Constructs a topological cover of real line's multiplicative group.
problem Topological cover of real line's multiplicative group.
method Homological algebra, 2D Lorentz geometry, high-school trigonometry.
result Interesting topological cover constructed.
We propose that a simple, Lagrangian 2d N=(0,2) duality interface between the 3d N=2 XYZ model and 3d N=2 SQED can be associated to the simplest triangulated 4-manifold: the 4-simplex. We then begin to flesh out a dictionary between more general triangulated 4-manifolds with boundar…
A novel method compresses point cloud attributes by folding them onto a 2D grid.
problem Efficiently compressing point cloud attributes for storage and transmission.
method Interpreting point clouds as 2D manifolds, folding onto a grid, and mapping attributes to the grid using optimized methods.
result The proposed folding-based approach achieves performance comparable to state-of-the-art codecs.
Minimalistic model captures head direction system properties.
problem Representing head direction system in a high-dimensional space.
method A minimalistic representation model of the rotation group U(1), including fully connected and convolutional versions.
result Emergence of Gaussian-like tuning profiles and 2D circle geometry in both model versions.
Method finds domain of Laplace-Beltrami operator on 2D almost-Riemannian manifolds.
problem Determining the domain of the Laplace-Beltrami operator on 2D almost-Riemannian manifolds with tangency points.
method Using tools from Lie groupoids, natural domains of perturbations are found.
result Method allows treatment of geometries with tangency points.
Investigates stochastic networks on disordered lattices, converging to Brownian web in 2D.
problem Stochastic networks on disordered lattices.
method Directed spanning forests on randomly perturbed lattices.
result DSF converges to Brownian web in 2D under diffusive scaling.
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.
The study constructs AdS manifolds from Gromov-Thurston manifolds.
problem Creating hyperbolic and anti-de Sitter structures from Gromov-Thurston manifolds.
method Explicit correspondence between quasifuchsian AdS manifolds and compact quotients of Ø(2d,2)/U(d,1).
result Existence of quasifuchsian AdS manifolds and hyperbolic ends with specified boundary.
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…
Research explores Lorentzian distances on a specific geometric plane.
problem Investigating Lorentzian structures on a 2D geometric plane.
method Analyzes sectional curvature, attainable sets, and Lorentzian length maximizers.
result Describes distance properties and spheres in the context of Lorentzian geometry.
Surveying mass in 2D hyperbolic geometry, overcoming challenges via minimisation.
problem Defining mass in 2D hyperbolic geometry.
method Minimisation using positive energy theorem and gluing theorems.
result Construction of novel initial data sets with controlled mass.
Cone structures in quantum field theory linked to information geometry.
problem Understanding geometric structures in quantum field theory.
method Analyzing invariant cones under modular automorphism groups and their relation to Wishart laws.
result Explicit connection between CAH cones and Wishart laws.
We show that the smooth geometry of a hyperbolic 3-manifold emerges from a classical spin system defined on a 2d discrete lattice, and moreover show that the process of this "dimensional oxidation" is equivalent with the dimensional reduction of a supersymmetric gauge theory from 4d to 3d. More concretely, we propose a…
New geometries derived from symplectic Monge-Ampère structures.
problem Exploring new generalized geometries from symplectic Monge-Ampère structures.
method Inspired by Hu, Moraru, and Svoboda, constructing new geometries from non-degenerate 2D symplectic Monge-Ampère structures.
result Non-degenerate Monge-Ampère structures give rise to quadric surfaces of generalized almost geometries.
Arboricity of manifolds is explored, with specific results for 2D surfaces.
problem Understanding the arboricity of different types of manifolds.
method Analyzing discrete 2-spheres, other 2D surfaces, and d-manifolds of higher dimensions.
result Arboricity of 2D surfaces is 3 or 4, and for higher dimensions, it can be arbitrarily large.
