Tight embeddings of 2-tori in 3D space contain short loops.
problem Finding the shortest non-contractible loops in twisted 2-tori.
method Proving systolic inequalities for T2 embeddings in R3. result Highly twisted 2-tori contain non-contractible loops of small diameter.
A novel 3D shape registration method using spectral graph embedding and probabilistic matching.
problem Challenges in 3D shape analysis and registration, especially with large variability.
method Combining spectral graph matching with Laplacian embedding for large graphs, using commute-time embedding and PCA.
result A method to register shapes with different samplings and isometric deformations.
Study groups that can embed Heawood graph in 3D space.
problem Classifying topological symmetry groups of the Heawood graph.
method Analyzing embeddings of the Heawood graph in S3. result Identified all possible groups as topological symmetry groups.
Proves existence of at least two minimal spheres in any 3D space.
problem Existence of minimal spheres in arbitrary 3D spaces.
method Iterative relative min-max constructions.
result Proves existence of at least two embedded minimal spheres.
Generative model for 3D point clouds using invertible flows.
problem Generating realistic 3D point clouds.
method Invertible flow-based models for point cloud generation with parameter sharing and embedding vectors.
result The model generates high-quality 3D point clouds with good similarity.
Study of fundamental groups of knotted solenoid complements in 3D sphere.
problem Determining fundamental groups of knotted solenoid complements.
method Using canonical sequence of knot groups and embedding up to mirror reflection.
result Fundamental groups of knotted solenoid complements are solely determined by a sequence of knot groups and embedding up to mirror reflection.
New theorem on embedding Moebius bands in 3D space.
problem Proving the impossibility of placing uncountably many disjoint Moebius bands in 3D space.
method Generalization of Grushin and Palamodov's result to tame subsets in R^N and arbitrary topological embeddings in R^3.
result The impossibility of embedding uncountably many pairwise disjoint Moebius bands in 3D space, even for arbitrary topological embeddings.
Deep-learning method estimates bone 3D structure from X-ray images.
problem Estimating bone 3D structure from X-ray images.
method Triplet loss-trained neural network selecting closest 3D bone shape from predefined set.
result Average RMS distance of 1.08 mm between predicted and true shapes.
Alternative proof for ribbon surfaces in 3D space.
problem Proving ribbonness of surfaces in 3D space.
method Using a compact oriented proper surface in upper half 4-space.
result Link bounds a ribbon surface in upper half 4-space.
Study on surfaces of genus g≥1 in 3D contact sub-Riemannian manifolds, proving finiteness or infiniteness of induced distance.
problem Determining the finiteness of the induced distance on surfaces of genus g≥1 in 3D contact sub-Riemannian manifolds.
method Analyzing the structural stability of the finiteness/not-finiteness of the induced distance on closed surfaces of genus g≥1.
result Closed surfaces of genus g≥1 can be embedded in such a way that the induced distance is either always finite or always infinite.
Study investigates induced geometry on surfaces in 3D contact manifolds.
problem Understanding the metric structure on surfaces embedded in 3D contact sub-Riemannian manifolds.
method Defined a coefficient to characterize characteristic points and identified global conditions for finite induced distance.
result Proved induced distance finite for certain surfaces with isolated characteristic points.
Establishes smooth Ricci flows from convex surfaces in 3D space.
problem Existence and uniqueness of Ricci flow starting from convex surfaces.
method Smooth Ricci flows starting from smooth convex surfaces.
result Uniform convergence of metrics to initial convex surface.
Prove an isoperimetric inequality for compact bodies in 3D contact non-unimodular Lie groups.
problem Isoperimetric inequality for compact bodies in contact non-unimodular 3D Lie groups.
method Prove an isoperimetric inequality.
result Prove an isoperimetric inequality.
A new geometric perceptron model improves 3D shape classification.
problem Challenges in geometric tasks involving point clouds using machine learning.
method Introduces multilayer geometric perceptron (MLGP) with geometric neurons.
result MLGP outperforms vanilla MLP in 3D shape classification and noise resistance.
Paper tackles zero-shot activity recognition using video features and text embeddings.
problem Zero-shot activity recognition with videos.
method Auto-encoder model for multimodal joint embedding, 3D convolutional action recognition for visual features, GloVe word embeddings for textual features.
result Improved zero-shot recognition results with top-n accuracy and mean Nearest Neighbor Overlap.
New method tackles instance segmentation on 3D point clouds with improved metrics.
problem Evaluation metrics are affected by small regions containing few instances.
method Proposes a new method with O(Np) space complexity that learns embeddings for clusters of instances.
result Achieves state-of-the-art performance using both existing and proposed metrics.
