3D dual field theories for Virasoro minimal models constructed using Seifert fiber spaces.
problem Constructing 3D dual field theories for Virasoro minimal models.
method 3D-3D correspondence and Seifert fiber spaces.
result 3D dual field theories constructed for Virasoro minimal models.
The paper studies decay near singularities of 3d Yang-Mills-Higgs fields.
problem Understanding isolated singularities of 3d Yang-Mills-Higgs fields.
method Derives decay estimates and applies removable singularity theorems.
result Generalizes removable singularity theorems for 3d Yang-Mills-Higgs fields.
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.
The study classifies Lie algebras of vector fields in 3D.
problem Classifying Lie algebras of vector fields in 3D.
method Lifting Lie algebras from C2 to C2imesC and computing all types of transitive lifts. result Computed all types of transitive lifts for Lie algebras from Lie's classification.
We show that 3D gravity, in its pure connection formulation, admits a natural 6D interpretation. The 3D field equations for the connection are equivalent to 6D Hitchin equations for the Chern-Simons 3-form in the total space of the principal bundle over the 3-dimensional base. Turning this construction around one gets …
Proves strong Tits alternative for 3D automorphisms over zero char fields.
problem Tits alternative for 3D tame automorphisms over zero char fields.
method Proved strong Tits alternative using 3D tame automorphisms over zero char fields.
result Strong Tits alternative proven for 3D tame automorphisms over zero char fields.
A scalable 3D magnetic field SLAM method using smartphone data.
problem Scalable 3D magnetic field SLAM in buildings and objects.
method Gaussian process model, reduced-rank regression, hexagonal tiling, Rao-Blackwellised particle filter.
result Accurate position and orientation estimates from smartphone data.
Defines a map connecting 3d-index and skein module.
problem Connecting mathematical physics predictions with topological quantum field theory.
method Defines a map from skein module to Laurent series ring.
result The map fulfills a supersymmetry prediction and is part of a conjectural topological quantum field theory.
Paper connects 3D gravity averages to 2D CFT correlators.
problem Understanding 3D gravity partition functions.
method 3D topological field theories and mapping class group averages.
result Established a correspondence between 3D gravity averages and 2D CFT correlators.
Proposes a model to generate 3D-aware images from 2D images.
problem Generating 3D-aware images from 2D images.
method Likelihood-based top-down model using Neural Radiance Fields and energy-based latent variables.
result Model can infer 3D object structures from 2D images and generate novel views.
Study finds symmetries in a special 3D space with a diagonal metric.
problem Identifying symmetries in a specific 3D space.
method Determining Killing vector fields on a diagonal metric in R3. result Killing vector fields on the space R3 with a diagonal metric have been identified. 3D Steerable CNNs learn equivariant features for 3D data.
problem Learning rotationally equivariant features in volumetric data.
method SE(3)-equivariant convolutions using steerable kernel basis.
result 3D Steerable CNNs are effective for protein structure classification and amino acid propensity prediction.
Study 3d N=1 vacua from M-theory compactification on Spin(7) space.
problem Quantum corrections in 3d N=1 vacua from M-theory compactification.
method Use Higgs bundles to analyze 3d N=1 vacua and track corrections.
result Topological anomalies are robust and calculable in 3d effective field theory.
InSphereNet uses infilling spheres for 3D object classification, improving accuracy with fewer parameters.
problem 3D object classification using points, voxels, or images.
method Constructs infilling spheres from signed distance field (SDF) for classification.
result InSphereNet achieves superior accuracy with fewer inputs and parameters.
Classifies 3D F-manifolds with or without Euler fields.
problem Local classification of 3D F-manifolds.
method Integrability condition on multiplication in holomorphic tangent bundle.
result Local classification of 3D F-manifolds.
Proves helicity is the only regular Casimir for 3D hydrodynamics.
problem Identifying unique Casimir functions for 3D hydrodynamics.
method Normal forms, Poincaré-Birkhoff theorem, division lemma.
result Helicity is the only regular Casimir for volume-preserving diffeomorphisms.
