510 Mathematik
Refine
Year of publication
Document Type
- Article (187)
- Doctoral Thesis (129)
- Preprint (44)
- diplomthesis (38)
- Report (21)
- Book (17)
- Contribution to a Periodical (12)
- Master's Thesis (12)
- Conference Proceeding (11)
- Diploma Thesis (10)
Has Fulltext
- yes (498)
Is part of the Bibliography
- no (498)
Keywords
- Kongress (6)
- Kryptologie (5)
- Mathematik (5)
- Stochastik (5)
- Online-Publikation (4)
- Statistik (4)
- point process (4)
- Brownian motion (3)
- Finanzmathematik (3)
- LLL-reduction (3)
- Moran model (3)
- coalescent (3)
- contraction method (3)
- spike train (3)
- ALICE (2)
- Algebraische Geometrie (2)
- Arithmetische Gruppe (2)
- Commitment Scheme (2)
- FPGA (2)
- Finitely many measurements (2)
- Fisher information (2)
- Fractional Laplacian (2)
- Fuchsian groups (2)
- Geometrie (2)
- Heat kernel (2)
- Integral Geometry (2)
- Knapsack problem (2)
- Kombinatorische Optimierung (2)
- Krein space (2)
- Laplace operator on graphs (2)
- Lattice basis reduction (2)
- Machine learning (2)
- Martingal (2)
- MathCityMap (2)
- Oblivious Transfer (2)
- Positive polynomials (2)
- Quantum Zeno dynamics (2)
- San Jose (2)
- Semidefinite Programming (2)
- Shortest lattice vector problem (2)
- Stochastischer Prozess (2)
- Subset sum problem (2)
- Sums of arithmetic-geometric exponentials (2)
- Tropical geometry (2)
- Tropische Geometrie (2)
- Valuation Theory (2)
- Verzweigungsprozess (2)
- W*-dynamical system (2)
- X-Y model (2)
- Yule-Prozess (2)
- ancestral selection graph (2)
- binary search tree (2)
- central limit theorem (2)
- collective intelligence (2)
- combinatorial optimization (2)
- complexity (2)
- computational complexity (2)
- duality (2)
- firing patterns (2)
- fixation probability (2)
- genealogy (2)
- level of difficulty (2)
- mathematics education (2)
- phase coding (2)
- quantum spin systems (2)
- return to equilibrium (2)
- segments (2)
- task space (2)
- thought structure (2)
- Λ−coalescent (2)
- 11N45 (1)
- 14N10 (secondary) (1)
- 2-SAT (1)
- 30F30 (1)
- 32G15 (primary) (1)
- 3D modeling (1)
- A-Discriminant (1)
- ADM1 (1)
- ALICE experiment (1)
- Abelian (1)
- Actions in mathematical learning (1)
- Activity (1)
- Adaptive dynamics (1)
- Affirmative (1)
- Affirmativeness (1)
- Ageing (1)
- Algebra (1)
- Algebraic Hodge polynomial (1)
- Algebraic number theory (1)
- Algebraisches Modell (1)
- Algorithmus (1)
- Amoeba (1)
- Anabelian Geometry (1)
- Anaerobe Fermentation (1)
- Analyse von Algorithmen (1)
- Ancestral selection graph (1)
- Anisotropic Norm (1)
- Approximation (1)
- Approximation algorithm (1)
- Approximationsalgorithmus (1)
- Arbitrage (1)
- Arithmetic-geometric exponentials (1)
- Assignment Problem (1)
- Asymptotically Even Nonlinearity (1)
- Audio-podcast (1)
- Augmented Reality (1)
- Ausreißer <Statistik> (1)
- Automorphismengruppe (1)
- Autophagy (1)
- Autorschaft (1)
- Banach spaces (1)
- Bayesian Inference (1)
- Belief Propagation (1)
- Belirsizlik (1)
- Berkovich spaces (1)
- Bernoulli (1)
- Bifurcation Theory (1)
- Bilderwelten (1)
- Bildverarbeitung (1)
- Binomialmodell (1)
- Binärsuchbaum (1)
- Biographie (1)
- Biological sciences (1)
- Biçimsel diller (1)
- Black and Scholes Option Price theory (1)
- Black-Scholes (1)
- Blind Signature (1)
- Block Korkin—Zolotarev reduction (1)
- Blockplay (1)
- Blow-up (1)
- Bolthausen-Sznitman (1)
- Boolean Lattice (1)
- Bootstrap-Statistik (1)
- Boundary (1)
- Boundary Value Problems (1)
- Boundary elements (1)
- Branch and Bound (1)
- Branching particle systems (1)
- Branching process approximation (1)
- Breaking knapsack cryptosystems (1)
- Bruhat-Tits-Gebäude (1)
- Bulanık küme kuramı (1)
- C++ (1)
- CAT(0)-Räume (1)
- CAT(0)-spaces (1)
- CBM experiment (1)
- CIR-1 (1)
- COVID-19 pandemic (1)
- Calcium waves (1)
- Calderón operator (1)
- Calderón problem (1)
- Cannings model (1)
- Capital gains taxes (1)
- Catalan number (1)
- Cauchy-Anfangswertproblem (1)
- Cayley-Graph (1)
- Cellular Automaton (1)
- China-Restaurant-Prozess (1)
- Chinese Remainder Theorem (1)
- Chinese restaurant process (1)
- Chinese-restaurant-process (1)
- Chronic conditions (1)
- Chronology of disease (1)
- Circuit (1)
- Closest Vector Problem (1)
- Coamoeba (1)
- Coding Scheme (1)
- Coin tossing (1)
- Commitment (1)
- Commitment schemes (1)
- Communication (1)
- Computational complexity (1)
- Comunicación (1)
- Concentration Inequality (1)
- Concordance (1)
- Condensing (1)
- Containment (1)
- Contraction method (1)
- Convexity (1)
- Convolution quadrature (1)
