Study on a specific type of Riemannian manifolds constructed from 2D space-forms.
problem Characterizing and understanding new types of Riemannian manifolds.
method Constructed as a product of a real line and a 2-dimensional Riemannian space-form, with metrics derived from cone and hyperbolic extensions.
result Characterized and studied in terms of their curvature properties.
New model preserves symmetry in multivariate time series, improving performance.
problem Implicit ordering in MTS models violates inherent exchangeability.
method Permutation-equivariant 2D state space model with canonical architecture.
result Eliminates sequential dependency chains and simplifies stability analysis.
Study of curve evolution in 2D space forms converging to a circle.
problem Understanding curve evolution in 2D space forms.
method Inverse curvature flow with normal speed defined by weighted inverse curvature and support function.
result Solutions exist for all time and converge exponentially to a standard round geodesic circle.
New method for optimizing risk in financial models using Fourier transforms.
problem Optimizing risk in financial models with multi-period mean-CVaR.
method Strictly monotone 2D integration scheme via Fourier-trained transition kernels.
result Established robust and accurate optimization method for financial models.
Introduces a new phase space for 2D supersymmetric sigma models.
problem Developing a new Hamiltonian formulation for 2D supersymmetric sigma models.
method Introduces a phase space with spinorial momenta and derives a covariant Hamiltonian formulation.
result Shows the existence of additional supersymmetries in the new formulation.
We present algorithms to compute the topology of 2D and 3D hyperelliptic curves. The algorithms are based on the fact that 2D and 3D hyperelliptic curves can be seen as the image of a planar curve (the Weierstrass form of the curve), whose topology is easy to compute, under a birational mapping of the plane or the spac…
The paper classifies 2D complete Lagrangian self-expanders in complex 2-space.
problem Classifying complete Lagrangian self-expanders in complex 2-space.
method Obtained a classification theorem.
result A classification of 2D complete Lagrangian self-expanders with constant squared norm of the second fundamental form.
Paper classifies special slant surfaces with varying curvature.
problem Classifying surfaces with non-constant mean curvature.
method Analyzing special slant surfaces in complex space forms.
result Complete classification of surfaces with non-constant mean curvature.
This paper proposes grid cells encode position via a conformal isometric embedding of 2D physical space.
problem Hexagonal grid firing patterns in grid cells.
method Learning a distance-preserving position embedding in neural space using a recurrent neural network.
result The conformal isometric embedding of 2D physical space into neural space explains hexagonal grid firing patterns.
We build a connection between topology of smooth 4-manifolds and the theory of topological modular forms by considering topologically twisted compactification of 6d (1,0) theories on 4-manifolds with flavor symmetry backgrounds. The effective 2d theory has (0,1) supersymmetry and, possibly, a residual flavor symmetry. …
Designs a Cellular Automata rule for forming touching loop patterns.
problem Forming stable touching loop patterns in a 2D grid.
method Developed a Cellular Automata rule that uses templates to cover the space and match patterns.
result The rule successfully evolves stable touching loop patterns in a 2D grid.
In this paper, we study the bound states of quantum layers. We prove that for the quantum layer built over a parabolic manifold which is not totally geodesic, if the second fundamantal form decays sufficiently fast, then the bound states exist. In the 2d case, we prove that the quantum layer over a convex surface whose…
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.
Study of evolutoids and involutoids of convex curves in 2D space forms.
problem Characterizing evolutoids and involutoids of convex curves in various 2D space forms.
method Explicit parametrization and analysis of geodesics, singularity theory, and wavefronts.
result Existence and properties of involutoids for convex curves in M−1,0. Study classifies equidistant decompositions in 2D spaces.
problem Classifying equidistant decompositions in 2D spaces.
method Full classification of decompositions in Euclidean plane and sphere.
result Complete classification of equidistant decompositions in 2D spaces.
Curvature of 2D subsets preserved in their space.
problem Understanding curvature of subsets in 2D spaces.
method Analyzing subsets with vanishing first homology.
result Closed subsets inherit curvature bounds from ambient spaces.
Study Ricci vector fields on 2D space with diagonal metrics.
problem Understanding Ricci vector fields on 2D space with specific metrics.
method Examined Ricci vector fields on R2 with a diagonal metric. result Characterized Ricci vector fields on R2 with a diagonal metric. The paper studies how grid cell patterns emerge in neural networks.
problem Understanding how grid cells in the brain form hexagonal firing patterns.
method Training recurrent neural networks with conformal normalization of velocity inputs.
result Conformal normalization is crucial for the emergence of hexagonal grid patterns in neural networks.
This paper analyzes shallow ReLU networks in L^p and Sobolev spaces, focusing on approximation and generalization.
problem Approximation and generalization of shallow ReLU networks in L^p and Sobolev spaces.
method Spherical harmonic analysis and embeddings into spectral Barron spaces for L^p spaces, path-norm control for Sobolev spaces.
result Minimax-optimal rates for nonparametric regression with shallow ReLU networks under path-norm control.
Many mobile robots rely on 2D laser scanners for localization, mapping, and navigation. However, those sensors are unable to correctly provide distance to obstacles such as glass panels and tables whose actual occupancy is invisible at the height the sensor is measuring. In this work, instead of estimating the distance…
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 2D spaces with curvature, finding a graph structure.
problem Understanding the geometry of 2D spaces with curvature constraints.
method Analyzing spaces as unions of disks, identifying singular points.
result Obtained a graph structure of topological singular points.
