2549 papers
This paper introduces the concepts of vertex dismissible and scalable simplicial complexes as generalizations of vertex decomposability and shellability, establishing their algebraic characterizations via Alexander duality, proving their equivalence to weak connectedness for specific graph classes, and providing a unified skeletal framework that recovers numerous classical theorems.
This paper develops a theory of discrete averaging for discrete-time dynamical systems that utilizes weighted trajectory averages to directly approximate autonomous vector fields, thereby eliminating intermediate steps of classical averaging to provide explicit error bounds and establish the validity of adiabatic invariants for near-identity maps and resonant fixed points.
This paper proves that for sufficiently large , the uniform probability measures on three specific families of spanning subgraphs of the complete graph —namely connected spanning subgraphs, forests with exactly components, and connected spanning subgraphs with excess —satisfy the pairwise negative correlation property.
This paper proposes a memory-efficient, quasi matrix-free solver that leverages the self-similarity of lattice structures through a reduced-order modeling strategy within a domain-decomposition framework to enable fast, full fine-scale nonlinear simulations of complex hyperelastic metamaterials on standard hardware.
This paper generalizes previous work on toroidal averages by studying the cubic moments of special values of -functions for Dirichlet characters of prime modulus, while highlighting connections to bilinear forms of trace functions and the number of solutions to monoidal equations in finite fields.
This paper proposes a deep learning-based autoencoder architecture for the Randomized Distributed Function Computation (RDFC) framework that minimizes the total variation distance to an unknown target distribution using only data samples, demonstrating superior communication efficiency compared to traditional data compression methods, particularly under limited common randomness.
This paper proves a consistency result for the Domain of Dependence (DoD) cut cell stabilization method with arbitrary polynomial degrees and sufficiently regular exact solutions, thereby enabling a rigorous error analysis for high-order applications.
This paper introduces an antichain condition for non- subgroups in infinite groups and proves that, within the class of generalized radical groups, this condition is equivalent to the restricted chain condition (RCC), thereby establishing minimax-type dichotomies for various subgroup properties such as normality, permutability, and pronormality.
This paper establishes a novel connection between digraph extremal problems and uniform Turán densities of 3-graphs to provide verifiable conditions for determining specific density values, including identifying new classes of 3-graphs with densities such as , , and $4/271/27$.
This paper proposes a new "disguise-and-squeeze" PIR scheme for MDS-coded databases with colluding servers that generalizes previous counterexamples to the Freij-Hollanti conjecture, achieves a superior rate for specific parameters (proving optimality when ), and offers advantages in field size and adaptability to various generalized PIR models.
This paper investigates the asymptotic behavior of solutions to divergence-form linear elliptic equations in exterior domains with periodic coefficients, thereby generalizing the Liouville-type result originally established by Avellaneda and Lin.
This paper establishes the existence and Liouville-type results for quadratic growth solutions to fully nonlinear elliptic equations with periodic coefficients and right-hand sides, proving that under a small oscillation assumption, such solutions decompose into the sum of a quadratic polynomial and a periodic function.
This paper investigates the properties of tightly prime-divisor-finite domains (TPDF-domains), which are integral domains where every nonzero element has finitely many nonassociate prime divisors and every nonzero nonunit admits at least one prime divisor, while also examining how this property behaves under localization, constructions, and polynomial rings.
This paper establishes sharper polyhomogeneous mapping properties for the Radon transform and backprojection operator on the unit ball by constructing a double -fibration to desingularize the point-hyperplane relation and utilizing associated -fibration operations to improve upon classic Mellin-based estimates.
This paper establishes that a Cohen-Macaulay complete local ring with an infinite residue field is uniformly dominant with explicit bounds on its dominant index under various conditions, including codimension 2 non-complete intersections, Burch rings, quasi-fiber product rings, and rings with low multiplicity, thereby recovering and refining existing results on hypersurfaces and specific ring classes.
This paper establishes a unified framework for estimating the spectral deviation of concentration operators on reproducing kernel Hilbert spaces, demonstrating that discretized approximations like Gabor multipliers preserve the theoretical localization properties of their continuous counterparts with bounds uniform in the discretization step.
This paper presents new combinatorial perspectives on partitions with distinct even parts by connecting them to signed and bicolored partitions to derive several identities and provide bijective proofs that partially resolve open problems posed by Andrews-El Bachraoui and Kılıç-Kurşungöz.
This paper introduces the concept of strong regularity for subanalytic sheaves to establish microsupport estimates and derive initial value and division theorems for multi-microlocal objects, ultimately yielding a multi-microlocal version of Bochner's tube theorem for solutions of regular D-modules.
This paper proposes a stochastic geometry framework for Underwater Optical Wireless Communication that reveals a counter-intuitive "offset pointing" strategy, where intentionally misaligning the receiver by an optimal angle maximizes received power and reduces transmit power requirements by nearly 20%, thereby significantly extending network lifetime and improving energy efficiency.
This paper introduces new extensions of Khovanov, Lee, and Bar-Natan homologies for links in that are distinct from previous constructions and yield novel Rasmussen invariants.