- Critical mass (1)
- Curvature measure (1)
- Cycle class (1)
- Data Acquisition (1)
- Datenbank (1)
- Datenstruktur (1)
- Degenerate Linear Part (1)
- Dehn (1)
- Demuškin groups (1)
- Depth-Map (1)
- Derivate (1)
- Dessins d'enfants (1)
- Diagramme und Mathematiklernen (1)
- Diagrams and mathematical learning (1)
- Dichte <Stochastik> (1)
- Digital and analogue materials (1)
- Digital trees (1)
- Dimension 2 (1)
- Directional selection (1)
- Dirichlet bound (1)
- Dirichlet random measure (1)
- Dirichletsche L-Reihe; Nullstelle (1)
- Discordance (1)
- Discrete Logarithm (1)
- Diskrete Geometrie (1)
- Diskrete Mathematik (1)
- Diskreter Markov-Prozess (1)
- Distributional super-solution (1)
- Diversity in trait space (1)
- Donkers theorem (1)
- Doplicher-Haag-Roberts Axiomatik; Algebraische Quantenfeldtheorie; Superauswahlregeln und -sektoren; Quantenstatistik; Zopfgruppenstatistik (1)
- Dormancy (1)
- Dosis-Wirkungs-Modellierung (1)
- Dreiecksgruppe (1)
- Dreiecksgruppen (1)
- Dual cone (1)
- Duality (1)
- Early Childhood (1)
- Einbettung <Mathematik> (1)
- Elementar- und Primarbereich (1)
- Endliche Präsentation (1)
- Endlichkeitseigenschaften (1)
- Endoplasmic reticulum (1)
- Energie-Modell (1)
- Enseñanza universitaria (1)
- Entscheidung bei Risiko (1)
- Erasure-Correcting Codes (1)
- Error Bound (1)
- Erwartungswert (1)
- Event Buffering (1)
- Evolutionary branching (1)
- Evolving Yield Curves in the Real-World Measures (1)
- Ewens sampling formula (1)
- Examples (1)
- Exponential sums (1)
- Extended RMJBN Modell (1)
- External-memory graph algorithms (1)
- FEM-BEM-coupling (1)
- FID model (1)
- FIND algorithm (1)
- Factoring (1)
- Familie (1)
- Family (1)
- Feller branching with logistic growth (1)
- Fermats letzter Satz (1)
- Finite element methods (1)
- Finite elements (1)
- Fixation probability (1)
- Fixpunkt (1)
- Formal languages (1)
- Formale Sprache (1)
- Formel (1)
- Fractional Brownian Motion (1)
- Frankfurt <Main> / Universität (1)
- Frühe Bildung (1)
- Fuchs-Gruppe (1)
- Fuchssche Gruppe ; Modulare Einbettung (1)
- Fuchssche Gruppen (1)
- Functions (1)
- Funktionenkegel (1)
- Funktionenkörper ; Arithmetische Gruppe ; Auflösbare Gruppe ; Endlichkeit (1)
- Fuzzy set theory (1)
- Fuzzy-Logik (1)
- GPGPU (1)
- GPU Computing (1)
- Gale-dual pairs (1)
- Galerkin Approximation (1)
- Galilei (1)
- Galois group (1)
- Galois-Gruppe (1)
- Game Tree (1)
- Gaussian Random Field (1)
- Gaussian process (1)
- Gelfand-Shilov space (1)
- Gemischte Volumen (1)
- Genealogical construction (1)
- Genealogische Konstruktion (1)
- Genetischer Fingerabdruck (1)
- Genus One (1)
- Geodesics (1)
- Geometrische Gruppentheorie (1)
- Geometry (1)
- Gespräch (1)
- Gestaenge (1)
- Gesten beim Mathematiklernen (1)
- Gesten-Lautsprache-Relationen (1)
- Girsanov transform (1)
- Gitter <Mathematik> ; Basis <Mathematik> ; Reduktion ; Algorithmus ; Laufzeit ; L-unendlich-Norm ; Rucksackproblem ; Kryptosystem (1)
- Gitter <Mathematik> ; Basis <Mathematik> ; Reduktion ; Gauß-Algorithmus (1)
- Gram-Hadamard inequalities (1)
- Graph generation (1)
- Graph theory (1)
- Graphen (1)
- Greeks (1)
- Grenzwertsatz (1)
- Griffiths–Engen–McCloskey distribution (1)
- Group dynamics (1)
- Group shrinkage (1)
- Große Abweichung (1)
- Großinvestor (1)
- Gruppendynamiken (1)
- Gruppentheorie (1)
- HLT (1)
- Hadamard's Three-Lines Theorem (1)
- Halbeinfache algebraische Gruppe (1)
- Handelman (1)
- Handlung (1)
- Hardy’s inequality (1)
- Harmoniebox (1)
- Hebbian learning (1)
- Heisenberg algebra (1)
- Heston model (1)
- Hidden Markov Model (1)
- Hidden Markov models (1)
- High energy physics (1)
- High-Level-Trigger (1)
- Hodge bundle (1)
- Hodge conjecture (1)
- Holzklötzchen (1)
- Hopf algebroids (1)
- Hopf boundary lemma (1)
- Householder reflection (1)
- Hyperfunktion ; Asymptotische Entwicklung (1)
- Hypertext (1)
- Hypotrochoid (1)
- ICT (1)
- Ideal (1)
- Identification (1)
- Immigration (1)
- Immunology (1)
- Index at Infinity (1)
- Infrared singularity (1)
- Integer relations (1)
- Integraldarstellung (1)
- Interaction (1)
- Invariante (1)
- Inverse Problem (1)
- Inverse problems (1)
- Iteration (1)
- Jahr der Mathematik (1)
- Kapitalertragsteuern (1)
- Keller-Segel (1)
- Kettenbruchentwicklung ; Dimension n ; Diophantische Approximation (1)
- Kieferorthopädie (1)
- Klassifizierender Raum (1)
- Knotenabstand (1)
- Knotentiefe (1)
- Koaleszent (1)
- Kochen-Specker theorem (1)
- Kognitionswissenschaft (1)
- Kollektivintelligenz (1)
- Kombinatorische Gruppen (1)
