Related papers: Implicitization using approximation complexes
For solving linear ill-posed problems regularization methods are required when the right hand side is with some noise. In the present paper regularized solutions are obtained by implicit iteration methods in Hilbert scales. % By exploiting…
One major deficiency of most semantic representation techniques is that they usually model a word type as a single point in the semantic space, hence conflating all the meanings that the word can have. Addressing this issue by learning…
In this paper we develop the Hermitian refinement of symplectic Clifford analysis, by introducing a complex structure $\mathbb{J}$ on the canonical symplectic manifold $(\mathbb {R}^{2n},\omega_0)$. This gives rise to two symplectic Dirac…
Building upon works of Hironaka, Bierstone-Milman, Villamayor and Wlodarczyk, we give an a priori estimate for the complexity of the simplified Hironaka algorithm. As a consequence of this result, we show that there exists canonical…
Error bounds have been studied for more than seventy years, beginning with the seminal result of Hoffman (1952) [{\it J. Res. Natl. Bur. Standards}, 49 (1952), 263--265], which establishes an upper bound for the distance from an arbitrary…
The paper develops an abstract (over-approximating) semantics for double-pushout rewriting of graphs and graph-like objects. The focus is on the so-called materialization of left-hand sides from abstract graphs, a central concept in…
We introduce a new version of arithmetic in all finite types which extends the usual versions with primitive notions of extensionality and extensional equality. This new hybrid version allows us to formulate a strong form of extensionality,…
We introduce decomposition complexes of posets, which generalize order complexes. The main advantage of our construction is that decomposition complexes are closed under taking products. Other special instances of this theory include nested…
Implicit neural representation is a recent approach to learn shape collections as zero level-sets of neural networks, where each shape is represented by a latent code. So far, the focus has been shape reconstruction, while shape…
Faithfully flat descent of pseudo-coherent complexes in rigid geometry was proved by Mathew. In this paper, we generalize the result of Mathew to quasi-coherent complexes on rigid analytic varieties, which have been introduced by Clausen…
In order to generate prime implicants for a given cube (minterm), most of minimization methods increase the dimension of this cube by removing one literal from it at a time. But there are two problems of exponential complexity. One of them…
We introduce notions of a constraint metric approximation and of a constraint stability of a metric approximation. This is done in the language of group equations with coefficients. We give an example of a group which is not constraintly…
The ever-growing complexity of mathematical proofs makes their manual verification by mathematicians very cognitively demanding. Autoformalization seeks to address this by translating proofs written in natural language into a formal…
Synthesizing programs from examples requires searching over a vast, combinatorial space of possible programs. In this search process, a key challenge is representing the behavior of a partially written program before it can be executed, to…
This paper contains a short and simplified proof of desingularization over fields of characteristic zero, together with various applications to other problems in algebraic geometry (among others, the study of the behavior of…
We adapt the diagrammatic presentation of the Hecke category to the dg category formed by the standard representatives for the Rouquier complexes. We use this description to recover basic results about these complexes, namely the…
A parameterized surface can be represented as a projection from a certain toric surface. This generalizes the classical homogeneous and bihomogeneous parameterizations. We extend to the toric case two methods for computing the implicit…
In this paper, we describe a general method for computing Selberg-like integrals based on a formula, due to Kaneko, for Selberg-Jack integrals. The general principle consists in expanding the integrand \emph{w.r.t.} the Jack basis, which is…
This is a gentle introduction to Colombeau nonlinear generalized functions, a generalization of the concept of distributions such that distributions can freely be multiplied. It is intended to physicists and applied mathematicians who…
In this work we propose a novel postprocessing technique for compression-artifact reduction. Our approach is based on posing this task as an inverse problem, with a regularization that leverages on existing state-of-the-art image denoising…