Kaiserslautern - Fachbereich Mathematik
Refine
Year of publication
- 1999 (121)
- 2000 (35)
- 1997 (31)
- 1998 (30)
- 1995 (27)
- 1996 (27)
- 2014 (26)
- 1994 (22)
- 2001 (22)
- 2003 (19)
- 1991 (18)
- 1992 (18)
- 1993 (16)
- 2002 (14)
- 2005 (14)
- 2007 (14)
- 2013 (14)
- 2006 (13)
- 2015 (13)
- 2004 (11)
- 1990 (10)
- 2011 (10)
- 1985 (8)
- 2008 (8)
- 2009 (8)
- 1984 (7)
- 2016 (7)
- 1986 (6)
- 1987 (6)
- 1989 (6)
- 2012 (6)
- 1988 (5)
- 2010 (4)
- 2017 (3)
- 2018 (3)
- 1979 (1)
- 1981 (1)
- 1983 (1)
- 2019 (1)
- 2021 (1)
- 2023 (1)
Document Type
- Preprint (608) (remove)
Keywords
- Mehrskalenanalyse (10)
- Wavelet (9)
- Approximation (8)
- Boltzmann Equation (7)
- Inverses Problem (7)
- Location Theory (7)
- Numerical Simulation (7)
- Gravitationsfeld (5)
- integer programming (5)
- wavelets (5)
- Regularisierung (4)
- Sphäre (4)
- haptotaxis (4)
- multiscale model (4)
- nonparametric regression (4)
- time series (4)
- Cauchy-Navier equation (3)
- Combinatorial optimization (3)
- Geodäsie (3)
- Intensity modulated radiation therapy (3)
- Kugel (3)
- Modellierung (3)
- Multicriteria Optimization (3)
- Multicriteria optimization (3)
- Multiobjective optimization (3)
- Spherical Wavelets (3)
- Spline (3)
- Wavelet-Analyse (3)
- average density (3)
- consistency (3)
- hub location (3)
- lattice Boltzmann method (3)
- low Mach number limit (3)
- network flows (3)
- neural network (3)
- numerics (3)
- tangent measure distributions (3)
- Algebraic Optimization (2)
- Beam-on time (2)
- Brownian motion (2)
- CHAMP <Satellitenmission> (2)
- Cauchy-Navier-Gleichung (2)
- Change analysis (2)
- Combinatorial Optimization (2)
- Decomposition and Reconstruction Schemes (2)
- Decomposition cardinality (2)
- Field splitting (2)
- GOCE <Satellitenmission> (2)
- GRACE <Satellitenmission> (2)
- Galerkin-Methode (2)
- Geometrical Algorithms (2)
- Gravimetrie (2)
- Gröbner bases (2)
- Harmonische Spline-Funktion (2)
- Hypervolume (2)
- Integer-valued time series (2)
- Kugelflächenfunktion (2)
- Lokalisation (2)
- Mathematikunterricht (2)
- Mixture Models (2)
- Multileaf collimator sequencing (2)
- Multiobjective programming (2)
- Multiresolution Analysis (2)
- Multivariate Approximation (2)
- Neural networks (2)
- Palm distributions (2)
- Parallel volume (2)
- Particle Methods (2)
- Poisson-Gleichung (2)
- Randwertproblem / Schiefe Ableitung (2)
- Rarefied Gas Dynamics (2)
- Regularization (2)
- Sobolev-Raum (2)
- Spline-Approximation (2)
- Subset selection (2)
- Up Functions (2)
- Wills functional (2)
- approximate identity (2)
- asymptotic analysis (2)
- asymptotic behavior (2)
- autoregressive process (2)
- average densities (2)
- cancer cell invasion (2)
- combinatorial optimization (2)
- connectedness (2)
- consecutive ones property (2)
- convergence (2)
- coset enumeration (2)
- degenerate diffusion (2)
- delay (2)
- density distribution (2)
- facets (2)
- geometric ergodicity (2)
- global existence (2)
- harmonic density (2)
- heat equation (2)
- hidden variables (2)
- incompressible Navier-Stokes equations (2)
- inverse problems (2)
- isogeometric analysis (2)
- k-link shortest path (2)
- kinetic equations (2)
- lacunarity distribution (2)
- limit and jump relations (2)
- mixture (2)
- moment realizability (2)
- occupation measure (2)
- optimal control (2)
- optimization (2)
- order-two densities (2)
- pH-taxis (2)
- parabolic system (2)
- particle method (2)
- particle methods (2)
- praxisorientiert (2)
- pyramid scheme (2)
- radiotherapy (2)
- regular surface (2)
- regularization (2)
- regularization wavelets (2)
- reproducing kernel (2)
- reproduzierender Kern (2)
- satellite gravity gradiometry (2)
- stationarity (2)
- stationary radiative transfer equation (2)
- subgroup problem (2)
- uniqueness (2)
- universal objective function (2)
- valid inequalities (2)
- weak solution (2)
- 2-d kernel regression (1)
- AR-ARCH (1)
- Abel integral equations (1)
- Abelian groups (1)
- Abgeschlossenheit (1)
- Ableitung höherer Ordnung (1)
- Acid-mediated tumor invasion (1)
- Adjoint system (1)
- Algebraic Geometry (1)
- Algebraic optimization (1)
- Algorithmics (1)
- Alter (1)
- Analytic semigroup (1)
- Applications (1)
- Approximation Algorithms (1)
- Approximative Identität (1)
- Associative Memory Problem (1)
- Automatische Spracherkennung (1)
- Autoregression (1)
- Autoregressive time series (1)
- Bayes risk (1)
- Behinderter (1)
- Bernstein Kern (1)
- Bernstejn-Polynom (1)
- Bessel functions (1)
- Biorthogonalisation (1)
- Bisector (1)
- Black-Scholes model (1)
- Boundary Value Problem (1)
- Boundary Value Problems (1)
- Box Algorithms (1)
- Box-Algorithm (1)
- CFL type conditions (1)
- CHAMP (1)
- CHAMP-Mission (1)
- CUSUM statistic (1)
- Cantor sets (1)
- Capacity (1)
- Capital-at-Risk (1)
- Carreau law (1)
- Cauchy-Navier scaling function and wavelet (1)
- Chorin's projection scheme (1)
- Classification (1)
- Collision Operator (1)
- Collocation Method plus (1)
- Complexity (1)
- Complexity and performance of numerical algorithms (1)
- Convex Analysis (1)
- Convex geometry (1)
- Convexity (1)
- Cosine function (1)
- Coxeter groups (1)
- Decision Making (1)
- Decision support (1)
- Decomposition of integer matrices (1)
- Dense gas (1)
- Derivatives (1)
- Differential Cross-Sections (1)
- Dirichlet series (1)
- Dirichlet-Problem (1)
- Discrete Bicriteria Optimization (1)
- Discrete decision problems (1)
- Discrete velocity models (1)
- Domain Decomposition (1)
- Dynamic cut (1)
- Dynamische Topographie (1)
- EGM96 (1)
- EM algorith (1)
- EM algorithm (1)
- Earliest arrival augmenting path (1)
- Earth' (1)
- Earth's disturbing potential (1)
- Eigenschwingung (1)
- Elastische Deformation (1)
- Elastizität (1)
- Elliptic-parabolic equation (1)
- Enskog equation (1)
- Euler's equation of motion (1)
- Evolution Equations (1)
- Evolutionary Integral Equations (1)
- Experimental Data (1)
- FEM-FCT stabilization (1)
- Faltung (1)
- Faltung <Mathematik> (1)
- Families of Probability Measures (1)
- Fast Wavelet Transform (1)
- Feed-forward Networks (1)
- Fiber spinning (1)
- First--order optimality system (1)
- Fokker-Planck equation (1)
- Forbidden Regions (1)
- Fredholm integral equation of the second kind (1)
- Frequency Averaging (1)
- Function of bounded variation (1)
- Fuzzy Programming (1)
- GOCE <satellite mission> (1)
- GPS-satellite-to-satellite tracking (1)
- GRACE (1)
- GRACE <satellite mission> (1)
- Gauge Distances (1)
- Gaussian random noise (1)
- Geodätischer Satellit (1)
- Geometric Ergodicity (1)
- Geometrical algorithms (1)
- Geostrophisches Gleichgewicht (1)
- Geothermal Flow (1)
- Geothermal Systems (1)
- Gleichmäßige Approximation (1)
- Global Optimization (1)
- Global optimization (1)
- Glättung (1)
- Glättungsparameterwahl (1)
- Grad expansion (1)
- Graph coloring (1)
- Gravimetry (1)
- Gravitation (1)
- Gravitational Field (1)
- Gravitationsmodell (1)
- Greedy algorithm (1)
- Gröbner base (1)
- Gröbner bases in monoid and group rings (1)
- Hamiltonian (1)
- Hamiltonian groups (1)
- Harmonische Dichte (1)
- Harmonische Funktion (1)
- Helmholtz decomposition (1)
- Hierarchies (1)
- Higher Order Differentials as Boundary Data (1)
- Hochschild homology (1)
- Hochschild-Homologie (1)
- Homogeneous Relaxation (1)
- Homologietheorie (1)
- Hybrid Codes (1)
- Hydrological Gravity Variations (1)
- Hydrologie (1)
- Hyperbolic Conservation (1)
- INGARCH (1)
- Identifiability (1)
- Ill-Posed Problems (1)
- Ill-posed Problems (1)
- Ill-posed problem (1)
- Improperly posed problems (1)
- Impulse control (1)
- Industrial Applications (1)
- Information Theory (1)
- Integral Equations (1)
- Integral transform (1)
- Inverse Problem (1)
- Inverse problems in Banach spaces (1)
- Isotropy (1)
- Iterative Methods (1)
- Jeffreys' prior (1)
- K-best solution (1)
- K-cardinality trees (1)
- Kallianpur-Robbins law (1)
- Kinetic Schems (1)
- Kinetic Theory of Gases (1)
- Kinetic theory (1)
- Knapsack problem (1)
- Kohonen's SOM (1)
- Kompakter Träger <Mathematik> (1)
- Konstruktive Approximation (1)
- Konvergenz (1)
- Kugelfunktion (1)
- Kullback Leibler distance (1)
- L-curve Methode (1)
- L2-Approximation (1)
- Label correcting algorithm (1)
- Label setting algorithm (1)
- Lagrangian Functions (1)
- Laplace transform (1)
- Lavrentiev regularization (1)
- Lavrentiev regularization for equations with monotone operators (1)
- Learnability (1)
- Learning systems (1)
- Legendre Wavelets (1)
- Level sets (1)
- Lexicographic Order (1)
- Lexicographic max-ordering (1)
- Linear Integral Equations (1)
- Linear membership function (1)
- Lineare Algebra (1)
