Refine
Year of publication
Document Type
- Article (1087) (remove)
Keywords
- random point processes (18)
- statistical mechanics (18)
- stochastic analysis (18)
- data assimilation (8)
- Bayesian inference (7)
- ensemble Kalman filter (6)
- Navier-Stokes equations (5)
- discrepancy principle (5)
- linear term (5)
- 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)
- uncertainty quantification (4)
- Bayesian inverse problems (3)
- Bayesian inversion (3)
- Cauchy problem (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)
- multiplicative noise (3)
- regularization (3)
- relative rank (3)
- statistical seismology (3)
- stochastic differential equations (3)
- transformations (3)
- Aerosols (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)
- Fokker-Planck equation (2)
- Fredholm complexes (2)
- Gamma-convergence (2)
- Gaussian process (2)
- Gibbs point process (2)
- Graphs (2)
- Iran (2)
- Kompetenzen (2)
- Laplacian (2)
- Left-ordered groups (2)
- Levenberg-Marquardt method (2)
- Lidar (2)
- MCMC (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)
- Teamarbeit (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)
- 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)
- ground state (2)
- heterogeneity (2)
- hyperbolic tilings (2)
- inflammatory bowel disease (2)
- inverse problem (2)
- isotopic tiling theory (2)
- iterative regularization (2)
- linear formula (2)
- linear tree language (2)
- localization (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)
- 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)
- secular variation (2)
- sequential data assimilation (2)
- term (2)
- transfer operator (2)
- transition path theory (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)
- Achievement goal orientation (1)
- Al-26 (1)
- Algebraic Birkhoff factorisation (1)
- Algorithmic (1)
- Aluminium (1)
- Analyse (1)
- Analytic extension (1)
- Andere Fachrichtungen (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)
- Automotive (1)
- Averaging principle (1)
- BTZ black hole (1)
- Banach-valued process (1)
- Bayesian (1)
- Bayesian method (1)
- Beltrami equation (1)
- Bernstein inequality (1)
- Beweisaufgaben (1)
- Big Data (1)
- Biodiversity (1)
- Birkhoff theorem (1)
- Birman–Krein formula (1)
- Birth-and-death process (1)
- Bisectorial operator (1)
- Bivariant K-theory (1)
- Blended Learning (1)
- Blended learning (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)
- C-Test (1)
- CFD (1)
- CHAMP satellite (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)
- Clearance induction (1)
- Cloud Computing (1)
- Codeverständnis (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 Literacy (1)
- Data Science (1)
- Data augmentation (1)
- Data-driven modelling (1)
- De Rham complex (1)
- Decay of eigenfunctions (1)
- Decorated cones (1)
- Definitions (1)
- Degenerationsprozesse (1)
- Delaney--Dress (1)
- Dependent thinning (1)
- Derivation (1)
- Design Research (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)
- Dispositional learning analytics (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)
- Empirische Untersuchung (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)
- Exact solution (1)
- Explorative Datenanalyse (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)
- Fertigkeiten (1)
- Finite difference method (1)
- Finite energy sections (1)
- Finite transformation semigroup (1)
- Finsler distance (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)
- Formale Sprachen und Automaten (1)
- Formative assessment (1)
- Forschung (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)
- Full rank matrix filters (1)
- Functional calculus (1)
- Future time interval (1)
- Fuzzy logic (1)
- G-Wishart distribution (1)
- GPS (1)
- GRACE (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)
- Gestaltungsprinzipien (1)
- Gestures (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)
- Hamiltonian dynamics (1)
- Hamiltonicity (1)
- Harmonic measure (1)
- Hawkes process (1)
- Heat kernel coefficients (1)
- Heavy-tailed distributions (1)
- Helmholtz problem (1)
- Hermeneutik (1)
- Heuristics (1)
- High dimensional statistical inference (1)
- Hilbert Scales (1)
- Hochschule (1)
- Hochschulkurse (1)
- Hochschullehre (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)
- Indefinite (1)
- Index theory (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)
- Informatik (1)
- Informatik für alle (1)
- Informationskompetenz (1)
- Inhalte (1)
- Inhaltsanalyse (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 square root problem (1)
- Kegel space (1)
- Kernel regression (1)
- Kinesin V (1)
- Kollaboration (1)
- Kompetenzmessung (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 analytics (1)
- Learning dispositions (1)
- Learning theory (1)
- Lefschetz number (1)
- Lehre (1)
- Lehrevaluation (1)
- Lehrkräftebildung Mathematik (1)
- Leistungstests (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)
- Lückentext (1)
- MASCOT (1)
- MCMC modelling (1)
- MOSAiC (1)
- Machine learning (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)
- Matrix function approximation (1)
- Maximal subsemibands (1)
- McKean-Vlasov (1)
- Measure-preserving semiflow (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)
- PBPK (1)
- PBTK (1)
- PC-MRI (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)
- Permuted balance (1)
- Perron-Frobenius operator (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)
- Professionswissen (1)
- Programmierausbildung (1)
- Projekte (1)
- Proper orthogonal decomposition (1)
- Protein binding (1)
- Proving (1)
- Proxy forward modeling (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)
- 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)
- Re-Engineering (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)
- 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)
- Sociolinguistics (1)
- Software Engineering (1)
- Softwareentwicklung (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 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)
- Strukturverbesserung (1)
