相关论文: A First Look at Chebyshev-Sobolev Series for Digit…
In this paper, we show that for any integer $k \in \mathbb{N}$ there exists a Sobolev sheaf (in the sense of Lebeau) on any definable site of $\mathbb{R}^2$ that agrees with Sobolev spaces on cuspidal domains. We also provide a complete…
In this paper, a new deep-learning architecture for solving the non-linear Falkner-Skan equation is proposed. Using Legendre and Chebyshev neural blocks, this approach shows how orthogonal polynomials can be used in neural networks to…
We evaluate integrals of certain polynomials over spheres and balls in real or complex spaces. We also promote the use of the Pochhammer symbol which gives the values of our integrals in compact forms.
We consider the question of whether a domain with uniformly thick boundary at all locations and at all scales has a large portion of its boundary visible from the interior; here, "visibility" indicates the existence of John curves…
In this paper, we develop the theory of Sobolev spaces on locally finite graphs, including completeness, reflexivity, separability, and Sobolev inequalities. Since there is no exact concept of dimension on graphs, classical methods that…
The application of quantum computing to the field of image processing has produced several promising applications: quantum image representation techniques have been developed showing how, by taking advantage of quantum properties like…
Over the past years, various representation systems which sparsely approximate functions governed by anisotropic features such as edges in images have been proposed. We exemplarily mention the systems of contourlets, curvelets, and…
We prove that almost every level set of a Sobolev function in a planar domain consists of points, Jordan curves, or homeomorphic copies of an interval. For monotone Sobolev functions in the plane we have the stronger conclusion that almost…
Deep learning based on deep neural networks of various structures and architectures has been powerful in many practical applications, but it lacks enough theoretical verifications. In this paper, we consider a family of deep convolutional…
The paper is an introduction to the use of the classical Newton-Puiseux procedure, oriented to an algorithmic description of it. This procedure enables to get polynomial approximations for parameterizations of branches of an algebraic plane…
We present a certified algorithm based on subdivision for computing an isotopic approximation to any number of curves in the plane. Our algorithm is based on the certified curve approximation algorithm of Plantinga and Vegter. The main…
We present a certified algorithm based on subdivision for computing an isotopic approximation to any number of curves in the plane. Our algorithm is based on the certified curve approximation algorithm of Plantinga and Vegter. The main…
Corrected versions of the numerically invariant expressions for the affine and Euclidean signature of a planar curve proposed by E.Calabi et. al are presented. The new formulas are valid for fine but otherwise arbitrary partitions of the…
Reasoning about distance is indispensable for establishing or avoiding contact in manipulation tasks. To this end, we present an online approach for learning implicit representations of signed distance using piecewise polynomial basis…
Graph-level representations are crucial tools for characterising structural differences between graphs. However, comparing graphs with different cardinalities, even when sampled from the same underlying distribution, remains challenging.…
How to represent a jet is at the core of machine learning on jet physics. Inspired by the notion of point clouds, we propose a new approach that considers a jet as an unordered set of its constituent particles, effectively a "particle…
We classify the set of quadrilaterals that can be inscribed in convex Jordan curves, in the continuous as well as in the smooth case. This answers a question of Makeev in the special case of convex curves. The difficulty of this problem…
We investigate the automorphism groups of the algebraic curves \[ \mathcal{C}_d : y^d = \varphi_d(x), \] where $\varphi_d(x)$ denotes the Chebyshev polynomial of degree $d$, defined over a field $k$ with $p:=\operatorname{char}(k) \nmid…
Time series data mining is an important field of research in the era of "Big Data". Next generation astronomical surveys will generate data at unprecedented rates, creating the need for automated methods of data analysis. We propose a…
Digital architectures for Chebyshev interpolation are explored and a variation which is word-serial in nature is proposed. These architectures are contrasted with equispaced system structures. Further, Chebyshev interpolation scheme is…