- Konforme Feldtheorie (1)
- Konstruktiver Beweis (1)
- Kontaktprozess (1)
- Kontraktionsmethode (1)
- Konzentrationsungleichung (1)
- Korkin—Zolotarev reduction (1)
- Kreuzkorrelation (1)
- Kryptosystem (1)
- Kullback-Leibler Informational Divergence (1)
- L^p bounds (1)
- L^p means (1)
- Label cover (1)
- Lanzeitverhalten (1)
- Laplace-Differentialgleichung (1)
- Large Deviation (1)
- Lattice Reduction (1)
- Lattice path matroids (1)
- Leapfrog (1)
- Leerverkauf (1)
- Lernen (1)
- Limit mixed Hodge structures (1)
- Linear Filtering (1)
- Linear Preferential Attachment Trees (1)
- Linear-Implicit Scheme (1)
- Linkages (1)
- Lipschitz–Killing measures (1)
- Literarischer Stil (1)
- Literaturwissenschaft (1)
- Loewner monotonicity and convexity (1)
- Loewner order (1)
- Log convex sets (1)
- Logarithmic Laplacian (1)
- Long- Range Dependence (1)
- Long-Range Dependence (1)
- Long-time behaviour (1)
- Longitudinal Study (1)
- Lotka-Volterra system (1)
- Lovász Local Lemma (1)
- Low density subset sum algorithm (1)
- Lyapunov exponents (1)
- MINT-Bildung (1)
- Machine Learning (1)
- Malliavin calculus (1)
- Mallows model (1)
- Many-core computer architectures (1)
- Markov chain Monte Carlo Method (1)
- Markov chain imbedding technique (1)
- Markov model (1)
- Markov-Kette (1)
- Marshall, Alfred (1)
- Matematiksel dilbilim (1)
- Mathematical Giftedness (1)
- Mathematical Reasoning (1)
- Mathematical biosciences (1)
- Mathematical linguistics (1)
- Mathematical modelling (1)
- Mathematics Learning (1)
- Mathematikdidaktik (1)
- Mathematiker (1)
- Mathematikgeschichte <Fach> (1)
- Mathematische Bildung (1)
- Mathematische Linguistik (1)
- Mathematische Modellierung (1)
- Mathtrails (1)
- Max (1)
- Maximum length of association (1)
- Mc Kean martingale (1)
- McEliece (1)
- Mean Anisotropy (1)
- Methanogenese (1)
- Mixed Volumes (1)
- Mobile Learning (1)
- Modellierung (1)
- Modular Multiplication (1)
- Moduli space of semi-stable sheaves (1)
- Mollifier decorrelation (1)
- Mollifier multiscale reconstruction and decomposition (1)
- Monotonicity (1)
- Morava K-theory (1)
- Multi-Harmonie-Ansatz (1)
- Multiple lineare Regression (1)
- Multiplicative convexity (1)
- Multityp-Verzweigungsprozess mit Immigration (1)
- Multitype Branching with Immigration (1)
- NP-complete problems (1)
- NP-hard (1)
- NP-hardness (1)
- Nash-Gleichgewicht (1)
- Nelson-Siegel (1)
- Neoklassische Theorie (1)
- Neurophysiology (1)
- Neuroscience (1)
- Neurowissenschaft (1)
- Newton–Okounkov bodies (1)
- Nodal curves (1)
- Non-Malleability (1)
- Non-negativity certificate (1)
- Nonlinear Schrödinger equation (1)
- Nonlocal Neumann conditions (1)
- Nonlocal normal derivative (1)
- Nonlocal operators (1)
- Noticeable Probability (1)
- Numerale (1)
- Numerical simulation (1)
- Olumluluk (1)
- Optimal Mean-Square Filter (1)
- Optimal stopping problem (1)
- Optimales Stoppproblem (1)
- Oracle Query (1)
- Orbital stability (1)
- Parabolic SPDE (1)
- Parallel Computing (1)
- Parallel and SIMD calculations (1)
- Parisi conjecture (1)
- Partial Differential Equations (1)
- Participation (1)
- Partizipation (1)
- Patientenbewertung (1)
- Perception (1)
- Perfect graphs (1)
- Permutation (1)
- Permutationsgruppen (1)
- Pfadeigenschaften (1)
- Phragmén-Lindelöf principle (1)
- Piecewise-constant coefficient (1)
- Podospora anserina (1)
- Pointwise super-solution (1)
- Poisson Process (1)
- Poisson boundary (1)
- Poisson-Prozess (1)
- Polyedrische Kombinatorik (1)
- Polyhedron (1)
- Polymorphic evolution sequence (1)
- Polynomial Optimization (1)
- Pontrjagin space (1)
- Populationsdynamiken (1)
- Portfolios (1)
- Positive function (1)
- Positive signomials (1)
- Positivstellensatz (1)
- Potential methods in exploration (1)
- Potenzialtheorie (1)
- Prag <1999> (1)
- Preferential Attachment-Modelle (1)
- Private Information Retrieval (1)
- Probabilistic analysis of algorithms (1)
- Probabilistically checkable proofs (1)
- Probabilistische Analyse von Algorithmen (1)
- Probability distribution (1)
- Probability of fixation (1)
- Processor (1)
- Professionalisierung (1)
- Profil Likelihood (1)
- Projektionen (1)
- Protein-protein interaction (1)
- Pseudo-Riemannian manifolds (1)
- Public Key Cryptosystem (1)
- Public Parameter (1)
- Punktprozess (1)
- Pythagoreische Tripel (1)
- Pólya urn (1)
- Quadratic Residue (1)
- Quantenfeldtheorie ; Konforme Feldtheorie ; Algebraische Methode (1)
- Quantum Zeno Effect (1)
- Quantum Zeno effect (1)
- Quasi-Automorphismen (1)
- Quaternionenalgebra (1)
- Quickselect (1)
