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…
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48 results for “3D conformal structures”
New insights into 3D PDEs via Einstein-Weyl geometry.
problem Understanding second-order PDEs in 3D with Einstein-Weyl conformal structure.
method Analyzing solutions of second-order dispersionless integrable PDEs in 3D, relating them to Einstein-Weyl geometry.
result The covector w can be expressed in terms of the equation for generic second-order PDEs, providing a dispersionless integrability test.
In this paper a conformal classification of three dimensional left-invariant sub-Riemannian contact structures is carried out; in particular we will prove the following dichotomy: either a structure is locally conformal to the Heisenberg group , or its conformal classification coincides with the metric one…
The Fefferman metric connects CR manifolds to conformal geodesics in 3D.
problem Understanding the Fefferman metric on CR manifolds.
method Explicit description of the Fefferman metric and variational characterization of conformal geodesics.
result Conformal geodesics have lifts to chains and null chains, and are characterized by total torsion.
How to detect the spacetime curvature without rulers and clocks. II. Three-dimensional spacetimegr-qc
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.
The article explains Rao distances and conformal mappings for 3D objects.
problem Calculating distances and preserving angles in 3D objects.
method Proposed constructions of distances and angle-preserving mappings.
result Application to virtual tourism and line integrals in complex planes.
3D projective structures can be metrized with conformal structures.
problem Weyl metrizability of 3D projective structures.
method Interpreting Weyl metrizability as CR submanifolds in 7D.
result Beltrami's theorem extends to conformal structures in 3D.
This paper completes the classification of discrete conformal structures on surfaces.
problem Classifying discrete conformal structures on surfaces.
method Axiomatic approach and study of existing structures.
result Find new classes of discrete conformal structures, including generalized circle packing metrics.
Study on 3D manifolds with specific tensor structures and their properties.
problem Characterizing 3D Riemannian manifolds with tensor structures.
method Investigation of locally conformal Riemannian product manifolds and their associated structures.
result Conditions for additional structures to be parallel and properties of almost Einstein and Einstein manifolds.
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.
For several classes of second order dispersionless PDEs, we show that the symbols of their formal linearizations define conformal structures which must be Einstein-Weyl in 3D (or self-dual in 4D) if and only if the PDE is integrable by the method of hydrodynamic reductions. This demonstrates that the integrability of t…
The paper extends Weierstrass representation to non-minimal conformal immersions.
problem Understanding conformal immersions of Riemann surfaces into 3D space.
method Generalizing Weierstrass representation to arbitrary conformal immersions and studying spin structures and spinors.
result Immersions give rise to spin structures and spinors, allowing for new ways to study the immersions.
Paper proves rigidity of discrete conformal structures on polyhedral surfaces.
problem Rigidity of discrete conformal structures on polyhedral surfaces.
method Variational principles.
result Proves Glickenstein's conjecture on the rigidity of discrete conformal structures.
Study biharmonic conformal immersions into a 3D flat space, finding new examples and classifications.
problem Characterize and classify biharmonic conformal immersions into a conformally flat 3-space.
method Characterization of totally umbilical surfaces, method to produce biharmonic immersions, classification of maps, construction of examples.
result Construct many examples of biharmonic conformal immersions, including proper immersions and isometric ones.
Study on Ricci solitons and related metrics in 3D trans-Sasakian manifolds.
problem Exploring metrics like Ricci solitons in 3D trans-Sasakian manifolds.
method Analyzing properties of metrics and structure functions in 3D trans-Sasakian manifolds.
result Characterization of Ricci solitons and scalar curvature in 3D trans-Sasakian manifolds.
It is shown that 3D part of a spherically symmetric solution in conformal Weyl gravity interacting with Maxwell electrodynamics is a Yamabe flow as well. The Yamabe flow describes the transition from a horn of an initial wormhole to a 3D Euclidean space both filled with a radial electric field. It is supposed that such…
The paper defines and analyzes conformal trajectories in 3D space forms.
problem Understanding trajectories in curved 3D spaces.
method Defined conformal trajectories and studied their properties in , , and .
result Conformal trajectories in and have constant curvature and torsion.
