Related papers: Finding and Classifying Critical Points of 2D Vect…
In cosmic web analysis, complementary to traditional cosmological probes, the extrema (e.g. peaks and voids) two-point correlation functions (2PCFs) are of particular interest for the study of both astrophysical phenomena and cosmological…
With automated measurements, large data sets can be assembled with relative ease. Often these data sets have a large degree of variance. Nonetheless, we hope to find groups within the data set with shared distinguishing characteristics.…
We describe how to compute topological objects associated to a polynomial map of several complex variables with isolated singularities. These objects are: the affine critical values, the affine Milnor numbers for all irregular fibers, the…
Chip firing provides a way to study the sandpile group (also known as the Jacobian) of a graph. We use a generalized version of chip firing to bound the number of invariant factors of the critical group of an arithmetical structure on a…
Instead of evaluating the gradient field of the brightness map of an image, we propose the use of dipole vectors. This approach is obtained by adapting to the image gray-tone distribution the definition of the dipole moment of charge…
We describe all possible structures of discrete vector field (discrete Morse functions) with minimal number of critical cells on the regular CW-complex for the 2-disk (1 cell), the 2-sphere (2 cells), the cylinder (2 cells) and Mobius band…
Indices of singular points of a vector field or of a 1-form on a smooth manifold are closely related with the Euler characteristic through the classical Poincar\'e--Hopf theorem. Generalized Euler characteristics (additive topological…
We propose an approach to the problem of global reconstruction of an orientation field. The method is based on a geometric model called "bisector line fields", which maps a pair of vector fields to an orientation field, effectively…
We present two diagnostic methods based on ideas of Principal Component Analysis and demonstrate their efficiency for sophisticated processing of multicolour photometric observations of variable objects.
The critical point between varieties A and B of algebras is defined as the least cardinality of the semilattice of compact congruences of a member of A but of no member of B, if it exists. The study of critical points gives rise to a whole…
We compute by Monte Carlo numerical simulations the critical exponents of two-dimensional scalar field theories at the $\lambda\phi^6$ tricritical point. The results are in agreement with the Zamolodchikov conjecture based on conformal…
Fine-grained visual categorization is a classification task for distinguishing categories with high intra-class and small inter-class variance. While global approaches aim at using the whole image for performing the classification,…
We study the task of panoptic symbol spotting, which involves identifying both individual instances of countable things and the semantic regions of uncountable stuff in computer-aided design (CAD) drawings composed of vector graphical…
This paper presents a comprehensive analysis of critical point sets in two-layer neural networks. To study such complex entities, we introduce the critical embedding operator and critical reduction operator as our tools. Given a critical…
A non-negative integer invariant, estimating from below the number of geometrically different critical points of a smooth function $f$ defined in the 2-disk, $f:\mathbb{B}^{2}\rightarrow\mathbb{R}$, is considered. (We denote it by…
This paper explores optimal methods for obtaining one-dimensional (1D) powder pattern intensities from two-dimensional (2D) planar detectors with good estimates of their standard deviations. We describe methods to estimate uncertainties…
We present Patherea, a unified framework for point-based cell detection and classification that enables the development and fair evaluation of state-of-the-art methods. To support this, we introduce a large-scale dataset that replicates the…
From a fibered link in the 3-sphere may be constructed a field of not everywhere tangent 2-planes; when the fibered link is the link of an isolated critical point of a map from 4-space to the plane, the plane field is essentially the field…
We investigate bivariate interpolation problems in characteristic 2. Given a nonnegative integer $t$, we describe all the sub-linear systems generated by monomials, in which there is no curve passing through a general point with…
The aim of this paper is to introduce and investigate the Poincar\'e series associated with the Weierstra{\ss} semigroup of one and two rational points at a (not necessarily irreducible) non-singular projective algebraic curve defined over…