Related papers: Mapping on the HEALPix grid
Subspace clustering is a powerful unsupervised approach for hyperspectral image (HSI) analysis, but its high computational and memory costs limit scalability. Superpixel segmentation can improve efficiency by reducing the number of data…
Shape recognition is the main challenging problem in computer vision. Different approaches and tools are used to solve this problem. Most existing approaches to object recognition are based on pixels. Pixel-based methods are dependent on…
The cohomology theory known as Tmf, for "topological modular forms," is a universal object mapping out to elliptic cohomology theories, and its coefficient ring is closely connected to the classical ring of modular forms. We extend this to…
The focus in this paper is on elliptic homogenization of a certain kind of possibly non-periodic problems. A non-periodic and two-dimensional example is studied, where we numerically illustrate the homogenized matrix.
Iterative rounding has enjoyed tremendous success in elegantly resolving open questions regarding the approximability of problems dominated by covering constraints. Although iterative rounding methods have been applied to packing problems,…
Topological correctness plays a critical role in many image segmentation tasks, yet most networks are trained using pixel-wise loss functions, such as Dice, neglecting topological accuracy. Existing topology-aware methods often lack robust…
We study and classify a class of representations (called generalized geometric representations) of a Coxeter group of finite rank. These representations can be viewed as a natural generalization of the geometric representation. The…
This paper is mainly a semi-tutorial introduction to elementary algebraic topology and its applications to Ising-type models of statistical physics, using graphical models of linear and group codes. It contains new material on systematic…
Implicit neural representations (INRs) are increasingly being used as tools to map coordinates to signals, encompassing applications from neural fields to texture compression, shape representations, and beyond. Most INR methods are based on…
We prove that the set of non-degenerate second order maximally superintegrable systems in the complex Euclidean plane carries a natural structure of a projective variety, equipped with a linear isometry group action. This is done by…
The estimation of potential fields such as the gravitational or magnetic potential at the surface of a spherical planet from noisy observations taken at an altitude over an incomplete portion of the globe is a classic example of an…
The class of spherically symmetric Finsler metrics is studied and locally dually flat and projectively flat spherically symmetric Finsler metrics is classified.
We prove that for any infinite-type orientable surface S there exists a collection of essential curves {\Gamma} in S such that any homeomorphism that preserves the isotopy classes of the elements of {\Gamma} is isotopic to the identity. The…
Let $S$ be a closed orientable surface of genus at least two. We introduce a bordification of the moduli space $\mathcal{PT}(S)$ of complex projective structures, with a boundary consisting of projective classes of half-translation…
We provide isomorphism results for Hopf algebras that are obtained as graded twistings of function algebras on finite groups by cocentral actions of cyclic groups. More generally , we also consider the isomorphism problem for…
We define the notion of a hierarchically cocompact classifying space for a family of subgroups of a group. Our main application is to show that the mapping class group $\mbox{Mod}(S)$ of any connected oriented compact surface $S$, possibly…
We consider the numerical homogenization of a class of fractal elliptic interface problems inspired by related mechanical contact problems from the geosciences. A particular feature is that the solution space depends on the actual fractal…
We consider spaces for which there is a notion of harmonicity for complex valued functions defined on them. For instance, this is the case of Riemannian manifolds on one hand, and (metric) graphs on the other hand. We observe that it is…
Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to…
Graph-based collaborative filtering is capable of capturing the essential and abundant collaborative signals from the high-order interactions, and thus received increasingly research interests. Conventionally, the embeddings of users and…