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We establish a relationship between error terms appearing in estimates for the counting functions of smooth and rough numbers. We then apply this link to obtain an explicit upper bound for the error term in de Bruijn's approximation…
Let $\lambda(m)$ denote the maximal absolute projection constant over real $m$-dimensional subspaces. This quantity is extremely hard to determine exactly, as testified by the fact that the only known value of $\lambda(m)$ for $m>1$ is…
We present a simple algorithm to select multivariate interpolation stencil with a Cartesian grid. We show its applicability by using this algorithm in the embedded boundary method for solving the elliptic interface problem.
Estimates of the quantum accuracy threshold often tacitly assume that it is possible to interact arbitrary pairs of qubits in a quantum computer with a failure rate that is independent of the distance between them. None of the many physical…
Computing the determinant of a matrix with the univariate and multivariate polynomial entries arises frequently in the scientific computing and engineering fields. In this paper, an effective algorithm is presented for computing the…
Error probabilities of random codes for memoryless channels are considered in this paper. In the area of communication systems, admissible error probability is very small and it is sometimes more important to discuss the relative gap…
This paper contains a survey of results obtained by the authors mostly during the past few years and published by 2021. In particular, we present the best of known estimates of numerical characteristics related to the research theme.…
The critical temperature of thin Fe layers on Ir(100) is measured through M\"o{\ss}bauer spectroscopy as a function of the layer thickness. From a phenomenological finite-size scaling analysis, we find an effective shift exponent lambda =…
The notion of the higher rank numerical range $\Lambda_{k}(L(\lambda))$ for matrix polynomials $L(\lambda)=A_{m}\lambda^{m}+...+A_{1}\lambda+A_{0}$ is introduced here and some fundamental geometrical properties are investigated. Further,…
Traditional studies of multi-source, multi-terminal interference channels typically allow a vanishing probability of error in communication. Motivated by the study of network coding, this work addresses the task of quantifying the loss in…
Event-by-event fluctuations of hadronic patterns in heavy-ion collisions are studied in search for signatures of quark-hadron phase transition. Attention is focused on a narrow strip in the azimuthal angle with small $\Delta y$. The…
A set of complex numbers $\Lambda=\{\lambda_n,\mu_n\}_{n=1}^{\infty}$ with multiple terms \[ \{\lambda_n,\mu_n\}_{n=1}^{\infty}:= \{\underbrace{\lambda_1,\lambda_1,\dots,\lambda_1}_{\mu_1 - times},…
Critical phenomena in globally coupled excitable elements are studied by focusing on a saddle-node bifurcation at the collective level. Critical exponents that characterize divergent fluctuations of interspike intervals near the bifurcation…
The aim of this paper is to give a short overview on error bounds and to provide the first bricks of a unified theory. Inspired by the works of [8, 15, 13, 16, 10], we show indeed the centrality of the Lojasiewicz gradient inequality. For…
Structured Kernel Interpolation (SKI) (Wilson et al. 2015) helps scale Gaussian Processes (GPs) by approximating the kernel matrix via interpolation at inducing points, achieving linear computational complexity. However, it lacks rigorous…
In this paper, we analyze the accuracy of gradient estimates obtained by linear interpolation when the underlying function is subject to bounded measurement noise. The total gradient error is decomposed into a deterministic component…
We study uniform interpolation and forgetting in the description logic ALC. Our main results are model-theoretic characterizations of uniform inter- polants and their existence in terms of bisimula- tions, tight complexity bounds for…
The distortion-rate performance of certain randomly-designed scalar quantizers is determined. The central results are the mean-squared error distortion and output entropy for quantizing a uniform random variable with thresholds drawn…
The permanent of a multidimensional matrix is the sum of products of entries over all diagonals. By Minc's conjecture, there exists a reachable upper bound on the permanent of 2-dimensional (0,1)-matrices. In this paper we obtain some…
This paper contains a review of available methods for establishing improved interpolation inequalities on the sphere for subcritical exponents. Pushing further these techniques we also establish some new results, clarify the range of…