- Lineare Integralgleichung (1)
- Local completeness (1)
- Locally Supported Radial Basis Functions (1)
- Locally stationary processes (1)
- Location problems (1)
- Location theory (1)
- Logik (1)
- Lokalkompakte Kerne (1)
- Low-discrepancy sequences (1)
- MLE (1)
- MOCO (1)
- Machine Scheduling (1)
- Markov Chain (1)
- Markov process (1)
- Markov switching (1)
- Massendichte (1)
- Mathematische Modellierung (1)
- Matroids (1)
- Max-Ordering (1)
- Mehrdimensionale Spline-Funktion (1)
- Mehrkriterielle Optimierung (1)
- Mie representation (1)
- Minimum Principle (1)
- Minkowski space (1)
- Moduli Spaces (1)
- Molodensky Problem (1)
- Molodensky problem (1)
- Moment sequence (1)
- Monoid and group rings (1)
- Monotone dynamical systems (1)
- Monte Carlo method (1)
- Multicriteria Location (1)
- Multiple Criteria (1)
- Multiple Objective Programs (1)
- Multiple criteria analysis (1)
- Multiple criteria optimization (1)
- Multiple objective combinatorial optimization (1)
- Multiple objective optimization (1)
- Multiresolution analysis (1)
- Multiscale Methods (1)
- Multiscale model (1)
- Multisresolution Analysis (1)
- Multivariate (1)
- NP (1)
- NP-completeness (1)
- NURBS (1)
- Navier Stokes equation (1)
- Navier-Stokes-Gleichung (1)
- Network flows (1)
- Neumann-Problem (1)
- Newtonsches Potenzial (1)
- Non-convex body (1)
- Nonlinear dynamics (1)
- Nonlinear regression (1)
- Nonparametric AR-ARCH (1)
- Nonparametric regression (1)
- Nonsmooth contact dynamics (1)
- Nonstationary processes (1)
- Numerics (1)
- Numerische Mathematik (1)
- Numerisches Verfahren (1)
- On-line algorithm (1)
- Optimal Prior Distribution (1)
- Optimal control (1)
- Optimal portfolios (1)
- Optimal semiconductor design (1)
- Optimierung (1)
- Orthonormalbasis (1)
- POD (1)
- Palm distribution (1)
- Panel clustering (1)
- Pareto Optimality (1)
- Pareto Points (1)
- Pareto optimality (1)
- Perceptron (1)
- Perona-Malik filter (1)
- Poisson autoregression (1)
- Poisson regression (1)
- Polynomapproximation (1)
- Polynomial Eigenfunctions (1)
- Pontrjagin (1)
- Potential transform (1)
- Project prioritization (1)
- Project selection (1)
- Quasi-identities (1)
- Radiative Heat Trasfer (1)
- Radiative heat transfer (1)
- Random Errors (1)
- Random body (1)
- Random differential equations (1)
- Random number generation (1)
- Rarefied Gas Flows (1)
- Rarefied Gsa Dynamics (1)
- Rarefied Polyatomic Gases (1)
- Rayleigh Number (1)
- Reaction-diffusion equations (1)
- Rectifiability (1)
- Recurrent Networks (1)
- Recurrent neural networks (1)
- Reflection (1)
- Rehabilitation clinics (1)
- Representation (1)
- Resolvent Estimate (1)
- Resonant tunneling diode (1)
- Richtungsableitung (1)
- Riemann-Siegel formula (1)
- Riesz Transform (1)
- SPn-approximation (1)
- Saddle Points (1)
- Satellitendaten (1)
- Satellitengeodäsie (1)
- Satellitengradiogravimetrie (1)
- Scalar-type operator (1)
- Scattered-Data-Interpolation (1)
- Scheduling (1)
- Seismic Modeling (1)
- Seismische Tomographie (1)
- Seismische Welle (1)
- Semantik (1)
- Semigroups (1)
- Sequential test (1)
- Shannon capacity (1)
- Shannon optimal priors (1)
- Shannon-Capacity (1)
- Shearlets (1)
- Sheaves (1)
- Shock Wave Problem (1)
- Shortest path problem (1)
- Signalanalyse (1)
- Similarity measures (1)
- Skalierungsfunktion (1)
- Slender-Body Approximations (1)
- Smoothed Particle Hydrodynamics (1)
- Sobolev spaces (1)
- Sobolevräume (1)
- Spectral Analysis (1)
- Spherical (1)
- Spherical Harmonics (1)
- Spherical Multiresolution Analysis (1)
- Sphärische Wavelets (1)
- Spline-Interpolation (1)
- Spline-Wavelets (1)
- Split Operator (1)
- Split-Operator (1)
- Square-mean Convergence (1)
- Standortplanung (1)
- Standorttheorie (1)
- Statistical Experiments (1)
- Stieltjes transform (1)
- Stochastisches Feld (1)
- Stokes Flow (1)
- Stratifaltigkeiten (1)
- Structure Theory (1)
- Stücklisten (1)
- Tensorfeld (1)
- Theorem of Plemelj-Privalov (1)
- Tiefengeothermie (1)
- Time-Space Multiresolution Analysis (1)
- Timetabling (1)
- Translation planes (1)
- Triangular fuzzy number (1)
- Uniform matroids (1)
- Universal objective function (1)
- Unschärferelation (1)
- Value-at-Risk (1)
- Van Neumann-Kakutani transformation (1)
- Vektorfeld (1)
- Verkehsplanung (1)
- Verschlüsselung (1)
- Vetor optimization (1)
- Vigenere (1)
- Vollständigkeit (1)
- Voronoi diagram (1)
- Wavelet Analysis auf regulären Flächen (1)
- Wavelet-Transformation (1)
- Wavelets (1)
- Wavelets auf der Kugel und der Sphäre (1)
- Weißes Rauschen (1)
- Wellengeschwindigkeit (1)
- Word problem (1)
- Zeitabhängigkeit (1)
- Zeitliche Veränderungen (1)
- Zonal Kernel Functions (1)
- Zyklische Homologie (1)
- acid-mediated tumor invasion (1)
- activity-based model (1)
- adaptive grid generation (1)
- additive Gaussian noise (1)
- adjacency (1)
- adjoint approach (1)
- adjoints (1)
- aggressive space mapping (1)
- algebraic geometry (1)
- algorithm (1)
- anisotropic diffusion (1)
- approximation methods (1)
- approximative Identität (1)
- arbitrary function (1)
- area loss (1)
- associated Legendre functions (1)
- asymptotic expansions (1)
- asymptotic preserving numerical scheme (1)
- ball (1)
- bicriteria shortest path problem (1)
- bicriterion path problems (1)
- bipolar quantum drift diffusion model (1)
- body wave velocity (1)
- bootstrap (1)
- bottleneck (1)
- boundary-value problems of potent (1)
- branch and cut (1)
- cancer radiation therapy (1)
- cardinality constraint combinatorial optimization (1)
- cash management (1)
- center hyperplane (1)
- centrally symmetric polytope (1)
- change point (1)
- changepoint test (1)
- charged fluids (1)
- chemotaxis (1)
- chemotherapy (1)
- classical solutions (1)
- clo (1)
- common transversal (1)
- compact operator equation (1)
- competitive analysis (1)
- complete presentations (1)
- computational complexity (1)
- conditional quantile (1)
- conditional quantiles (1)
- confluence (1)
- consecutive ones matrix (1)
- constructive approximation (1)
- control theory (1)
- convex distance funtion (1)
- convex operator (1)
- convex optimization (1)
- cooling processes (1)
- count data (1)
- coverage error (1)
- crash modelling (1)
- cusp forms (1)
- cut (1)
- cut basis problem (1)
- cuts (1)
- cyclic homology (1)
- da (1)
- data structure (1)
- data-adaptive bandwidth choice (1)
- decrease direction (1)
- deficiency (1)
- deflections of the vertical (1)
- delay management problem (1)
- denoising (1)
- density gradient equation (1)
- derivative-free iterative method (1)
- descent algorithm (1)
- diffusive scaling (1)
- direct product (1)
- directional derivative (1)
- discrete element method (1)
- discrete measure (1)
- discrete velocity models (1)
- discretization (1)
- displacement problem (1)
- distribution (1)
- domain decomposition (1)
- domain decomposition methods (1)
- drift diffusion (1)
- drift-diffusion limit (1)
- dynamical topography (1)
- efficient solution (1)
- elasticity problem (1)
- energy transport (1)
- epsilon-constraint method (1)
- equilibrium state (1)
- equilibrium strategies (1)
- estimation (1)
- exact fully discrete vectorial wavelet transform (1)
- exact solution (1)
- exchange rate (1)
- explicit representation (1)
- explicit representations (1)
- explizite Darstellung (1)
- exponential rate (1)
- f-dissimilarity (1)
- facility location (1)
- fast approximation (1)
- film casting (1)
- final prediction error (1)
- finite difference method (1)
- finite pointset method (1)
- finite volume methods (1)
- finite-difference methods (1)
- fixpoint theorem (1)
- fluid dynamic equations (1)
- formulation as integral equation (1)
- fractals (1)
- free boundary (1)
- frequency bands (1)
- freqzency bands (1)
- fundamental cut (1)
- fundamental systems (1)
- gas dynamics (1)
- gauge (1)
- general multidimensional moment problem (1)
- generalized Gummel itera (1)
- generalized inverse Gaussian diffusion (1)
- geodetic (1)
- geomagnetic field modelling from MAGSAT data (1)
- geometric measure theory (1)
- geometrical algorithms (1)
- geometry of measures (1)
- geopotential determination (1)
- global optimization (1)
- go-or-grow (1)
- go-or-grow dichotomy (1)
- gradient descent reprojection (1)
- granular flow (1)
- graph and network algorithm (1)
- gravimetry (1)
- gravitational field recovery (1)
- growing sub-quadratically (1)
- growth optimal portfolios (1)
- harmonic WFT (1)
- harmonic balance (1)
- harmonic scaling functions and wavelets (1)
- harmonic wavelets (1)
- harmonische Dichte (1)
- heat radiation (1)
- heuristic (1)
- hidden Markov (1)
- higher order (1)
- higher-order moments (1)
- homological algebra (1)
