Related papers: Closed-Form Bounds for the Rice $Ie$-Function
We provide an explicit characterization of the properties of primitive recursive functions that are decidable or semi-decidable, given a primitive recursive index for the function. The result is much more general as it applies to any c.e.…
The convolution of a function with an isotropic Gaussian appears in many contexts such as differential equations, computer vision, signal processing, and numerical optimization. Although this convolution does not always have a closed form…
The Fisher-Rao distance is the geodesic distance between probability distributions in a statistical manifold equipped with the Fisher metric, which is a natural choice of Riemannian metric on such manifolds. It has recently been applied to…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
This article establishes a complete approximate axiomatization for the real-closed field $\mathbb{R}$ expanded with all differentially-defined functions, including special functions such as $\sin(x), \cos(x), e^x, \dots$. Every true…
We show how to find upper and lower bounds to the median of a gamma distribution, over the entire range of shape parameter $k > 0$, that are the tightest possible bounds of the form $2^{-1/k} (A + Bk)$, with closed-form parameters $A$ and…
Open Information Extraction (OpenIE) facilitates domain-independent discovery of relational facts from large corpora. The technique well suits many open-world natural language understanding scenarios, such as automatic knowledge base…
Simple upper and lower bounds are obtained for the integral $\int_0^x\mathrm{e}^{-\gamma t}t^\nu I_\nu(t)\,\mathrm{d}t$, $x>0$, $\nu>-\frac{1}{2}$, $0<\gamma<1$. Most of our bounds for this integral are tight as $x\rightarrow\infty$. We…
The Lieb-Oxford bound is a constraint upon approximate exchange-correlation functionals. We explore a non-empirical tightening of that bound in both universal and electron-number-dependent form. The test functional is PBE. Regarding both…
In this paper, capacity bounds for the two-user Interference Channel (IC) with cooperative receivers via conferencing links of finite capacities is investigated. The capacity results known for this communication scenario are limited to a…
Based on two point spline approximations of arbitrary order, a series of functions that define lower bounds for sin(x) and sin(x)/x, over the interval [0,Pi/2], with increasingly low relative errors and smaller relative errors than…
Provable lower bounds are presented for the information rate I(X; X+S+N) where X is the symbol drawn independently and uniformly from a finite-size alphabet, S is a discrete-valued random variable (RV) and N is a Gaussian RV. It is well…
Single hidden layer feedforward neural networks can represent multivariate functions that are sums of ridge functions. These ridge functions are defined via an activation function and customizable weights. The paper deals with best…
This letter presents a detailed performance analysis of the intelligent reflecting surface (IRS) aided single-input single-output communication systems, taking into account of the direct link between the transmitter and receiver. A…
Finite differences have been widely used in mathematical theory as well as in scientific and engineering computations. These concepts are constantly mentioned in calculus. Most frequently-used difference formulas provide excellent…
A statistical characterization of the fundamental performance bounds of an intelligent reflective surface (IRS) intended for aiding wireless communications is presented. To this end, the outage probability, average symbol error probability,…
Sample size criteria are often expressed in terms of the concentration of the posterior density, as controlled by some sort of error bound. Since this is done pre-experimentally, one can regard the posterior density as a function of the…
We provide closed-form approximations to the performance gain achieved in a RIS-assisted communication. We then consider a network deployment of RIS and Transmitter-Receiver pairs and use these approximate expressions to provide equivalence…
We derive an analytical expression for the effective indices of modes of circular step-index fibers valid near their cutoff wavelengths. The approximation, being a first-order Taylor series of a smooth function, is also valid for the real…
Many functions have approximately-known upper and/or lower bounds, potentially aiding the modeling of such functions. In this paper, we introduce Gaussian process models for functions where such bounds are (approximately) known. More…