2d dualities linked to 4-simplex triangulation.
problem Exploring dualities between 2d and 3d theories via 4-manifold geometry.
method Using Pachner moves and supersymmetric half-indices.
result Identified IR dualities and abelian dualities.
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48 results for “2d $\mathcal{N}=(0”
Kontsevich flow simplified for 2D Poisson structures.
problem Formality conjecture for 2D Poisson structures.
method Universal flow construction and Poisson-cohomology triviality proof.
result For , the flow is Poisson-cohomology trivial.
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.
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 layers and complexity.
result Exceeds convolutional and graph neural network baselines in long-range dependency modeling.
A new complex space resolves projective structures on surfaces.
problem Understanding projective structures on compact surfaces.
method Proposed a complex analytic space and analyzed it for .
result The space naturally resolves the orbifold locus of .
New 4-manifold invariants derived from vertex algebras.
problem Computing 4-manifold invariants, including new and old ones.
method Using chiral correlation functions in half-twisted 2d theories from compactified fivebranes.
result Prediction of structural properties of multi-monopole invariants and non-abelian generalizations.
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.
2d GLSM connects Berry connections to Coulomb branch via difference equations.
problem Connecting Berry connections to Coulomb branch via difference equations.
method Boundary 2d GLSM, 3d A-twisted gauge theory, spectral data of monopoles.
result Coulomb branch algebra actions derived from 2d GLSM.
New method speeds up Bayesian optimization in high dimensions.
problem High-dimensional expensive function optimization struggles.
method Structured automatic differentiation for kernel matrices.
result First-order Bayesian optimization scalable to high dimensions.
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.
FIRAL is a scalable active learning algorithm for multiclass classification.
problem Scalability issues with FIRAL in large datasets.
method Proposed an approximate algorithm with reduced storage and computational complexity.
result Demonstrated strong scalability and accuracy on large datasets.
Abstract M5 branes on ADE singularities yields BPS spectrum and partition functions.
problem Determine the BPS spectrum and partition functions for M5 branes on ADE singularities.
method Analyze 6d SCFTs on geometric backgrounds, using contributions from BPS strings and particles.
result Explicit expressions for BPS string and particle contributions to partition functions.
This paper improves 3D pose recovery from 2D images using non-convex regularization.
problem 3D object pose recovery from 2D images.
method Proposes non-convex regularization with leaky capped ℓ1-norm (LCNR) and multi-stage optimization.
result Theoretical analysis shows estimation error decreases with optimization stages.
In this paper we classify maps from a torus phase space to , the space of , non-singular hermitian operators up to equivariant homotopy. The equivariance is with respect to a time-reversal involution on and an involution on defining a certain symmetry class. Furthe…
Study Berry connections for 2d GLSMs, linking to cohomology theories.
problem Quantise ground states of 2d GLSMs on a circle.
method Relate periodic monopole solutions to difference modules and vector bundles with filtrations.
result Derive novel difference equations for brane amplitudes and vortex partition functions.
Method constructs quantum holonomies for BPS states on line defects.
problem Determining spins of BPS states on line defects in 4d theories.
method Combines spectral networks and skein algebra.
result Confirms positivity conjectures in physics and math.
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.
Theoretical analysis of CNNs' inductive biases and their efficiency in approximating functions.
problem Understanding and optimizing the inductive biases in deep CNNs.
method Theoretical analysis combining multichanneling, downsampling, weight sharing, and locality.
result Deep CNNs with depth can approximate any continuous function, and require samples for sparse functions.
We propose a new description of 3d theories which do not admit conventional Lagrangians. Given a quiver and a mutation sequence on it, we define a 3d theory in such a way that the partition function of the theory coincides with the cluster partition f…
Compactifies strata of d-differentials in genus 0.
problem Compactify strata of d-differentials in genus 0.
method Specify an ideal sheaf and show isomorphism to blow-up of .
result Incidence variety compactification is isomorphic to the blow-up of .
We give, using an explicit expression obtained in [V. Jones, Ann. of Math. 126, 335 (1987)], a basic hypergeometric representation of the HOMFLY polynomial of torus knots, and present a number of equivalent expressions, all related by Heine's transformations. Using this result the s…
Study of surface defects in gauge theories leads to duality and separation of variables.
problem Understanding surface observables and their transitions in gauge theories.
method Utilized Fourier transformations and spectral problems to derive dualities and separation of variables.
result Exact duality between spectral problems of spin chains and Gaudin models.
Study of 2d gauged linear sigma models to derive difference equations and spectral data.
problem Understanding monopole solutions and their spectral data in 2d gauged models.
method Analyzing ground states and cohomology of supercharges to derive difference modules and equations.
result Derived novel difference equations for brane amplitudes and hemisphere partition functions.