3D Axial-Attention improves lung nodule classification accuracy.
problem Limited 3D attention in existing methods.
method Proposes 3D Axial-Attention network with 3D positional encoding.
result 3D Axial-Attention achieves state-of-the-art performance.
Minimal surfaces span periodic curves in 3D space.
problem Existence of minimal surfaces spanning periodic curves.
method Proof of existence for minimal surfaces using periodic curves in R3. result Existence of noncompact simply connected periodic minimal surfaces.
Proposes a neural network for recognizing 3D skeleton-based interactions.
problem Recognizing two-person interactions from 3D skeleton sequences.
method Uses Gaussian distributions and Riemannian geometry of SPD matrices and matrix groups.
result Achieves competitive results on three benchmarks for 3D human activity understanding.
We study supersymmetric probe M5-branes in the AdS_4 solution that arises from M5-branes wrapped on a hyperbolic 3-manifold M_3. This amounts to introducing internal defects within the framework of the 3d-3d correspondence. The BPS condition for a probe M5-brane extending along all of AdS_4 requires it to wrap a surfac…
Optimizes master faces for 2D and 3D face verification using evolutionary algorithms and neural networks.
problem Impersonation attacks using master faces for face-based identity authentication.
method Evolutionary algorithm in latent space of StyleGAN, neural network to direct search, 2D and 3D face reconstruction.
result Obtains high impersonation rates with fewer master faces for 2D and 3D face verification.
Graphs embeddable on torus and linklessly in 3D can be embedded linklessly in standard torus.
problem Embedding linklessly in a standard torus for graphs embeddable on torus and in 3D.
method Analyzing graphs of order 9 and below, showing linkless embedding in standard torus.
result For graphs of order 9 and below, linkless embedding in standard torus is possible.
3D analog of Whitney's planarity criterion for 2-complexes.
problem Embedding 2-complexes in 3-space.
method Proving dual matroids of 2-complexes are graphic if and only if the complexes embed in 3-space.
result Simply connected and locally 2-dimensional complexes embed in 3-space if and only if their dual matroids are graphic.
New relations link knot theory to quiver representations in 3d physics.
problem Exploring new connections between knot theory and quiver representations.
method Observing multi-cover skein relations and embedding them into M-theory.
result Obtained dualities of 3d N=2 theories associated to quivers. EuLearn creates diverse 3D topological datasets for machine learning.
problem Training machine learning systems to discern topological features.
method Developed novel sampling and neural network architectures for graph and manifold data.
result Incorporating topological information improves deep learning performance on EuLearn datasets.
Standardizes surfaces in 3D handlebodies using Morse theory.
problem Classifying and identifying incompressible surfaces in 3D handlebodies.
method Applied Morse theory to provide a standard form and a condition for incompressibility.
result Developed a practical algorithm to determine incompressibility of surfaces in standard form.
System converts 3D lung nodule images into embeddings for retrieval.
problem Retrieving similar 3D lung nodule images for radiologist decision support.
method 3D deep learning, semantic representation, transfer learning, similarity score.
result System can measure similarity between nodule annotations and CBIR results.
We present a method of generating high resolution 3D shapes from natural language descriptions. To achieve this goal, we propose two steps that generating low resolution shapes which roughly reflect texts and generating high resolution shapes which reflect the detail of texts. In a previous paper, the authors have show…
Study Schrödinger evolution on surfaces in 3D contact sub-Riemannian manifolds.
problem Analyzing the Schrödinger evolution on surfaces embedded in 3D contact sub-Riemannian manifolds.
method Relating self-adjointness of the Schrödinger operator to geometric invariants of the foliation.
result Classification of self-adjoint extensions yielding disjoint dynamics.
pyLOT library simplifies machine learning on 3D point clouds via linearized optimal transport.
problem Performing machine learning tasks on 3D point clouds.
method Linearized optimal transport (LOT) to embed distributions into Hilbert space, enabling linear machine learning.
result Downstream tasks on embedded representations are simplified to linear operations.
Study the embedding space of a Hopf link in 3D and 3-manifolds.
problem Homotopy equivalence of embedding spaces of Hopf links.
method Prove homotopy equivalence using subspace inclusions and manifold properties.
result Embedding spaces are homotopy equivalent to specific 3-manifolds.
Paper constructs an infinite 3-7 surface in 3D space.
problem Can an infinite 3-7 surface be embedded in Euclidean space?
method Constructs an immersed, but not embedded, infinite 3-7 surface in R^3.
result Realizes an infinite 3-7 surface as a cover of Klein's quartic.