- Radix sort (1)
- Random CSP (1)
- Random Graphs (1)
- Random Matrices (1)
- Random Oracle (1)
- Random Split Trees (1)
- Random String (1)
- Random environment (1)
- Random graphs (1)
- Random variables (1)
- Randomisieren (1)
- Ray-Knight representation (1)
- Reale vs. risikoneutrale Welt in der Finanzmathematik (1)
- Reflexive polytopes (1)
- Regional Laplacian (1)
- Regional fractional Laplacian (1)
- Regularized regression (1)
- Rekursiver Algorithmus (1)
- Relatives Risiko (1)
- Relaxation (1)
- Representación (1)
- Representation (1)
- Representation Problem (1)
- Riemann surfaces (1)
- Riemannsche Fläche (1)
- Riemannsche Flächen (1)
- Ringtheorie (1)
- Risiko (1)
- Risikoanalyse (1)
- Risikobewertung (1)
- Risikomanagement (1)
- Risikotheorie (1)
- Ryanodine receptors (1)
- Rückkopplungseffekt (1)
- S-arithmetic groups (1)
- SIMD (1)
- SLLL-reduction (1)
- STEM education (1)
- Sackgassen (1)
- San Francisco (1)
- Santa Barbara (1)
- Schizophrenia (1)
- Schwarz triangel functions (1)
- Schwinger model (1)
- Second-order cone (1)
- Security Parameter (1)
- Semidefinite Optimierung (1)
- Semidefinite Optimization (1)
- Semiotics according to C. S. Peirce (1)
- Semiotik nach C. S. Peirce (1)
- Sequence analysis (1)
- Sigma-Invariante (1)
- Sigma-invariant (1)
- Sign-changing solutions (1)
- Signalverarbeitung (1)
- Signature (1)
- Signed Birkhoff polytopes (1)
- Simplicial complexes (1)
- Small Worlds (1)
- Small order expansion (1)
- Smartphone (1)
- Spectrahedra (1)
- Spectral Theory (1)
- Spiel (1)
- Spielbaum (1)
- Spielbaum-Suchverfahren (1)
- Stable reduction algorithm (1)
- Standard monomials (1)
- Standing waves (1)
- State dependent branching rate (1)
- Stationarity (1)
- Stochastic Analysis of Square Zero Variation Processes (1)
- Stonesches Spektrum (1)
- Strong Taylor Scheme (1)
- Structure-function interplay (1)
- Sublinear circuit (1)
- Suchbaum (1)
- Suchoperation (1)
- Sudoku (1)
- Sum of Squares (1)
- Sums of non-negative circuit polynomials (1)
- Sums of nonnegative circuit polynomials (SONC) (1)
- Supervised hierarchical clustering (1)
- Support (1)
- Symmetrie (1)
- Symmetries (1)
- Symmetrischer Raum (1)
- Symmetry (1)
- Symmetry Breaking (1)
- Sympatric speciation (1)
- TIC (1)
- TRD (1)
- Tail Bound (1)
- Tailschranke (1)
- Talk (1)
- Teacher-Education (1)
- Thermoelastic wave equation (1)
- Thorne Kishino Felsenstein model (1)
- Topic Model (1)
- Transcriptome analysis (1)
- Transparent boundary conditions (1)
- Transylvanian cultural history (1)
- Trapdoor (1)
- Trinomial (1)
- Tropical Geometry (1)
- Tropical Grassmannians (1)
- Tropical bases (1)
- Tropical varieties (1)
- Tropische Basen (1)
- Trotter's product formula (1)
- Turkish immigrants (1)
- Typ-In-Algebra (1)
- Typology (1)
- Türkisch (1)
- Unconditional polytopes (1)
- Uniform regularity (1)
- Unimodular triangulations (1)
- Unterstützung (1)
- UrQMD (1)
- Vagheit (1)
- Vagueness (1)
- Valuation (1)
- Valuation on functions (1)
- Varianz (1)
- Variational Methods (1)
- Vectorization (1)
- Verdeckung (1)
- Vertexoperator (1)
- Verzweigende Teilchensysteme (1)
- Virasoro-Algebra (1)
- Vision (1)
- Wahrgenommenes Risiko (1)
- Wahrscheinlichkeit (1)
- Wahrscheinlichkeitsverteilung (1)
- Wavelet decomposition (1)
- Weak super-solution (1)
- Weyl principle (1)
- Wiener Index (1)
- Wiener index (1)
- Wiener-Index (1)
- Wirtschaftswissenschaften (1)
- Wissenssoziologie (1)
- Yule process (1)
- Yule-process (1)
- Zinsstrukturmodelle (1)
- Zinsänderungsrisiko (1)
- Zolotarev metric (1)
- Zolotarev-Metrik (1)
- Zopfgruppe ; Lineare Darstellung ; Kettengruppe ; Homologiegruppe ; Automorphismengruppe ; Kettenkomplex (1)
- Zufall (1)
- Zufallsgraph (1)
- Zufällige Umgebung (1)
- Zustandsabhängige Verzweigungsrate (1)
- Zweiphasen-Biogasreaktor (1)
- Zweistufen-Biogasreaktor (1)
- abelian differentials (1)
- abstract potential theory (1)
- algebraic curves (1)
- algebraic thinking (1)
- algebraic values (1)
- alpha-stable branching (1)
- ampleness (1)
- anabelian geometry (1)
- analysis of algorithms (1)
- anti-Zeno effect (1)
- approximation algorithms (1)
- arithmetic ball quotients (1)
- arithmetic geometry (1)
- arithmetic group (1)
- assignment problem (1)
- atopic dermatitis (1)
- augmented and restricted base loci (1)
- autocorrelograms (1)
- bid-ask spread (1)
- bistable perception (1)
- bordism theory (1)
- branching processes (1)
- branching random walk in random medium (1)
- buildings (1)
- cancer cell dormancy (1)
- canonical divisors (1)