- hub covering (1)
- hybrid method (1)
- hyper-quasi-identities (1)
- hyperbolic conservation laws (1)
- hyperbolic systems of conservation laws (1)
- hypergeometric functions (1)
- hyperplane transversal (1)
- hyperquasivarieties (1)
- image denoising (1)
- image processing (1)
- image restoration (1)
- incident wave (1)
- incompressible Euler equation (1)
- incompressible limit (1)
- information (1)
- initial temperature (1)
- initial temperature reconstruction (1)
- instantaneous phase (1)
- integer GARCH (1)
- integer-valued time series (1)
- intensity map segmentation (1)
- interest oriented portfolios (1)
- internal approximation (1)
- intersection local time (1)
- intra- and extracellular proton dynamics (1)
- invariant theory (1)
- inverse Fourier transform (1)
- inverse optimization (1)
- inverse problem (1)
- inversion method (1)
- iterative bandwidth choice (1)
- jump diffusion (1)
- junction (1)
- k-cardinality minimum cut (1)
- k-max (1)
- kernel estimate (1)
- kernel estimates (1)
- kinetic approach (1)
- kinetic models (1)
- kinetic semiconductor equations (1)
- kinetic theory (1)
- label setting algorithm (1)
- large deviations (1)
- level set method (1)
- limit models (1)
- linear programming (1)
- linear transport equation (1)
- local bandwidths (1)
- local multiscale (1)
- local orientation (1)
- local search algorithm (1)
- local stationarity (1)
- local support (1)
- localization (1)
- localizing basis (1)
- locally compact (1)
- locally compact kernels (1)
- locally maximal clone (1)
- locally supported (Green's) vector wavelets (1)
- location (1)
- location problem (1)
- location theory (1)
- log averaging methods (1)
- log-utility (1)
- logarithmic average (1)
- logarithmic averages (1)
- logarithmic utility (1)
- logical analysis (1)
- logische Analyse (1)
- lokal kompakt (1)
- lokaler Träger (1)
- lokalisierende Basis (1)
- lokalisierende Kerne (1)
- low discrepancy (1)
- martingale measu (1)
- matrix decomposition (1)
- maximum a posteriori estimation (1)
- maximum capacity path (1)
- maximum entropy (1)
- maximum entropy moment (1)
- maximum flows (1)
- maximum likelihood estimation (1)
- maximum-entropy (1)
- mehrwertig (1)
- mesh-free method (1)
- minimal paths (1)
- minimax estimation (1)
- minimax risk (1)
- minimum cost flows (1)
- minimum cut (1)
- minimum fundamental cut basis (1)
- mixing (1)
- mixture models (1)
- mixture of quantum fluids and classical fluids (1)
- modal derivatives (1)
- model reduction (1)
- moduli spaces (1)
- moment methods (1)
- monlinear vibration (1)
- monogenic signals (1)
- monoid- and group-presentations (1)
- monotropic programming (1)
- multicriteria minimal path problem is presented (1)
- multicriteria optimization (1)
- multidimensional Kohonen algorithm (1)
- multileaf collimator (1)
- multileaf collimator sequencing (1)
- multiliead collimator sequencing (1)
- multiple collision frequencies (1)
- multiple objective (1)
- multiplicative noise (1)
- multiresolution analysis (1)
- multiscale analysis (1)
- multiscale approximation on regular telluroidal surfaces (1)
- multiscale modeling (1)
- multiscale models (1)
- mutiresolution (1)
- neighborhood search (1)
- network flow (1)
- network location (1)
- neural networks (1)
- never-meet property (1)
- non-commutative geometry (1)
- non-convex body (1)
- non-convex optimization (1)
- non-linear wavelet thresholding (1)
- non-local filtering (1)
- non-stationary time series (1)
- noninformative prior (1)
- nonlinear finite element method (1)
- nonlinear heat equation (1)
- nonlinear inverse problem (1)
- nonlinear thresholding (1)
- nonlocal sample dependence (1)
- norm (1)
- normal cone (1)
- normal mode (1)
- normality (1)
- normed residuum (1)
- number of objectives (1)
- numeraire portfolios (1)
- numerical integration (1)
- numerical methods for stiff equations (1)
- one-dimensional self-organization (1)
- online optimization (1)
- optimal portfolios (1)
- order selection (1)
- order-three density (1)
- order-two density (1)
- orthogonal bandlimited and non-bandlimited wavelets (1)
- ovoids (1)
- parallel numerical algorithms (1)
- parameter choice (1)
- parameter identification (1)
- partial differential equations (1)
- partial differential-algebraic equations (1)
- partition of unity (1)
- penalization (1)
- personnel scheduling (1)
- physicians (1)
- planar Brownian motion (1)
- polycyclic group rings (1)
- polyhedral analysis (1)
- polyhedral norm (1)
- polynomial weight functions (1)
- porous media (1)
- porous media flow (1)
- portfolio optimisation (1)
- portfolio optimization (1)
- positivity preserving time integration (1)
- potential operators (1)
- prefix reduction (1)
- prefix string rewriting (1)
- prefix-rewriting (1)
- preservation of relations (1)
- projected quasi-gradient method (1)
- projection method (1)
- properly efficient solution (1)
- pseudospectral methods (1)
- pyramid schemes (1)
- quadratic forms (1)
- qualitative threshold model (1)
- quantile autoregression (1)
- quasi-P (1)
- quasi-SH (1)
- quasi-SV (1)
- quasivarieties (1)
- radiative heat transfer (1)
- random noise (1)
- rarefied gas flows (1)
- rate of convergence (1)
- ratio ergodic theorem (1)
- reaction-diffusion-taxis equations (1)
- reaction-diffusion-transport equations (1)
- reconstruction formula (1)
- reference prior (1)
- refraction (1)
- regularization by wavelets (1)
- reguläre Fläche (1)
- reinitialization (1)
- rela (1)
- representative systems (1)
- residual based error formula (1)
- resource constrained shortest path problem (1)
- rewriting (1)
- robustness (1)
- rostering (1)
- s external gravitational field (1)
- satellite gradiometry (1)
- satellite-to-satellite tracking (1)
- scalar conservation laws (1)
- scalarization (1)
- scale discrete spherical vector wavelets (1)
- scale-space (1)
- scaled translates (1)
- scaling functions (1)
- scheduling (1)
- scheduling theory (1)
- schlecht gestellt (1)
- schnelle Approximation (1)
- second order upwind discretization (1)
- seismic wave (1)
- semi-classical limits (1)
- set covering (1)
- severely ill-posed inverse problems (1)
- shape optimization (1)
- shear flow (1)
- shock wave (1)
- shortest path problem (1)
- sieve estimate (1)
- singular fluxes (1)
- singular optimal control (1)
- singular spaces (1)
- singuläre Räume (1)
- sink location (1)
- slope limiter (1)
- smoothing (1)
- solution formula (1)
- special entropies (1)
- spectral sequences (1)
- sphere (1)
- spherical approximation (1)
- spherical splines (1)
- spline (1)
- spline and wavelet based determination of the geoid and the gravitational potential (1)
- spline-wavelets (1)
- splitting function (1)
- squares (1)
- stability (1)
- stability uniformly in the mean free path (1)
- stationary solutions (1)
- statistical experiment (1)
- steady Boltzmann equation (1)
- stochastic differential equations (1)
- stochastic interest rate (1)
- stochastic stability (1)
- stop location (1)
- strictly quasi-convex functions (1)
- strong theorems (1)
- strongly polynomial-time algorithm (1)
- subgroup presentation problem (1)
- superstep cycles (1)
- systems (1)
- tension problems (1)
- test (1)
- thermal equilibrium state (1)
- threshold choice (1)
- time-delayed carrying capacities (1)
- time-dependent shortest path problem (1)
- time-varying autoregression (1)
- time-varying covariance (1)
- traffic planning (1)
- trial systems (1)
- triclinic medium (1)
- tumor acidity (1)
- tumor cell invasion (1)
- tumor cell migration (1)
- two-scale expansion (1)
- uncapacitated facility location (1)
- uncertainty principle (1)
- uniform central limit theorem (1)
- uniform consistency (1)
- uniform ergodicity (1)
- value preserving portfolios (1)
- value-at-risk (1)
- vector wavelets (1)
- vectorial multiresolution analysis (1)
- vehicular traffic (1)
- verication theorem (1)
- viscosity solutions (1)
- wavelet estimators (1)
- wavelet transform (1)
- weak dependence (1)
- weak solutions (1)
- weight optimization (1)
- well-posedness (1)
- windowed Fourier transform (1)
- winner definition (1)
- worst-case scenario (1)
Faculty / Organisational entity
This paper considers the numerical solution of a transmission boundary-value problem for the time-harmonic Maxwell equations with the help of a special finite volume discretization. Applying this technique to several three-dimensional test problems, we obtain large, sparse, complex linear systems, which are solved by using BiCG, CGS, BiCGSTAB resp., GMRES. We combine these methods with suitably chosen preconditioning matrices and compare the speed of convergence.