Researchers found 5 local fields to uniquely describe 3D director fields, related through 6 differential relations.
problem Understanding the compatibility conditions for 3D director fields.
method Employed the method of moving frames.
result A director field is fully determined by five local fields related through six differential relations.
Model learns tool affordances from vision, enabling tool selection.
problem Learning tool affordances from visual input.
method Vision-based generative model with task predictor.
result Agents can select appropriate tools based on task success criteria.
3D Schoenflies theorem for simply-connected 2-complexes.
problem Embedding simply-connected 2-complexes in 3-space uniquely.
method Proving a 3-dimensional Schoenflies theorem for 3-connected link graphs.
result Essentially unique locally flat embedding into 3-sphere.
ED-NeRF efficiently edits 3D scenes using latent space NeRF and improved loss functions.
problem Slow training speeds and inadequate editing loss functions in existing NeRF editing techniques.
method Embedding real-world scenes into latent space of LDM, using a unique refinement layer and an improved loss function.
result ED-NeRF achieves faster editing speed and improved output quality compared to state-of-the-art models.
Regularizes 3D inverse scattering with tangent-point energy for better solutions.
problem Ill-conditioned inverse obstacle scattering problems in 3D.
method Tikhonov regularization using tangent-point energy to penalize surface roughness and ensure well-posedness.
result Regularized solutions converge to true solution as noise level decreases.
The sigma invariant is studied for torus, K3 surface, and 3d manifolds.
problem Investigating the sigma invariant for specific manifolds.
method Analyzing isometric embeddings and scalar curvature functionals.
result Sigma invariant is zero for torus, K3 surface, and certain 3d manifolds.
Characterizes weakly linked pairs of complete graphs in 3D space.
problem Identifying pairs of complete graphs that are weakly linked.
method Algebraic characterisation and geometric analysis of linking cycles.
result Characterization of weakly linked pairs of complete graphs.
The paper studies minimal surfaces in 3D spheres and balls, confirming conjectures and identifying new surfaces.
problem Understanding minimal surfaces in 3D spheres and balls with low area.
method Equivariant optimization of Laplace and Steklov eigenvalues to construct minimal surfaces of prescribed topology.
result Sharp area estimates and varifold limits for minimal surfaces in large topology regimes.
In neural networks, it is often desirable to work with various representations of the same space. For example, 3D rotations can be represented with quaternions or Euler angles. In this paper, we advance a definition of a continuous representation, which can be helpful for training deep neural networks. We relate this t…
A neural flow method minimizes Willmore energy for 2-surfaces in 3D space.
problem Minimizing Willmore energy for closed oriented 2-surfaces in 3D space.
method Introducing neural Willmore flow to model and minimize the Willmore energy using neural architectures.
result The neural flow reproduces expected round sphere and Clifford torus for genus 0 and 1 surfaces, respectively, and finds minimal Willmore surfaces for genus 2.
New maximally linkless graphs found with fewer edges.
problem Finding graphs without any links in 3D space.
method Demonstrated new maximally linkless graphs with improved edge count.
result Found maximally linkless graphs with m≤514n edges. Proves local isometric embedding of low-differentiability metrics in 3D space.
problem Isometric embedding of metrics of low differentiability in Euclidean 3-space.
method Simplified notation, geodesic and level parameters, solutions of initial value problems for first order non-linear PDEs, classical linear algebraic systems.
result Local isometric embedding exists for metrics of C1 differentiability.
The paper explores linearly free graphs and their embeddings into 3D space.
problem Understanding the conditions under which a graph's embedding into 3D space is free.
method Developed a sufficient condition for a linear embedding to be free and applied it to specific graph cases.
result Established sufficient conditions for a graph to be linearly free and provided examples and counterexamples.
Paper proposes Roweisposes for 3D action recognition using generalized eigenvalue problem.
problem Need for basic methods in 3D action recognition.
method Roweisposes uses Roweis discriminant analysis for generalized subspace learning.
result Roweisposes is effective for 3D action recognition.
This paper embeds surfaces in 3D spheres and balls with minimal area.
problem Embed surfaces with boundary in B3 as minimal surfaces. method Optimizing Laplace and Steklov eigenvalues with symmetry groups.
result Proves existence of minimal surfaces in B3 with area below 2π. Classifies minimal surfaces of finite genus in 3D space.
problem Classifying minimal surfaces of finite genus in 3D space.
method Four-step classification, lamination techniques, dynamics theorem, and topology bounds.
result Classification of minimal surfaces of genus zero and infinite topology.