- catastrophe modeling (1)
- changepoint (1)
- chosen ciphertext attack (1)
- clique problem (1)
- colorabdity (1)
- colored graphs (1)
- compact Riemann surfaces (1)
- complex multiplication (1)
- composition (1)
- computational geometry (1)
- concurrent composition (1)
- condensing (1)
- confirmatory factor analysis (1)
- confirmatory factory analysis (1)
- consensus (1)
- contact process (1)
- continued fraction algorithm (1)
- controlled homotopy (1)
- convexity (1)
- convolution quadrature (1)
- cooperative systems (1)
- cover times (1)
- cross correlation (1)
- crowd behaviour (1)
- cryptography (1)
- cycle structure of permutations (1)
- data parallel (1)
- dead ends (1)
- deep learning (1)
- deformable model (1)
- degenerate semigroup (1)
- delay equation (1)
- depth of a nod (1)
- dessins d’enfants (1)
- dichotomization (1)
- dichotomous data (1)
- difference sets (1)
- digital learning (1)
- digital search tree (1)
- digitization (1)
- discrete dynamical system (1)
- discrete logarithm (1)
- discrete logarithm (DL) (1)
- diskrete Mathematik (1)
- distance learning (1)
- dose-resoponse modelling (1)
- doubly stochastic point process (1)
- dynamic algorithms (1)
- educational technology (1)
- eigenvalue (1)
- elastodynamic wave equation (1)
- endliche metrische Räume (1)
- equity and access to technology (1)
- erasure codes (1)
- error bounds (1)
- error correction codes (1)
- evacuation (1)
- event reconstruction (1)
- excess kurtosis (1)
- expectile (1)
- exponentiation (1)
- external branch (1)
- extreme value theory (1)
- fake projective planes (1)
- families of hash functions (1)
- feedback effect (1)
- finite resolution (1)
- finiteness-properties (1)
- flat surfaces (1)
- floating norms (1)
- floating point arithmetic (1)
- floating point errors (1)
- foliated Schwarz symmetry (1)
- forming a group (1)
- fractional Brownian motion (1)
- fractional Fourier transform (1)
- fractions of exponentiation (1)
- fringe tree (1)
- frühkindliche Erziehung (1)
- fuchsian group (1)
- functional limit theorem (1)
- functional limit theorems (1)
- fundamental theorem of asset pricing (1)
- generic algorithm (1)
- generic algorithms (1)
- generic complexity (1)
- generic group model (1)
- graph coloring (1)
- graph isomorphism (1)
- guiding principle (1)
- h-transform (1)
- hard bit (1)
- hardcore subsets (1)
- harmonic function (1)
- heavy tails (1)
- hidden Markov model (1)
- hierarchical fields (1)
- hierarchical mean-field limit (1)
- highly regular nearby points (1)
- hyperbolische Geometrie (1)
- hypergeometric functions (1)
- hypervariable region (1)
- höhere Momente (1)
- identifying moment conditions (1)
- indefinite inner product space (1)
- independence number (1)
- independent component analysis (1)
- individual-based models (1)
- influenza (1)
- information processing (1)
- information set (1)
- information transfer (1)
- inner product (1)
- inquiry-based education (1)
- integer relation (1)
- integer vector (1)
- interacting particle Systems (1)
- interdisziplinäre Lehre (1)
- internal diffusion limited aggregation (1)
- internal path length (1)
- interval-level data (1)
- inverse coefficient problem, (1)
- iterated subsegments (1)
- key comparisons (1)
- knapsack cryptosystems (1)
- kontrollierte Homotopie (1)
- large deviations (1)
- large trader (1)
- latent structure (1)
- latent variance (1)
- lattice basis reduction (1)
- lattices (1)
- leapfrog (1)
- length defect (1)
- limit order markets (1)
- local LLL-reduction (1)
- local LLLreduction (1)
- local coordinates (1)
- local randomness (1)
- local time (1)
- local time drift (1)
- logarithmic geometry (1)
- logical networks (1)
- lookdown construction (1)
- loss function (1)
- manifold and geodesic (1)
- market making (1)
- math trails (1)
- mathematical description (1)
- mathematical modelling (1)
- mathematician and philosopher János Bolyai (1)
- mathematics (1)
- mathematische Beschreibung (1)
- measurement (1)
- mehrdimensionale Ausreißererkennung (1)
- message-passing algorithm (1)
- modelling (1)
- modular automorphism group (1)
- modular group (1)
- moduli spaces (1)
- multi-agents system (1)
- multi-drug treatment (1)
- multiharmony (1)
- multilevel branching (1)
- mutation parameter estimation (1)
- neural ordinary differential equation (1)
- neuronal code (1)
- neuronaler Kode (1)
- neuroscience (1)
- nichtlineare stochastische Integration (1)
- no unbounded profit with bounded risk (1)
- non-archimedean geometry (1)
- non-autonomous dynamical systems (1)
- non-malleability (1)
