Related papers: Testing zero-dimensionality of varieties at a poin…
Monocular depth estimation is scale-ambiguous, and thus requires scale supervision to produce metric predictions. Even so, the resulting models will be geometry-specific, with learned scales that cannot be directly transferred across…
We give an overview of invariants of algebraic singularities over perfect fields. We then show how they lead to a synthetic proof of embedded resolution of singularities of 2-dimensional schemes.
We investigate the zero set of a stationary Gaussian process on the real line, and in particular give lower bounds for the variance of the number of points on a large interval, in all generality. We prove that this point process is never…
We present a collection of algorithms which utilize dimensional reduction to perform mesh refinement and study possibly singular solutions of time-dependent partial differential equations. The algorithms are inspired by constructions used…
We study bihomogeneous systems defining, non-zero dimensional, biprojective varieties for which the projection onto the first group of variables results in a finite set of points. To compute (with) the 0-dimensional projection and the…
We present a zero decomposition theorem and an algorithm based on Wu's method, which computes a zero decomposition with multiplicity for a given zero-dimensional polynomial system. If the system satisfies some condition, the zero…
We present an algorithm which, given a deformation with trivial section of a reduced plane curve singularity, computes equations for the equisingularity stratum (that is, the mu-constant stratum in characteristic 0) in the parameter space…
Parameter testing algorithms are using constant number of queries to estimate the value of a certain parameter of a very large finite graph. It is well-known that graph parameters such as the independence ratio or the edit-distance from…
This paper explores variants of the subspace iteration algorithm for computing approximate invariant subspaces. The standard subspace iteration approach is revisited and new variants that exploit gradient-type techniques combined with a…
We propose a novel zeroth-order optimization algorithm based on an efficient sampling strategy. Under mild global regularity conditions on the objective function, we establish non-asymptotic convergence rates for the proposed method.…
Based on the partition of parameter space, two algorithms for computing the rational univariate representation of zero-dimensional ideals with parameters are presented in the paper. Unlike the rational univariate representation of…
A low-degree polynomial model for a response curve is used commonly in practice. It generally incorporates a linear or quadratic function of the covariate. In this paper we suggest methods for testing the goodness of fit of a general…
Multiparameter persistence is a natural extension of the well-known persistent homology, which has attracted a lot of interest. However, there are major theoretical obstacles preventing the full development of this promising theory. In this…
The purpose of this paper is to analyze the singularities of a well known benchmark problem ``Andrews' squeezing mechanism''. We show that for physically relevant parameter values this system admits singularities. The method is based on…
We present an algorithm for computing zero-dimensional tropical varieties using projections. Our main tools are fast unimodular transforms of lexicographical Gr\"obner bases. We prove that our algorithm requires only a polynomial number of…
A theory of simultaneous resolution of singularities for families of embedded varieties (over a field of characteristic zero) parametrized by the spectrum of a suitable artinian ring, and compatible with a given algorithm of resolution, is…
We study one parameter deformations of a pair consisting of an analytic singular space $X_0$ and a function $f_0$ on it, in case this defines an isolated singularity. We prove, under general conditions, a bouquet decomposition of the Milnor…
This paper describes the systematic application of local topological methods for detecting interfaces and related anomalies in complicated high-dimensional data. By examining the topology of small regions around each point, one can…
We describe a design methodology for modifying the refractive index profile of graded-index optical instruments that incorporate singularities or zeros in their refractive index. The process maintains the device performance whilst resulting…
We propose a conservative algorithm to test the geometrical validity of simplicial (triangles, tetrahedra), tensor product (quadrilaterals, hexahedra), and mixed (prisms) elements of arbitrary polynomial order as they deform over a…