相关论文: An error estimate for counting $S_3$-sextic number…

Third order chiral perturbation theory accounts for the $\pi-N$ scattering phase shift data out to energies slightly below the position of the $\Delta$ resonance. The low energy constants are not accurately determined. Explicit inclusion of…

We describe in some detail the derivation of a power counting formula for the soft-collinear effective theory (SCET). This formula constrains which operators are required to correctly describe the infrared at any order in the Lambda_QCD/Q…

In this paper we present a short and elementary proof for the error in Simpson's rule.

Building an accurate load forecasting model with minimal underpredictions is vital to prevent any undesired power outages due to underproduction of electricity. However, the power consumption patterns of the residential sector contain…

We present a framework that relates preconditioning with a posteriori error estimates in finite element methods. In particular, we use standard tools in subspace correction methods to obtain reliable and efficient error estimators. As a…

We design a new provably efficient algorithm for episodic reinforcement learning with generalized linear function approximation. We analyze the algorithm under a new expressivity assumption that we call "optimistic closure," which is…

We improve upon the traditional error term in the truncated Perron formula for the logarithm of an $L$-function. All our constants are explicit.

In the tensor completion problem, one seeks to estimate a low-rank tensor based on a random sample of revealed entries. In terms of the required sample size, earlier work revealed a large gap between estimation with unbounded computational…

We compute the next-to-leading order QCD and electroweak corrections to $Z$ and $W$ pole observables using the dimension-6 Standard Model effective field theory and present numerical results that can easily be included in global fitting…

Building on the concept of pretentious multiplicative functions, we give a new and largely elementary proof of the best result known on the counting function of primes in arithmetic progressions.

The Functional Machine Calculus (Heijltjes 2022) is an extension of the lambda-calculus that preserves confluent reduction and typed termination, while enabling both call-by-name and call-by-value reduction behaviour and encoding the…

We construct an objective function that consists of a quadratic approximation term and a penalty term. Thanks to the quadratic approximation, we can deal with various kinds of loss functions into a unified way, and by taking advantage of…

A strong form of the Manin-Peyre conjecture with a power saving error term is proved for a certain cubic fourfold.

Resonance counting is an intuitive and widely used tool in Random Matrix Theory and Anderson Localization. Its undoubted advantage is its simplicity: in principle, it is easily applicable to any random matrix ensemble. On the downside, the…

In this paper we improve drastically the estimate for the multiplicity of a binary recurrence. The main contribution comes from an effective version of the Faltings' Product Theorem.

Super-symmetric tensors - a higher-order extension of scatter matrices - are becoming increasingly popular in machine learning and computer vision for modelling data statistics, co-occurrences, or even as visual descriptors. However, the…

We prove that the average error term when counting square-free values of polynomials is the quartic root of the main term.

We consider the problem setting of prediction with expert advice with possibly heavy-tailed losses, i.e. the only assumption on the losses is an upper bound on their second moments, denoted by $\theta$. We develop adaptive algorithms that…

We consider a one-dimensional singularly perturbed 4th order problem with the additional feature of a shift term. An expansion into a smooth term, boundary layers and an inner layer yields a formal solution decomposition, and together with…

In this manuscript, we investigate some properties of certain counting functions, associated to the ergodic sums computed along the periodic orbits of the skew-product map, related to a finitely generated rational semigroup. To be precise,…