7150 papers
This paper derives explicit formulae for the -dissection of a product of quintuple products when is a prime expressible as a sum of two squares, determines the sign patterns of the resulting Taylor series coefficients, and presents combinatorial applications of these findings.
The paper establishes that the Kazhdan-Lusztig category of W-algebras associated with simple, simply-laced Lie algebras at irrational levels is braided tensor equivalent to the corresponding Kazhdan-Lusztig category of affine vertex algebras via quantum Hamiltonian reduction.
This paper proposes and analyzes two consistent and asymptotically normal estimators for the edge existence probability of a dynamic Erdős–Rényi graph by observing only the population distribution of individuals moving across its vertices, without direct access to the graph's structure.
This paper proposes a post-processing method that significantly improves the accuracy of physics-informed neural networks (PINNs) by finding the best approximation in a function space associated with the network, achieving errors four to five orders of magnitude lower than standard PINNs while enabling transfer learning and providing a metric for optimal basis function selection.
This paper utilizes family index theory to generalize well-known modular forms to the family setting, thereby deriving new anomaly cancellation formulas for determinant line bundles, index gerbes, eta invariants, and residue Chern forms.
This paper establishes a polynomial upper bound for the nodal sets of solutions to bi-Laplace equations by deriving delicate monotonicity and propagation of smallness results via Carleman estimates, thereby avoiding the use of frequency functions central to Logunov's work.
This paper establishes uniform convergence rates for kernel averages under fixed, equally-spaced design points with heterogeneous dependent data, offering a non-stationary alternative to existing random-design results and applying these findings to local linear estimators in nonparametric regression with time-varying autoregressive errors.
This paper develops a unified theory of second-order asymptotic optimality for sequential multiple testing with independent data streams, demonstrating that certain first-order optimal procedures are also second-order optimal with uniformly bounded excess sample sizes and deriving a refined asymptotic expansion for the minimal achievable sample size.
This paper introduces an augmented van Trees inequality that provides uniformly tighter lower bounds on minimax squared Bayes risk than the classical version, accommodates priors with non-vanishing boundary densities, and enables the derivation of sharper or exact minimax constants for various nonparametric estimation problems, including high-dimensional regression.
This paper establishes the strong consistency and convergence rates of a local linear estimator for generalized regression with dependent functional data, demonstrating its superior performance over the local constant estimator through both theoretical analysis and empirical applications in energy forecasting.
This paper investigates the continuous and Borel regulation numbers of rectangular partitions for free -actions on $0$-dimensional Polish spaces, establishing that while the value is 3 for , it increases to 5 for and is bounded between and for higher dimensions, thereby revealing a fundamental distinction in Borel combinatorics between two-dimensional and higher-dimensional cases.
This paper demonstrates that for Oldroyd-B viscoelastic fluids, the stress tensor and elastic components decay at rates that cause the fluid to exhibit almost Newtonian behavior over large time scales, as the elastic part vanishes faster than the Newtonian deformation.
This paper proves a conjecture by Gyárfás and Király by showing that the vertices of a complete -partite -uniform hypergraph with a spanning -edge-coloring (where ) can be covered by at most monochromatic connected components, while also establishing a related bound for complete bipartite graphs.
This paper characterizes the graphs maximizing the number of -convex sets, establishes the -completeness of counting these sets on split graphs, and provides efficient linear-time algorithms for trees and threshold graphs alongside a novel exact exponential-time approach for general graphs.
This paper introduces a time-discrete Variational Physics-Informed Neural Network (VPINN) that minimizes the residual's dual norm at each time step to effectively model the temperature-dependent heat conduction dynamics of industrial coffee extract freezing.
This paper proposes a hybrid methodology combining theoretical modeling with empirical benchmarking to accurately determine the optimal allocation of Prefill-Decode disaggregated hardware resources for Large Language Model inference while satisfying throughput, SLO, and request characteristic constraints.
This paper proposes an explicit truncated Euler-Maruyama scheme with time and space truncation to approximate the invariant probability measures of super-linear stochastic functional differential equations with infinite delay, establishing strong convergence and proving that the numerical invariant measure converges to the exact one in Wasserstein distance with an explicit rate.
This paper proposes a rare event-aware control method for power systems that utilizes a Fleming-Viot particle approach within a multistage stochastic programming framework to generate biased scenarios of prolonged renewable energy shortfalls, thereby enabling cost-effective and robust ramping of conventional power plants.
This paper establishes a dimension-independent lower bound on the cotype constant for normed spaces generated by random polytopes with Gaussian vertices, demonstrating that under specific density conditions on the number of vertices relative to dimension, these spaces satisfy a cotype inequality with high probability.
This paper proposes a robust estimation method for diffusion processes using -divergence to mitigate the impact of outliers in high-frequency data, establishing its asymptotic properties and bounded influence functions through Gaussian approximation of transition densities.