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.
Deep generative architectures provide a way to model not only images but also complex, 3-dimensional objects, such as point clouds. In this work, we present a novel method to obtain meaningful representations of 3D shapes that can be used for challenging tasks including 3D points generation, reconstruction, compression…
Python tools for 3D shape analysis on Kendall's space.
problem Lack of practical utilities for advanced 3D shape analysis.
method Developed Python tools for 3D shape analysis on Kendall's 3D Shape Space.
result Efficient, accessible software solutions for researchers.
New method reconstructs 3D shapes from 2D images using Kendall's shape space.
problem Reconstruct 3D shapes from 2D images, especially for rare specimens.
method Kendall's shape space approach with prior information.
result More robust and plausible shapes compared to previous methods.
Non-trivialization probability of arc system in 3D space
problem Defining and generalizing the knotting probability of an arc diagram in 3D space
method Transforming polygonal arcs in 3D space into unique arc diagrams
result Introducing and generalizing the Non-Trivialization probability (NT probability) for arc systems in 3D space
NT probability measures knotting in 3D arc systems.
problem Measuring knotting in 3D arc systems.
method Transforming polygonal arcs into unique diagrams, generalizing NT probability.
result Properties of NT probability for 3D arc systems are shown.
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.
3D spaces without boundaries are found that aren't manifolds.
problem Finding compact aspherical Alexandrov spaces without boundaries.
method Constructing specific examples of 3D spaces.
result Examples of 3D spaces without boundaries that are not topological manifolds.
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.
To give a Cartan calculus on the extended quantum 3d space, the noncommutative differential calculus on the extended quantum 3d space is extended by introducing inner derivations and Lie derivatives.
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 …
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.
LION generates high-quality 3D shapes using hierarchical latent diffusion models.
problem Creating high-quality 3D shapes for digital artists.
method Hierarchical Latent Point Diffusion Model (LION) with a global shape latent and point-structured latent space.
result LION achieves state-of-the-art generation performance on ShapeNet benchmarks.
(1,1) non-L-space knots are foliar in 3D space.
problem Proving (1,1) non-L-space knots are foliar.
method Analyzing (1,1) non-L-space knots in S3 and lens spaces. result (1,1) non-L-space knots are persistently foliar.
Approximate 3D elastic curves with exact constraints
problem Designing and approximating 3D elastic curves
method Numerically stable method for recovering 11 parameters
result Fast and stable approximation of arbitrary curves
Sharp 3D Alexandrov inequality applied to volume-preserving flows.
problem Volume-preserving geometric flows in 3D space.
method Sharp quantitative Alexandrov inequality for C2-regular sets. result Established a 3D sharp quantitative version of the Alexandrov inequality.
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.
In this paper, a neural architecture search (NAS) framework is proposed for 3D medical image segmentation, to automatically optimize a neural architecture from a large design space. Our NAS framework searches the structure of each layer including neural connectivities and operation types in both of the encoder and deco…
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. 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.
Scientific imaging techniques such as optical and electron microscopy and computed tomography (CT) scanning are used to study the 3D structure of an object through 2D observations. These observations are related to the original 3D object through orthogonal integral projections. For common 3D reconstruction algorithms, …
Classifies polar actions on 3D homogeneous spaces.
problem Classifying polar isometric actions on 3D homogeneous spaces.
method Orbit equivalence classification and study of cohomogeneity one actions.
result Classification of extrinsically homogeneous surfaces and orbit foliations.
Study of 3D vacuum static spaces with specific curvature properties.
problem Classifying 3D vacuum static spaces with certain curvature conditions.
method Used generalized maximum principle to classify 3D spaces.
result Gave a complete classification of 3D complete vacuum static spaces.
Pix2Shape learns 3D scene representations from single images without supervision.
problem Learning 3D scene information from a single image without supervision.
method Pix2Shape uses an encoder, decoder, and critic network to generate 2.5D surfel-based reconstructions.
result Pix2Shape can generate complex 3D scenes from a single image, scaling with on-screen resolution.
The study characterizes constant curvature manifolds using ruled surfaces.
problem Characterizing manifolds of constant curvature using ruled surfaces.
method Investigating ruled surfaces in 3d Riemannian manifolds, finding stiction curve, distribution parameter, and fundamental forms.
result Identifies necessary and sufficient conditions for extrinsically flat surfaces to be ruled and proves manifold properties.