Self attention mechanisms have become a key building block in many state-of-the-art language understanding models. In this paper, we show that the self attention operator can be formulated in terms of 1x1 convolution operations. Following this observation, we propose several novel operators: First, we introduce a 2D ve…
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.
The Grove-Searle theorem on 2d manifolds with 8 or less symmetry groups has positive Euler characteristic.
problem Proving positive Euler characteristic for 2d manifolds with specific symmetry groups.
method Direct proof and analysis of fixed point components N with geodesic properties.
result Fixed point components N have amazing geodesic properties and can be S^2, RP^2, CP^d, HP^d, etc.
Study of symmetries in a 2D space with specific metric properties.
problem Understanding symmetries in a 2D space with diagonal metrics.
method Analyzing Killing vector fields under specific restrictions on Lamé coefficients.
result Concretely described symmetries of the metric under given conditions.
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.
The Strominger conjecture is confirmed for compact Hermitian manifolds in 2D and special higher dimensions.
problem Determining conditions for a Hermitian metric to be Kähler based on the Strominger connection's curvature.
method Analyzing the Strominger connection's holomorphic sectional curvature in compact Hermitian manifolds.
result The Strominger conjecture is confirmed in 2D and special higher dimensions.
We present a local formulation for 2D Discrete Exterior Calculus (DEC) similar to that of the Finite Element Method (FEM), which allows a natural treatment of material heterogeneity (element by element). It also allows us to deduce, in a robust manner, anisotropic fluxes and the DEC discretization of the pullback of 1-…
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.
Study 2D spaces with curvature, focusing on structure and approximations.
problem Characterize and understand 2D metric spaces with curvature constraints.
method Lipschitz homotopy approximations, curvature measures, convergence analysis.
result Established Gauss-Bonnet Theorem and characterized spaces.
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.
iSTFTNet2 improves iSTFTNet's speed and lightness with 1D-2D CNN.
problem Efficiently synthesizing high-fidelity speech.
method Improved iSTFTNet using 1D-2D CNNs for temporal and spectrogram structures.
result iSTFTNet2 is faster and more lightweight with comparable speech quality.
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.
Sharp inequalities for star bodies in 2D space.
problem Understanding star bodies in 2D space.
method Sharp inequalities for star bodies in R2. result New inequalities and proofs for star bodies.
Existing techniques to compress point cloud attributes leverage either geometric or video-based compression tools. We explore a radically different approach inspired by recent advances in point cloud representation learning. Point clouds can be interpreted as 2D manifolds in 3D space. Specifically, we fold a 2D grid on…
Develops unisolvent weights for Nédélec second family finite elements in 2D.
problem Finding efficient degrees of freedom for Nédélec second family finite elements.
method Uses techniques of homological algebra to obtain degrees of freedom for differential forms.
result Provides a family of unisolvent and minimal physical degrees of freedom for Nédélec second family finite elements.
New neural model processes 2D data with long-range dependencies efficiently.
problem Limited receptive field of convolutions for complex 2D tasks.
method Proposes Matrix Shuffle-Exchange network with O(logn) layers and O(n2logn) complexity. result Exceeds convolutional and graph neural network baselines in long-range dependency modeling.
Open 2D TFTs extend to closed theories with circle value as Hochschild homology.
problem Extending open 2D TFTs to closed theories.
method Using symmetric monoidal ∞-categories and Hochschild homology.
result Open 2D TFTs admit initial open-closed extensions.
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.
Paper finds new criteria for conjugate points in fluid flows.
problem Finding conjugate points in steady 2D Euler flows.
method Develops a new sufficient criterion for conjugate points, applies to any rotational cell, and uses a general construction of steady fluid surfaces.
result Improves on existing criteria and captures all known conjugate points in rotational cells.
Modeling financial market dynamics with 2D Levy flights.
problem Capturing the complex, scaling laws in financial market dynamics.
method 2D Lévy flight model applied to S\&P 500 index prices.
result Empirical spectral properties match model predictions.
Study geodesic curvature in 2D Alexandrov spaces, generalizing results from spaces with curvature above.
problem Geodesic curvature in Alexandrov spaces with curvature below.
method Comparison and rigidity theorems for geodesic curvatures.
result Generalized known results for geodesic curvature in spaces with curvature above.
The paper simplifies complex 2D functions near their critical points.
problem Simplifying smooth functions on 2-manifolds near critical points.
method Explicit construction of coordinate changes to canonical form.
result Estimates the radius of required neighbourhoods for specific singularity types.
We propose a method to generate multiple diverse and valid human pose hypotheses in 3D all consistent with the 2D detection of joints in a monocular RGB image. We use a novel generative model uniform (unbiased) in the space of anatomically plausible 3D poses. Our model is compositional (produces a pose by combining par…
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.
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.
In this work we reduce undersampling artefacts in two-dimensional (2D) golden-angle radial cine cardiac MRI by applying a modified version of the U-net. We train the network on 2D spatio-temporal slices which are previously extracted from the image sequences. We compare our approach to two 2D and a 3D Deep Lear…