectations (1)
- percolation (1)
- periodic entanglement (1)
- permanental and determinantal point processes (MSC 2010) 35K55 (1)
- personalised medicine (1)
- pharmacodynamics (1)
- pharmacokinetic (1)
- pharmacokinetic/pharmacodynamic (1)
- pharmacokinetics (1)
- pharmacometrics (1)
- phase dynamics (1)
- phase-locked loop (PLL) (1)
- photometer (1)
- physical SRB measures (1)
- physiologically-based pharmacokinetics (PBPK) (1)
- pi-inverse monoid (1)
- piperacillin/tazobactam (1)
- planar rotors (1)
- polyhedra and polytopes (1)
- positive correlation (1)
- positive mass theorem (1)
- positive operators (1)
- positive scalar curvature (1)
- posterior distribution (1)
- power amplifier (PA) (1)
- power series (1)
- presentations (1)
- principle (1)
- probabilistic modeling (1)
- probability of target attainment (1)
- problem (1)
- problem-solving (1)
- problems (1)
- proposal densities (1)
- proteasome (1)
- protein degradation (1)
- proteolysis (1)
- pseudo-differential boundary value problems (1)
- pseudo-differential operators (1)
- pseudospectral method (1)
- quantification (1)
- quasiconformal mapping (1)
- quasilinear Fredholm operators (1)
- quasimodes (1)
- r-hypersubstitution (1)
- r-term (1)
- radar (1)
- radiation mechanisms: thermal (1)
- random KMM-measure (1)
- random matrix theory (1)
- random walk on Abelian group (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)
- red blood cells (1)
- regimen (1)
- regular and singular inverse Sturm-Liouville problems (1)
- regular figures (1)
- regular monoid (1)
- regular polyhedra (1)
- regular solutions (1)
- regularisation (1)
- regularization method (1)
- regularization methods (1)
- regularly varying Levy process (1)
- rekonstruktive Fallanalyse (1)
- relative isoperimetric inequality (1)
- relative ranks (1)
- representations of groups as automorphism groups of (1)
- resampling (1)
- resolvents (1)
- resonances (1)
- restricted isometry property (1)
- rho-invariants (1)
- right limits (1)
- rock mechanics (1)
- rooted trees (1)
- rough metrics (1)
- saccades (1)
- sampling (1)
- scalable (1)
- seismic hazard (1)
- seismicity (1)
- semi-Lagrangian method (1)
- semi-classical limit (1)
- semiclassical Agmon estimate (1)
- semigroup representations (1)
- semigroup theory (1)
- semigroups on infinite chain (1)
- sequential learning (1)
- shallow-water equations (1)
- short-range prediction (1)
- signal detection (1)
- simulations (1)
- singular Sturm-Liouville (1)
- singular foliation (1)
- singular manifolds (1)
- singular points (1)
- skew Brownian motion (1)
- skew diffusions (1)
- small ball probabilities (1)
- small ball probabilities; (1)
- small noise asymptotic (1)
- small noise asymptotics (1)
- smooth drift dependence (1)
- smoother (1)
- spacecraft operations (1)
- sparsity (1)
- spectral cut-off (1)
- spectral flow (1)
- spectral regularization (1)
- spectral theory (1)
- spread correction (1)
- stability (1)
- stability and accuracy (1)
- stable limit cycle (1)
- stable variety (1)
- star product (1)
- starker Halbverband von Halbgruppen (1)
- stars: early-type (1)
- stars: individual: Vega (1)
- stars: oscillations (1)
- stars: rotation (1)
- starspots (1)
- statistical (1)
- statistical methods (1)
- statistical model selection (1)
- statistics (1)
- step-up (1)
- stiff ODE (1)
- stochastic Marcus (canonical) differential equation (1)
- stochastic bridge (1)
- stochastic completeness (1)
- stochastic models (1)
- stochastic process (1)
- stochastic reaction diffusion equation with heavy-tailed Levy noise (1)
- stochastic systems (1)
- stopping rules (1)
- stress variability (1)
- strong Feller property (1)
- strongly tempered stable Levy measure (1)
- structured cantilever (1)
- sub-grid scale (1)
- subspaces (1)
- superposition (1)
- superposition of n-ary operations and n-ary (1)
- superposition of operations (1)
- surgery (1)
- surrogate loss (1)
- symbols (1)
- tangles (1)
- target dimensions (1)
- targeted antineoplastic drugs (1)
- temporal discretization (1)
- terms (1)
- terms and (1)
- theorem (1)
- theory (1)
- therapeutic (1)
- thermospheric wind (1)
- thymoproteasome (1)
- thymus (1)
- tiling theory (1)
- time (1)
- time-fractional derivative (1)
- topic modeling (1)
- torsion forms (1)
- trace formula (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)
- triply periodic minimal surface (1)
- truncated SVD (1)
- two-dimensional topology (1)
- tyrosine kinase inhibitors (1)
- ulcerative colitis (1)
- ultracontractivity (1)
- uncertainty (1)
- universal Hopf algebra of renormalization (1)
- unknown variance (1)
- unsteady flow (1)
- upper atmosphere model (1)
- vagal sympathetic activity (1)
- value problems (1)
- variable Ricci curvature (1)
- variational iteration method (1)
- variational stability (1)
- verification (1)