- noncommutative ring spectra (1)
- nondetermmistlc Turing machines (1)
- nonlinear stochastic integration (1)
- numerical experiments (1)
- objective functions (1)
- observable Funktion (1)
- octonions (1)
- one-more decryption attack (1)
- one-way function (1)
- one-way functions (1)
- online bayesian change point detection (1)
- operator algebra (1)
- optimal coding (1)
- optimal transport (1)
- optimality of point forecasts (1)
- option pricing (1)
- outdoors (1)
- pair HMM (1)
- parallel file systems (1)
- parallel programming (1)
- parameter dependent semimartingales (1)
- parameterabhängige Semimartingale (1)
- partial match queries (1)
- path properties (1)
- patricia trie (1)
- permutation groups (1)
- phase transitions (1)
- platonischer Körper (1)
- pneumonia (1)
- point inversion (1)
- poisson process (1)
- polynomial random number generator (1)
- portfolio optimization (1)
- positivity of line bundles (1)
- positivity preserving property (1)
- preferential attachment (1)
- preferential attachment models (1)
- probabilistic analysis of algorithms (1)
- probability (1)
- probability metric (1)
- profile likelihood (1)
- projections (1)
- projective planes (1)
- proportional transaction costs (1)
- psoriasis (1)
- q-binomial theorem (1)
- quantile (1)
- quantum field theory (1)
- quasi-automorphisms (1)
- quaternion algebra (1)
- quincunx (1)
- random assignment problem (1)
- random energy model (1)
- random environment (1)
- random function generator (1)
- random graphs (1)
- random measures (1)
- random media (1)
- random metric (1)
- random move (1)
- random number generator (1)
- random oracle model (1)
- random partition (1)
- random recursive tree (1)
- random rekursiv tree (1)
- random tree (1)
- random trees (1)
- random walks (1)
- raum-zeitliche Muster (1)
- reactant-catalyst systems (1)
- recursive distributional equation (1)
- reguläre Parkettierung (1)
- representation learning (1)
- resistance mutation (1)
- reversibility (1)
- riemann surfaces (1)
- risk assessment (1)
- risk theory (1)
- rotating plane method (1)
- rough paths theory (1)
- satisfiability problem (1)
- satlsfiablhty (1)
- scaling (1)
- search operation (1)
- searchtrees (1)
- section conjecture (1)
- secure bit (1)
- security analysis of protocols (1)
- self-organizing groups (1)
- self-organizing groups; population dynamics; collective intelligence; forming groups; metric on finite sets (1)
- semidefinite optimization (1)
- semimartingales (1)
- sequence alignment (1)
- set-valued pullback attractors (1)
- shadow price (1)
- shape prior (1)
- short integer relation (1)
- shortest lattice vector (1)
- shrinkage correction (1)
- signed ElGamal encryption (1)
- simultaneous diophantine approximations (1)
- simultaneous security of bits (1)
- small worlds (1)
- spatio-temporal patterns (1)
- spike timing (1)
- spin group (1)
- split tree (1)
- statistic analysis (1)
- statistical alignment (1)
- statistical shape analysis (1)
- statistische Analyse (1)
- statistischer Test (1)
- stoch. Analyse von Algorithmen (1)
- stochastic filtering (1)
- stochastic integration (1)
- stochastic model (1)
- stochastic modeling (1)
- stochastic population dynamics (1)
- stochastic volatility (1)
- stochastische Prozesse (1)
- storage (1)
- strong transience (1)
- subgroup growth (1)
- subset sum problems (1)
- sum of squared factor loadings (1)
- switching systems (1)
- synaptic plasticity (1)
- synchronous teaching (1)
- task design (1)
- teaching with technology (1)
- technology-enhanced learning (1)
- the origin and places linked to his and his ancestorsʼ biography (1)
- therapy evasion (1)
- topological entropy (1)
- torsion function (1)
- trading strategies (1)
- transcendence (1)
- transfer entropy (1)
- treatment protocol design (1)
- treatment success (1)
- triangle group (1)
- triangle groups (1)
- tropical geometry (1)
- tropical universal Jacobian (1)
- tropicalization (1)
- universal compactified Jacobian (1)
- urn model (1)
- vaccination (1)
- valuation (1)
- vectorization (1)
- von Neumann algebra (1)
- von Neumann algebras (1)
- von Neumann-Algebra (1)
- weak convergence (1)
- zufälliger Algorithmus (1)
- zufälliger rekursiver Baum (1)
- zufälliges Assignment Problem (1)
- Λ-coalescent (1)
- σ-field (1)
- 𝒮-cone (1)
Institute
- Mathematik (320)
- Informatik und Mathematik (93)
- Informatik (54)
- Präsidium (13)
- Frankfurt Institute for Advanced Studies (FIAS) (9)
- Physik (9)
- Medizin (4)
- Goethe-Zentrum für Wissenschaftliches Rechnen (G-CSC) (3)