- Studiengänge (1)
- Studierendenperformance (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)
- TIMSS (1)
- Taphonomy (1)
- Technology (1)
- TerraSAR-X/TanDEM-X (1)
- Testfähigkeit (1)
- The Yamabe (1)
- Theoretische Informatik (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)
- 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)
- Verknüpfung Fachwissenschaft und Fachdidaktik (1)
- Visuospatial reasoning (1)
- Volterra operator (1)
- WKB ansatz (1)
- WKB approximation (1)
- WKB expansion (1)
- Warped product (1)
- Wartung von Lehrveranstaltungen (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)
- Wissenschaftliches Arbeiten (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)
- aptitude tests (1)
- archaeomagnetism (1)
- articulation (1)
- assimilation (1)
- association (1)
- asteroseismology (1)
- asymptotic (1)
- asymptotic approximation (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)
- boundary element method (1)
- boundary regularity (1)
- bridge (1)
- category equivalence of clones (1)
- characterization of point processes (1)
- chemical master equation (1)
- chemistry (1)
- classification with partial labels (1)
- clathrin (1)
- clone of operations (1)
- cluster (1)
- clustering (1)
- coarea formula (1)
- coherent set (1)
- collegial supervision (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)
- 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)
- corner Sobolev spaces with double weights (1)
- corner parametrices (1)
- correlated noise (1)
- cortisol (1)
- coupling methods (1)
- critically ill (1)
- crossed product (1)
- curvature varifold (1)
- data-driven (1)
- decomposition (1)
- delaney-dress tiling theory (1)
- density estimation (1)
- derivative-free optimization (1)
- design elements (1)
- design research (1)
- dht-symmetric category (1)
- difference operator (1)
- diffusion maps (1)
- dimension independent bound (1)
- dimension reduction (1)
- disagreement percolation (1)
- discrete Schrodinger (1)
- discrete spectrum (1)
- disease activity (1)
- distribution (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)
- duale IT-Ausbildung (1)
- duality formula (1)
- dynamical models (1)
- e-Assessment (1)
- e-Learning (1)
- early mathematical education (1)
- earthquake hazards (1)
- earthquake interaction (1)
- earthquake precursor (1)
- eigenfunction (1)
- eigenvalue asymptotics (1)
- eigenvalue decay (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)
- 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)
- 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)
- forschungsorientiertes Lernen (1)
- fosfomycin (1)
- fractional calculus (1)
- fracture (1)
- fracture network (1)
- frameworks (1)
- frequency-modulated continuous-wave (FMCW) (1)
- functional calculus (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 (1)
- graph Laplacian (1)
- green function (1)
- group (1)
- group ring (1)
- groups (1)
- hard core interaction (1)
- heat kernel (1)
- helicates (1)
- hemodynamics (1)
- hermeneutics (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)
- 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)
- infinite-dimensional diffusion (1)
- infinite-dimensional diffusions (1)
- infinitesimal generator (1)
- infliximab (1)
- infliximab dosing (1)
- integral equation (1)
- integration by parts formula (1)
- interacting particle system (1)
- interacting particle systems (1)
- interacting particles (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)
- ionospheric convection (1)
- ionospheric precursors of earthquakes (1)
- isoperimetric estimates (1)
- iterated asymptotics (1)
- jump process (1)
- kernel methods (1)
- kernel operator (1)
- knots (1)
- kollegiale Supervision (1)
- label noise (1)
- large deviations principle (1)
- laser remote sensing (1)
- lattice packing and covering (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)
- linking of subject science and didactic (1)
- lithospheric field (1)
- local time (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)
- morphology (1)
- motion correction (1)
- motivic Feynman rules (1)
- multi-hypersubstitutions (1)
- multi-modular morphology (1)
- multi-scale diffusion processes (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 equations (1)
- nonparametric hypothesis testing (1)
- nonparametric statistics (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 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 methods (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)
- 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)
- professional knowledge (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)
- regular and singular inverse Sturm-Liouville problems (1)
- regular figures (1)
- regular monoid (1)
- regular polyhedra (1)
- regular solutions (1)
- regularization method (1)
- regularization methods (1)
- regularly varying Levy process (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)
- reversible measure (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)
- semi-Lagrangian method (1)
- semi-classical limit (1)
- semiclassical Agmon estimate (1)
- semigroup representations (1)
- semigroups on infinite chain (1)
- shallow-water equations (1)
- short-range prediction (1)
- signal detection (1)
- simulations (1)
- singular Sturm-Liouville (1)
- singular foliation (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)
- 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)
- tangles (1)
- target dimensions (1)
- targeted antineoplastic drugs (1)
- teacher training mathematics (1)
- temporal discretization (1)
- terms (1)
- terms and (1)
- test ability (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 (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)
- tunneling (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)
- 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 (1087) (remove)
Devising optimal interventions for constraining stochastic systems is a challenging endeavor that has to confront the interplay between randomness and dynamical nonlinearity.
