Related papers: New Techniques for Computing Geometric Index
We are presenting an algorithm capable of simplifying tensor polynomials with indices when the building tensors have index symmetry properties. These properties include simple symmetry, cyclicity and those due to the presence of covariant…
We present an approach of computing the intersection curve $\mathcal{C}$ of two rational parametric surface $\S_1(u,s)$ and $\S_2(v,t)$, one being projectable and hence can easily be implicitized. Plugging the parametric surface to the…
Clustering is indispensable for data analysis in many scientific disciplines. Detecting clusters from heavy noise remains challenging, particularly for high-dimensional sparse data. Based on graph-theoretic framework, the present paper…
Computing the topology of an algebraic plane curve $\mathcal{C}$ means to compute a combinatorial graph that is isotopic to $\mathcal{C}$ and thus represents its topology in $\mathbb{R}^2$. We prove that, for a polynomial of degree $n$ with…
The coherence attribute is one of the most commonly used attributes in seismic interpretation. In this paper, we propose building on the recently introduced Generalized Tensor-based Coherence (GTC) attribute to make it directionally…
Intersection graphs of planar geometric objects such as intervals, disks, rectangles and pseudo-disks are well studied. Motivated by various applications, Butman et al. in SODA 2007 considered algorithmic questions in intersection graphs of…
Geodesic models are known as an efficient tool for solving various image segmentation problems. Most of existing approaches only exploit local pointwise image features to track geodesic paths for delineating the objective boundaries.…
We present an efficient dynamic data structure that supports geodesic nearest neighbor queries for a set of point sites $S$ in a static simple polygon $P$. Our data structure allows us to insert a new site in $S$, delete a site from $S$,…
In this paper a new technique is presented that extracts the geometry of lumbar vertebral bodies from spiral CT scans. Our new multi-step segmentation approach yields highly accurate and precise measurement of the bone mineral density (BMD)…
We show that geometric inference of a point cloud can be calculated by examining its kernel density estimate with a Gaussian kernel. This allows one to consider kernel density estimates, which are robust to spatial noise, subsampling, and…
In this paper, we consider enumeration of geodesics on a polyhedron, where a geodesic means locally-shortest path between two points. Particularly, we consider the following preprocessing problem: given a point $s$ on a polyhedral surface…
In 1980, Onishchik introduced the index of a Riemannian symmetric space as the minimal codimension of a (proper) totally geodesic submanifold. He calculated the index for symmetric spaces of rank less than or equal to 2, but for higher rank…
We consider the homotopical dynamics on compact orientable surfaces of positive genus g. We establish a sufficient and necessary algebraic criterion for homotopy classes with infinitely many periodic points of maps on such surfaces in terms…
We explore the path integration -- upon the contour of hermitian (non-auxliary) field configurations -- of topologically twisted $\mathcal{N}=2$ Chern-Simons-matter theory (TTCSM) on $\mathbb{S}_2$ times a segment. In this way, we obtain…
Geometric graphs appear in many real-world data sets, such as road networks, sensor networks, and molecules. We investigate the notion of distance between embedded graphs and present a metric to measure the distance between two geometric…
We propose three fast algorithms for solving the inverse problem of the thermoacoustic tomography corresponding to certain acquisition geometries. Two of these methods are designed to process the measurements done with point-like detectors…
The purpose of this note is to give an exposition of some interesting combinatorics and convex geometry concepts that appear in algebraic geometry in relation to counting the number of solutions of a system of polynomial equations in…
Let $d_G(v)$ be the degree of the vertex $v$ in a graph $G$. The Sombor index of $G$ is defined as $SO(G) =\sum_{uv\in E(G)}\sqrt{d^2_G(u)+d^2_G(v)}$, which is a new degree-based topological index introduced by Gutman. Let…
The current discourse delves into the effectiveness of h-index as an author level metric. It further reviews and explains the algorithmic complexity of calculating h-index through algebraic method. To conduct the algebraic analysis…
A geometric graph is a graph embedded in the plane with vertices at points and edges drawn as curves (which are usually straight line segments) between those points. The average transversal complexity of a geometric graph is the number of…