相关论文: Sphere recognition lies in NP

Associated to an embedded surface in the $3$-sphere, we construct a diagram of fundamental groups, and prove that it is a complete invariant, wherefrom we deduce complete invariants of handlebody links, tunnels of handlebody links, and…

In this article, we shall describe some of the most interesting topics in the subject of Complexity Science for a general audience. Anyone with a solid foundation in high school mathematics (with some calculus) and an elementary…

In this article, we prove that the commensurability class of a closed, orientable, hyperbolic 3-manifold is determined by the surface subgroups of its fundamental group. Moreover, we prove that there can be only finitely many closed,…

An affine hypersurface $M$ is said to admit a pointwise symmetry, if there exists a subgroup $G$ of ${\rm Aut}(T_p M)$ for all $p\in M$, which preserves (pointwise) the affine metric $h$, the difference tensor $K$ and the affine shape…

Many practical problems in almost all scientific and technological disciplines have been classified as computationally hard (NP-hard or even NP-complete). In life sciences, combinatorial optimization problems frequently arise in molecular…

The Perspective-Three-Point Problem (P3P) is solved by first focusing on determining the directions of the lines through pairs of control points, relative to the camera, rather than the distances from the camera to the control points. The…

3D object detection and pose estimation from a single image are two inherently ambiguous problems. Oftentimes, objects appear similar from different viewpoints due to shape symmetries, occlusion and repetitive textures. This ambiguity in…

This study investigate the effectiveness of using Deep Learning (DL) for the classification of planetary nebulae (PNe). It focusses on distinguishing PNe from other types of objects, as well as their morphological classification. We adopted…

The complete lists of vector hyperbolic equations on the sphere that have integrable third order vector isotropic and anisotropic symmetries are presented. Several new integrable hyperbolic vector models are found. By their integrability we…

We describe the constructible derived category of sheaves on the $n$-sphere, stratified in a point and its complement, as a dg module category of a formal dg algebra. We prove formality by exploring two different methods: As a combinatorial…

By assuming some widely-believed arithmetic conjectures, we show that the task of accepting a number that is representable as a sum of $d\geq2$ squares subjected to given congruence conditions is NP-complete. On the other hand, we develop…

In this paper, helicoidal flat surfaces in the $3$-dimensional sphere $\mathbb{S}^3$ are considered. A complete classification of such surfaces is given in terms of their first and second fundamental forms and by linear solutions of the…

A simple free-surface particle detection method for two and three-dimensional SPH simulation has been implemented. The method uses sphere representation for the SPH particle. The fluid domain is covered by overlapping spheres. A sphere…

The main goal of this paper is to show that shellability is NP-hard for triangulated d-balls (this also gives hardness for triangulated d-manifolds/d-pseudomanifolds with boundary) as soon as d is at least 3. This extends our earlier work…

Differentiable rendering has received increasing interest for image-based inverse problems. It can benefit traditional optimization-based solutions to inverse problems, but also allows for self-supervision of learning-based approaches for…

In this paper, we present three necessary conditions for recognizing point visibility graphs. We show that this recognition problem lies in PSPACE. We state new properties of point visibility graphs along with some known properties that are…

We consider the problem of deciding whether a polygonal knot in 3-dimensional Euclidean space is unknotted, capable of being continuously deformed without self-intersection so that it lies in a plane. We show that this problem, {\sc…

In this study, we introduce an autonomous method for addressing the detection and classification of quantum entanglement, a core element of quantum mechanics that has yet to be fully understood. We employ a multi-layer perceptron to…

For a 3-manifold M, the twist group Twist(M) is the subgroup of the mapping class group Mod(M) generated by twists about embedded 2-spheres. We study the Nielsen realization problem for subgroups of Twist(M). We prove that a nontrivial…

We prove a sharp three sphere inequality for solutions to third order perturbations of a product of two second order elliptic operators with real coefficients. Then we derive various kinds of quantitative estimates of unique continuation…