Related papers: Algorithms for Skein Manipulation in a Genus-2 Han…
Schoof's classic algorithm allows point-counting for elliptic curves over finite fields in polynomial time. This algorithm was subsequently improved by Atkin, using factorizations of modular polynomials, and by Elkies, using a theory of…
Existing RGB-based 2D hand pose estimation methods learn the joint locations from a single resolution, which is not suitable for different hand sizes. To tackle this problem, we propose a new deep learning-based framework that consists of…
In this paper, we study the arithmetics of skew polynomial rings over finite fields, mostly from an algorithmic point of view. We give various algorithms for fast multiplication, division and extended Euclidean division. We give a precise…
Robotic kitting has attracted considerable attention in logistics and industrial settings. However, existing kitting methods encounter challenges such as low precision and poor efficiency, limiting their widespread applications. To address…
We present an accelerated Schoof-type point-counting algorithm for curves of genus 2 equipped with an efficiently computable real multiplication endomorphism. Our new algorithm reduces the complexity of genus 2 point counting over a finite…
Skein lasagna modules are a recent tool developed for the study of 4-manifolds. We provide general formula for 1-, 2-, and 3-handle attachments for skein modules defined with any functorial link theory in $S^3 \times I$ generalizing…
The proof of Witten's finiteness conjecture established that the Kauffman bracket skein modules of closed $3$-manifolds are finitely generated over $\mathbb Q(A)$. In this paper, we develop a novel method for computing these skein modules.…
We present robust algorithms for set operations and Euclidean transformations of curved shapes in the plane using approximate geometric primitives. We use a refinement algorithm to ensure consistency. Its computational complexity is…
A piecewise Chebyshevian spline space is good for design when it possesses a B-spline basis and this property is preserved under knot insertion. The interest in such kind of spaces is justified by the fact that, similarly as for polynomial…
General skinning techniques aim to deform the surface of an articulated model following the pose change of a skeleton. Their rapidity makes them ideal tools for real-time animation purposes. However, popular skinning algorithms are simple,…
Skeletonization extracts thin representations from images that compactly encode their geometry and topology. These representations have become an important topological prior for preserving connectivity in curvilinear structures, aiding…
A complex of incompressible surfaces in a handlebody is constructed so that it contains, as a subcomplex, the complex of curves of the boundary of the handlebody. For genus 2 handlebodies, the group of automorphisms of this complex is used…
Skew polynomials are a class of non-commutative polynomials that have several applications in computer science, coding theory and cryptography. In particular, skew polynomials can be used to construct and decode evaluation codes in several…
This article deals with equivalence of links in 3-manifolds of Heegaard genus 2. Starting from a description of such a manifold introduced by Casali et al., that uses 6-tuples of integers and determines a Heegaard decomposition of the…
In recent years, high-performance computer vision models have achieved remarkable success in medical imaging, with some skin lesion classification systems even surpassing dermatology specialists in diagnostic accuracy. However, such models…
Generating sketches with specific patterns as expected, i.e., manipulating sketches in a controllable way, is a popular task. Recent studies control sketch features at stroke-level by editing values of stroke embeddings as conditions.…
Clustering is a hard discrete optimization problem. Nonconvex approaches such as low-rank semidefinite programming (SDP) have recently demonstrated promising statistical and local algorithmic guarantees for cluster recovery. Due to the…
An important problem in computational arithmetic geometry is to find changes of coordinates to simplify a system of polynomial equations with rational coefficients. This is tackled by a combination of two techniques, called minimisation and…
We describe a new method of producing equations for the canonical component of representation variety of a knot group into $PSL_2(\mathbb{C})$. Unlike known methods, this one does not involve any polyhedral decomposition or triangulation of…
Visually sorted grid layouts provide an efficient method for organizing high-dimensional vectors in two-dimensional space by aligning spatial proximity with similarity relationships. This approach facilitates the effective sorting of…