Extends Double Field Theory with new kinematical structure.
problem Formalizing Double Field Theory on para-Hermitian manifolds.
method Constructing a canonical connection and generalised Lie derivative for a Leibniz algebroid.
result Integrability conditions for symmetry algebra closure under non-flat and non-constant and .
Statistical and machine-learning algorithms are frequently applied to high-dimensional data. In many of these applications data is scarce, and often much more costly than computation time. We provide the first sample-efficient polynomial-time estimator for high-dimensional spherical Gaussian mixtures. For mixtures of a…
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.
5D gauge theories are dual to 3D and 2D models via Floer homologies.
problem Exploring dualities in 5D gauge theories and their 3D and 2D counterparts.
method Using Landau-Ginzburg models and Floer homologies, the paper establishes dualities between different gauge theories and their associated homologies.
result Dual -categories of Floer homologies are derived, proving mirror symmetry and Langlands duality.
Introduces Lax-Kirchhoff moduli spaces for quivers and Lie groups.
problem Constructing moduli spaces for quivers and Lie groups.
method Introduces Lax equations and Kirchhoff conditions, constructs slices, and uses Marsden-Weinstein reduction.
result Proves is a finite-dimensional smooth symplectic manifold with a Hamiltonian action of .
Quantum memory limits set by relativity theory.
problem Quantum memory efficiency and relativity constraints.
method Relativistic quantum field theory and Lieb-Robinson bounds.
result Quantum memory capacity is limited by fundamental physics.
A new algorithm reduces the time and space complexity for multinomial logistic bandits.
problem High-dimensional feedback in multinomial logistic bandits makes existing algorithms inefficient.
method Integrates frequent directions matrix sketching into OFUL-MLogB to reduce time and space complexity.
result Achieves a regret bound of .
New method reduces computational cost of Gaussian process regression.
problem High computational cost of exact Gaussian process inference for large datasets.
method Sparse variational inference with inducing variables.
result KL-divergence between approximate and exact posterior can be made arbitrarily small.
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.
This research uses PointNets to detect 2D objects from radar data.
problem Detecting 2D objects from sparse radar data for automated driving.
method Adapting PointNets for radar data, performing 2D object classification and bounding box regression.
result Demonstrates the potential of PointNets for 2D object detection in radar data.
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
The study proves that in normal tilings, at least two vertices are required per cell.
problem Understanding the minimum number of vertices required in normal tilings.
method The research examines both periodic and monohedral tilings in 2D, proving the minimum number of non-smooth vertices required.
result The study confirms that for normal tilings, at least two vertices are necessary per cell.
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.
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 that separates two subsystems of quantum strongly coupled SU(N) superconformal gauge theory. We extend this result and calculate en…
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.
Paper classifies brain signals using eigenvalues for 2D and 3D educational content questions.
problem Classifying brain signals for 2D and 3D educational content questions.
method Eigenvalues of covariance matrix used as features; KNN and SVM classifiers applied.
result No significant difference in learning, memory retention, and recall between 2D and 3D educational content.
The paper explores gauge theory invariants and their duals via topological-holomorphic twist.
problem Understanding gauge theory invariants and their duals in 4d and 2d.
method Topological-holomorphic twist of N=4 supersymmetric gauge theory.
result Derived novel topological and holomorphic invariants and their Langlands duals.
2D tissue model predicts neurotoxicity more accurately and robustly.
problem Fast and accurate prediction of developmental neurotoxicity.
method Machine learning on 2D bio-engineered tissue models.
result 2D model outperforms 3D model in accuracy and robustness.
Paper presents efficient algorithms for robust PCA with reduced computational complexity.
problem Robust PCA in fully and partially observed settings, especially when corruptions are present.
method Non-convex optimization approach using gradient descent.
result Significant reduction in computational complexity compared to existing algorithms.
Flexible pipeline for 3D vehicle detection from 2D images.
problem Current methods lack 3D perception of vehicles and other objects.
method Adopt any 2D detection network, fuse with 3D point cloud, develop model fitting algorithm, refine with CNN.
result 3D detection results rank second among algorithms, demonstrating competencies.
Proves a unique connection for Born geometry.
problem Consistency of string dynamics under T-duality.
method Proves a unique connection preserving the Born structure.
result Resolves a fundamental ambiguity in double field theory.
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.
Geometric interpretation of 2d-4d wall-crossing formulas.
problem Understanding wall-crossing phenomena in coupled 2d-4d systems.
method Deformation theory of holomorphic pairs and relation to scattering diagrams.
result Geometric interpretation of wall-crossing formulas.
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.