相关论文: Fingerprints, lemniscates and quadratic differenti…
Differential quantities, including normals, curvatures, principal directions, and associated matrices, play a fundamental role in geometric processing and physics-based modeling. Computing these differential quantities consistently on…
A lemniscate of a complex polynomial $Q_n$ of degree $n$ is a sublevel set of its modulus, i.e., of the form $\{z \in \mathbb{C}: |Q_n(z)| < t\}$ for some $t>0.$ In general, the number of connected components of this lemniscate can vary…
The deployment of machine learning models in operational contexts represents a significant investment for any organisation. Consequently, the risk of these models being misappropriated by competitors needs to be addressed. In recent years,…
We consider the problem of extracting curve skeletons of three-dimensional, elongated objects given a noisy surface, which has applications in agricultural contexts such as extracting the branching structure of plants. We describe an…
The algebraic method enables one to study the properties of the spectrum of a quadratic Hamiltonian through the mathematical properties of a matrix representation called regular or adjoint. This matrix exhibits exceptional points where it…
This paper, motivated by problems in Diophantine analysis which can be formulated as problems of finding rational points on the intersection of two quadrics, presents an explicit construction of a rationally defined isomorphism (biregular…
The paper deals with a comprehensive theory of mappings, whose local behavior can be described by means of linear subspaces, contained in the graphs of two (primal and dual) generalized derivatives. This class of mappings includes the…
The elliptic 2-Hessian equation is a fully nonlinear partial differential equation (PDE) that is related to intrinsic curvature for three dimensional manifolds. We introduce two numerical methods for this PDE: the first is provably…
In the first part of this paper, we survey results that are associated with three types of Laplacian matrices:difference, normalized, and signless. We derive eigenvalue and eigenvector formulaes for paths and cycles using circulant matrices…
Medieval paper, a handmade product, is made with a mould which leaves an indelible imprint on the sheet of paper. This imprint includes chain lines, laid lines and watermarks which are often visible on the sheet. Extracting these features…
Obtaining complete information about the shape of an object by looking at it from a single direction is impossible in general. In this paper, we theoretically study obtaining differential geometric information of an object from orthogonal…
Understanding peptide properties is often assumed to require modeling long-range molecular interactions, motivating the use of complex graph neural networks and pretrained transformers. Yet, whether such long-range dependencies are…
Macdonald polynomials are orthogonal polynomials associated to root systems, and in the type A case, the symmetric kind is a common generalization of Schur functions, Macdonald spherical functions, and Jack polynomials. We use the…
Zernike polynomials are a basis of orthogonal polynomials on the unit disk that are a natural basis for representing smooth functions. They arise in a number of applications including optics and atmospheric sciences. In this paper, we…
This paper contributes to the theory of singularities of meromorphic linear ODEs in traceless $2\times2$ cases, focusing on their deformations and confluences. It is divided into two parts: The first part addresses individual singularities…
This survey paper discusses some of the recent progress in the study of rational curves on algebraic varieties. It was written for the survey volume of the priority programme "Global Methods in Complex Geometry", supported by the DFG. To…
The paper is devoted to differential geometric invariants determining a Frenet curve in up to a direct similarity These invariants can be presented by the Euclidean curvatures in terms of an arc lengths of the spherical indicatrices. Then,…
In this note we mainly study the fine Jordan-Chevalley decomposition: a refinement of the classical Jordan-Chevalley decomposition of a matrix and we pay a particular attention to the field of the coefficients of the matrix. Moreover we…
In this work, we define the notions of Wronskian and simplified Wronskian for Stieltjes derivatives and study some of their properties in a similar manner to the context of time scales or the usual derivative. Later, we use these tools to…
We discuss the problem of recovering geometric objects from the spectrum of a quantum integrable system. In the case of one degree of freedom, precise results exist. In the general case, we report on the recent notion of good labellings of…