相关论文: A First Look at Chebyshev-Sobolev Series for Digit…
The theme of symbolic computation in algebraic categories has become of utmost importance in the last decade since it enables the automatic modeling of modern algebra theories. On this theoretical background, the present paper reveals the…
We apply numerical algebraic geometry to the invariant-theoretic problem of detecting symmetries between two plane algebraic curves. We describe an efficient equality test which determines, with "probability-one", whether or not two…
With the great promise of deep learning, discoveries of new particles at the Large Hadron Collider (LHC) may be imminent. Following the discovery of a new Beyond the Standard model particle in an all-hadronic channel, deep learning can also…
Extracting planes from a 3D scene is useful for downstream tasks in robotics and augmented reality. In this paper we tackle the problem of estimating the planar surfaces in a scene from posed images. Our first finding is that a surprisingly…
Perturbation theory is a powerful tool for studying large-scale structure formation in the universe and calculating observables such as the power spectrum or bispectrum. However, beyond linear order, typically this is done by assuming a…
Signature is an infinite graded sequence of statistics known to characterize geometric rough paths, which includes the paths with bounded variation. This object has been studied successfully for machine learning with mostly applications in…
High-dimensional time series are common in many domains. Since human cognition is not optimized to work well in high-dimensional spaces, these areas could benefit from interpretable low-dimensional representations. However, most…
The sequential data observed in earth science can be regarded as paths in multidimensional space. To read the path effectively, it is useful to convert it into a sequence of numbers called the signature, which can faithfully describe the…
Connected components of real algebraic sets are semi-algebraic, i.e. they are described by a boolean formula whose atoms are polynomial constraints with real coefficients. Computing such descriptions finds topical applications in optical…
In the field of document forensics, ink analysis plays a crucial role in determining the authenticity of legal and historic documents and detecting forgery. Visual examination alone is insufficient for distinguishing visually similar inks,…
In this article we provide another method for obtaining explicit formulas yielding counts of secant planes to a projective curve. We formulate the problem in terms of Segre classes of suitable bundles over the symmetric product of the curve…
It is shown that, under some mild technical conditions, representations of prime numbers by binary quadratic forms can be computed in polynomial complexity by exploiting Schoof's algorithm, which counts the number of $\mathbb F_q$-points of…
In this article, using an exemplar-based approach, we investigate the inpainting problem, introducing a new mathematical functional, whose minimization determines the quality of the reconstructions. The new functional expression takes into…
This work is unique in the use of discrete wavelets that were built from or derived from Chebyshev polynomials of the second and third kind, filter the Discrete Second Chebyshev Wavelets Transform (DSCWT), and derive two effective filters.…
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 propose a framework of principal manifolds to model high-dimensional data. This framework is based on Sobolev spaces and designed to model data of any intrinsic dimension. It includes principal component analysis and principal curve…
In this work, we define a parabolic equation on digital spaces and study its properties. The equation can be used in investigation of mechanical, aerodynamic, structural and technological properties of a Moebius strip, which is used as a…
Approximating adequate number of clusters in multidimensional data is an open area of research, given a level of compromise made on the quality of acceptable results. The manuscript addresses the issue by formulating a transductive…
We propose a platform-independent multi-threaded function library that provides data structures to generate, differentiate and render both the ordinary basis and the normalized B-basis of a user-specified extended Chebyshev (EC) space that…
A general framework is presented which unifies the treatment of wavelet-like, quasidistribution, and tomographic transforms. Explicit formulas relating the three types of transforms are obtained. The case of transforms associated to the…