- Wirtschaftswissenschaften (3)
- Biochemie und Chemie (2)
Muller's ratchet, in its prototype version, models a haploid, asexual population whose size~N is constant over the generations. Slightly deleterious mutations are acquired along the lineages at a constant rate, and individuals carrying less mutations have a selective advantage. The classical variant considers {\it fitness proportional} selection, but other fitness schemes are conceivable as well. Inspired by the work of Etheridge et al. ([EPW09]) we propose a parameter scaling which fits well to the ``near-critical'' regime that was in the focus of [EPW09] (and in which the mutation-selection ratio diverges logarithmically as N→∞). Using a Moran model, we investigate the``rule of thumb'' given in [EPW09] for the click rate of the ``classical ratchet'' by putting it into the context of new results on the long-time evolution of the size of the best class of the ratchet with (binary) tournament selection, which (other than that of the classical ratchet) follows an autonomous dynamics up to the time of its extinction. In [GSW23] it was discovered that the tournament ratchet has a hierarchy of dual processes which can be constructed on top of an Ancestral Selection graph with a Poisson decoration. For a regime in which the mutation/selection-ratio remains bounded away from 1, this was used in [GSW23] to reveal the asymptotics of the click rates as well as that of the type frequency profile between clicks. We will describe how these ideas can be extended to the near-critical regime in which the mutation-selection ratio of the tournament ratchet converges to 1 as N→∞.
Motivated by the question of the impact of selective advantage in populations with skewed reproduction mechanims, we study a Moran model with selection. We assume that there are two types of individuals, where the reproductive success of one type is larger than the other. The higher reproductive success may stem from either more frequent reproduction, or from larger numbers of offspring, and is encoded in a measure Λ for each of the two types. Our approach consists of constructing a Λ-asymmetric Moran model in which individuals of the two populations compete, rather than considering a Moran model for each population. Under certain conditions, that we call the "partial order of adaptation", we can couple these measures. This allows us to construct the central object of this paper, the Λ−asymmetric ancestral selection graph, leading to a pathwise duality of the forward in time Λ-asymmetric Moran model with its ancestral process. Interestingly, the construction also provides a connection to the theory of optimal transport. We apply the ancestral selection graph in order to obtain scaling limits of the forward and backward processes, and note that the frequency process converges to the solution of an SDE with discontinous paths. Finally, we derive a Griffiths representation for the generator of the SDE and use it to find a semi-explicit formula for the probability of fixation of the less beneficial of the two types.
Motivated by the question of the impact of selective advantage in populations with skewed reproduction mechanims, we study a Moran model with selection. We assume that there are two types of individuals, where the reproductive success of one type is larger than the other. The higher reproductive success may stem from either more frequent reproduction, or from larger numbers of offspring, and is encoded in a measure Λ for each of the two types. Our approach consists of constructing a Λ-asymmetric Moran model in which individuals of the two populations compete, rather than considering a Moran model for each population. Under certain conditions, that we call the ``partial order of adaptation'', we can couple these measures. This allows us to construct the central object of this paper, the Λ−asymmetric ancestral selection graph, leading to a pathwise duality of the forward in time Λ-asymmetric Moran model with its ancestral process. Interestingly, the construction also provides a connection to the theory of optimal transport. We apply the ancestral selection graph in order to obtain scaling limits of the forward and backward processes, and note that the frequency process converges to the solution of an SDE with discontinous paths. Finally, we derive a Griffiths representation for the generator of the SDE and use it to find a semi-explicit formula for the probability of fixation of the less beneficial of the two types.
