Related papers: Tight Approximations for the Two Dimensional Gauss…
The p - q duality is a relation between the (p,q) model and the (q,p) model of two-dimensional quantum gravity. Geometrically this duality corresponds to a relation between the two relevant points of the Sato Grassmannian. Kharchev and…
The purpose of this note is to provide an alternative proof of two quadratic transformation formulas contiguous to that of Gauss using a differential equation approach.
Gauss quadrature integral approximation is extended to include integrals with a measure consisting of continuous as well as discrete components. That is, we give an approximation for the integral of a function plus its sum over a discrete…
This work is devoted to the derivation of novel analytic expressions and bounds for a family of special functions that are useful in wireless communication theory. These functions are the well-known Nuttall $Q{-}$function, the incomplete…
In the present paper we use the expansion formula of the polylogarithm function to construct approximations of the Caputo derivative which are related to the midpoint approximation of the integral in the definition of the Caputo derivative.…
Near-Gaussian probability densities are common in many important physical applications. Here we develop an asymptotic expansion methodology for computing entropic functionals for such densities. The expansion proposed is a close relative of…
The increased demand for online prediction and the growing availability of large data sets drives the need for computationally efficient models. While exact Gaussian process regression shows various favorable theoretical properties…
We investigate the characters of some finite-dimensional representations of the quantum affine algebras $U_q(\hat{g})$ using the action of the copy of $U_q(g)$ embedded in it. First, we present an efficient algorithm for computing the…
From two q-summation formulas we deduce certain series expansion formulas involving the q-gamma function. With these formulas we can give q-analogues of series expansions for certain constants.
When computing bounds, spatial branch-and-bound algorithms often linearly outer approximate convex relaxations for non-convex expressions in order to capitalize on the efficiency and robustness of linear programming solvers. Considering…
The present work stemmed from the study of the problem of harmonic analysis on the infinite-dimensional unitary group U(\infty). That problem consisted in the decomposition of a certain 4-parameter family of unitary representations, which…
Gaussian universality results assert that the properties of many estimators remain unchanged when the input data are replaced by Gaussians. Such results have gained popularity in high-dimensional statistics and machine learning, as…
Directed q-analysis is a recent extension of q-analysis, an established method for extracting structure from networks, to directed graphs. Until recently, a lack of efficient algorithms heavily restricted the application of this technique:…
We present an analytical closed form expression, which gives a good approximate propagator for diffusion on the sphere. Our formula is the spherical counterpart of the Gaussian propagator for diffusion on the plane. While the analytical…
In this paper, a novel gamma-shadowed two-ray with diffuse power (GS-TWDP) composite fading model is proposed. The model is intended for modeling propagation in the emerging wireless networks working at millimeter wave (mmWave) frequencies,…
If $f\in L^2(R^d)$ and if the function $f(x)f(y)$ is close in $L^2(R^{2d})$ norm to a radially symmetric function of $(x,y)$ then $f$ is close in $L^2$ norm to a centered Gaussian function. This is proved in a quantitative form with the…
We consider $q$-analytic derivations of the $q$-Gauss summation formula for a $\, _2\phi _1$ that respect the symmetry in its upper parameters.
The aghq package for implementing approximate Bayesian inference using adaptive quadrature is introduced. The method and software are described, and use of the package in making approximate Bayesian inferences in several challenging low-…
Effective image tokenization is crucial for both multi-modal understanding and generation tasks due to the necessity of the alignment with discrete text data. To this end, existing approaches utilize vector quantization (VQ) to project…
We consider approximation of functions of $s$ variables, where $s$ is very large or infinite, that belong to weighted anchored spaces. We study when such functions can be approximated by algorithms designed for functions with only very…