We test the 3d-3d correspondence for theories that are labelled by Lens spaces. We find a full agreement between the index of the 3d N=2 "Lens space theory" T[L(p,1)] and the partition function of complex Chern-Simons theory on L(p,1). In particular, for p=1, we show how the familiar S3 partition func…
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.
Study circular tractrices and pseudospheres in 3D space.
problem Geometric properties of circular tractrices and pseudospheres.
method Exploration of geometric properties through analysis.
result Characterization of circular tractrices and pseudospheres.
Existing networks directly learn feature representations on 3D point clouds for shape analysis. We argue that 3D point clouds are highly redundant and hold irregular (permutation-invariant) structure, which makes it difficult to achieve inter-class discrimination efficiently. In this paper, we propose a two-faceted sol…
We solve 6-DoF localisation and 3D reconstruction using deep state-space models.
problem 6-DoF localisation and dense 3D reconstruction in spatial environments.
method Approximate Bayesian inference in a deep state-space model combining learning and domain knowledge.
result Near state-of-the-art performance on UAV flight data.
Study complete 3D λ-translators in Minkowski space with constant properties.
problem Classify 3D space-like λ-translators with specific constant properties.
method Obtained classification theorem through analysis of constant norm and f4. result Classification theorem for 3D complete space-like λ-translators.
We describe a family of 3d topological B-models whose target spaces are Hilbert schemes of points in C2. The interfaces separating theories with different numbers of points correspond to braid strands. The Hilbert space of the picture of a closed braid is the HOMFLY-PT homology of the corresponding link.
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.
New bounds on Heegaard distance for link complements in 3D space.
problem Finding bounds on Heegaard distance for link complements.
method Constructing specific links with given properties.
result Existence of links with specific Heegaard distances.
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 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.
Teichmüller TQFT is a unitary 3d topological theory whose Hilbert spaces are spanned by Liouville conformal blocks. It is related but not identical to PSL(2,R) Chern-Simons theory. To physicists, it is known in particular in the context of 3d-3d correspondence and also in the holographic description of Virasoro conform…
The common assertion that the Ricci flows of Einstein spaces with cosmological constant can be modelled by certain classes of nonholonomic frame, metric and linear connection deformations resulting in nonhomogeneous Einstein spaces is examined in the light of the role played by topological three dimensional (3D) Taub-N…
The tangent space is constructed in sub-Finsler geometry, leading to the failure of the CD condition in 3D-contact manifolds.
problem The failure of the CD condition in sub-Finsler geometry.
method Construction of the tangent space in the measured Gromov-Hausdorff sense, application of nilpotent approximation.
result The CD condition fails in 3D-contact sub-Finsler manifolds.
SU(2) flat connection on 2D Riemann surface is shown to relate to the generalized twisted geometry in 3D space with cosmological constant. Various flat connection quantities on Riemann surface are mapped to the geometrical quantities in discrete 3D space. We propose that the moduli space of SU(2) flat connections on Ri…
The study classifies flows of finite curvature in 3D space.
problem Classifying flows of finite curvature in 3D space.
method Partial classification of eternal mean convex flows.
result Topologically nonplanar flows must exit a catenoid.
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.
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.
Only vertical planes are asymptotic to other planes in 3D space.
problem Characterizing asymptotic planes in 3D space.
method Proof of uniqueness for complete translators with finite topology.
result Vertical planes are the only asymptotic planes in 3D space.
3D object classification and segmentation using deep neural networks has been extremely successful. As the problem of identifying 3D objects has many safety-critical applications, the neural networks have to be robust against adversarial changes to the input data set. There is a growing body of research on generating h…
Study on flat metrics on 3D and 4D manifolds, focusing on topology and algebra.
problem Topology and algebraic structure of flat metrics on manifolds.
method Algebraic and topological descriptions of moduli spaces.
result Algebraic description and topology of moduli spaces for 4D manifolds with a single holonomy generator.
3D filament plots visualize curves in datasets, avoiding visual clutter.
problem Visualizing high-dimensional data relationships in scatterplots of points.
method Construct 3D filament plots using linear isometries and Frenet-Serret systems.
result 3D filament plots preserve Euclidean distances and avoid visual clutter.
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.