- wave structure (1)
- weak boundary values (1)
- weak dependence (1)
- weakly almost periodic (1)
- weight-based formulations (1)
- weighted (1)
- weighted Sobolev spaces (1)
- weighted edge and corner spaces (1)
- weighted graphs (1)
- well-posedness (1)
- когомологии (1)
- комплекс де Рама (1)
- проблема Неймана (1)
- теория Ходжа (1)
Institute
- Institut für Mathematik (1645) (remove)
The author considers the heat equation in dimension one with singular drift and inhomogeneous space-time white noise. In particular, the quadratic variation measure of the white noise is not required to be absolutely continuous w.r.t. the Lebesgue measure, neither in space nor in time. Under some assumptions the author gives statements on strong and weak existence as well as strong and weak uniqueness of continuous solutions.
Extreme value statistics is a popular and frequently used tool to model the occurrence of large earthquakes. The problem of poor statistics arising from rare events is addressed by taking advantage of the validity of general statistical properties in asymptotic regimes. In this note, I argue that the use of extreme value statistics for the purpose of practically modeling the tail of the frequency-magnitude distribution of earthquakes can produce biased and thus misleading results because it is unknown to what degree the tail of the true distribution is sampled by data. Using synthetic data allows to quantify this bias in detail. The implicit assumption that the true M-max is close to the maximum observed magnitude M-max,M-observed restricts the class of the potential models a priori to those with M-max = M-max,M-observed + Delta M with an increment Delta M approximate to 0.5... 1.2. This corresponds to the simple heuristic method suggested by Wheeler (2009) and labeled :M-max equals M-obs plus an increment." The incomplete consideration of the entire model family for the frequency-magnitude distribution neglects, however, the scenario of a large so far unobserved earthquake.
Paleoearthquakes and historic earthquakes are the most important source of information for the estimation of long-term earthquake recurrence intervals in fault zones, because corresponding sequences cover more than one seismic cycle. However, these events are often rare, dating uncertainties are enormous, and missing or misinterpreted events lead to additional problems. In the present study, I assume that the time to the next major earthquake depends on the rate of small and intermediate events between the large ones in terms of a clock change model. Mathematically, this leads to a Brownian passage time distribution for recurrence intervals. I take advantage of an earlier finding that under certain assumptions the aperiodicity of this distribution can be related to the Gutenberg-Richter b value, which can be estimated easily from instrumental seismicity in the region under consideration. In this way, both parameters of the Brownian passage time distribution can be attributed with accessible seismological quantities. This allows to reduce the uncertainties in the estimation of the mean recurrence interval, especially for short paleoearthquake sequences and high dating errors. Using a Bayesian framework for parameter estimation results in a statistical model for earthquake recurrence intervals that assimilates in a simple way paleoearthquake sequences and instrumental data. I present illustrative case studies from Southern California and compare the method with the commonly used approach of exponentially distributed recurrence times based on a stationary Poisson process.
Convergence of the frequency-magnitude distribution of global earthquakes - maybe in 200 years
(2013)
I study the ability to estimate the tail of the frequency-magnitude distribution of global earthquakes. While power-law scaling for small earthquakes is accepted by support of data, the tail remains speculative. In a recent study, Bell et al. (2013) claim that the frequency-magnitude distribution of global earthquakes converges to a tapered Pareto distribution. I show that this finding results from data fitting errors, namely from the biased maximum likelihood estimation of the corner magnitude theta in strongly undersampled models. In particular, the estimation of theta depends solely on the few largest events in the catalog. Taking this into account, I compare various state-of-the-art models for the global frequency-magnitude distribution. After discarding undersampled models, the remaining ones, including the unbounded Gutenberg-Richter distribution, perform all equally well and are, therefore, indistinguishable. Convergence to a specific distribution, if it ever takes place, requires about 200 years homogeneous recording of global seismicity, at least.