A 2D Riemannian space has only 2 injective geodesics.
problem Characterizing geodesics in Riemannian planes.
method Perturbation of a surface of revolution with contracting ends.
result Found a complete Riemannian plane with exactly two injective geodesics.
In this note we obtain the characterization for asymptotic directions on various subgroups of the diffeomorphism group. We give a simple proof of non-existence of such directions for area-preserving diffeomorphisms of closed surfaces of non-zero curvature. Finally, we exhibit the common origin of the Monge-Ampere equat…
Lectures detail field theory dynamics and exact WKB analysis.
problem Understanding quantum field theories with four supercharges.
method Combining WKB analysis with 2D quantum field theories.
result Partition function characterizes non-perturbative dynamics.
The paper develops a theory linking Hamiltonian and quasi-Hamiltonian manifolds.
problem Understanding the deformation of Hamiltonian quasi-Poisson manifolds to Hamiltonian Poisson manifolds.
method Introduces a generalized Hamiltonian deformation theory and constructs a topological quantum field theory.
result Shows that the imploded cross section of the double $D(G)_\imp$ deforms to the implosion of the cotangent bundle $T^*G_\imp$.
Six quaternionic lines with optimal angles found in 2D quaternion space.
problem Finding optimal configurations of quaternionic lines in 2D space.
method Simple presentation of lines as orbit of a reflection group, finding other optimal designs.
result Optimal spherical designs of 10, 15, and 20 lines in quaternion space.
Langmuir-Blodgett films (LB-films) consist from few LB-monolayers which are high structured nanomaterials that are very promising materials for applications. We use a geometrical approach to describe structurization into LB-monolayers. Consequently, we develop on the 1-jet space J^1([0,\infty),R^2) the single-time Lagr…
In this paper, we present a deep-learning based method for estimating the 3D structure of a bone from a pair of 2D X-ray images. Our triplet loss-trained neural network selects the most closely matching 3D bone shape from a predefined set of shapes. Our predictions have an average root mean square (RMS) distance of 1.0…
2D CNNs approximate Korobov functions with near-optimal rates.
problem Approximating Korobov functions using 2D CNNs.
method Constructive approach for 2D CNNs with ReLU activations and fully connected layers.
result 2D CNNs achieve near-optimal approximation rates for Korobov functions.
We use the conformal invariance and the holographic correspondence to fully specify the dependence of entanglement entropy on the extrinsic geometry of the 2d surface Σ that separates two subsystems of quantum strongly coupled N=4 SU(N) superconformal gauge theory. We extend this result and calculate en…
It has been known for a while that the effective geometrical description of compactified strings on d-dimensional target spaces implies a generalization of geometry with a doubling of the sets of tangent space directions. This generalized geometry involves an O(d,d) pairing η and an O(2d) generalized metric $\m…
Let (M,g,J) be a compact Hermitian manifold with a smooth boundary. Let Δp and Dp be the realizations of the real and complex Laplacians on p forms with either Dirichlet or Neumann boundary conditions. We generalize previous results in the closed setting to show that (M,g,J) is Kaehler if and only if $Spec(Δ_p)=S…
Study of 2D Lorentzian anti-de Sitter plane using geometric control theory.
problem Understanding extremal trajectories and reachable set on anti-de Sitter plane.
method Geometric control theory and differential geometry.
result Construction of optimal synthesis and description of Lorentzian distance.
Study optimizes submatrices in 2D spaces, linking to polygon geometry.
problem Optimizing submatrices in 2-dimensional linear subspaces. method Optimization problem for isoperimetric polygons in Euclidean spaces.
result New geometrical perspective on a linear subspace problem.
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.
Derive bihamiltonian structure for rational reduction of 2D-Toda hierarchy
problem Derive bihamiltonian structure for rational reduction of 2D-Toda hierarchy
method Direct computations
result Derive local bihamiltonian structure
We study geometric consistency relations between angles on 3-dimensional (3D) circular quadrilateral lattices -- lattices whose faces are planar quadrilaterals inscribable into a circle. We show that these relations generate canonical transformations of a remarkable ``ultra-local'' Poisson bracket algebra defined on di…
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.
