Related papers: Complex-Valued Hough Transforms for Circles
Stable and reliable numerical integration of second-order radial equations in the fields of classical black holes can be performed by using the Pr\"ufer transformation and by passing to the use of phase functions, which allows uniquely…
In the present paper we extend the concepts of multiplicative de- rivative and integral to complex-valued functions of complex variable. Some drawbacks, arising with these concepts in the real case, are explained satis- factorily.…
The field of computational complexity is concerned both with the intrinsic hardness of computational problems and with the efficiency of algorithms to solve them. Given such a problem, normally one designs an algorithm to solve it and sets…
A new simple geometrical interpretation of complex numbers is presented. It differs from their usual interpretation as points in the complex plane. From the new point of view the complex numbers are rather operations on vectors than points.…
The $\texttt{IntegerHull}$ function is part of Maple's $\texttt{PolyhedralSets}$ library, which calculates the integer hull of a given polyhedral set. This algorithm works by translating the supporting hyperplanes of the facets of the input…
Black box variational inference allows researchers to easily prototype and evaluate an array of models. Recent advances allow such algorithms to scale to high dimensions. However, a central question remains: How to specify an expressive…
Complex-valued data is ubiquitous in signal and image processing applications, and complex-valued representations in deep learning have appealing theoretical properties. While these aspects have long been recognized, complex-valued deep…
Representing complex shapes with simple primitives in high accuracy is important for a variety of applications in computer graphics and geometry processing. Existing solutions may produce suboptimal samples or are complex to implement. We…
We use hyperbolic wavelet regression for the fast reconstruction of high-dimensional functions having only low dimensional variable interactions. Compactly supported periodic Chui-Wang wavelets are used for the tensorized hyperbolic wavelet…
Convexity prior is one of the main cue for human vision and shape completion with important applications in image processing, computer vision. This paper focuses on characterization methods for convex objects and applications in image…
In this paper, we formulate a simple algorithm that detects contours around a region of interest in an image. After an initial smoothing, the method is based on viewing an image as a topographic surface and finding convex and/or concave…
In this work we detail the application of a fast convolution algorithm computing high dimensional integrals to the context of multiplicative noise stochastic processes. The algorithm provides a numerical solution to the problem of…
The use of Shap scores has become widespread in Explainable AI. However, their computation is in general intractable, in particular when done with a black-box classifier, such as neural network. Recent research has unveiled classes of…
A variational model for learning convolutional image atoms from corrupted and/or incomplete data is introduced and analyzed both in function space and numerically. Building on lifting and relaxation strategies, the proposed approach is…
We present a method to perform the exact convolution of the model prediction for bispectrum multipoles in redshift space with the survey window function. We extend a widely applied method for the power spectrum convolution to the…
Capture calculus has recently been proposed as a solution to effect checking, achieved by tracking the captured references of terms in the types. Boxes, along with the box and unbox operations, are a crucial construct in capture calculus,…
. The choice of a suitable random matrix model of a complex system is very sensitive to the nature of its complexity. The statistical spectral analysis of various complex systems requires, therefore, a thorough probing of a wide range of…
Cohomology and cohomology ring of three-dimensional (3D) objects are topological invariants that characterize holes and their relations. Cohomology ring has been traditionally computed on simplicial complexes. Nevertheless, cubical…
We describe algorithms for computing central values of twists of $L$-functions associated to Hilbert modular forms, carry out such computations for a number of examples, and compare the results of these computations to some heuristics and…
Feature selection for a given model can be transformed into an optimization task. The essential idea behind it is to find the most suitable subset of features according to some criterion. Nature-inspired optimization can mitigate this…