4897 papers
This paper presents a visual, intuition-driven guide to key information theory concepts such as entropy, mutual information, and channel capacity, demonstrating how they derive from basic probability to define the fundamental limits of data compression and reliable communication.
This paper proves that for the standard triangle polygon (corresponding to the toric surface ), the spectral transform establishes a birational isomorphism between the Goncharov-Kenyon cluster integrable system and the Beauville integrable system by showing that it intertwines their respective Poisson structures, thereby demonstrating that Beauville integrable systems admit cluster algebra structures.
This paper employs pseudodifferential arithmetic to construct an explicit operator that allegedly disproves the Riemann hypothesis by showing the real parts of non-trivial zeros have a measure of at least 0.5, while simultaneously claiming to prove the Lindelöf hypothesis.
These lecture notes provide a brief introduction to category theory concepts, specifically initial algebras and monads, tailored to their applications in defining datatypes, recursive functions, and effects within functional programming.
This paper generalizes the construction of mixed Hodge module structures to tautological systems associated with homogeneous spaces via a functorial approach, thereby providing a complete solution to the holonomic rank problem for these systems.
This paper addresses geometric programming problems with inaccurate parameters by introducing triangular and trapezoidal two-fold uncertain variables, developing reduction methods to convert them into single-fold uncertainties, and solving the resulting models using a chance-constrained framework.
This paper establishes structural results for NIP integral domains, proving that non-field NIP Noetherian domains are semilocal of Krull dimension 1 with characteristic 0 fraction fields, that finite dp-rank domains are henselian local rings, and providing a classification of dp-minimal Noetherian domains.
This paper proves that the Quillen posets of -extensions of simple unitary groups have non-zero homology in the largest possible dimension, thereby establishing the 1992 Aschbacher-Smith conjecture and confirming Quillen's conjecture for odd primes.
This paper investigates the topological properties of negatively associated and negatively correlated distributions within the space of probability measures, demonstrating that while the class of negatively associated distributions has a non-empty interior under the total variation metric, it lacks this property in the weak topology unless the underlying space is finite, while also analyzing their convexity, connectedness, and behavior on the Boolean cube.
This paper introduces surface area notions for discrete graphs linked to the inverse degree to define new connectivity measures and a class of "social graphs," while deriving spectral estimates that yield an improved upper bound on the second eigenvalue for planar graphs.
This paper introduces a canonical -algebra of operators with finite dynamical propagation for non-singular group actions, establishing its isomorphism to the algebraic crossed product under free actions to characterize ergodicity and to describe the Roe algebras of warped spaces and warped cones.
This paper establishes that in doubling metric measure spaces supporting a -Poincaré inequality, domains with uniformly thick boundaries possess a large "visible" portion accessible via John curves, and that the traces of Sobolev functions on these domains belong to the Besov class of the visible boundary.
This paper employs a constructive gluing approach to establish the existence of global-in-time solutions to the 2D incompressible Euler equations that asymptotically behave as a superposition of two traveling vortex-antivortex pairs moving in opposite directions.
This paper establishes the descriptive complexity of various mathematical structures by proving that the Hindman ideal, the ideal , and specific families of trees are -complete, while also exploring the connections between ideals on and classical tree types like Sacks and Miller.
This paper establishes limit theorems for the number of fixed points in random pattern-avoiding permutations under a biased distribution, revealing a phase transition where the limiting behavior shifts from negative binomial to Rayleigh to normal depending on the bias parameter.
This paper determines the unique birationally rigid induction datum for every -equivariant nilpotent cover of a nilpotent coadjoint orbit in a semisimple simply connected algebraic group of exceptional type over .
This paper extends the complex multipoint Schwarz-Pick Lemma to the quaternionic setting of slice regular functions using iterated hyperbolic difference quotients, thereby deriving new estimates and providing an algorithm for constructing interpolating functions with real nodes.
This paper defines a quaternionic analog of the classical Maass Spezialschar on split , characterizing this space of level one quaternionic modular forms via theta lifts from and period integrals, while also proposing and verifying a conjecture regarding the Dirichlet series of their standard -functions.
This paper investigates the local-triviality dimensions of actions on -algebras within noncommutative Borsuk-Ulam theory, demonstrating that free actions do not necessarily possess finite weak local-triviality dimensions and that these invariants can exhibit discontinuity or exceed fiber values in continuous fields, while establishing conditions for upper semicontinuity through examples involving noncommutative tori and spheres.
This paper establishes the existence and uniqueness of equilibrium for a stochastic mean-field game of optimal investment involving identical firms interacting through a time-dependent price, covering both finite and infinite time horizons as well as a deterministic counterpart.