We investigate spatio-temporal properties of earthquake patterns in the San Jacinto fault zone (SJFZ), California, between Cajon Pass and the Superstition Hill Fault, using a long record of simulated seismicity constrained by available seismological and geological data. The model provides an effective realization of a large segmented strike-slip fault zone in a 3D elastic half-space, with heterogeneous distribution of static friction chosen to represent several clear step-overs at the surface. The simulated synthetic catalog reproduces well the basic statistical features of the instrumental seismicity recorded at the SJFZ area since 1981. The model also produces events larger than those included in the short instrumental record, consistent with paleo-earthquakes documented at sites along the SJFZ for the last 1,400 years. The general agreement between the synthetic and observed data allows us to address with the long-simulated seismicity questions related to large earthquakes and expected seismic hazard. The interaction between m a parts per thousand yen 7 events on different sections of the SJFZ is found to be close to random. The hazard associated with m a parts per thousand yen 7 events on the SJFZ increases significantly if the long record of simulated seismicity is taken into account. The model simulations indicate that the recent increased number of observed intermediate SJFZ earthquakes is a robust statistical feature heralding the occurrence of m a parts per thousand yen 7 earthquakes. The hypocenters of the m a parts per thousand yen 5 events in the simulation results move progressively towards the hypocenter of the upcoming m a parts per thousand yen 7 earthquake.
Based on an analysis of continuous monitoring of farm animal behavior in the region of the 2016 M6.6 Norcia earthquake in Italy, Wikelski et al., 2020; (Seismol Res Lett, 89, 2020, 1238) conclude that animal activity can be anticipated with subsequent seismic activity and that this finding might help to design a "short-term earthquake forecasting method." We show that this result is based on an incomplete analysis and misleading interpretations. Applying state-of-the-art methods of statistics, we demonstrate that the proposed anticipatory patterns cannot be distinguished from random patterns, and consequently, the observed anomalies in animal activity do not have any forecasting power.
The injection of fluids is a well-known origin for the triggering of earthquake sequences. The growing number of projects related to enhanced geothermal systems, fracking, and others has led to the question, which maximum earthquake magnitude can be expected as a consequence of fluid injection? This question is addressed from the perspective of statistical analysis. Using basic empirical laws of earthquake statistics, we estimate the magnitude M-T of the maximum expected earthquake in a predefined future time window T-f. A case study of the fluid injection site at Paradox Valley, Colorado, demonstrates that the magnitude m 4.3 of the largest observed earthquake on 27 May 2000 lies very well within the expectation from past seismicity without adjusting any parameters. Vice versa, for a given maximum tolerable earthquake at an injection site, we can constrain the corresponding amount of injected fluids that must not be exceeded within predefined confidence bounds.
The Groningen gas field serves as a natural laboratory for production-induced earthquakes, because no earthquakes were observed before the beginning of gas production. Increasing gas production rates resulted in growing earthquake activity and eventually in the occurrence of the 2012M(w) 3.6 Huizinge earthquake. At least since this event, a detailed seismic hazard and risk assessment including estimation of the maximum earthquake magnitude is considered to be necessary to decide on the future gas production. In this short note, we first apply state-of-the-art methods of mathematical statistics to derive confidence intervals for the maximum possible earthquake magnitude m(max). Second, we calculate the maximum expected magnitude M-T in the time between 2016 and 2024 for three assumed gas-production scenarios. Using broadly accepted physical assumptions and 90% confidence level, we suggest a value of m(max) 4.4, whereas M-T varies between 3.9 and 4.3, depending on the production scenario.
In the present study, we summarize and evaluate the endeavors from recent years to estimate the maximum possible earthquake magnitude m(max) from observed data. In particular, we use basic and physically motivated assumptions to identify best cases and worst cases in terms of lowest and highest degree of uncertainty of m(max). In a general framework, we demonstrate that earthquake data and earthquake proxy data recorded in a fault zone provide almost no information about m(max) unless reliable and homogeneous data of a long time interval, including several earthquakes with magnitude close to m(max), are available. Even if detailed earthquake information from some centuries including historic and paleoearthquakes are given, only very few, namely the largest events, will contribute at all to the estimation of m(max), and this results in unacceptably high uncertainties. As a consequence, estimators of m(max) in a fault zone, which are based solely on earthquake-related information from this region, have to be dismissed.