We have presented here a two-dimensional kinetical scheme for equations governing the motion of a compressible flow of an ideal gas (air) based on the Kaniel method. The basic flux functions are computed analytically and have been used in the organization of the flux computation. The algorithm is implemented and tested for the 1D shock and 2D shock-obstacle interaction problems.
The classic approach in robust optimization is to optimize the solution with respect to the worst case scenario. This pessimistic approach yields solutions that perform best if the worst scenario happens, but also usually perform bad on average. A solution that optimizes the average performance on the other hand lacks in worst-case performance guarantee.
In practice it is important to find a good compromise between these two solutions. We propose to deal with this problem by considering it from a bicriteria perspective. The Pareto curve of the bicriteria problem visualizes exactly how costly it is to ensure robustness and helps to choose the solution with the best balance between expected and guaranteed performance.
Building upon a theoretical observation on the structure of Pareto solutions for problems with polyhedral feasible sets, we present a column generation approach that requires no direct solution of the computationally expensive worst-case problem. In computational experiments we demonstrate the effectivity of both the proposed algorithm, and the bicriteria perspective in general.
We consider the problem of evacuating a region with the help of buses. For a given set of possible collection points where evacuees gather, and possible shelter locations where evacuees are brought to, we need to determine both collection points and shelters we would like to use, and bus routes that evacuate the region in minimum time.
We model this integrated problem using an integer linear program, and present a branch-cut-and-price algorithm that generates bus tours in its pricing step. In computational experiments we show that our approach is able to solve instances of realistic size in sufficient time for practical application, and considerably outperforms the usage of a generic ILP solver.
In this paper we give the definition of a solution concept in multicriteria combinatorial optimization. We show how Pareto, max-ordering and lexicographically optimal solutions can be incorporated in this framework. Furthermore we state some properties of lexicographic max-ordering solutions, which combine features of these three kinds of optimal solutions. Two of these properties, which are desirable from a decision maker" s point of view, are satisfied if and only of the solution concept is that of lexicographic max-ordering.
In this paper we develop a data-driven mixture of vector autoregressive models with exogenous components. The process is assumed to change regimes according to an underlying Markov process. In contrast to the hidden Markov setup, we allow the transition probabilities of the underlying Markov process to depend on past time series values and exogenous variables. Such processes have potential applications to modeling brain signals. For example, brain activity at time t (measured by electroencephalograms) will can be modeled as a function of both its past values as well as exogenous variables (such as visual or somatosensory stimuli). Furthermore, we establish stationarity, geometric ergodicity and the existence of moments for these processes under suitable conditions on the parameters of the model. Such properties are important for understanding the stability properties of the model as well as deriving the asymptotic behavior of various statistics and model parameter estimators.
Treating polyatomic gases in kinetic gas theory requires an appropriate molecule model taking into account the additional internal structure of the gas particles. In this paper we describe two such models, each arising from quite different approaches to this problem. A simulation scheme for solving the corresponding kinetic equations is presented and some numerical results to 1D shockwaves are compared.
Simulation methods like DSMC are an efficient tool to compute rarefied gas flows. Using supercomputers it is possible to include various real gas effects like vibrational energies or chemical reactions in a gas mixture. Nevertheless it is still necessary to improve the accuracy of the current simulation methods in order to reduce the computational effort. To support this task the paper presents a comparison of the classical DSMC method with the so called finite Pointset Method. This new approach was developed during several years in the framework of the European space project HERMES. The comparison given in the paper is based on two different testcases: a spatially homogeneous relaxation problem and a 2-dimensional axisymmetric flow problem at high Mach numbers.
We consider the problem of evacuating an urban area caused by a natural or man-made disaster. There are several planning aspects that need to be considered in such a scenario, which are usually considered separately, due to their computational complexity. These aspects include: Which shelters are used to accommodate evacuees? How to schedule public transport for transit-dependent evacuees? And how do public and individual traffic interact? Furthermore, besides evacuation time, also the risk of the evacuation needs to be considered.
We propose a macroscopic multi-criteria optimization model that includes all of these questions simultaneously. As a mixed-integer programming formulation cannot handle instances of real-world size, we develop a genetic algorithm of NSGA-II type that is able to generate feasible solutions of good quality in reasonable computation times.
We extend the applicability of these methods by also considering how to aggregate instance data, and how to generate solutions for the original instance starting from a reduced solution.
In computational experiments using real-world data modelling the cities of Nice in France and Kaiserslautern in Germany, we demonstrate the effectiveness of our approach and compare the trade-off between different levels of data aggregation.
A new algorithm for optimization problems with three objective functions is presented which computes a representation for the set of nondominated points. This representation is guaranteed to have a desired coverage error and a bound on the number of iterations needed by the algorithm to meet this coverage error is derived. Since the representation does not necessarily contain nondominated points only, ideas to calculate bounds for the representation error are given. Moreover, the incorporation of domination during the algorithm and other quality measures are discussed.
We present a deterministic simulation scheme for the Boltzmann Semiconductor Equation. The convergence of the method is shown for a simplified space homogeneous case. Numerical experiments, which are very promising, are also given in this situation. The extension for the application to the space inhomogeneous equation with a self consistent electric field is quoted. Theoretical considerations in that case are in preparation.
Many discrepancy principles are known for choosing the parameter \(\alpha\) in the regularized operator equation \((T^*T+ \alpha I)x_\alpha^\delta = T^*y^\delta\), \(||y-y^d||\leq \delta\), in order to approximate the minimal norm least-squares solution of the operator equation \(Tx=y\). In this paper we consider a class of discrepancy principles for choosing the regularization parameter when \(T^*T\) and \(T^*y^\delta\) are approximated by \(A_n\) and \(z_n^\delta\) respectively with \(A_n\) not necessarily self - adjoint. Thisprocedure generalizes the work of Engl and Neubauer (1985),and particular cases of the results are applicable to the regularized projection method as well as to a degenerate kernel method considered by Groetsch (1990).
A distributional solution framework is developed for systems consisting of linear hyperbolic partial differential equations (PDEs) and switched differential algebraic equations (DAEs) which are coupled via boundary conditions. The unique solvability is then characterize in terms of a switched delay DAE. The theory is illustrated with an example of electric power lines modeled by the telegraph equations which are coupled via a switching transformer where simulations confirm the predicted impulsive solutions.
Compared to conventional techniques in computational fluid dynamics, the lattice Boltzmann method (LBM) seems to be a completely different approach to solve the incompressible Navier-Stokes equations. The aim of this article is to correct this impression by showing the close relation of LBM to two standard methods: relaxation schemes and explicit finite difference discretizations. As a side effect, new starting points for a discretization of the incompressible Navier-Stokes equations are obtained.
A single facility problem in the plane is considered, where an optimal location has to be
identified for each of finitely many time-steps with respect to time-dependent weights and
demand points. It is shown that the median objective can be reduced to a special case of the
static multifacility median problem such that results from the latter can be used to tackle the
dynamic location problem. When using block norms as distance measure between facilities,
a Finite Dominating Set (FDS) is derived. For the special case with only two time-steps, the
resulting algorithm is analyzed with respect to its worst-case complexity. Due to the relation
between dynamic location problems for T time periods and T-facility problems, this algorithm
can also be applied to the static 2-facility location problem.
