Mathematik
Refine
Year of publication
Document Type
- Article (112) (remove)
Has Fulltext
- yes (112)
Is part of the Bibliography
- no (112)
Keywords
- Biographie (2)
- Brownian motion (2)
- Finanzmathematik (2)
- Frankfurt <Main> / Universität (2)
- Krein space (2)
- Mathematik (2)
- Mathematiker (2)
- Perception (2)
- Statistik (2)
- Stochastik (2)
- Tropical geometry (2)
- Vision (2)
- coalescent (2)
- complexity (2)
- genealogy (2)
- level of difficulty (2)
- task space (2)
- thought structure (2)
- Abelian (1)
- Action potential (1)
- Adaptive dynamics (1)
- Ancestral selection graph (1)
- Anisotropic Norm (1)
- Arbitrage (1)
- Asymptotically Even Nonlinearity (1)
- Axon (1)
- Berkovich spaces (1)
- Binomialmodell (1)
- Black and Scholes Option Price theory (1)
- Black-Scholes (1)
- Boundary Value Problems (1)
- Branching process approximation (1)
- Breaking knapsack cryptosystems (1)
- Burst (1)
- Cannings model (1)
- Catalan number (1)
- Chinese restaurant process (1)
- Cognitive psychology (1)
- Degenerate Linear Part (1)
- Dehn (1)
- Derivate (1)
- Directional selection (1)
- Dirichlet bound (1)
- Dirichlet random measure (1)
- Diskrete Mathematik (1)
- Diversity in trait space (1)
- Dopamine (1)
- Dormancy (1)
- Duality (1)
- Evolutionary branching (1)
- Ewens sampling formula (1)
- Examples (1)
- FEM-BEM-coupling (1)
- FIND algorithm (1)
- Face (1)
- Face recognition (1)
- Feller branching with logistic growth (1)
- Finite element methods (1)
- Finitely many measurements (1)
- Fixation probability (1)
- Fractional Brownian Motion (1)
- Fractional Laplacian (1)
- Fuchsian groups (1)
- Functions (1)
- Galerkin Approximation (1)
- Gaussian Random Field (1)
- Gaussian process (1)
- Gelfand-Shilov space (1)
- Girsanov transform (1)
- Gram-Hadamard inequalities (1)
- Griffiths–Engen–McCloskey distribution (1)
- Hadamard's Three-Lines Theorem (1)
- Heat kernel (1)
- Heisenberg algebra (1)
- Hidden Markov models (1)
- Hodge bundle (1)
- Hopf algebroids (1)
- Index at Infinity (1)
- Infrared singularity (1)
- Internet (1)
- Inverse problems (1)
- Jahr der Mathematik (1)
- Klebsiella pneumoniae (1)
- Knapsack problem (1)
- Kongress (1)
- Kryptosystem (1)
- Kullback-Leibler Informational Divergence (1)
- L^p bounds (1)
- L^p means (1)
- Laplace operator on graphs (1)
- Lattice basis reduction (1)
- Leerverkauf (1)
- Linear Filtering (1)
- Linear-Implicit Scheme (1)
- Logarithmic Laplacian (1)
- Long- Range Dependence (1)
- Long-Range Dependence (1)
- Longitudinal Study (1)
- Malliavin calculus (1)
- Mallows model (1)
- Mathematical Giftedness (1)
- Mathematical Reasoning (1)
- Mathematical modelling (1)
- Max (1)
- Mean Anisotropy (1)
- Mooney faces (1)
- Moran model (1)
- Morava K-theory (1)
- Mouse (1)
- NP-complete problems (1)
- NP-hardness (1)
- Nash-Gleichgewicht (1)
- Neural encoding (1)
- Neurophysiology (1)
- Neuroscience (1)
- Neurowissenschaft (1)
- Newton–Okounkov bodies (1)
- Optimal Mean-Square Filter (1)
- Parabolic SPDE (1)
- Pause (1)
- Phragmén-Lindelöf principle (1)
- Piecewise-constant coefficient (1)
- Poisson boundary (1)
- Polymorphic evolution sequence (1)
- Pontrjagin space (1)
- Portfolios (1)
- Probability distribution (1)
- Probability of fixation (1)
- Quantum Zeno dynamics (1)
- Quantum Zeno effect (1)
- Quickselect (1)
- Random variables (1)
- Randomisieren (1)
- Ray-Knight representation (1)
- Reaction time (1)
- Rechenzentrum (1)
- Research article (1)
- Riemann surfaces (1)
- Riemannsche Fläche (1)
- Schizophrenia (1)
- Schwinger model (1)
- Sensory perception (1)
- Sensory processing (1)
- Shortest lattice vector problem (1)
- Signalverarbeitung (1)
- Small order expansion (1)
- Stochastic Analysis of Square Zero Variation Processes (1)
- Striatum (1)
- Strong Taylor Scheme (1)
- Stummel, Friedrich (1)
- Subset sum problem (1)
- Sudoku (1)
- Sympatric speciation (1)
- Tropical Grassmannians (1)
- Tropical varieties (1)
- Typology (1)
- Uniform regularity (1)
- W*-dynamical system (1)
- Wiener index (1)
- X-Y model (1)
- Zufall (1)
- abelian differentials (1)
- algebraic curves (1)
- alpha-stable branching (1)
- ampleness (1)
- argumentation (1)
- arithmetic ball quotients (1)
- augmented and restricted base loci (1)
- binary search tree (1)
- bordism theory (1)
- branching processes (1)
- branching random walk in random medium (1)
- canonical divisors (1)
- chosen ciphertext attack (1)
- clique problem (1)
- colorabdity (1)
- composition (1)
