Related papers: On capacity computation for symmetric polygonal co…
A poly-log time method to compute the truncated theta function, its derivatives, and integrals is presented. The method is elementary, rigorous, explicit, and suited for computer implementation. We repeatedly apply the Poisson summation…
We introduce a novel method for bounding high-order multi-dimensional polynomials in finite element approximations. The method involves precomputing optimal piecewise-linear bounding boxes for polynomial basis functions, which can then be…
We present an effective harmonic density interpolation method for the numerical evaluation of singular and nearly singular Laplace boundary integral operators and layer potentials in two and three spatial dimensions. The method relies on…
We address a major flaw in the abovementioned paper, which proposes to calculate effective capacity of random channels by the use of central limit theorem. We analytically show that the authors are incorrect in finding the effective…
We present analytic results for all planar two-loop Feynman integrals contributing to five-particle scattering amplitudes with one external massive leg. We express the integrals in terms of a basis of algebraically-independent…
We provide tools to help automate the error analysis of algorithms that evaluate simple functions over the floating-point numbers. The aim is to obtain tight relative error bounds for these algorithms, expressed as a function of the unit…
This paper presents a novel, model-based compressive antenna design method for high sensing capacity imaging applications. Given a set of design constraints, the method maximizes the sensing capacity of the compressive antenna by varying…
This paper introduces a highly efficient rectenna (rectifying antenna) using a binary optimization algorithm. A novel pixelated receiving antenna has been developed to match the diode impedance of a rectifier, eliminating the need for a…
For the discretization of the integral fractional Laplacian $(-\Delta)^s$, $0 < s < 1$, based on piecewise linear functions, we present and analyze a reliable weighted residual a posteriori error estimator. In order to compensate for a lack…
First, we study geometric variants of the standard set cover motivated by assignment of directional antenna and shipping with deadlines, providing the first known polynomial-time exact solutions. Next, we consider the following general…
For interior-point algorithms in linear programming, it is well-known that the selection of the centering parameter is crucial for proving polynomility in theory and for efficiency in practice. However, the selection of the centering…
We present a parallel algorithm for calculating very large determinants with arbitrary precision on computer clusters. This algorithm minimises data movements between the nodes and computes not only the determinant but also all minors…
In this article we develop function-based a posteriori error estimators for the solution of linear second order elliptic problems considering hierarchical spline spaces for the Galerkin discretization. We prove a global upper bound for the…
In a previous paper it was shown that a machine learning regression problem can be solved within the framework of random function theory, with the optimal kernel analytically derived from symmetry and indifference principles and coinciding…
Optimal rates for achieving an information processing task are often characterized in terms of regularized information measures. In many cases of quantum tasks, we do not know how to compute such quantities. Here, we exploit the symmetries…
For the singular integral definition of the fractional Laplacian, we consider an adaptive finite element method steered by two-level error indicators. For this algorithm, we show linear convergence in two and three space dimensions as well…
We consider the problem of estimating an upper bound on the capacity of a memoryless channel with unknown channel law and continuous output alphabet. A novel data-driven algorithm is proposed that exploits the dual representation of…
In this paper, we develop a unified framework able to certify both exponential and subexponential convergence rates for a wide range of iterative first-order optimization algorithms. To this end, we construct a family of parameter-dependent…
A LMTO implementation of Aversa and Sipe's length-gauge formalism for calculating the full frequency dependent second-harmonic generation in the independent particle approximation is presented. It is applied to GaAs, GaP, 3C-SiC, c-BN and…
In this paper we further develop the ideas from Geometric Function Theory initially introduced in [arXiv:2206.13206], to derive capacity estimate in metastability for arbitrary configurations. The novelty of this paper is twofold. First,…