Computes knot types using HOMFLY-PT polynomial.
problem Determining chiral knot and link types with small crossing numbers.
method Uses the HOMFLY-PT polynomial to compute knot types from 3D coordinates.
result Efficacy of HOMFLY-PT for knot types up to crossing number 16.
3D dust map of the Milky Way improves resolution and accuracy.
problem Reconstructing the 3D dust distribution in the Milky Way.
method Gaussian process regression on spherical coordinates with iterative grid refinement.
result Improved 3D dust map with increased resolution and accuracy.
Equivariant diffusion model generates 3D molecules efficiently.
problem Generating high-quality 3D molecules efficiently.
method Equivariant Diffusion Model (EDM) that operates on atom coordinates and types.
result Significantly outperforms previous methods in molecule quality and training efficiency.
Proposes local coordinate frames for improving model performance in complex dynamical systems.
problem Improving model performance in complex, non-linear, and time-dependent dynamical systems.
method Introduces roto-translation invariant local coordinate frames for geometric graphs.
result The approach outperforms state-of-the-art models in various complex scenarios.
HLTF generates chemically valid 3D molecules with improved topology control.
problem Generating chemically valid 3D molecules is challenging due to bond topology errors.
method HLTF uses a latent multi-scale plan for global context and a constraint-aware sampler to suppress topology-driven failures.
result HLTF achieves high validity and uniqueness on QM9 and GEOM-DRUGS datasets.
Study how large-scale flows align small-scale vortices in 3D Euler equations.
problem Understanding how large-scale flows align small-scale vortices in 3D Euler equations.
method Constructing a Lagrangian coordinate to identify when the Lie bracket is zero and investigating the locality of the pressure term.
result Clarified conditions under which small-scale vortices are aligned by large-scale flows.
Unified 3D R-matrices from quantum cluster algebra.
problem Constructing new solutions to the tetrahedron equation.
method Symmetric butterfly quiver, quantum cluster algebra, quantum dilogarithms, q-Weyl algebra.
result Unified 3D R-matrices from various sources.
Improved 3D LiDAR data classification using product coefficients.
problem Enhancing accuracy in 3D LiDAR data classification.
method Introducing product coefficients derived from measure theory as additional features in the classification process, alongside PCA.
result Significant improvement in classification accuracy with product coefficients.
Extracts object-centric frames from unlabeled images.
problem Extracting abstract models of 3D objects from visual measurements.
method Viewpoint factorization and dense equivariant labelling neural network.
result Extracts dense object-centric coordinate frames invariant to deformations.
Study on tubes with specific Gauss map properties in 3D space.
problem Characterizing surfaces with a specific Gauss map property in 3D space.
method Analyzing tubes in Euclidean 3-space with Gauss map n satisfying ΔIn = Λn.
result Circular cylinders are the only surfaces of coordinate finite I-type Gauss map.
VecMol generates 3D molecules as continuous vector fields, overcoming modality and geometry constraints.
problem Challenges in generating 3D molecules, especially in drug discovery and materials science.
method VecMol reimagines molecular representation by modeling 3D molecules as continuous vector fields over Euclidean space, parameterized by a neural field and generated using a latent diffusion model.
result Vector-field-based representations show promise for 3D molecular generation, validated on benchmarks.
DECAF optimizes molecular graphs for ensemble properties, improving drug design accuracy.
problem Designing molecules with ensemble properties rather than single conformations.
method DECAF uses Boltzmann-expected design with decoupled annealing flows to optimize molecular graphs.
result DECAF optimizes molecular graphs to shift ensemble properties towards targets, improving accuracy over single-conformer methods.
A neural atlas simplifies 3D geometry simulation by avoiding meshing.
problem Simulation of complex 3D geometries with thin features or non-trivial topology.
method Learned geometric representation of overlapping volumetric coordinate charts, trained from point-cloud or level-set data.
result The learned atlas enables different solvers without re-meshing or re-parametrization.
Overview of methods for rotating 2D and 3D data.
problem Processing data with equivariance/invariance under rotations.
method An overview of methods for 2D and 3D rotations.
result Identification of commonalities and links between methods.
New form of D4−-singularities for fronts in 3D space.
problem Understanding singularities of fronts in 3D space.
method Coordinate transformation on source and isometry on target.
result Computed differential geometric invariants near D4−-singularity. Study of motion constraints and path-following on 3D space.
problem Path-following with non-holonomic constraints on R3. method Exploration of geometric structure and construction of guiding vector fields.
result General principles for constructing guiding vector fields for path-following.