In continous location problems we are given a set of existing facilities and we are looking for the location of one or several new facilities. In the classical approaches weights are assigned to existing facilities expressing the importance of the new facilities for the existing ones. In this paper, we consider a pointwise defined objective function where the weights are assigned to the existing facilities depending on the location of the new facility. This approach is shown to be a generalization of the median, center and centdian objective functions. In addition, this approach allows to formulate completely new location models. Efficient algorithms as well as structure results for this algebraic approach for location problems are presented. Extensions to the multifacility and restricted case are also considered.
We develop a framework for shape optimization problems under state equation con-
straints where both state and control are discretized by B-splines or NURBS. In other
words, we use isogeometric analysis (IGA) for solving the partial differential equation and a nodal approach to change domains where control points take the place of nodes and where thus a quite general class of functions for representing optimal shapes and their boundaries becomes available. The minimization problem is solved by a gradient descent method where the shape gradient will be defined in isogeometric terms. This
gradient is obtained following two schemes, optimize first–discretize then and, reversely,
discretize first–optimize then. We show that for isogeometric analysis, the two schemes yield the same discrete system. Moreover, we also formulate shape optimization with respect to NURBS in the optimize first ansatz which amounts to finding optimal control points and weights simultaneously. Numerical tests illustrate the theory.
Facility Location Problems are concerned with the optimal location of one or several new facilities, with respect to a set of existing ones. The objectives involve the distance between new and existing facilities, usually a weighted sum or weighted maximum. Since the various stakeholders (decision makers) will have different opinions of the importance of the existing facilities, a multicriteria problem with several sets of weights, and thus several objectives, arises. In our approach, we assume the decision makers to make only fuzzy comparisons of the different existing facilities. A geometric mean method is used to obtain the fuzzy weights for each facility and each decision maker. The resulting multicriteria facility location problem is solved using fuzzy techniques again. We prove that the final compromise solution is weakly Pareto optimal and Pareto optimal, if it is unique, or under certain assumptions on the estimates of the Nadir point. A numerical example is considered to illustrate the methodology.
A General Hilbert Space Approach to Wavelets and Its Application in Geopotential Determination
(1999)
A general approach to wavelets is presented within a framework of a separable functional Hilbert space H. Basic tool is the construction of H-product kernels by use of Fourier analysis with respect to an orthonormal basis in H. Scaling function and wavelet are defined in terms of H-product kernels. Wavelets are shown to be 'building blocks' that decorrelate the data. A pyramid scheme provides fast computation. Finally, the determination of the earth's gravitational potential from single and multipole expressions is organized as an example of wavelet approximation in Hilbert space structure.
In this paper we consider the problem of optimizing a piecewise-linear objective function over a non-convex domain. In particular we do not allow the solution to lie in the interior of a prespecified region R. We discuss the geometrical properties of this problems and present algorithms based on combinatorial arguments. In addition we show how we can construct quite complicated shaped sets R while maintaining the combinatorial properties.
A way to derive consistently kinetic models for vehicular traffic from microscopic follow the leader models is presented. The obtained class of kinetic equations is investigated. Explicit examples for kinetic models are developed with a particular emphasis on obtaining models, that give realistic results. For space homogeneous traffic flow situations numerical examples are given including stationary distributions and fundamental diagrams.
In this paper the kinetic model for vehicular traffic developed in [3,4] is considered and theoretical results for the space homogeneous kinetic equation are presented. Existence and uniqueness results for the time dependent equation are stated. An investigation of the stationary equation leads to a boundary value problem for an ordinary differential equation. Existence of the solution and some properties are proved. A numerical investigation of the stationary equation is included.
Multiobjective combinatorial optimization problems have received increasing attention in recent years. Nevertheless, many algorithms are still restricted to the bicriteria case. In this paper we propose a new algorithm for computing all Pareto optimal solutions. Our algorithm is based on the notion of level sets and level curves and contains as a subproblem the determination of K best solutions for a single objective combinatorial optimization problem. We apply the method to the Multiobjective Quadratic Assignment Problem (MOQAP). We present two algorithms for ranking QAP solutions and nally give computational results comparing the methods.
It is often helpful to compute the intrinsic volumes of a set of which only a pixel image is observed. A computational efficient approach, which is suggested by several authors and used in practice, is to approximate the intrinsic volumes by a linear functional of the pixel configuration histogram. Here we want to examine, whether there is an optimal way of choosing this linear functional, where we will use a quite natural optimality criterion that has already been applied successfully for the estimation of the surface area. We will see that for intrinsic volumes other than volume or surface area this optimality criterion cannot be used, since estimators which ignore the data and return constant values are optimal w.r.t. this criterion. This shows that one has to be very careful, when intrinsic volumes are approximated by a linear functional of the pixel configuration histogram.
In this article a new numerical solver for simulations of district heating networks is presented. The numerical method applies the local time stepping introduced in [11] to networks of linear advection equations. In combination with the high order approach of [4] an accurate and very efficient scheme is developed. In several numerical test cases the advantages for simulations of district heating networks are shown.
In the Black-Scholes type financial market, the risky asset S 1 ( ) is supposed to satisfy dS 1 ( t ) = S 1 ( t )( b ( t ) dt + Sigma ( t ) dW ( t ) where W ( ) is a Brownian motion. The processes b ( ), Sigma ( ) are progressively measurable with respect to the filtration generated by W ( ). They are known as the mean rate of return and the volatility respectively. A portfolio is described by a progressively measurable processes Pi1 ( ), where Pi1 ( t ) gives the amount invested in the risky asset at the time t. Typically, the optimal portfolio Pi1 ( ) (that, which maximizes the expected utility), depends at the time t, among other quantities, on b ( t ) meaning that the mean rate of return shall be known in order to follow the optimal trading strategy. However, in a real-world market, no direct observation of this quantity is possible since the available information comes from the behavior of the stock prices which gives a noisy observation of b ( ). In the present work, we consider the optimal portfolio selection which uses only the observation of stock prices.
It is of basic interest to assess the quality of the decisions of a statistician, based on the outcoming data of a statistical experiment, in the context of a given model class P of probability distributions. The statistician picks a particular distribution P , suffering a loss by not picking the 'true' distribution P' . There are several relevant loss functions, one being based on the the relative entropy function or Kullback Leibler information distance. In this paper we prove a general 'minimax risk equals maximin (Bayes) risk' theorem for the Kullback Leibler loss under the hypothesis of a dominated and compact family of distributions over a Polish observation space with suitably integrable densities. We also find that there is always an optimal Bayes strategy (i.e. a suitable prior) achieving the minimax value. Further, we see that every such minimax optimal strategy leads to the same distribution P in the convex closure of the model class. Finally, we give some examples to illustrate the results and to indicate, how the minimax result reflects in the structure of least favorable priors. This paper is mainly based on parts of this author's doctorial thesis.
The original publication is available at www.springerlink.com. This original publication also contains further results. We study a spherical wave propagating in radius- and latitude-direction and oscillating in latitude-direction in case of fibre-reinforced linearly elastic material. A function system solving Euler's equation of motion in this case and depending on certain Bessel and associated Legendre functions is derived.
The Multiple Objective Median Problem involves locating a new facility so that a vector of performance criteria is optimized over a given set of existing facilities. A variation of this problem is obtained if the existing facilities are situated on two sides of a linear barrier. Such barriers like rivers, highways, borders, or mountain ranges are frequently encountered in practice. In this paper, theory of the Multiple Objective Median Problem with line barriers is developped. As this problem is nonconvex but specially-structured, a reduction to a series of convex optimization problems is proposed. The general results lead to a polynomial algorithm for finding the set of efficient solutions. The algorithm is proposed for bi-criteria problems with different measures of distance.
Starting from the two-scale model for pH-taxis of cancer cells introduced in [1], we consider here an extension accounting for tumor heterogeneity w.r.t. treatment sensitivity and a treatment approach including chemo- and radiotherapy. The effect of peritumoral region alkalinization on such therapeutic combination is investigated with the aid of numerical simulations.
We propose a model for acid-mediated tumor invasion involving two different scales: the microscopic one, for the dynamics of intracellular protons and their exchange with their extracellular counterparts, and the macroscopic scale of interactions between tumor cell and normal cell populations, along with the evolution of extracellular protons. We also account for the tactic behavior of cancer cells, the latter being assumed to biase their motion according to a gradient of extracellular protons (following [2,31] we call this pH taxis). A time dependent (and also time delayed) carrying capacity for the tumor cells in response to the effects of acidity is considered as well. The global well posedness of the resulting multiscale model is proved with a regularization and fixed point argument. Numerical simulations are performed in order to illustrate the behavior of the model.
We consider the multiscale model for glioma growth introduced in a previous work and extend it to account
for therapy effects. Thereby, three treatment strategies involving surgical resection, radio-, and
chemotherapy are compared for their efficiency. The chemotherapy relies on inhibiting the binding
of cell surface receptors to the surrounding tissue, which impairs both migration and proliferation.
Minmax regret optimization aims at finding robust solutions that perform best in the worst-case, compared to the respective optimum objective value in each scenario. Even for simple uncertainty sets like boxes, most polynomially solvable optimization problems have strongly NP-hard minmax regret counterparts. Thus, heuristics with performance guarantees can potentially be of great value, but only few such guarantees exist.
A very easy but effective approximation technique is to compute the midpoint solution of the original optimization problem, which aims at optimizing the average regret, and also the average nominal objective. It is a well-known result that the regret of the midpoint solution is at most 2 times the optimal regret. Besides some academic instances showing that this bound is tight, most instances reveal a way better approximation ratio.