Motivated by the question of the impact of selective advantage in populations with skewed reproduction mechanisms, we study a Moran model with selection. We assume that there are two types of individuals, where the reproductive success of one type is larger than the other. The higher reproductive success may stem from either more frequent reproduction, or from larger numbers of offspring, and is encoded in a measure Λ for each of the two types. Λ-reproduction here means that a whole fraction of the population is replaced at a reproductive event. Our approach consists of constructing a Λ-asymmetric Moran model in which individuals of the two populations compete, rather than considering a Moran model for each population. Provided the measure are ordered stochastically, we can couple them. This allows us to construct the central object of this paper, the Λ−asymmetric ancestral selection graph, leading to a pathwise duality of the forward in time Λ-asymmetric Moran model with its ancestral process. We apply the ancestral selection graph in order to obtain scaling limits of the forward and backward processes, and note that the frequency process converges to the solution of an SDE with discontinuous paths. Finally, we derive a Griffiths representation for the generator of the SDE and use it to find a semi-explicit formula for the probability of fixation of the less beneficial of the two types.
We show explicit formulas for the evaluation of (possibly higher-order) fractional Laplacians (-△)ˢ of some functions supported on ellipsoids. In particular, we derive the explicit expression of the torsion function and give examples of s-harmonic functions. As an application, we infer that the weak maximum principle fails in eccentric ellipsoids for s ∈ (1; √3 + 3/2) in any dimension n ≥ 2. We build a counterexample in terms of the torsion function times a polynomial of degree 2. Using point inversion transformations, it follows that a variety of bounded and unbounded domains do not satisfy positivity preserving properties either and we give some examples.
Therapy evasion – and subsequent disease progression – is a major challenge in current oncology. An important role in this context seems to be played by various forms of cancer cell dormancy. For example, therapy-induced dormancy, over short timescales, can create serious obstacles to aggressive treatment approaches such as chemotherapy, and long-term dormancy may lead to relapses and metastases even many years after an initially successful treatment. The underlying dormancy-related mechanisms are complex and highly diverse, so that the analysis even of basic patterns of the population-level consequences of dormancy requires abstraction and idealization, as well as the identification of the relevant specific scenarios.
In this paper, we focus on a situation in which individual cancer cells may switch into and out of a dormant state both spontaneously as well as in response to treatment, and over relatively short time-spans. We introduce a mathematical ‘toy model’, based on stochastic agent-based interactions, for the dynamics of cancer cell populations involving individual short-term dormancy, and allow for a range of (multi-drug) therapy protocols. Our analysis shows that in our idealized model, even a small initial population of dormant cells can lead to therapy failure under classical (and in the absence of dormancy successful) single-drug treatments. We further investigate the effectiveness of several multidrug regimes (manipulating dormant cancer cells in specific ways) and provide some basic rules for the design of (multi-)drug treatment protocols depending on the types and parameters of dormancy mechanisms present in the population.
Highlights
• We study dormancy in the ‘rare mutation’ regime of stochastic adaptive dynamics.
• We first derive the polymorphic evolution sequence, based on prior work.
• Our evolutionary branching criterion extends a result by Champagnat and Méléard.
• In a classical model dormancy can favour evolutionary branching.
• Dormancy also affects several more population characteristics.
Abstract
In this paper, we investigate the consequences of dormancy in the ‘rare mutation’ and ‘large population’ regime of stochastic adaptive dynamics. Starting from an individual-based micro-model, we first derive the Polymorphic Evolution Sequence of the population, based on a previous work by Baar and Bovier (2018). After passing to a second ‘small mutations’ limit, we arrive at the Canonical Equation of Adaptive Dynamics, and state a corresponding criterion for evolutionary branching, extending a previous result of Champagnat and Méléard (2011).
The criterion allows a quantitative and qualitative analysis of the effects of dormancy in the well-known model of Dieckmann and Doebeli (1999) for sympatric speciation. In fact, quite an intuitive picture emerges: Dormancy enlarges the parameter range for evolutionary branching, increases the carrying capacity and niche width of the post-branching sub-populations, and, depending on the model parameters, can either increase or decrease the ‘speed of adaptation’ of populations. Finally, dormancy increases diversity by increasing the genetic distance between subpopulations.
The hierarchical feature regression (HFR) is a novel graph-based regularized regression estimator, which mobilizes insights from the domains of machine learning and graph theory to estimate robust parameters for a linear regression. The estimator constructs a supervised feature graph that decomposes parameters along its edges, adjusting first for common variation and successively incorporating idiosyncratic patterns into the fitting process. The graph structure has the effect of shrinking parameters towards group targets, where the extent of shrinkage is governed by a hyperparameter, and group compositions as well as shrinkage targets are determined endogenously. The method offers rich resources for the visual exploration of the latent effect structure in the data, and demonstrates good predictive accuracy and versatility when compared to a panel of commonly used regularization techniques across a range of empirical and simulated regression tasks.
A convex body is unconditional if it is symmetric with respect to reflections in all coordinate hyperplanes. We investigate unconditional lattice polytopes with respect to geometric, combinatorial, and algebraic properties. In particular, we characterize unconditional reflexive polytopes in terms of perfect graphs. As a prime example, we study the signed Birkhoff polytope. Moreover, we derive constructions for Gale-dual pairs of polytopes and we explicitly describe Gröbner bases for unconditional reflexive polytopes coming from partially ordered sets.