- computational complexity (1)
- confirmatory factory analysis (1)
- continued fraction algorithm (1)
- contraction method (1)
- convexity (1)
- convolution quadrature (1)
- cryptography (1)
- delay equation (1)
- dessins d’enfants (1)
- difference sets (1)
- digital search tree (1)
- digital tools (1)
- discrete logarithm (DL) (1)
- diskrete Mathematik (1)
- eigenvalue (1)
- elastodynamic wave equation (1)
- emergence (1)
- external branch (1)
- face inversion (1)
- face perception (1)
- fake projective planes (1)
- flat surfaces (1)
- floating point arithmetic (1)
- fractional Brownian motion (1)
- functional limit theorem (1)
- generic algorithm (1)
- generic algorithms (1)
- generic complexity (1)
- generic group model (1)
- geometry (1)
- graph isomorphism (1)
- h-transform (1)
- hardcore subsets (1)
- harmonic function (1)
- heavy tails (1)
- hierarchical mean-field limit (1)
- hyperbolische Geometrie (1)
- indefinite inner product space (1)
- integer relation (1)
- interacting particle Systems (1)
- interdisziplinäre Lehre (1)
- internal diffusion limited aggregation (1)
- internal path length (1)
- key comparisons (1)
- kinetic fingerprint (1)
- knapsack cryptosystems (1)
- large deviations (1)
- latent variance (1)
- lattice basis reduction (1)
- lattices (1)
- leapfrog (1)
- local time (1)
- local time drift (1)
- logical networks (1)
- lookdown construction (1)
- mathematical modeling (1)
- mathematical modelling (1)
- modular group (1)
- moduli spaces (1)
- multilevel branching (1)
- non-autonomous dynamical systems (1)
- noncommutative ring spectra (1)
- nondetermmistlc Turing machines (1)
- numerical experiments (1)
- one-more decryption attack (1)
- perceptual closure (1)
- phage (1)
- phage therapy (1)
- platonischer Körper (1)
- population dynamics (1)
- positivity of line bundles (1)
- probabilistic analysis of algorithms (1)
- professional development (1)
- projective planes (1)
- q-binomial theorem (1)
- quantum field theory (1)
- quantum spin systems (1)
- quincunx (1)
- random environment (1)
- random media (1)
- random oracle model (1)
- random partition (1)
- random recursive tree (1)
- random trees (1)
- random walks (1)
- reactant-catalyst systems (1)
- reguläre Parkettierung (1)
- resistance (1)
- return to equilibrium (1)
- reversibility (1)
- rough paths theory (1)
- satlsfiablhty (1)
- scaling (1)
- set-valued pullback attractors (1)
- signed ElGamal encryption (1)
- simultaneous diophantine approximations (1)
- stochastische Prozesse (1)
- strong transience (1)
- subset sum problems (1)
- sum of squared factor loadings (1)
- switching systems (1)
- synergistic interaction (1)
- topological entropy (1)
- urn model (1)
- von Neumann algebra (1)
- Λ-coalescent (1)
- σ-field (1)
Institute
- Mathematik (112)
- Informatik (13)
- Medizin (2)
- Frankfurt Institute for Advanced Studies (FIAS) (1)
- MPI für Hirnforschung (1)
- MPI für empirische Ästhetik (1)
- Physik (1)
- Präsidium (1)
- Psychologie (1)
Über Elementarkettenbrüche, lineare Substitutionen und indefinite binäre quadratische Formen : I.
(1919)
Über Elementarkettenbrüche, lineare Substitutionen und indefinite binäre quadratische Formen : II.
(1921)
Die Hilbertsche Grundlegung der Geometrie darf für alle analogen Untersuchungen als vorbildlich gelten. Zwei ihrer Eigenschaften sind es, auf die es hier ankommt. Erstens wird von allen sprachlichen Definitionen der Objekte, mit denen sie operiert, wie Punkt, Gerade, zwischen usw. abgesehen; nur ihre gegenseitigen Beziehungen und deren Grundgesetze werden axiomatisch an die Spitze gestellt. Zweitens werden die Axiome in verschiedene Gruppen gewisser Eigenart und Tragweite gespalten (die des Schneidens und Verbindens, die Axiome der Ordnung, der Kongruenz usw.), und es ist eine wesentliche Aufgabe des axiomatischen Aufbaues, zu prüfen, bis zu welchen Resultaten eine einzelne oder mehrere dieser Gruppen für sich führen. Die gleiche Behandlung eignet sich für die Mengenlehre. Von sprachlicher Einführung der Begriffe Menge, Bereich usw. ist daher ebenso abzusehen , wie von der des Punktes oder Raumes. Ebenso kann man hier gewiisse Axiomgruppen unterscheiden, die Axiome der Aquivalenz, die Axiome der Ordnung usw., und kann die gleichen Fragen stellen, wie im Gebiet der Geometrie. Dies soll im folgenden geschehen und zwar für denjenigen Teii, der nur mit dar Äquivalenz der Mengen, der Mengenteilung und Mengenverbindung, sowie der Mengenvergleichung operiert.....