Paper introduces conformal prediction for reliable uncertainty quantification in landmark localization.
problem Systematic underestimation of total predictive uncertainty in landmark localization.
method Conformal prediction framework for multi-output regression, generating flexible prediction regions.
result Methods outperform existing approaches in validity and efficiency across 2D and 3D datasets.
We address the problem of surface inpainting, which aims to fill in holes or missing regions on a Riemann surface based on its surface geometry. In practical situation, surfaces obtained from range scanners often have holes where the 3D models are incomplete. In order to analyze the 3D shapes effectively, restoring the…
Study finds all conformal Ricci collineations on specific 3D Lorentzian groups.
problem Identifying conformal Ricci collineations on three-dimensional Lorentzian Lie groups.
method Analysis of Levi-Civita connection on specific Lie groups.
result Determined all conformal Ricci collineations associated with the Levi-Civita connection.
Proves Lorentzian manifold properties for analytic 3D spaces.
problem Analyzing properties of Lorentzian manifolds.
method Analyzes compact, real-analytic, three-dimensional Lorentzian manifolds.
result Identity conformal group preserves metric or manifold is flat.
Study on filling 3D metrics with 4D Poincaré-Einstein structures.
problem Finding a conformal filling by a Poincaré-Einstein metric in 4D.
method Compactness result for conformally compact Einstein 4-manifolds under invariant conditions, with a rigidity result for hyperbolic metrics.
result Established compactness results and derived existence results for conformal fillings.
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…
Study properties of Kenmotsu manifolds with conformal η-Einstein soliton metrics.
problem Properties of Kenmotsu manifolds with specific soliton metrics.
method Investigated properties and constructed a 3D example.
result Properties and construction of 3D Kenmotsu manifold with conformal η-Einstein soliton.
Quasi-conformal (QC) theory is an important topic in complex analysis, which studies geometric patterns of deformations between shapes. Recently, computational QC geometry has been developed and has made significant contributions to medical imaging, computer graphics and computer vision. Existing computational QC theor…
Farey Bryophyllamath.GT
The paper generalizes Farey tessellation to 3D hyperbolic space.
problem Generalizing Farey tessellation to higher dimensions.
method Introducing conformal bryophylla and classifying them.
result Properties of conformal bryophylla's limiting sets studied.
New 3D protein analysis methods improve accuracy.
problem Lack of suitable learning algorithms for protein data.
method Intrinsic-Extrinsic Convolution and Pooling for 3D protein structures.
result Outperforms state-of-the-art methods on protein analysis tasks.
Compact 3D Cotton-parallel manifolds are always conformally flat.
problem Understanding the properties of compact 3D Cotton-parallel manifolds.
method Analyzing the Cotton tensor and its parallelism condition.
result Compact 3D Cotton-parallel manifolds are conformally flat.
Researchers found spiraling conformal geodesics in 3D space.
problem Existence of spiraling conformal geodesics in Euclidean signature.
method Constructed an example in 3D Euclidean signature, answering a question posed by Friedrich and Tod.
result Found an example of spiraling conformal geodesics in 3D space, not real analytic.
In 3D, conformal geodesics are variational.
problem Whether conformal geodesics are variational in 3D.
method Demonstrated that the equation for unparametrized conformal geodesics is variational.
result Variationality of conformal geodesics in 3D.
Develops a method for conformal parameterization of point clouds without fixed boundaries.
problem Desirable distortion in fixed-boundary parameterizations of point clouds.
method Free-boundary conformal parameterization method involving approximation of point cloud Laplacian and boundary treatment.
result High-quality point cloud meshing achieved through the proposed method.