Paper uses tensor regression to analyze point clouds for process optimization.
problem Challenges in modeling and analyzing high-dimensional point cloud data.
method Utilizes multilinear algebra and tensor regression techniques.
result Successfully models and links point cloud variational patterns to process variables.
STRING improves 2D and 3D position encodings for better performance.
problem Efficient and accurate position encoding for 2D and 3D applications.
method STRING extends Rotary Position Encodings with a unifying theoretical framework, maintaining translation invariance and low computational cost.
result STRING shows substantial gains in open-vocabulary object detection and robotics.
Convolutional neural networks improve human pose estimation from videos.
problem Estimating 3D pose of humans from monocular vision.
method 3D CNN applied to RGB videos, encoding time as the 3rd dimension.
result Achieves state-of-the-art performance on Human3.6M dataset.
Detect spacetime curvature without rulers and clocks in 3D.
problem Detecting spacetime curvature without traditional measurement tools.
method Generalized results from 2D to 3D spacetime, proving well-stitched spacetime for conformally flat cases.
result A 3D spacetime is well-stitched if and only if it is conformally flat, providing a tool for curvature detection.
Generative models learn 3D scenes without explicit maps.
problem Learning models for visual 3D localization without explicit maps.
method Generative Query Networks (GQNs) with attention mechanisms.
result GQNs can capture complex 3D scenes and perform localization.
Only helicoids and spheres satisfy a specific surface equation in 3D space.
problem Characterizing surfaces in 3D space based on a specific differential equation.
method Analyzing ruled and quadric surfaces in 3D Euclidean space satisfying a particular differential equation.
result Helicoids and spheres are the only surfaces satisfying the given differential equation.
Study caustics of an elliptical paraboloid and extend Apollonius problem solution.
problem Apollonius problem on paraboloid normals.
method Two methods: Cartesian and parabolic coordinates.
result Complete classification of caustic intersections with paraboloid.
End-to-end model predicts protein interfaces from atomic coordinates.
problem Improving protein interface prediction using large datasets.
method Developed SASNet, an end-to-end learning model using only atomic coordinates.
result SASNet outperforms state-of-the-art methods trained on gold-standard data.
New classification of complex hypersurfaces in 3D.
problem Classifying simply-transitive Levi non-degenerate hypersurfaces in C3. method Novel Lie algebraic approach, new coordinate-free formula for quartic tensor.
result Unique non-tubular model with geometric relations to planar equi-affine geometry.
Method predicts spinal deformity progression using 3D models and machine learning.
problem Predicting the progression of spinal deformities in scoliosis patients.
method Discriminative probabilistic manifold embedding for 3D spine models.
result 81% classification rate and 2.1° prediction difference in curve angulation.
A 1D-fully convolutional network classifies 3D point clouds efficiently.
problem Efficiently classifying 3D point clouds with reliable features.
method Directly consumes terrain-normalized points and spectral data, implicitly learning contextual features.
result Ranked second in ISPRS 3D Semantic Labeling Contest with 81.6% overall accuracy.
Defines Vassiliev complexity measures for open and closed curves in 3D space.
problem Measuring complexity of curves in 3D space.
method Using enhanced Jones polynomial coefficients and Gauss code diagrams.
result Second Vassiliev measure converges to knot invariants as curve ends coincide.
Unified framework for nuclear reactor perturbation analysis using CNN and LSTM.
problem Monitoring reactor cores for safety and perturbation identification.
method 3D-CNN and LSTM networks for frequency and time domain analysis, respectively.
result High accuracy in recognising perturbation type and precise source localisation in frequency domain.
AniDS improves molecular force field modeling by learning anisotropic noise.
problem Molecular force field modeling suffers from oversimplified assumptions about atomic motions.
method AniDS introduces anisotropic noise generation for better modeling of directional and structural variability.
result AniDS outperforms existing methods on benchmarks, achieving significant improvements in force prediction accuracy.
Deep learning predicts protein structures accurately.
problem Predicting the 3D structure of proteins from amino acid sequences.
method Embeddings and deep learning models for backbone atom distance matrices and torsion angles.
result Competitive results in CASP13 and CASP12, surpassing previous winners.
New method uses scalar-based models to approximate spherical tensors efficiently.
problem Efficiently approximating spherical tensors with equivariant functions.
method Expressing equivariant functions as the product of a scalar function and a small tensor basis.
result Approximations are fast, simple to implement, and accurate in practical settings.