We introduce a new lower bound for the optimal value of the minmax regret problem. Using this lower bound we state an algorithm that gives an instance dependent performance guarantee of the midpoint solution for combinatorial problems that is at most 2. The computational complexity of the algorithm depends on the minmax regret problem under consideration; we show that the sharpened guarantee can be computed in strongly polynomial time for several classes of combinatorial optimization problems.
To illustrate the quality of the proposed bound, we use it within a branch and bound framework for the robust shortest path problem. In an experimental study comparing this approach with a bound from the literature, we find a considerable improvement in computation times.
Compared to standard numerical methods for hyperbolic systems of conservation laws, Kinetic Schemes model propagation of information by particles instead of waves. In this article, the wave and the particle concept are shown to be closely related. Moreover, a general approach to the construction of Kinetic Schemes for hyperbolic conservation laws is given which summarizes several approaches discussed by other authors. The approach also demonstrates why Kinetic Schemes are particularly well suited for scalar conservation laws and why extensions to general systems are less natural.
Finding a delivery plan for cancer radiation treatment using multileaf collimators operating in ''step-and-shoot mode'' can be formulated mathematically as a problem of decomposing an integer matrix into a weighted sum of binary matrices having the consecutive-ones property - and sometimes other properties related to the collimator technology. The efficiency of the delivery plan is measured by both the sum of weights in the decomposition, known as the total beam-on time, and the number of different binary matrices appearing in it, referred to as the cardinality, the latter being closely related to the set-up time of the treatment. In practice, the total beam-on time is usually restricted to its minimum possible value, (which is easy to find), and a decomposition that minimises cardinality (subject to this restriction) is sought.
This paper presents a new similarity measure and nonlocal filters for images corrupted by multiplicative noise. The considered filters are generalizations of the nonlocal means filter of Buades et al., which is known to be well suited for removing additive Gaussian noise. To adapt to different noise models, the patch comparison involved in this filter has first of all to be performed by a suitable noise dependent similarity measure. To this purpose, we start by studying a probabilistic measure recently proposed for general noise models by Deledalle et al. We analyze this measure in the context of conditional density functions and examine its properties for images corrupted by additive and multiplicative noise. Since it turns out to have unfavorable properties for multiplicative noise we deduce a new similarity measure consisting of a probability density function specially chosen for this type of noise. The properties of our new measure are studied theoretically as well as by numerical experiments. To obtain the final nonlocal filters we apply a weighted maximum likelihood estimation framework, which also incorporates the noise statistics. Moreover, we define the weights occurring in these filters using our new similarity measure and propose different adaptations to further improve the results. Finally, restoration results for images corrupted by multiplicative Gamma and Rayleigh noise are presented to demonstrate the very good performance of our nonlocal filters.
A new solution approach for solving the 2-facility location problem in the plane with block norms
(2015)
Motivated by the time-dependent location problem over T time-periods introduced in
Maier and Hamacher (2015) we consider the special case of two time-steps, which was shown
to be equivalent to the static 2-facility location problem in the plane. Geometric optimality
conditions are stated for the median objective. When using block norms, these conditions
are used to derive a polygon grid inducing a subdivision of the plane based on normal cones,
yielding a new approach to solve the 2-facility location problem in polynomial time. Combinatorial algorithms for the 2-facility location problem based on geometric properties are
deduced and their complexities are analyzed. These methods differ from others as they are
completely working on geometric objects to derive the optimal solution set.
A Nonlinear Ray Theory
(1994)
A proof of the famous Huygens" method of wavefront construction is reviewed and it is shown that the method is embedded in the geometrical optics theory for the calculation of the intensity of the wave based on high frequency approximation. It is then shown that Huygens" method can be extended in a natural way to the construction of a weakly nonlinear wavefront. This is an elegant nonlinear ray theory based on an approximation published by the author in 1975 which was inspired by the work of Gubkin. In this theory, the wave amplitude correction is incorporated in the eikonal equation itself and this leads to a sytem of ray equations coupled to the transport equation. The theory shows that the nonlinear rays stretch due to the wave amplitude, as in the work of Choquet-Bruhat (1969), followed by Hunter, Majda, Keller and Rosales, but in addition the wavefront rotates due to a non-uniform distribution of the amplitude on the wavefront. Thus the amplitude of the wave modifies the rays and the wavefront geometry, which in turn affects the growth and decay of the amplitude. Our theory also shows that a compression nonlinear wavefront may develop a kink but an expansion one always remains smooth. In the end, an exact solution showing the resolution of a linear caustic due to nonlinearity has been presented. The theory incorporates all features of Whitham" s geometrical shock dynamics.
A nonlocal stochastic model for intra- and extracellular proton dynamics in a tumor is proposed.
The intracellular dynamics is governed by an SDE coupled to a reaction-diffusion
equation for the extracellular proton concentration on the macroscale. In a more general context
the existence and uniqueness of solutions for local and nonlocal
SDE-PDE systems are established allowing, in particular, to analyze the proton dynamics model both,
in its local version and the case with nonlocal path dependence.
Numerical simulations are performed
to illustrate the behavior of solutions, providing some insights into the effects of randomness on tumor acidity.
The problem of finding an optimal location X* minimizing the maximum Euclidean distance to existing facilities is well solved by e.g. the Elzinga-Hearn algorithm. In practical situations X* will however often not be feasible. We therefore suggest in this note a polynomial algorithm which will find an optimal location X^F in a feasible subset F of the plane R^2
In this paper, we study the inverse maximum flow problem under \(\ell_\infty\)-norm and show that this problem can be solved by finding a maximum capacity path on a modified graph. Moreover, we consider an extension of the problem where we minimize the number of perturbations among all the optimal solutions of Chebyshev norm. This bicriteria version of the inverse maximum flow problem can also be solved in strongly polynomial time by finding a minimum \(s - t\) cut on the modified graph with a new capacity function.
Groups can be studied using methods from different fields such as combinatorial group theory or string rewriting. Recently techniques from Gröbner basis theory for free monoid rings (non-commutative polynomial rings) respectively free group rings have been added to the set of methods due to the fact that monoid and group presentations (in terms of string rewriting systems) can be linked to special polynomials called binomials. In the same mood, the aim of this paper is to discuss the relation between Nielsen reduced sets of generators and the Todd-Coxeter coset enumeration procedure on the one side and the Gröbner basis theory for free group rings on the other. While it is well-known that there is a strong relationship between Buchberger's algorithm and the Knuth-Bendix completion procedure, and there are interpretations of the Todd-Coxeter coset enumeration procedure using the Knuth-Bendix procedure for special cases, our aim is to show how a verbatim interpretation of the Todd-Coxeter procedure can be obtained by linking recent Gröbner techniques like prefix Gröbner bases and the FGLM algorithm as a tool to study the duality of ideals. As a side product our procedure computes Nielsen reduced generating sets for subgroups in finitely generated free groups.
Linear half-space problems can be used to solve domain decomposition problems between Boltzmann and aerodynamic equations. A new fast numerical method computing the asymptotic states and outgoing distributions for a linearized BGK half-space problem is presented. Relations with the so-called variational methods are discussed. In particular, we stress the connection between these methods and Chapman-Enskog type expansions.
An asymptotic-induced scheme for kinetic semiconductor equations with the diffusion scaling is developed. The scheme is based on the asymptotic analysis of the kinetic semiconductor equation. It works uniformly for all ranges of mean free paths. The velocity discretization is done using quadrature points equivalent to a moment expansion method. Numerical results for different physical situations are presented.
Estimation of P(R kl/gleich S) is considered for the simple stress-strength model of failure. Using the Pareto and Power distributions together with their combined form a useful parametric solution is obtained and is illustrated numerically. It is shown that these models are also applicable when only the tails of distributions for R and S are considered. An application to the failure study concerning the fractures is also included.
The problem of providing connectivity for a collection of applications is largely one of data integration: the communicating parties must agree on thesemantics and syntax of the data being exchanged. In earlier papers [#!mp:jsc1!#,#!sg:BSG1!#], it was proposed that dictionaries of definitions foroperators, functions, and symbolic constants can effectively address the problem of semantic data integration. In this paper we extend that earlier work todiscuss the important issues in data integration at the syntactic level and propose a set of solutions that are both general, supporting a wide range of dataobjects with typing information, and efficient, supporting fast transmission and parsing.
We consider a scale discrete wavelet approach on the sphere based on spherical radial basis functions. If the generators of the wavelets have a compact support, the scale and detail spaces are finite-dimensional, so that the detail information of a function is determined by only finitely many wavelet coefficients for each scale. We describe a pyramid scheme for the recursive determination of the wavelet coefficients from level to level, starting from an initial approximation of a given function. Basic tools are integration formulas which are exact for functions up to a given polynomial degree and spherical convolutions.