Existing intervention methods that employ stochastic path sampling scale poorly with increasing system dimension and are slow to converge.
Here we propose a generally applicable and practically feasible methodology that computes the optimal interventions in a noniterative scheme.
We formulate the optimal dynamical adjustments in terms of deterministically sampled probability flows approximated by an interacting particle system.
Applied to several biologically inspired models, we demonstrate that our method provides the necessary optimal controls in settings with terminal, transient, or generalized collective state constraints and arbitrary system dynamics.
We consider the case of scattering by several obstacles in Rd for d ≥ 2.
In this setting, the absolutely continuous part of the Laplace operator Δ with Dirichlet boundary conditions and the free Laplace operator Δ0 are unitarily equivalent.
For suitable functions that decay sufficiently fast, we have that the difference g(Δ) - g(Δ0) is a trace-class operator and its trace is described by the Krein spectral shift function.
In this article, we study the contribution to the trace (and hence the Krein spectral shift function) that arises from assembling several obstacles relative to a setting where the obstacles are completely separated. In the case of two obstacles, we consider the Laplace operators Δ1 and Δ2 obtained by imposing Dirichlet boundary conditions only on one of the objects.
Our main result in this case states that then g(Δ) - g(Δ1) - g(Δ2) C g(Δ0) is a trace-class operator for a much larger class of functions (including functions of polynomial growth) and that this trace may still be computed by a modification of the Birman–Krein formula. In case g(x) D x 2 , 1 the relative trace has a physical meaning as the vacuum energy of the massless scalar field and is expressible as an integral involving boundary layer operators.
Such integrals have been derived in the physics literature using nonrigorous path integral derivations and our formula provides both a rigorous justification as well as a generalization.
We present the extension of the Kalmag model, proposed as a candidate for IGRF-13, to the twentieth century.
The dataset serving its derivation has been complemented by new measurements coming from satellites, ground-based observatories and land, marine and airborne surveys.
As its predecessor, this version is derived from a combination of a Kalman filter and a smoothing algorithm, providing mean models and associated uncertainties. These quantities permit a precise estimation of locations where mean solutions can be considered as reliable or not.
The temporal resolution of the core field and the secular variation was set to 0.1 year over the 122 years the model is spanning.
Nevertheless, it can be shown through ensembles a posteriori sampled, that this resolution can be effectively achieved only by a limited amount of spatial scales and during certain time periods.
Unsurprisingly, highest accuracy in both space and time of the core field and the secular variation is achieved during the CHAMP and Swarm era. In this version of Kalmag, a particular effort was made for resolving the small-scale lithospheric field.
Under specific statistical assumptions, the latter was modeled up to spherical harmonic degree and order 1000, and signal from both satellite and survey measurements contributed to its development.
External and induced fields were jointly estimated with the rest of the model. We show that their large scales could be accurately extracted from direct measurements whenever the latter exhibit a sufficiently high temporal coverage.
Temporally resolving these fields down to 3 hours during the CHAMP and Swarm missions, gave us access to the link between induced and magnetospheric fields. In particular, the period dependence of the driving signal on the induced one could be directly observed.
The model is available through various physical and statistical quantities on a dedicated website at https://ionocovar.agnld.uni-potsdam.de/Kalmag/.
We consider the initial value problem for the Navier-Stokes equations over R-3 x [0, T] with time T > 0 in the spatially periodic setting.
We prove that it induces open injective mappings A(s): B-1(s) -> B-2(s-1) where B-1(s), B-2(s-1) are elements from scales of specially constructed function spaces of Bochner-Sobolev typeparametrized with the smoothness index s is an element of N.