Classifies 3D non-degenerate left-symmetric algebras.
problem Classifying left-symmetric algebras in 3D.
method Using Nijenhuis geometry and algebraic independence of coefficients in characteristic polynomial.
result Classification of differentially non-degenerate LSA in dimension 3.
TarMAC targets and coordinates multi-agent communication for cooperative tasks.
problem Coordinating multi-agent reinforcement learning in partially observable environments.
method Targeted multi-round communication approach without supervision.
result Improved performance and sample efficiency in diverse environments.
Deep RL learns grasping from 2.5D images.
problem Grasping objects from 2.5D images.
method Deep Reinforcement Learning (DRL) in a simulated environment.
result Successfully learned grasping from 2.5D images.
Extends quantum trace map to SL3(C) for 3D surfaces.
problem Generalizing quantum trace map to higher dimensions.
method Definition of SL3(C) quantum trace invariant.
result Construction of SL3(C) quantum trace map.
Neural network learns atomic coordinates from Patterson maps in a simplified case.
problem Training a neural network to infer atomic coordinates from Patterson maps.
method Synthetic data training, centering output maps, removing centrosymmetric inversion, and adding empty space.
result The network can generalize to infer atom positions from Patterson maps not in the training set.
New method reconstructs 3D protein structures from cryo-EM images.
problem Reconstructing continuous protein structures from noisy cryo-EM projections.
method Neural network-based approach that models structural heterogeneity in Fourier space.
result Demonstrated successful ab initio reconstruction of 3D protein complexes.
New algorithm beats traditional methods for seismic data interpolation.
problem Efficiently filling in missing seismic data volumes.
method Primal-dual alternating approach using matrix factors and block-coordinate algorithm.
result Successfully interpolated a large 5D seismic data volume from a 3D model.
The paper constructs and classifies 3D Walker manifolds with specific structures.
problem Classifying 3D Walker manifolds with specific paracontact structures.
method Constructing structures using a unit space-like vector field and a function, characterizing the Lorentzian metric.
result Necessary and sufficient conditions for the manifold to belong to specific classes of almost paracontact metric manifolds.
New neural network predicts accurate protein complex structures.
problem Predicting accurate protein complex structures from atomic coordinates.
method Rotation-equivariant neural network combining point-based representation, equivariance, local convolutions, and hierarchical subsampling.
result Significant improvement in identifying accurate structural models.
Unsupervised mesh disentanglement separates identity and pose.
problem Geometric disentanglement for 3D deformable models.
method CFAN-VAE architecture using conformal factor and normal features.
result CFAN-VAE achieves state-of-the-art performance on unsupervised geometric disentanglement.
New method characterizes minimal surfaces in 3D space.
problem Characterizing minimal surfaces in 3D space.
method Alexandrov Reflection Method
result Embedded minimal free boundary annuli in B3 are the critical catenoid. Method estimates section thickness and XY anisotropy in ssEM images.
problem Accurate 3D reconstructions require precise section thickness and XY anisotropy estimates.
method Non-parametric Bayesian regression of image statistics.
result Method has lower estimation error compared to existing methods.
Study b-6j symbols linking anti-de Sitter tetrahedra to hyperbolic geometry.
problem Analyzing b-6j symbols for quantum invariants. method Examining asymptotics and analytic extensions of 6j-symbols. result Connection between anti-de Sitter tetrahedra and hyperbolic geometry.
Neural network Kalman filtering improves 3D ultrasound object tracking.
problem Accurate and robust 3D positional estimation from 2D ultrasound data.
method Neural network training for out-of-plane offset estimation, combined with Kalman filtering.
result Mean error of 0.1mm for simulated data, 0.2mm for experimental data.
Bayesian model classifies X-ray binaries as black holes, neutron stars, or bursters.
problem Uncertainty in classifying X-ray binaries as black holes or neutron stars.
method Developed a Bayesian statistical model using 3D coordinates from X-ray spectral data.
result Accurate prediction of X-ray binary types, but non-pulsing neutron stars near black hole boundary misclassified.
Extends Wigner's representation to study super hyperbolic geometry.
problem Understanding geometry in super hyperbolic three-space.
method Extended Wigner's representation of the Lorentz group to OSp_C(1|2) and applied to Minkowski (3,1|4)-dimensional super space.
result Proof of divergence of the volume of a typical ideal tetrahedron in super hyperbolic three-space.