We consider a multiple objective linear program (MOLP) max{Cx|Ax = b,x in N_{0}^{n}} where C = (c_ij) is the p x n - matrix of p different objective functions z_i(x) = c_{i1}x_1 + ... + c_{in}x_n , i = 1,...,p and A is the m x n - matrix of a system of m linear equations a_{k1}x_1 + ... + a_{kn}x_n = b_k , k=1,...,m which form the set of constraints of the problem. All coefficients are assumed to be natural numbers or zero. The set M of admissable solutions {hat x} is an admissible solution such that there exists no other admissable solution x' with C{hat x} Cx'. The efficient solutions play the role of optimal solutions for the MOLP and it is our aim to determine the set of all efficient solutions
In this paper we consider the problem of locating one new facility in the plane with respect to a given set of existing facility where a set of polygonal barriers restricts traveling. This non-convex optimization problem can be reduced to a finite set of convex subproblems if the objective function is a convex function of the travel distances between the new and the existing facilities (like e.g. the Median and Center objective functions). An exact Algorithm and a heuristic solution procedure based on this reduction result are developed.
A compact subset E of the complex plane is called removable if all bounded analytic functions on its complement are constant or, equivalently, i f its analytic capacity vanishes. The problem of finding a geometric characterization of the removable sets is more than a hundred years old and still not comp letely solved.
The asymptotic behaviour of a singular-perturbed two-phase Stefan problem due to slow diffusion in one of the two phases is investigated. In the limit the model equations reduce to a one-phase Stefan problem. A boundary layer at the moving interface makes it necessary to use a corrected interface condition obtained from matched asymptotic expansions. The approach is validated by numerical experiments using a front-tracking method.
Linearized flows past slender bodies can be asymptotically described by a linear Fredholm integral equation. A collocation method to solve this equation is presented. In cases where the spectral representation of the integral operator is explicitly known, the collocation method recovers the spectrum of the continuous operator. The approximation error is estimated for two discretizations of the integral operator and the convergence is proved. The collocation scheme is validated in several test cases and extended to situations where the spectrum is not explicit.
We present a particle method for the numerical simulation of boundary value problems for the steady-state Boltzmann equation. Referring to some recent results concerning steady-state schemes, the current approach may be used for multi-dimensional problems, where the collision scattering kernel is not restricted to Maxwellian molecules. The efficiency of the new approach is demonstrated by some numerical results obtained from simulations for the (two-dimensional) BEnard's instability in a rarefied gas flow.
We consider investment problems where an investor can invest in a savings account, stocks and bonds and tries to maximize her utility from terminal wealth. In contrast to the classical Merton problem we assume a stochastic interest rate. To solve the corresponding control problems it is necessary to prove averi cation theorem without the usual Lipschitz assumptions.
In this paper we propose a phenomenological model for the formation of an interstitial gap between the tumor and the stroma. The gap
is mainly filled with acid produced by the progressing edge of the tumor front. Our setting extends existing models for acid-induced tumor invasion models to incorporate
several features of local invasion like formation of gaps, spikes, buds, islands, and cavities. These behaviors are obtained mainly due to the random dynamics at the intracellular
level, the go-or-grow-or-recede dynamics on the population scale, together with the nonlinear coupling between the microscopic (intracellular) and macroscopic (population)
levels. The wellposedness of the model is proved using the semigroup technique and 1D and 2D numerical simulations are performed to illustrate model predictions and draw
conclusions based on the observed behavior.
Cancer research is not only a fast growing field involving many branches of science, but also an intricate and diversified field rife with anomalies. One such anomaly is the
consistent reliance of cancer cells on glucose metabolism for energy production even in a normoxic environment. Glycolysis is an inefficient pathway for energy production and normally is used during hypoxic conditions. Since cancer cells have a high demand for energy
(e.g. for proliferation) it is somehow paradoxical for them to rely on such a mechanism. An emerging conjecture aiming to explain this behavior is that cancer cells
preserve this aerobic glycolytic phenotype for its use in invasion and metastasis. We follow this hypothesis and propose a new model
for cancer invasion, depending on the dynamics of extra- and intracellular protons, by building upon the existing ones. We incorporate random perturbations in the intracellular proton dynamics to account
for uncertainties affecting the cellular machinery. Finally, we address the well-posedness of our setting and use numerical simulations to illustrate the model predictions.
The efficient numerical treatment of the Boltzmann equation is a very important task in many fields of application. Most of the practically relevant numerical schemes are based on the simulation of large particle systems that approximate the evolution of the distribution function described by the Boltzmann equation. In particular, stochastic particle systems play an important role in the construction of various numerical algorithms.
Spline functions that approximate data given on the sphere are developed in a weighted Sobolev space setting. The flexibility of the weights makes possible the choice of the approximating function in a way which emphasizes attributes desirable for the particular application area. Examples show that certain choices of the weight sequences yield known methods. A convergence theorem containing explicit constants yields a usable error bound. Our survey ends with the discussion of spherical splines in geodetically relevant pseudodifferential equations.
The Earth's surface is an almost perfect sphere. Deviations from its spherical shape are less than 0,4% of its radius and essentially arise from its rotation. All equipotential surfaces are nearly spherical, too. In consequence, multiscale modelling of geoscientifically relevant data on the sphere involving rotational symmetry of the trial functions used for the approximation plays an important role. In this paper we deal with isotropic kernel functions showing local support and (one-dimensional) polynomial structure (briefly called isotropic finite elements) for reconstructing square--integrable functions on the sphere. Essential tool is the concept of multiresolution analysis by virtue of the spherical up function. The main result is a tree algorithm in terms of (low--order) isotropic finite elements.
We consider the problem of scheduling a bus fleet to evacuate persons from an endangered region. As most of the planning data is subject to uncertainty, we develop a two-stage bicriteria robust formulation, which considers both the evacuation time, and the vulnerability of the schedule to changing evacuation circumstances.
As the resulting integer program is too large to solve it directly using an off-the-shelf solver, we develop an iterative algorithm that successively adds new scenarios to the currently considered subproblem. In computational experiments, we show that this approach is fast enough to deal with an instance modeling an evacuation case within the city of Kaiserslautern, Germany.
In this paper we introduce a new type of single facility location problems on networks which includes as special cases most of the classical criteria in the literature. Structural results as well as a finite dominationg set for the optimal locations are developed. Also the extension to the multi-facility case is discussed.
We consider an autoregressive process with a nonlinear regression function that is modeled by a feedforward neural network. We derive a uniform central limit theorem which is useful in the context of change-point analysis. We propose a test for a change in the autoregression function which - by the uniform central limit theorem - has asymptotic power one for a large class of alternatives including local alternatives.
By means of the limit and jump relations of classical potential theory with respect to the vectorial Helmholtz equation a wavelet approach is established on a regular surface. The multiscale procedure is constructed in such a way that the emerging scalar, vectorial and tensorial potential kernels act as scaling functions. Corresponding wavelets are defined via a canonical refinement equation. A tree algorithm for fast decomposition of a complex-valued vector field given on a regular surface is developed based on numerical integration rules. By virtue of this tree algorithm, an effcient numerical method for the solution of vectorial Fredholm integral equations on regular surfaces is discussed in more detail. The resulting multiscale formulation is used to solve boundary-value problems for the time harmonic Maxwell's equations corresponding to regular surfaces.
We develop a test for stationarity of a time series against the alternative of a time-changing covariance structure. Using localized versions of the periodogram, we obtain empirical versions of a reasonable notion of a time-varying spectral density. Coefficients w.r.t. a Haar wavelet series expansion of such a time-varying periodogram are a possible indicator whether there is some deviation from covariance stationarity. We propose a test based on the limit distribution of these empirical coefficients.
Some new approximation methods are described for harmonic functions corresponding to boundary values on the (unit) sphere. Starting from the usual Fourier (orthogonal) series approach, we propose here nonorthogonal expansions, i.e. series expansions in terms of overcomplete systems consisting of localizing functions. In detail, we are concerned with the so-called Gabor, Toeplitz, and wavelet expansions. Essential tools are modulations, rotations, and dilations of a mother wavelet. The Abel-Poisson kernel turns out to be the appropriate mother wavelet in approximation of harmonic functions from potential values on a spherical boundary.
Selection of new projects is one of the major decision making activities in any company. Given a set of potential projects to invest, a subset which matches the company's strategy and internal resources best has to be selected. In this paper, we propose a multicriteria model for portfolio selection of projects, where we take into consideration that each of the potential projects has several - usually conflicting - values.
The paper presents some adaptive load balance techniques for the simulation of rarefied gas flows on parallel computers. It is shown that a static load balance is insufficient to obtain a scalable parallel efficiency. Hence, two adaptive techniques are investigated which are based on simple algorithms. Numerical results show that using heuristic techniques one can achieve a sufficiently high efficiency over a wide range of different hardware platforms.
We present the concept of a universal adaptive tracking controller for classes of linear systems. For the class of scalar minimum phase systems of relative degree one, adaptive tracking is shown for arbitrary finite dimensional reference signals. The controller requires no identificaiton of the system parameters. Robustness properties are explored.
In this article we present a method to extend high order finite volume schemes
to networks of hyperbolic conservation laws with algebraic coupling conditions. This method is based on an ADER approach in time to solve the
generalized Riemann problem at the junction. Additionally to the high order accuracy, this approach maintains an exact conservation of quantities if
stated by the coupling conditions. Several numerical examples confirm the
benefits of a high order coupling procedure for high order accuracy and stable
shock capturing.
