Related papers: Computational procedures for weighted projective s…
We present a technique for translating a black-box machine-learned classifier operating on a high-dimensional input space into a small set of human-interpretable observables that can be combined to make the same classification decisions. We…
We classify all closed 1-connected manifolds $M$ which look like projective planes, i.e. with integral homology $H_*(M)=Z^3$. Furthermore, we give an explicit construction of these manifolds as Thom spaces of open disk bundles.
We study certain foliated complex manifolds that behave similarly to complete nonsingular toric varieties. We classify them by combinatorial objects that we call marked fans. We describe the basic cohomology algebras of them in terms of…
We define fake weighted projective spaces as a generalisation of weighted projective spaces. We introduce the notions of fundamental group in codimension 1 and of universal covering in codimension 1. We prove that for every fake weighted…
We introduce the notion of real phase structure on rational polyhedral fans in Euclidean space. Such a structure consists of an assignment of affine spaces over $\mathbb{Z}/2\mathbb{Z}$ to each top dimensional face of the fan subject to two…
The present article is concerned scattered data approximation for higher dimensional data sets which exhibit an anisotropic behavior in the different dimensions. Tailoring sparse polynomial interpolation to this specific situation, we…
As the Imaging X-ray Polarimetry Explorer (IXPE) measures increasingly faint sources, the need for precise polarimetry extraction becomes paramount. In addition to previously described neural-net (NN) weights, we introduce here point-spread…
Weighted model counting (WMC) consists of computing the weighted sum of all satisfying assignments of a propositional formula. WMC is well-known to be #P-hard for exact solving, but admits a fully polynomial randomized approximation scheme…
We characterize building sets whose associated nonsingular projective toric varieties are Fano. Furthermore, we show that all such toric Fano varieties are obtained from smooth Fano polytopes associated to finite directed graphs.
Data visualisation helps understanding data represented by multiple variables, also called features, stored in a large matrix where individuals are stored in lines and variable values in columns. These data structures are frequently called…
We survey a collection of closely related methods for generalizing fans of toric varieties, include skeletons, Kato fans, Artin fans, and polyhedral cone complexes, all of which apply in the wider context of logarithmic geometry. Under…
Little publicly available data exists for polarimetric measurements. When designing task specific polarimetric systems, the statistical properties of the task specific data becomes important. Until better polarimetric datasets are available…
Weighted projective space arises when we consider the usual geometric definition for projective space and allow for non-trivial weights. On its own, this extra freedom gives rise to more than enough interesting phenomena, but it is the fact…
In this paper we provide a computational approach to the shape of curves which are rational in polar coordinates, i.e. which are defined by means of a parametrization (r(t),\theta(t)) where both r(t),\theta(t) are rational functions. Our…
Given complex numbers $w_1, \ldots, w_n$, we define the weight $w(X)$ of a set $X$ of 0-1 vectors as the sum of $w_1^{x_1} \cdots w_n^{x_n}$ over all vectors $(x_1, \ldots, x_n)$ in $X$. We present an algorithm, which for a set $X$ defined…
Cylindrical algebraic decomposition (CAD) is an important tool, both for quantifier elimination over the reals and a range of other applications. Traditionally, a CAD is built through a process of projection and lifting to move the problem…
Mapper and Ball Mapper are Topological Data Analysis tools used for exploring high dimensional point clouds and visualizing scalar-valued functions on those point clouds. Inspired by open questions in knot theory, new features are added to…
Data-driven machine learning models often require extensive datasets, which can be costly or inaccessible, and their predictions may fail to comply with established physical laws. Current approaches for incorporating physical priors…
PatchMatch Multi-View Stereo (PatchMatch MVS) is one of the popular MVS approaches, owing to its balanced accuracy and efficiency. In this paper, we propose Polarimetric PatchMatch multi-view Stereo (PolarPMS), which is the first method…
Tensor decompositions have become essential tools for feature extraction and compression of multiway data. Recent advances in tensor operators have enabled desirable properties of standard matrix algebra to be retained for multilinear…