Related papers: Algorithms for Low-Dimensional Topology

In this paper, we introduce the concept of 3-alterfolds with embedded separating surfaces. When the separating surface is decorated by a spherical fusion category, we obtain quantum invariants of 3-alterfold, which is consistent with many…

We present a novel 3D shape completion method that operates directly on unstructured point clouds, thus avoiding resource-intensive data structures like voxel grids. To this end, we introduce KAPLAN, a 3D point descriptor that aggregates…

High dimensionality, i.e. data having a large number of variables, tends to be a challenge for most machine learning tasks, including classification. A classifier usually builds a model representing how a set of inputs explain the outputs.…

Affine Cartesian codes were first discussed by Geil and Thomsen in 2013 in a broader framework and were formally introduced by L\'opez, Renter\'ia-M\'arquez and Villarreal in 2014. These are linear error-correcting codes obtained by…

Geodesics are essential in many geometry processing applications. However, traditional algorithms for computing geodesic distances and paths on 3D mesh models are often inefficient and slow. This makes them impractical for scenarios that…

Thanks to recent advances, the 4D quantum Hall (QH) effect is becoming experimentally accessible in various engineered set-ups. In this paper, we propose a new type of 4D topological system that, unlike other 2D and 4D QH models, does not…

A new hybrid scheme for numerical relativity will be presented. The scheme will employ a 3-dimensional spacelike lattice to record the 3-metric while using the standard 3+1 ADM equations to evolve the lattice. Each time step will involve…

We introduce a simple initial working system in which relations (such as part-whole) are directly represented via an architecture with operating and learning rules fundamentally distinct from standard artificial neural network methods.…

This paper proposes a Kolmogorov high order deep neural network (K-HOrderDNN) for solving high-dimensional partial differential equations (PDEs), which improves the high order deep neural networks (HOrderDNNs). HOrderDNNs have been…

Artificial intelligence techniques are considered an effective means to accelerate flow field simulations. However, current deep learning methods struggle to achieve generalization to flow field resolutions while ensuring computational…

We consider ultracold atoms in a two-dimensional optical lattice of the dice geometry in a tight-binding regime. The atoms experience a laser-assisted tunneling between the nearest neighbour sites of the dice lattice accompanied by the…

We introduce a unified framework for counting representations of knot groups into $SU(2)$ and $SL(2, \mathbb{R})$. For a knot $K$ in the 3-sphere, Lin and others showed that a Casson-style count of $SU(2)$ representations with fixed…

We develop a novel framework to study smooth and strongly convex optimization algorithms, both deterministic and stochastic. Focusing on quadratic functions we are able to examine optimization algorithms as a recursive application of linear…

We present a new class of fast polylog-linear algorithms based on the theory of structured matrices (in particular low displacement rank) for integrating tensor fields defined on weighted trees. Several applications of the resulting fast…

Khovanov homology is a topological knot invariant that categorifies the Jones polynomial, recognizes the unknot, and is conjectured to appear as an observable in $4D$ supersymmetric Yang--Mills theory. Despite its rich mathematical and…

The Kolmogorov-Arnold representation is a proven adequate replacement of a continuous multivariate function by an hierarchical structure of multiple functions of one variable. The proven existence of such representation inspired many…

Designing the topology of three-dimensional structures is a challenging problem due to its memory and time consumption. In this paper, we present a robust and efficient algorithm for solving large-scale 3D topology optimization problems.…

We characterize the complexity of the lattice decoding problem from a neural network perspective. The notion of Voronoi-reduced basis is introduced to restrict the space of solutions to a binary set. On the one hand, this problem is shown…

The goal of this project is to learn a 3D shape representation that enables accurate surface reconstruction, compact storage, efficient computation, consistency for similar shapes, generalization across diverse shape categories, and…

We present an algorithm to recover a minimal local apolar scheme to a homogeneous polynomial $F$. The socle degree of the scheme determines whether it is evinced by a Generalized Additive Decomposition (GAD) of $F$ or of an extension. We…