Algorithmic ideal theory
(1999)
Algebraic geometers have used Gröbner bases as the main computational tool for many years, either to prove a theorem or to disprove a conjecture or just to experiment with examples in order to obtain a feeling about the structure of an algebraic variety. Non-trivial mathematical problems usually lead to non-trivial Gröbner basis computations, which is the reason why several improvements and efficient implementations have been provided by algebraic geometers (for example, the systems CoCoA, Macaulay and SINGULAR). The present paper starts with an introduction to some concepts of algebraic geometry which should be understood by people with (almost) no knowledge in this field. In the second chapter we introduce standard bases (generalization of Gröbner bases to non-well-orderings), which are needed for applications to local algebraic geometry (singularity theory), and a method for computing syzygies and free resolutions. In the third chapter several algorithms for primary decomposition of polynomial ideals are presented, together with a discussion of improvements and preferable choices. We also describe a newly invented algorithm for computing the normalization of a reduced affine ring. The last chapter gives an elementary introduction to singularity theory and then describes algorithms, using standard bases, to compute infinitesimal deformations and obstructions, which are basic for the deformation theory of isolated singularities. It is impossible to list all papers where Gröbner basis have been used in local and global algebraic geometry, and even more impossible to give an overview about these contributions. We have, therefore, included only a few references to papers which contain interesting applications and which are not mentioned in this tutorial paper. The interested reader will find many more in the other contributions of this volume and in the literature cited there.
We generalize the classical shortest path problem in two ways. We consider two - in general contradicting - objective functions and introduce a time dependency of the cost which is caused by a traversal time on each arc. The resulting problem, called time-dependent bicriteria shortest path problem (TdBiSP) has several interesting practical applications, but has not attained much attention in the literature.
In this paper we generalize the classical shortest path problem in two ways. We consider two objective functions and time-dependent data. The resulting problem, called the time-dependent bicriteria shortest path problem (TdBiSP), has several interesting practical applications, but has not gained much attention in the literature.
Algorithms in Singular
(1999)
The ordered weighted averaging objective (OWA) is an aggregate function over multiple optimization criteria which received increasing attention by the research community over the last decade. Different to the ordered weighted sum, weights are attached to ordered objective functions (i.e., a weight for the largest value, a weight for the second-largest value and so on). As this contains max-min or worst-case optimization as a special case, OWA can also be considered as an alternative approach to robust optimization.
For linear programs with OWA objective, compact reformulations exist, which result in extended linear programs. We present new such reformulation models with reduced size. A computational comparison indicates that these formulations improve solution times.
In this paper we present a domain decomposition approach for the coupling of Boltzmann and Euler equations. Particle methods are used for both equations. This leads to a simple implementation of the coupling procedure and to natural interface conditions between the two domains. Adaptive time and space discretizations and a direct coupling procedure leads to considerable gains in CPU time compared to a solution of the full Boltzmann equation. Several test cases involving a large range of Knudsen numbers are numerically investigated.
The paper discusses the approximation of scattered data on the sphere which is one of the major tasks in geomathematics. Starting from the discretization of singular integrals on the sphere the authors devise a simple approximation method that employs locally supported spherical polynomials and does not require equidistributed grids. It is the basis for a hierarchical approximation algorithm using differently scaled basis functions, adaptivity and error control. The method is applied to two examples one of which is a digital terrain model of Australia.
This paper is concerned with the development of a self-adaptive spatial descretization for PDEs using a wavelet basis. A Petrov-Galerkin method [LPT91] is used to reduce the determination of the unknown at the new time step to the computation of scalar products. These have to be discretized in an appropriate way. We investigate this point in detail and devise an algorithm that has linear operation count with respect to the number of unknowns. It is tested with spline wavelets and Meyer wavelets retaining the latter for their better localisation at finite precision. The algorithm is then applied to the one dimensional thermodiffusive equations. We show that the adaption strategy merits to be modified in order to take into account the particular and very strong nonlinearity of this problem. Finally, a supplementary Fourier discretization permits the computation of two dimensional flame fronts.
The polynomial approach introduced in Fuhrmann [1991] is extended to cover the crucial area of AAK theory, namely the characterization of zero location of the Schmidt vectors of the Hankel operators. This is done using the duality theory developed in that paper but with a twist. First we get the standard, lower bound, estimates on the number of unstable zeroes of the minimal degree Schmidt vectors of the Hankel operator. In the case of the Schmidt vector corresponding to the smallest singular the lower bound is in fact achieved. This leads to a solution of a Bezout equation. We use this Bezout equation to introduce another Hankel operator which have singular values that are the inverse of the singular values of the original Hankel operator.
Questions arising from Statistical Decision Theory, Bayes Methods and other probability theoretic fields lead to concepts of orthogonality of a family of probability measures. In this paper we therefore give a sketch of a generalized information theory which is very helpful in considering and answering those questions. In this adapted information theory Shannon's classical transition channels modelled by finite stochastic matrices are replaced by compact families of probability measures that are uniformly integrable. These channels are characterized by concepts such as information rate and capacity and by optimal priors and the optimal mixture distribution. For practical studies we introduce an algorithm to calculate the capacity of the whole probability family which is appli cable even for general output space. We then explain how the algorithm works and compare its numerical costs with those of the classical Arimoto-Blahut-algorithm.
This paper is a continuation of a joint paper with B. Martin [MS] dealing with the problem of direct sum decompositions. The techniques of that paper areused to decide wether two modules are isomorphic or not. An positive answer to this question has many applications - for example for the classification ofmaximal Cohen-Macaulay module over local algebras as well as for the study of projective modules. Up to now computer algebra is normally dealing withequality of ideals or modules which depends on chosen embeddings. The present algorithm allows to switch to isomorphism classes which is more natural inthe sense of commutative algebra and algebraic geometry.
The paper presents the shuffle algorithm proposed by Baganoff, which can be implemented in simulation methods for the Boltzmann equation to simplify the binary collision process. It is shown that the shuffle algborithm is a discrete approximation of an isotropic collision law. The transition probability as well as the scattering cross section of the shuffle algorithm are opposed to the corresponding quantities of a hard-sphere model. The discrepancy between measures on a sphere is introduced in order to quantify the approximation error by using the shuffle algorithm.
This paper provides an annotated bibliography of multiple objective combinatorial optimization, MOCO. We present a general formulation of MOCO problems, describe the main characteristics of MOCO problems, and review the main properties and theoretical results for these problems. One section is devoted to a brief description of the available solution methodology, both exact and heuristic. The main part of the paper is devoted to an annotation of the existing literature in the field organized problem by problem. We conclude the paper by stating open questions and areas of future research. The list of references comprises more than 350 entries.
An asymptotic-induced scheme for nonstationary transport equations with thediffusion scaling is developed. The scheme works uniformly for all ranges ofmean free paths. It is based on the asymptotic analysis of the diffusion limit ofthe transport equation. A theoretical investigation of the behaviour of thescheme in the diffusion limit is given and an approximation property is proven.Moreover, numerical results for different physical situations are shown and atheuniform convergence of the scheme is established numerically.
Non-smooth contact dynamics provides an increasingly popular simulation framework for granular material. In contrast to classical discrete element methods, this approach is stable for arbitrary time steps and produces visually acceptable results in very short computing time. Yet when it comes to the prediction of draft forces, non-smooth contact dynamics is typically not accurate enough. We therefore propose to combine the method class with an interior point algorithm for higher accuracy. Our specific algorithm is based on so-called Jordan algebras and exploits the relation to symmetric cones in order to tackle the conical constraints that are intrinsic to frictional contact problems. In every interior point iteration a linear system has to be solved. We analyze how the interior point method behaves when it is combined with Krylov subspace solvers and incomplete factorizations. We show that efficient preconditioners and efficient linear solvers are essential for the method to be applicable to large-scale problems. Using BiCGstab as a linear solver and incomplete Cholesky factorizations, we substantially improve the accuracy in comparison to the projected Gauss-Jacobi solver.
For the determination of the earth" s gravity field many types of observations are available nowadays, e.g., terrestrial gravimetry, airborne gravimetry, satellite-to-satellite tracking, satellite gradiometry etc. The mathematical connection between these observables on the one hand and gravity field and shape of the earth on the other hand, is called the integrated concept of physical geodesy. In this paper harmonic wavelets are introduced by which the gravitational part of the gravity field can be approximated progressively better and better, reflecting an increasing flow of observations. An integrated concept of physical geodesy in terms of harmonic wavelets is presented. Essential tools for approximation are integration formulas relating an integral over an internal sphere to suitable linear combinations of observation functionals, i.e., linear functionals representing the geodetic observables. A scale discrete version of multiresolution is described for approximating the gravitational potential outside and on the earth" s surface. Furthermore, an exact fully discrete wavelet approximation is developed for the case of band-limited wavelets. A method for combined global outer harmonic and local harmonic wavelet modelling is proposed corresponding to realistic earth" s models. As examples, the role of wavelets is discussed for the classical Stokes problem, the oblique derivative problem, satellite-to-satellite tracking, satellite gravity gradiometry, and combined satellite-to-satellite tracking and gradiometry.
In this paper we consider generalizations of multifacility location problems in which as an additional constraint the new facilities are not allowed to be located in a presprcified region. We propose several different solution schemes for this non-convex optimization problem. These include a linear programming type approach, penalty approaches and barrier approaches. Moreover, structural results as well as illustratrive examples showing the difficulties of this problem are presented
This report is intended to provide an introduction to the method of SmoothedParticle Hydrodynamics or SPH. SPH is a very versatile, fully Lagrangian, particle based code for solving fluid dynamical problems. Many technical aspects of the method are explained which can then be employed to extend the application of SPH to new problems.