Finally, we prove that a map Asis surjective if and only if the inverse image A(s)(- 1) (K) of any pre compact set K from the range of the map Asis bounded in the Bochner space L-s([0, T], L-r(T-3))with the Ladyzhenskaya-Prodi-Serrin numbers s, r.
We consider Bayesian inference for large-scale inverse problems, where computational challenges arise from the need for repeated evaluations of an expensive forward model.
This renders most Markov chain Monte Carlo approaches infeasible, since they typically require O(10(4)) model runs, or more.
Moreover, the forward model is often given as a black box or is impractical to differentiate.
Therefore derivative-free algorithms are highly desirable. We propose a framework, which is built on Kalman methodology, to efficiently perform Bayesian inference in such inverse problems.
The basic method is based on an approximation of the filtering distribution of a novel mean-field dynamical system, into which the inverse problem is embedded as an observation operator.
Theoretical properties are established for linear inverse problems, demonstrating that the desired Bayesian posterior is given by the steady state of the law of the filtering distribution of the mean-field dynamical system, and proving exponential convergence to it.
This suggests that, for nonlinear problems which are close to Gaussian, sequentially computing this law provides the basis for efficient iterative methods to approximate the Bayesian posterior.
Ensemble methods are applied to obtain interacting particle system approximations of the filtering distribution of the mean-field model; and practical strategies to further reduce the computational and memory cost of the methodology are presented, including low-rank approximation and a bi-fidelity approach.
The effectiveness of the framework is demonstrated in several numerical experiments, including proof-of-concept linear/nonlinear examples and two large-scale applications: learning of permeability parameters in subsurface flow; and learning subgrid-scale parameters in a global climate model.
Moreover, the stochastic ensemble Kalman filter and various ensemble square-root Kalman filters are all employed and are compared numerically.
The results demonstrate that the proposed method, based on exponential convergence to the filtering distribution of a mean-field dynamical system, is competitive with pre-existing Kalman-based methods for inverse problems.
In this paper, we define a variant of Roe algebras for spaces with cylindrical ends and use this to study questions regarding existence and classification of metrics of positive scalar curvature on such manifolds which are collared on the cylindrical end.
We discuss how our constructions are related to relative higher index theory as developed by Chang, Weinberger, and Yu and use this relationship to define higher rho-invariants for positive scalar curvature metrics on manifolds with boundary.
This paves the way for the classification of these metrics.
Finally, we use the machinery developed here to give a concise proof of a result of Schick and the author, which relates the relative higher index with indices defined in the presence of positive scalar curvature on the boundary.
In this paper we consider surfaces which are critical points of the Willmore functional subject to constrained area.
In the case of small area we calculate the corrections to the intrinsic geometry induced by the ambient curvature.
These estimates together with the choice of an adapted geometric center of mass lead to refined position estimates in relation to the scalar curvature of the ambient manifold.
As the loop space of a Riemannian manifold is infinite-dimensional, it is a non-trivial problem to make sense of the "top degree component " of a differential form on it.
In this paper, we show that a formula from finite dimensions generalizes to assign a sensible "top degree component " to certain composite forms, obtained by wedging with the exponential (in the exterior algebra) of the canonical presymplectic 2-form on the loop space.
This construction is a crucial ingredient for the definition of the supersymmetric path integral on the loop space.
We present general existence and uniqueness results for marked models with pair interactions, exemplified through Gibbs point processes on path space.
More precisely, we study a class of infinite-dimensional diffusions under Gibbsian interactions, in the context of marked point configurations: the starting points belong to R-d, and the marks are the paths of Langevin diffusions.
We use the entropy method to prove existence of an infinite-volume Gibbs point process and use cluster expansion tools to provide an explicit activity domain in which uniqueness holds.
The Gutenberg-Richter (GR) and the Omori-Utsu (OU) law describe the earthquakes' energy release and temporal clustering and are thus of great importance for seismic hazard assessment. Motivated by experimental results, which indicate stress-dependent parameters, we consider a combined global data set of 127 main shock-aftershock sequences and perform a systematic study of the relationship between main shock-induced stress changes and associated seismicity patterns. For this purpose, we calculate space-dependent Coulomb Stress (& UDelta;CFS) and alternative receiver-independent stress metrics in the surrounding of the main shocks. Our results indicate a clear positive correlation between the GR b-value and the induced stress, contrasting expectations from laboratory experiments and suggesting a crucial role of structural heterogeneity and strength variations. Furthermore, we demonstrate that the aftershock productivity increases nonlinearly with stress, while the OU parameters c and p systematically decrease for increasing stress changes. Our partly unexpected findings can have an important impact on future estimations of the aftershock hazard.