Related papers: Re-Embeddings of Special Border Basis Schemes
A general graded reflection equation algebra is proposed and the corresponding boundary quantum inverse scattering method is formulated. The formalism is applicable to all boundary lattice systems where an invertible R-matrix exists. As an…
The study of band connectivity is a fundamental problem in condensed matter physics. Here, we develop a new method for analyzing band connectivity, which completely solves the outstanding questions of the reducibility and decomposition of…
Image segmentation is a popular area of research in computer vision that has many applications in automated image processing. A recent technique called piecewise flat embeddings (PFE) has been proposed for use in image segmentation; PFE…
In this paper we study scalar multivariate subdivision schemes with general integer expanding dilation matrix. Our main result yields simple algebraic conditions on the symbols of such schemes that characterize their polynomial…
We study the existence of proper holomorphic embeddings of bordered Riemann surfaces into the complex plane C^2. Denote by M(R) the moduli space consisting of all equivalence classes of complex structures J on a given smooth oriented…
High-order finite difference methods are efficient, easy to program, scales well in multiple dimensions and can be modified locally for various reasons (such as shock treatment for example). The main drawback have been the complicated and…
A surface integral representation of Maxwell's equations allows the efficient electromagnetic (EM) modeling of three-dimensional structures with a two-dimensional discretization, via the boundary element method (BEM). However, existing BEM…
We present several new algorithms for computing factorization invariant values over affine semigroups. In particular, we give (i) the first known algorithm to compute the delta set of any affine semigroup, (ii) an improved method of…
Border complexity captures functions that can be approximated by low-complexity ones. Debordering is the task of proving an upper bound on some non-border complexity measure in terms of a border complexity measure, thus getting rid of…
The affine Grassmannian is a noncompact smooth manifold that parameterizes all affine subspaces of a fixed dimension. It is a natural generalization of Euclidean space, points being zero-dimensional affine subspaces. We will realize the…
Matrices are typically considered over fields or rings. Motivated by applications in parametric differential equations and data-driven modeling, we suggest to study matrices with entries from a Hilbert space and present an elementary theory…
This paper presents a matrix-free approach for implementing the shifted boundary method (SBM) in finite element analysis. The SBM is a versatile technique for solving partial differential equations on complex geometries by shifting boundary…
An axiomatic approach to signal reconstruction is formulated, involving a sample consistent set and a guiding set, describing desired reconstructions. New frame-less reconstruction methods are proposed, based on a novel concept of a…
We show that the cohomology ring of Hilbert scheme of $n$-points in the affine plane is isomorphic to the coordinate ring of $\mathbb{G}_{m}$-fixed point scheme of the $n$-th symmetric product of $\mathbb{C}^{2}$ for a natural…
We consider practical aspects of reconstructing planar curves with prescribed Euclidean or affine curvatures. These curvatures are invariant under the special Euclidean group and the equi-affine groups, respectively, and play an important…
Higher-dimensional rewriting is founded on a duality of rewrite systems and cell complexes, connecting computational mathematics to higher categories and homotopy theory: the two sides of a rewrite rule are two halves of the boundary of an…
Let Hilb^p be the Hilbert scheme parametrizing the closed subschemes of P^n with Hilbert polynomial p\in Q[t] over a field K of characteristic zero. By bounding below the cohomological Hilbert functions of the points of Hilb^p we define…
This paper proposes ReBNet, an end-to-end framework for training reconfigurable binary neural networks on software and developing efficient accelerators for execution on FPGA. Binary neural networks offer an intriguing opportunity for…
Let X be a smooth projective surface of irregularity 0. The Hilbert scheme of n points on X parameterizes zero-dimensional subschemes of X of length n. In this paper, we discuss general methods for studying the cone of ample divisors on the…
Distributed adaptive conforming refinement requires multiple iterations of the serial refinement algorithm and global communication as the refinement can be propagated over several processor boundaries. We show bounds on the maximum number…