Deep learning predicts molecular functions from 3D fields.
problem Predicting molecular functions from 3D fields.
method Deep learning models trained on approximated electron density and electrostatic potential fields.
result Deep learning achieves comparable performance to state-of-the-art methods.
Physics-constrained neural nets solve EM fields of charged particle beams.
problem Solving Maxwell's equations for intense charged particle beams.
method 3D Convolutional Neural Networks (CNNs) constrained by physics.
result 3D CNNs generate electromagnetic fields from current and charge densities.
The paper explores the connection between 3d gravity and Chern-Simons theory using affine group connections.
problem Exploring the relationship between 3d gravity and Chern-Simons theory.
method A variational problem of Chern-Simons type on a principal fiber bundle with general affine group structure is studied. The connection is established through a generalized notion of extension and reduction of connections.
result Established a correspondence between 3d gravity and Chern-Simons theory using affine group connections.
Generative model calibrates 3D battery cathode morphologies from 2D images.
problem Calibrate 3D morphologies of all-solid-state battery cathodes from 2D microscopy images.
method Combining GANs with excursion sets of Gaussian random fields.
result Calibrated digital twins enable systematic exploration of morphological scenarios.
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.
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.
3D-PRNN generates shapes from depth images using recurrent neural networks.
problem Representing 3D shapes from limited sensor data.
method Generative Recurrent Neural Network (3D-PRNN) with Gaussian Fields.
result 3D-PRNN synthesizes plausible shapes from primitives, outperforming nearest-neighbor methods.
3D HQFTs constructed using graded monoidal categories.
problem Constructing 3D HQFTs with specific targets.
method Using spherical χ-fusion categories and the state sum method.
result 3D HQFTs constructed with target Bχ.
Overview of 3D TQFTs and 3-manifold invariants.
problem Quantum invariants of 3-manifolds.
method Recall and review of TQFTs, fusion categories, and recent generalizations.
result Overview of various 3D TQFTs and their invariants.
Improved QSM maps from MRI using deep learning.
problem Inaccurate susceptibility maps due to ill-posed dipole inversion.
method 3D GAN with increased receptive field and WGAN with gradient penalty.
result Significantly better QSM maps from single orientation phase maps.
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.
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.
ObSuRF converts a single image into a 3D model with NeRFs.
problem Creating a 3D model from a single image with object segmentation.
method Unsupervised volume segmentation using Neural Radiance Fields (NeRFs).
result ObSuRF can segment a 3D scene into objects from a single image.
We present a string inspired 3D Euclidean field theory as the starting point for a modified Ricci flow analysis of the Thurston conjecture. In addition to the metric, the theory contains a dilaton, an antisymmetric tensor field and a Maxwell-Chern Simons field. For constant dilaton, the theory appears to obey a Birkhof…
DreamFusion uses text-to-image diffusion models to create 3D images efficiently.
problem Lack of large-scale 3D datasets and efficient architectures for 3D synthesis.
method Adapting a 2D diffusion model to 3D synthesis using a loss based on probability density distillation.
result A 3D model can be optimized from a 2D diffusion model, allowing for text-to-3D synthesis.
Study magnetic flows on 3D contact sub-Riemannian manifolds using Rumin complex.
problem Understanding magnetic flows on 3D contact sub-Riemannian manifolds.
method Introducing horizontal magnetic flows via closed Rumin differential two-forms and analyzing the lifted sub-Riemannian structure.
result Horizontal magnetic flows can be interpreted as geodesic flows on a suitably lifted structure, which is of Engel type when the magnetic field is non-vanishing.
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.
Improved 3D scene understanding from partial point sets using multiview fusion.
problem Challenging task of 3D scene semantic understanding from partial point clouds.
method Multiview representation of 360° point clouds and fusion with original data.
result Overall increase of 31.9% and 4.3% in segmentation accuracy for partial and complete scenes.
