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.
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48 results for “3D HQFTs”
We show that for every spherical category $\C$ with invertible dimension, the Turaev-Viro TQFT admits a splitting into blocks which come from an HQFT, called the Turaev-Viro HQFT. The Turaev-Viro HQFT has the classifying space $B\grad$ as target space, where $\grad$ is a group obtained from the category $\C$. This cons…
Surgery HQFTmath.QA
Homotopy Quantum Field Theories (HQFTs) generalize more familiar Topological Quantum Field Theories (TQFTs). In generalization of the surgery construction of 3-dimensional TQFTs from modular categories, we use surgery to derive 3-dimensional HQFTs from G-modular categories.
In a previous work arXiv:0903.4512, we have built an homotopical Turaev-Viro invariant and an HQFT from the universal graduation of a spherical category. In the present paper, we show that every graduation of a spherical category $\C$ defines an homotopical Turaev-Viro invariant $HTV_{\C}^{(G,p)}$ and an HQFT $…
We introduce and study algebraic structures underlying 2-dimensional Homotopy Quantum Field Theories (HQFTs) with arbitrary target spaces. These algebraic structures are formalized in the notion of a twisted Frobenius algebra. Our work generalizes results of Brightwell, Turner, and the second author on 2-dimensional HQ…
Defines a new 2+1-G-HQFT using graded skein modules.
problem Developing a new quantum field theory for groups.
method G-graded chromatic maps and skein modules.
result Recover modified Turaev-Viro invariants.
Let G be a discrete group and C be an additive spherical G-fusion category. We prove that the state sum 3-dimensional HQFT derived from C is isomorphic to the surgery 3-dimensional HQFT derived from the G-center of C.
A 3-dimensional homotopy quantum field theory (HQFT) can be described as a TQFT for surfaces and 3-cobordisms endowed with homotopy classes of maps into a given space. For a group , we introduce a notion of a modular crossed -category and show that such a category gives rise to a 3-dimensional HQFT with target sp…
Two link diagrams on compact surfaces are strongly equivalent if they are related by Reidemeister moves and orientation preserving homeomorphisms of the surfaces. They are stably equivalent if they are related by the two previous operations and adding or removing handles. Turaev and Turner constructed a link homology f…
For a group G, the notion of a ribbon G-category was introduced by the second author in a previous work with a view towards constructing 3-dimensional homotopy quantum field theories (HQFT's) with target K(G,1). We discuss here how to derive ribbon G-categories from a simple complex Lie algebra g where G is the center …
Given a discrete group G and a spherical G-fusion category whose neutral component has invertible dimension, we use the state-sum method to construct a 3-dimensional Homotopy Quantum Field Theory (HQFT) with target the Eilenberg-MacLane space K(G,1).
We study knots in 3d Chern-Simons theory with complex gauge group , in the context of its relation with 3d theory (the so-called 3d-3d correspondence). The defect has either co-dimension 2 or co-dimension 4 inside the 6d theory, which is compactified on a 3-manifold . …
Study of 3d-3d correspondence involving -Weyl algebra and 3d-index.
problem Understanding the action of a -Weyl algebra on the 3d-index of knots.
method Investigation of the -Weyl algebra's module action on the 3d-index, conjecturing structural properties.
result Bilinear factorization, pair of linear -difference equations, and rational function matrix for the 3d-index determination.
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.
3D flying wings created for any angle asymptotic cones.
problem Creating 3D steady gradient Ricci solitons with any angle asymptotic cones.
method Constructing 3D flying wings for any angle asymptotic cones.
result 3D flying wings constructed for any angle asymptotic cones.
for 3d theorieshep-th
Proposes a new effective central charge for 3d N=2 theories.
problem Understanding the effective central charge in 3d N=2 theories.
method Analyzes the superconformal index to propose a new quantity and discusses its properties and computation.
result Proposes a new effective central charge for 3d N=2 theories.
Autonomous driving requires 3D perception of vehicles and other objects in the in environment. Much of the current methods support 2D vehicle detection. This paper proposes a flexible pipeline to adopt any 2D detection network and fuse it with a 3D point cloud to generate 3D information with minimum changes of the 2D d…
Smooth 3D flows from non-smooth starting points.
problem Creating smooth Ricci flows from non-smooth initial conditions.
method Generalized singular Ricci flow applied to 3D complete manifolds.
result Existence of smooth Ricci flows starting from non-smooth initial conditions.
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.
3D steady gradient Ricci solitons are all O(2)-symmetric.
problem Characterizing 3D steady gradient Ricci solitons.
method Analyzing asymptotic behavior and using O(2) symmetry.
result All 3D steady gradient Ricci solitons are O(2)-symmetric.
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.
3D Convolutional Neural Networks (3D-CNN) have been used for object recognition based on the voxelized shape of an object. However, interpreting the decision making process of these 3D-CNNs is still an infeasible task. In this paper, we present a unique 3D-CNN based Gradient-weighted Class Activation Mapping method (3D…
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…
Graph Neural Networks improve 3D object detection in LiDAR point clouds.
problem Challenges in processing LiDAR data due to its 3D geometry and massive volume.
method Proposes a Graph Neural Network (GNN) based framework for 3D object detection.
result GNNs successfully identify objects in 3D LiDAR point clouds.