In dem Artikel ,,Zur Axiomatik der Mengenlehre" habe ich die Axiome, die sich mit den Gebieten der Äquivalenz, der Mengenteilung und Mengenuergleichung beschäftigen, einer Erörterung unterzogen. An zwei Resultate dieses Artikels knüpfe ich hier an. Erstens einmal, da die in ihm durchgeführten Untersuchungen auf die Elemente der Mengen gar nicht eingehen, so stellen sie, allgemein gesprochen, axiomatische Betrachtungen über Größen und Größenbeziehungen dar, an denen die Mengen ja Teil haben; und zweitens hatte eine der dort analysierten Beziehungen den Gedanken nahegelegt, auch Größen entgegengesetzter Art (resp. Mengen von zweierlei Art von Elementen) in Betracht zu ziehen, und auf sie die oben genannten Operationen auszudehnen. Hier nun gebe ich im folgenden einige Ergänzungen. Bereits a. a. O.war bemerkt worden, daß es naturgemäß der Untersuchung bedarf, ob für die so charakterisierten Mengen die weiteren allgemeinen Sätze der Cantorschen Theorie in Kraft bleiben. Inzwischen hat mir Herr A. Fränkel mitgetelt, daß für das von mir konstruierte Beispiel schon ein Teil der in meinem Artikel zugrunde gelegten Axiome versagt; und zwar ein Teil der Axiome über Teilmengen. Über Teilmengen habe ich zwei Axiome an die Spitze gestellt. ......
Considered are the classes QL (quasilinear) and NQL (nondet quasllmear) of all those problems that can be solved by deterministic (nondetermlnlsttc, respectively) Turmg machines in time O(n(log n) ~) for some k Effloent algorithms have time bounds of th~s type, it is argued. Many of the "exhausUve search" type problems such as satlsflablhty and colorabdlty are complete in NQL with respect to reductions that take O(n(log n) k) steps This lmphes that QL = NQL iff satisfiabdlty is m QL CR CATEGORIES: 5.25
Public key signature schemes are necessary for the access control to communication networks and for proving the authenticity of sensitive messages such as electronic fund transfers. Since the invention of the RSA scheme by Rivest, Shamir and Adleman (1978) research has focused on improving the e±ciency of these schemes. In this paper we present an efficient algorithm for generating public key signatures which is particularly suited for interactions between smart cards and terminals.
The general subset sum problem is NP-complete. However, there are two algorithms, one due to Brickell and the other to Lagarias and Odlyzko, which in polynomial time solve almost all subset sum problems of sufficiently low density. Both methods rely on basis reduction algorithms to find short nonzero vectors in special lattices. The Lagarias-Odlyzko algorithm would solve almost all subset sum problems of density < 0.6463 . . . in polynomial time if it could invoke a polynomial-time algorithm for finding the shortest non-zero vector in a lattice. This paper presents two modifications of that algorithm, either one of which would solve almost all problems of density < 0.9408 . . . if it could find shortest non-zero vectors in lattices. These modifications also yield dramatic improvements in practice when they are combined with known lattice basis reduction algorithms.
Let b1, . . . , bm 2 IRn be an arbitrary basis of lattice L that is a block Korkin Zolotarev basis with block size ¯ and let ¸i(L) denote the successive minima of lattice L. We prove that for i = 1, . . . ,m 4 i + 3 ° 2 i 1 ¯ 1 ¯ · kbik2/¸i(L)2 · ° 2m i ¯ 1 ¯ i + 3 4 where °¯ is the Hermite constant. For ¯ = 3 we establish the optimal upper bound kb1k2/¸1(L)2 · µ3 2¶m 1 2 1 and we present block Korkin Zolotarev lattice bases for which this bound is tight. We improve the Nearest Plane Algorithm of Babai (1986) using block Korkin Zolotarev bases. Given a block Korkin Zolotarev basis b1, . . . , bm with block size ¯ and x 2 L(b1, . . . , bm) a lattice point v can be found in time ¯O(¯) satisfying kx vk2 · m° 2m ¯ 1 ¯ minu2L kx uk2.
Parallel FFT-hashing
(1994)
We propose two families of scalable hash functions for collision resistant hashing that are highly parallel and based on the generalized fast Fourier transform (FFT). FFT hashing is based on multipermutations. This is a basic cryptographic primitive for perfect generation of diffusion and confusion which generalizes the boxes of the classic FFT. The slower FFT hash functions iterate a compression function. For the faster FFT hash functions all rounds are alike with the same number of message words entering each round.