3658 papers
This paper provides a self-contained tutorial on finite block length rate-distortion theory for a Bernoulli source with Hamming distortion, deriving the classical rate-distortion function, illustrating its computation via the Blahut-Arimoto algorithm, and analyzing finite-length refinements governed by rate-distortion dispersion with accompanying numerical examples.
This paper presents a new proof of the generalized Chapple-Euler relation for triangles inscribed in a circle and circumscribed about a central conic, establishing that the sum of the squared side lengths of such Poncelet triangles is invariant if and only if the circle is centered at either the conic's center or one of its foci.
This paper details a previously unrecorded error in Guy and Kelly's 2004 heuristic argument for the no-three-in-line problem, identified by Gabor Ellmann, and presents the resulting correction to their conjectured upper bound.
This paper introduces a new method utilizing syzygies to demonstrate that certain numerical semigroups are not Weierstrass, notably providing the first known examples of non-Weierstrass semigroups with multiplicity 6 and genus 13.
This paper establishes faster minimax convergence rates for a binary plug-in classification procedure applied to time-homogeneous SDE paths with space-dependent coefficients under low-noise conditions, by deriving a crucial exponential inequality and analyzing the lower bound on the empirical classifier's excess risk.
This paper constructs fractional Sobolev spaces with variable orders on arbitrary time scales and their product domains, establishing their functional-analytic properties and trace frameworks to derive Euler-Lagrange equations for variational problems involving variable-order Riemann-Liouville and Caputo fractional operators.
This paper establishes the global well-posedness and uniform exponential stabilization of the critical quintic wave equation in a 3D bounded domain with locally distributed Kelvin-Voigt damping by combining frequency-space Littlewood-Paley analysis, critical Strichartz estimates, and microlocal defect measures to overcome derivative loss and geometric obstructions.
This paper provides a complete proof for the previously proposed upper bound of on the double domination number of maximal outerplanar graphs, correcting an earlier incomplete proof by Abd Aziz, Rad, and Kamarulhaili.
This paper solves an intertemporal utility maximization problem with a no-borrowing constraint and stochastic excess returns in the Kim-Omberg framework by employing Lagrange duality to transform the primal problem into a dual singular control problem, which is then characterized via an auxiliary two-dimensional optimal stopping problem to derive optimal consumption and portfolio strategies.
This paper investigates the existence of invariant transversals for normal subgroups and provides counterexamples to a conjecture in the specific case where the subgroup is abelian and the group is finite.
This paper presents a geometrically convergent exact solution and a highly parallelizable algorithm for spatial hypercube queueing models with heterogeneous service rates, demonstrating significant computational speedups over traditional solvers and simulations for large-scale emergency service applications.
This paper investigates the distributional and asymptotic properties of the supremum and infimum of Brownian motion with drift and exponential resetting, deriving explicit renewal formulas, survival function approximations, and new expressions for the finite-dimensional distributions in the stationary case.
This paper extends the known concentration of the largest induced tree size in random graphs to all vanishing edge probabilities and demonstrates that for sparser graphs where , this size fails to concentrate around the standard expectation threshold.
This paper proposes the Wright-Euler Mersenne Exponent Hypothesis, which utilizes Euler's quadratic polynomial combined with nearest-integer rounding to identify candidate exponents for Mersenne primes, demonstrating a significantly higher accuracy and lower error rate compared to exponential regression models while effectively narrowing the search space for GIMPS testing.
This paper introduces a two-time scale neurodynamic duplex approach utilizing projection equations to solve distributionally robust geometric joint chance-constrained optimization problems with unknown distributions, demonstrating convergence to the global optimum through neural networks in applications such as shape optimization and telecommunications.
This paper provides a comprehensive review of the Partial Information Decomposition (PID) framework by integrating diverse formalisms into a unified language, systematically evaluating their adherence to known properties, mapping theorems that reveal relationships and incompatibilities between these properties, and charting a path for future theoretical and empirical advancements.
This paper investigates the analytic continuation and prime-restricted theory of arctanh sums , establishing their meromorphic extension with specific poles and zeros, deriving Laurent expansions and Mittag-Leffler decompositions, and proving the unconditional transcendence of their prime-restricted analogues via a -cancellation mechanism.
This paper employs the AlphaEvolve computational engine to explore three combinatorial problems—graph reconstruction, the Alon-Tarsi parity problem, and Rota's Basis Conjecture—by iteratively refining local correcting steps to generate explicit algorithms and structural patterns that serve as foundations for future traditional mathematical proofs.
This paper utilizes Markov models and Monte Carlo simulations to analyze how the average duration of Chutes and Ladders changes as die roll probabilities approach certainty and to evaluate the impact of six distinct strategies involving optional coin-flip moves on game length.
This paper introduces a unified recursive framework that constructs elliptic extensions of Clausen-type functions by replacing trigonometric seeds with Jacobi theta functions, thereby establishing a structural correspondence between circular and elliptic settings while organizing the hierarchy into a single analytic object.