Transthoracic echo is one of the most common means of cardiac studies in the clinical routines. During the echo exam, the sonographer captures a set of standard cross sections (echo views) of the heart. Each 2D echo view cuts through the 3D cardiac geometry via a unique plane. Consequently, different views share some l…
A new privacy-preserving mechanism for shapes on manifolds.
problem Privacy-preserving sanitization of shapes on curved manifolds.
method Developed a K-norm gradient mechanism on Riemannian manifolds.
result The K-norm gradient mechanism offers better control over sensitivity than the Laplace mechanism on positively curved manifolds.
Geometric proof shows regularity of anisotropic minimal surfaces in 2D.
problem Regularity of anisotropic minimal surfaces in 2D.
method Geometric proof using surface energy and strict convexity.
result All anisotropic surface minimizers in 2D are locally disjoint unions of line segments.
The paper quantizes Hessian structures on R^2 using KV-algebras.
problem Quantizing Hessian structures on a 2D space.
method Deformation quantization within Koszul-Vinberg algebras.
result Established links between deformation theory and Hessian geometry.
The central problem of strip theory is the calculation of potential flowaround 2D sections. One particular method of solutions to this problem is conformal mapping of the body section to the unit circle over which a solution of potential flow is available. Here, a new multiparameter conformal mapping method is presente…
For many automated driving functions, a highly accurate perception of the vehicle environment is a crucial prerequisite. Modern high-resolution radar sensors generate multiple radar targets per object, which makes these sensors particularly suitable for the 2D object detection task. This work presents an approach to de…
We review the construction of homological evolutionary vector fields on infinite jet spaces and partial differential equations. We describe the applications of this concept in three tightly inter-related domains: the variational Poisson formalism (e.g., for equations of Korteweg-de Vries type), geometry of Liouville-ty…
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.
Framework predicts Navier-Stokes solutions on 2D domains using graph neural networks.
problem Predicting stationary Navier-Stokes solutions in non-parametrized 2D geometries.
method Graph-based multi-fidelity learning framework combining reduced-order models, Transformers, and Mamba architectures.
result Mamba architecture reduces computational cost while maintaining performance.
The paper establishes T-duality for 2D σ-models with H-flux.
problem T-duality for 2D σ-models with H-flux.
method Localization and graded T-duality map (graded Hori morphism).
result Establishes the most general version of T-duality for Type II String Theory.
New theorem shows embedding restrictions for manifold skeletons.
problem Embedding restrictions for triangulated manifolds.
method Proves van Kampen-Flores theorem for manifolds with specific Stiefel-Whitney classes.
result Triangulated manifolds with non-trivial Stiefel-Whitney classes cannot embed into R2d. Computes a new metric quantity Y(M) for Riemannian 2d-manifolds.
problem No simple metric quantity exists for Riemannian manifolds.
method Defines Y(M) and Y_disc(M) involving sectional curvatures and computes them for specific manifolds.
result Y(M) and Y_disc(M) differ from the Euler characteristic and can be positive or negative.
We develop a theory to represent dislocated single crystals at the mesoscopic scale by considering concentrated effects, governed by the distribution theory combined with multiple-valued kinematic fields. Our approach gives a new understanding of the continuum theory of defects as developed by Kroener (1980) and other …
A simple Almost-Riemmanian Structure on a Lie group G is defined by a linear vector field and dim(G)-1 left-invariant ones. We state results about the singular locus, the abnormal extremals and the desingularization of such ARS's, and these results are illustrated by examples on the 2D affine and the Heisenberg groups.…
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.
Transformer-M learns molecular data in 2D or 3D formats.
problem Learning models for molecules are limited to specific data formats.
method Developed a Transformer-based model that can handle 2D and 3D molecular data.
result Transformer-M achieves strong performance on both 2D and 3D molecular tasks.