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The main goal of this article is to relate asymptotic geometric properties on a tower of coverings of a non-compact K\"ahler manifold of finite volume with reasonable geometric assumptions to its universal covering. Applicable examples…
Bilevel optimization, addressing challenges in hierarchical learning tasks, has gained significant interest in machine learning. The practical implementation of the gradient descent method to bilevel optimization encounters computational…
The aim of this article is to introduce standard bases of ideals in polynomial rings with respect to a class of orderings which are not necessarily semigroup orderings. Our approach generalises the concept of standard bases with respect to…
This paper studies the concept and the computation of approximately vanishing ideals of a finite set of data points. By data points, we mean that the points contain some uncertainty, which is a key motivation for the approximate treatment.…
This paper presents a point-wise divergence-free projection method for numerical approximations of photonic quasicrystals problems. The original three-dimensional quasiperiodic Maxwell's system is transformed into a periodic one in higher…
We propose a differential geometric construction for families of low-rank covariance matrices, via interpolation on low-rank matrix manifolds. In contrast with standard parametric covariance classes, these families offer significant…
We generalize quasi-arithmetic means beyond scalars by considering the gradient map of a Legendre type real-valued function. The gradient map of a Legendre type function is proven strictly comonotone with a global inverse. It thus yields a…
Quasimodules for vertex algebras are generalizations of modules for vertex algebras. These new objects arise from a generalization of locality for fields. Quasimodules tie together module theory and twisted module theory, and both twisted…
Generalizing our earlier work, we construct quasi-particle bases of principal subspaces of standard module $L_{X_l^{(1)}}(k\Lambda_0)$ and generalized Verma module $N_{X_l^{(1)}}(k\Lambda_0)$ at level $k\geq 1$ in the case of affine Lie…
Near isometric orthogonal embeddings to lower dimensions are a fundamental tool in data science and machine learning. In this paper, we present the construction of such embeddings that minimizes the maximum distortion for a given set of…
In a Freud-type weighted ($w$) space, introducing another weight ($v$) with infinitely many roots, we give a complete and minimal system with respect to $vw$, by deleting infinitely many elements from the original orthonormal system with…
Solving multihomogeneous systems, as a wide range of structured algebraic systems occurring frequently in practical problems, is of first importance. Experimentally, solving these systems with Gr\"obner bases algorithms seems to be easier…
In this paper, applied strictly monotonic increasing scaled maps, a kind of well-conditioned linear barycentric rational interpolations are proposed to approximate functions of singularities at the origin, such as $x^\alpha$ for $\alpha \in…
The first part of this paper completes the classification of Whitney towers in the 4-ball that was started in three related papers. We provide an algebraic framework allowing the computations of the graded groups associated to geometric…
We establish a correspondence (or duality) between the characters and the crystal bases of finite-dimensional representations of quantum groups associated to Langlands dual semi-simple Lie algebras. This duality may also be stated purely in…
We propose a level-set-based semi-Lagrangian method on graded adaptive Cartesian grids to address the problem of surface reconstruction from point clouds. The goal is to obtain an implicit, high-quality representation of real shapes that…
Generalizing supertropical algebras, we present a "layered" structure, "sorted" by a semiring which permits varying ghost layers, and indicate how it is more amenable than the "standard" supertropical construction in factorizations of…
We develop and analyze a broad family of stochastic/randomized algorithms for inverting a matrix. We also develop specialized variants maintaining symmetry or positive definiteness of the iterates. All methods in the family converge…
The notion of equivalence of maximally entangled bases of bipartite d-dimensional Hilbert spaces is introduced. An explicit method of inequivalent bases construction is presented.
We introduce a new construction of towers of algebraic curves over finite fields and provide a simple example of an optimal tower.