The paper defines analogs of volume and action for curves in flag manifolds.
problem Investigating invariants for curves in flag manifolds.
method Using the correspondence between anti-de Sitter 3-space and (1,1)-conformal metrics, defining analogs of $\cW$-volume, Epstein surfaces, and Liouville action.
result Obtained finite invariants for positive curves in flag manifolds.
Study finds metrics maximizing one Laplace eigenvalue on 3D and higher manifolds.
problem Maximizing a Laplace eigenvalue on n-dimensional manifolds.
method Existence and regularity results for metrics of same volume in a conformal class.
result Existence and regularity of metrics maximizing the Laplace eigenvalue.
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…
Formula derived for ALH manifolds, showing existence of specific 3D manifolds.
problem Energy calculation and existence of specific 3D conformally compact ALH manifolds.
method Derivation of energy formula and application to manifold existence.
result Existence of 3D conformally compact ALH manifolds with specific properties.
Compact metrics found with specific curvature properties on 3D surfaces.
problem Finding compact metrics with constant curvature on 3D surfaces.
method Blow-up analysis of Yamabe equation with critical Sobolev exponents.
result Proved the compactness of conformal metrics with constant scalar curvature and boundary mean curvature.
Single-particle electron cryomicroscopy is an essential tool for high-resolution 3D reconstruction of proteins and other biological macromolecules. An important challenge in cryo-EM is the reconstruction of non-rigid molecules with parts that move and deform. Traditional reconstruction methods fail in these cases, resu…
A key goal of computer vision is to recover the underlying 3D structure from 2D observations of the world. In this paper we learn strong deep generative models of 3D structures, and recover these structures from 3D and 2D images via probabilistic inference. We demonstrate high-quality samples and report log-likelihoods…
Point cloud is the most fundamental representation of 3D geometric objects. Analyzing and processing point cloud surfaces is important in computer graphics and computer vision. However, most of the existing algorithms for surface analysis require connectivity information. Therefore, it is desirable to develop a mesh st…
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, …
The paper proves a new inequality linking mass and volume in 3D space.
problem Relating mass and volume in 3D space with a sharp inequality.
method Using a monotonicity formula for level sets of a 3-harmonic function.
result Sharp lower bound for ADM mass in terms of Euclidean volume of Ω.
"Ends of hyperbolic 3-manifolds should support canonical Wick Rotations, so they realize effective interactions of their ending globally hyperbolic spacetimes of constant curvature." We develop a consistent sector of WR-rescaling theory in 3D gravity, that, in particular, concretizes the above guess for many geometrica…
Study of 3D trans-Sasakian manifolds using Newman--Penrose formalism.
problem Characterizing and understanding the geometry of 3D trans-Sasakian manifolds.
method Using Newman--Penrose formalism to encode the geometry of the structure vector field.
result Derivation of curvature and Laplacian identities for trans-Sasakian manifolds and their subclasses, including rigidity results.
NeRF-VAE generates 3D scenes with geometric structure from few images.
problem Generating 3D scenes from few images with geometric consistency.
method Combines NeRF and VAE, incorporating shared geometric structure.
result NeRF-VAE can infer and render geometrically-consistent scenes from unseen environments.
The paper classifies isometries on specific Lie groups.
problem Classifying isometries on nonnilpotent, solvable 3D Lie groups.
method Proving automorphisms are the only isometries for rank two Almost-Riemannian Structures.
result A classification result for rank two ARSs on nonnilpotent, solvable 3D Lie groups.
Solves Yamabe problem for 3D metrics of Sobolev class .
problem Yamabe problem on closed 3-manifolds for Sobolev metrics.
method Developed elliptic theory for conformal Laplacian on rough metrics.
result Existence, regularity, and blow-up analysis for Green function.
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.
We present a three-dimensional graph convolutional network (3DGCN), which predicts molecular properties and biochemical activities, based on 3D molecular graph. In the 3DGCN, graph convolution is unified with learning operations on the vector to handle the spatial information from molecular topology. The 3DGCN model ex…