Related papers: Complex-Valued Hough Transforms for Circles
We study two recent conjectures for holographic complexity: the complexity=action conjecture and the complexity=volume conjecture. In particular, we examine the structure of the UV divergences appearing in these quantities, and show that…
Integral transformations are used to estimate high order derivatives of various special functions. Applications are given to numerical integration, where estimates of high order derivatives of the integrand are needed to achieve bounds on…
In this paper, we further develop the theory of circles of partition by introducing the notion of complex circles of partition. This work generalizes the classical framework, extending from subsets of the natural numbers as base sets to…
We consider probabilistic shaping to maximize the achievable information rate of coded modulation (CM) with hard decision decoding. The proposed scheme using binary staircase codes outperforms its uniform CM counterpart by more than 1.3 dB…
This paper introduces a circle detection method based on Differential Evolution (DE) optimization. Just as circle detection has been lately considered as a fundamental component for many computer vision algorithms, DE has evolved as a…
We develop new closed form representations of sums of (n + {\alpha})th shifted harmonic numbers and reciprocal binomial coefficients in terms of {\alpha}th shifted harmonic numbers. Some interesting new consequences and illustrative…
We extend the two-dimensional Cartesian shapelet formalism to d-dimensions. Concentrating on the three-dimensional case, we derive shapelet-based equations for the mass, centroid, root-mean-square radius, and components of the quadrupole…
We present a novel and effective binary representation for convex shapes. We show the equivalence between the shape convexity and some properties of the associated indicator function. The proposed method has two advantages. Firstly, the…
A quantum computer has a clear advantage over a classical computer for exhaustive search. The quantum mechanical algorithm for exhaustive search was originally derived by using subtle properties of a particular quantum mechanical operation…
In complex analysis, the winding number measures the number of times a path (counter-clockwise) winds around a point, while the Cauchy index can approximate how the path winds. We formalise this approximation in the Isabelle theorem prover,…
We present some interesting observations on the 3x+1 problem. We propose a new algorithm which eliminates certain steps while we check the action of 3x+1 procedure on a number. Also, we propose a reason why many numbers follow a similar…
A novel high-order numerical scheme is proposed to compute the covariant derivative, particularly for divergence and curl, on any curved surface. The proposed scheme does not require the construction of a curved axis or metric tensor, which…
Fast Fourier transform algorithms are an arsenal of effective tools for solving various problems of analysis and high-speed processing of signals of various natures. Almost all of these algorithms are designed to process sequences of…
Large-scale Hierarchical Classification (HC) involves datasets consisting of thousands of classes and millions of training instances with high-dimensional features posing several big data challenges. Feature selection that aims to select…
It is common to have to process signals or images whose values are cyclic and can be represented as points on the complex circle, like wrapped phases, angles, orientations, or color hues. We consider a Tikhonov-type regularization model to…
The efficacy of using complex numbers for understanding geometric questions related to polar equations and general cycloids is demonstrated.
Calculations of the Fourier transform of a constant quantity over an area or volume defined by polygons (connected vertices) are often useful in modeling wave scattering, or in fourier-space filtering of real-space vector-based volumes and…
Visual place recognition tasks often encounter significant challenges in landmark detection due to the presence of irrelevant objects such as humans, cars, and trees, despite the remarkable progress achieved by previous models, especially…
Complex polynomial optimization has recently gained more and more attention in both theory and practice. In this paper, we study the optimization of a real-valued general conjugate complex form over various popular constraint sets including…
Fractional moments have been investigated by many authors to represent the density of univariate and bivariate random variables in different contexts. Fractional moments are indeed important when the density of the random variable has…