Related papers: Comparing representations for function spaces in c…
Is analogical reasoning a task that must be learned to solve from scratch by applying deep learning models to massive numbers of reasoning problems? Or are analogies solved by computing similarities between structured representations of…
The rapid developments of various machine learning models and their deployments in several applications has led to discussions around the importance of looking beyond the accuracies of these models. Fairness of such models is one such…
Smoothed Wigner transforms have been used in signal processing, as a regularized version of the Wigner transform, and have been proposed as an alternative to it in the homogenization and / or semiclassical limits of wave equations. We…
By using Cauchy integral formula in the theory of complex functions, the authors establish some integral representations for the principal branches of several complex functions involving the logarithmic function, find some properties, such…
In this paper, we provide a comprehensive rigorous modeling for multidimensional spaces with hierarchically structured dimensions in several layers of abstractions and data cubes that live in such spaces. We model cube queries and their…
Finite dimensional subspaces spanned by exponential functions in the space of square integrable functions on a finite interval of the real line are considered. Their limiting positions are studied and described in terms of expo-polynomials.
We point out that a proper use of the Hoeffding--ANOVA decomposition for symmetric statistics of finite urn sequences, previously introduced by the author, yields a decomposition of the space of square-integrable functionals of a…
In classical complex analysis analyticity of a complex function $f$ is equivalent to differentiability of its real and imaginary parts $u$ and $v$, respectively, together with the Cauchy-Riemann equations for the partial derivatives of $u$…
In this thesis we will present and discuss various results pertaining to tiling problems and mathematical logic, specifically computability theory. We focus on Wang prototiles, as defined in [32]. We begin by studying Domino Problems, and…
Shape analysis and compuational anatomy both make use of sophisticated tools from infinite-dimensional differential manifolds and Riemannian geometry on spaces of functions. While comprehensive references for the mathematical foundations…
There is a well known intrinsic trade-off between the fairness of a representation and the performance of classifiers derived from the representation. Due to the complexity of optimisation algorithms in most modern representation learning…
Conceptual spaces are geometric representations of conceptual knowledge, in which entities correspond to points, natural properties correspond to convex regions, and the dimensions of the space correspond to salient features. While…
For a compact subset $K$ of the complex plane $\mathbb C,$ let $C(K)$ denote the algebra of continuous functions on $K$. For an open subset $U \subset K,$ let $A(K,U) \subset C(K)$ be the algebra of functions that are analytic in $U.$ We…
We address in this paper the following two closely related problems: 1. How to represent functions with singularities (up to a prescribed accuracy) in a compact way? 2. How to reconstruct such functions from a small number of measurements?…
To enable the study of open sets in computational approaches to mathematics, lots of extra data and structure on these sets is assumed. For both foundational and mathematical reasons, it is then a natural question, and the subject of this…
We provide explicit commutative sequence space representations for classical function and distribution spaces on the real half-line. This is done by evaluating at the Fourier transforms of the elements of an orthonormal wavelet basis.
In this paper we consider polynomial representability of functions defined over $Z_{p^n}$, where $p$ is a prime and $n$ is a positive integer. Our aim is to provide an algorithmic characterization that (i) answers the decision problem: to…
This preprint is dedicated to a self contained simple proof of the classical criteria for representability of algebraic functions of several complex variables by radicals. It also contains a criteria for representability of algebroidal…
In a previous paper, the sup-interpretation method was proposed as a new tool to control memory resources of first order functional programs with pattern matching by static analysis. Basically, a sup-interpretation provides an upper bound…
We investigate the uniform computational content of the open and clopen Ramsey theorems in the Weihrauch lattice. While they are known to be equivalent to $\mathrm{ATR_0}$ from the point of view of reverse mathematics, there is not a…