This paper defines directional derivatives and solves Maxwell's equations in curved 3D space.
problem Analyzing electromagnetic fields in curved non-flat 3D space.
method Defined directional derivatives and used Frenet formulas to express Serret-Frenet relations. Solved Maxwell's equations for electric and magnetic fields.
result Solved Maxwell's equations for electromagnetic fields in curved 3D space.
Geometric GNNs model 3D atomic systems with rotations and translations.
problem Modeling 3D atomic systems with geometric graphs and machine learning.
method Invariant, equivariant, and unconstrained GNN architectures.
result Geometric GNNs leverage physical symmetries and chemical properties.
Classifies left invariant Kundt structures on 3D Lie groups.
problem Understanding Kundt spacetimes and their properties.
method Analyzes local structure and properties of left invariant Kundt structures.
result Classifies all left invariant Kundt structures on 3D simply connected unimodular Lie groups.
New approach connects 3D Chern-Simons theory to spectral networks.
problem Understanding Chern-Simons invariants in 3D manifolds.
method Constructing equivalences between bundles and spectral networks.
result New formulas for Chern-Simons invariants of 3D manifolds.
The paper tackles mapping tori by proposing a new approach to 3d-3d correspondence.
problem No existing approach fully describes 3d N=2 SCFTs for all types of 3-manifolds. method Systematic study of 3d N=2 gauge theories with non-linear matter fields. result Recovery of 3-manifold invariants from T[M3] indices and proposal of new q-series invariants. New method uses resurgent analysis to determine growth rate of quantum field theory coefficients.
problem Determining the growth rate of quantum field theory coefficients.
method Resurgence analysis on the Stokes line, leading to transseries decomposition and continued across natural boundary.
result Essential exponent of growth has Cardy-like interpretation as effective central charge.
New methods reveal compatible liquid crystal phases in 3D.
problem Understanding compatible director fields in 3D liquid crystals.
method Re-derived compatibility conditions using vector calculus.
result Characterized a wide range of compatible liquid crystal phases.
Study of IR phases in 3D class R theories linked to non-hyperbolic 3-manifolds.
problem Understanding IR phases of 3D class R theories associated with non-hyperbolic 3-manifolds.
method Analysis of IR phenomena through `exceptional' Dehn fillings and gauging of flavor symmetries.
result 3D class R theories associated with certain atoroidal non-hyperbolic 3-manifolds exhibit supersymmetry enhancement at low energy.
Extracts airways from 3D CT data using graph refinement methods.
problem Extracting airway trees from volumetric CT data.
method Two methods: mean-field approximation and graph neural networks.
result Both methods improve airway detection accuracy.
Study bends 2D surfaces in 3D space using special equations.
problem Investigate infinitesimal bendings of 2D surfaces in 3D space.
method Use Bers-Vekua type equations and systems of differential equations with periodic coefficients.
result Construct bending fields for specific classes of 2D surfaces.
3D good continuation model explains stereo vision using neurogeometry.
problem Understanding how the brain processes 3D visual correspondence.
method Developed a neurogeometric model involving spatial and orientation disparities.
result Provides insight into neural organization and correspondence problem.
Generic 3D vector fields have singularly hyperbolic transitive sets.
problem Understanding the dynamics of generic three-dimensional vector fields.
method Analyzing C1 generic vector fields on closed 3-manifolds. result Generic vector fields have singularly hyperbolic transitive sets.
3D manifolds with certain projective fields are projectively flat.
problem Geodesic rigidity of Levi-Civita connections with essential projective vector fields.
method Proved projective flatness for specific manifolds with projective vector fields.
result Connected 3D Riemannian and closed semi-Riemannian manifolds with non-linearizable projective singularities are projectively flat.
A scalable deep learning framework accelerates training of large neural networks for solving 3D Poisson equations.
problem Training large-scale neural networks for solving complex PDEs efficiently.
method Combines multigrid techniques with distributed deep learning to accelerate training.
result Solves 3D Poisson equations up to 512x512x512 resolution efficiently.