The study connects knot complements to 3d theories via half-index calculations.
problem Understanding the relationship between knot complements and 3d theories.
method Using half-index calculations and inverted Habiro series, the study realizes knot complements as homological blocks.
result The colored Jones polynomial is derived from choosing specific poles in the half-index integral expression.
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…
GCDM generates valid large 3D molecules and optimizes existing molecules.
problem Lack of geometric properties in 3D molecule generation models.
method Introduces Geometry-Complete Diffusion Model (GCDM) using equivariant GNNs.
result Significantly outperforms existing models in 3D molecule generation and optimization.
Generates coherent 3D scenes from monocular videos without supervision.
problem Lack of 3D scene modeling in video generation models.
method Trains a model to generate 3D scenes with moving objects and a background from monocular videos.
result Trained model generates coherent 3D scenes with multiple moving objects and a background.
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.
Researchers discover a new family of 3D solitons that are flying wings.
problem Verifying a conjecture about 3D steady gradient Ricci solitons.
method Analyzing a family of 3D flying wing solitons and proving properties of these solitons.
result 3D flying wing solitons are non-collapsed and have non-zero scalar curvature at infinity.
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.
Study large N oscillations in 3D theories related to black hole physics.
problem Understanding large N sign oscillations in 3D theories via holography.
method Holographic computation of on-shell actions for Euclidean supergravity solutions, Wick rotation of magnetically charged AdS4 black holes.
result Proposed a non-trivial mathematical conjecture regarding phase factors of twisted Reidemeister-Ray-Singer torsion.
Enhances 2D face recognition with 3D features using active illumination.
problem Improving robustness of 2D face recognition to spoofing attacks and low-light conditions.
method Projecting a high spatial frequency pattern onto the face to recover 3D information and a 2D image simultaneously.
result Significantly boosts face recognition performance and dramatically improves robustness to spoofing attacks.
Early diagnosis, playing an important role in preventing progress and treating the Alzheimer\{'}s disease (AD), is based on classification of features extracted from brain images. The features have to accurately capture main AD-related variations of anatomical brain structures, such as, e.g., ventricles size, hippocamp…
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.
A framework for generating 3D shapes by sequentially assembling primitives.
problem Combinatorial complexity in generating 3D shapes.
method Bayesian optimization for efficient exploration and exploitation of feasible combinations.
result Successfully generates realistic combinatorial 3D shapes.
3D object detection improved using energy-based models.
problem Accurate 3D object detection in cluttered environments from sparse LiDAR data.
method Designing a differentiable pooling operator for 3D bounding boxes integrated into a state-of-the-art 3D object detector.
result Our approach consistently outperforms the SA-SSD baseline across all 3DOD metrics on the KITTI dataset.
Early diagnosis, playing an important role in preventing progress and treating the Alzheimer's disease (AD), is based on classification of features extracted from brain images. The features have to accurately capture main AD-related variations of anatomical brain structures, such as, e.g., ventricles size, hippocampus …
Dimofte, Gaiotto and Gukov introduced a powerful invariant, the 3D-index, associated to a suitable ideal triangulation of a 3-manifold with torus boundary components. The 3D-index is a collection of formal power series in with integer coefficients. Our goal is to explain how the 3D-index is a generating serie…
Understanding the three-dimensional (3D) structure of the genome is essential for elucidating vital biological processes and their links to human disease. To determine how the genome folds within the nucleus, chromosome conformation capture methods such as HiC have recently been employed. However, computational methods…
3D adversarial logos can fool object detectors in real-world settings.
problem Creating robust adversarial attacks in 3D rendering views.
method Constructing 3D adversarial logos via texture mapping and differentiable rendering.
result 3D adversarial logos are more versatile and robust than traditional adversarial patches.
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.
GIBLy adds geometric priors to 3D segmentation models, improving performance with minimal overhead.
problem Lack of explicit geometric information in 3D semantic segmentation models.
method Introduces GIBLy, a lightweight geometric inductive bias layer that integrates learnable geometric priors into existing 3D segmentation pipelines.
result Consistent performance gains across multiple benchmarks, including up to +11.5% mIoU on TS40K with PTV3.
Paper extends 2D ZSAD to 3D MRI without training, achieving robust anomaly detection.
problem Challenges in extending zero-shot anomaly detection to 3D medical images.
method Constructs localized volumetric tokens by aggregating 2D slices processed by 2D foundation models.
result Training-free, batch-based ZSAD effectively extends from 2D encoders to full 3D MRI volumes.
Sharp 3D Alexandrov inequality applied to volume-preserving flows.
problem Volume-preserving geometric flows in 3D space.
method Sharp quantitative Alexandrov inequality for -regular sets.
result Established a 3D sharp quantitative version of the Alexandrov inequality.
Noise2Filter: fast, self-supervised learning and real-time reconstruction for 3D Computed Tomographyeess.IV
Noise2Filter improves 3D tomography reconstruction efficiency and accuracy.
problem Efficiently reconstructing 3D tomographic images in real-time with limited data.
method Self-supervised learning and a learned filter method.
result Noise2Filter achieves real-time reconstruction with limited loss of accuracy.
The importance of training robust neural network grows as 3D data is increasingly utilized in deep learning for vision tasks in robotics, drone control, and autonomous driving. One commonly used 3D data type is 3D point clouds, which describe shape information. We examine the problem of creating robust models from the …
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.