Improved sleep stage classification using FT surrogates for class-balanced data.
problem Class imbalance in noisy signals for sleep stage classification.
method Generated FT surrogates to balance the CAPSLPDB database and trained a CNN.
result Surrogate-based augmentation improved mean F1-score by 7%.
A hybrid framework uses machine learning to price options faster and more accurately.
problem Rapid recalibration of option pricing models in dynamic markets.
method Integrates smooth offset algorithm with supervised machine learning models.
result Surrogate pricing operators achieve up to 1000x speedup over direct SOA evaluation.
DAFNO learns surrogates for complex systems on irregular geometries.
problem Learning accurate surrogates for complex physical systems on irregular geometries.
method DAFNO incorporates a smoothed characteristic function in the integral layer architecture of FNOs, leveraging FFT for rapid computations.
result DAFNO achieves state-of-the-art accuracy on material modeling and airfoil simulation datasets.
Paper proves Fourier transform for valuations, simplifying previous work.
problem Existence of isomorphism for translation-invariant smooth valuations.
method Directly describes Alesker's isomorphism in terms of Fourier transform on functions.
result Simple proofs of Alesker's Fourier transform properties, including a previously conjectured result.
Simplified Butterfly-Net2 improves CNN efficiency in solving PDEs and signal processing tasks.
problem Improving CNN efficiency in solving PDEs and signal processing tasks.
method Introducing BNet2, a simplified Butterfly-Net, and Fourier transform initialization.
result BNet2 achieves similar accuracy as CNN but with fewer parameters and improves accuracy over randomly initialized CNN.
A new algorithm computes Fourier coefficients for a specified range efficiently.
problem Inefficiency in FFT due to fixed output size for all applications.
method Fast Partial Fourier Transform (PFT) that allows specifying the range of Fourier coefficients to compute.
result PFT achieves significant speedup over state-of-the-art FFT algorithms for small output sizes.
Paper computes link determinants using Fourier-Hadamard transforms.
problem Computing determinants of complex link structures.
method Fourier-Hadamard transforms of Boolean functions.
result Determinant of centrally symmetric links with even components equals zero.
The Fourier transform of Heegaard Floer d-invariants helps classify 3-manifolds.
problem Classifying 3-manifolds up to integer homology cobordism.
method Exploring the Fourier transform of Heegaard Floer d-invariants.
result Lens spaces are cancellable in the monoid of 3-manifolds up to integer homology cobordism.
X-ray transform on H-type groups solved, revealing function injectivity.
problem Injectivity in sub-Riemannian geometry.
method Fourier Slice Theorem adapted to H-type groups.
result Integrable functions on H-type groups are uniquely determined by their integrals over geodesics.
Proves conditions for Fourier transforms in rank 1 symmetric spaces.
problem Understanding Fourier transform bounds in symmetric spaces.
method Proves sufficient and necessary conditions using Lipschitz and Fourier type integral conditions.
result Establishes bounds for Fourier transforms in rank 1 symmetric spaces with specific moduli of continuity.
This work improves Fourier pricing for multi-asset options using RQMC with domain transformation.
problem Efficiently pricing multi-asset options in high dimensions with Fourier methods.
method Randomized quasi-Monte Carlo (RQMC) with domain transformation to handle singularities.
result RQMC with domain transformation provides accurate and scalable Fourier pricing for multi-asset options.
New graph Fourier transform distinguishes directions in multi-dimensional signals.
problem Existing graph Fourier transform fails to distinguish directions in multi-dimensional signals.
method Algebraic properties of Cartesian products rearrange 1-D spectra into multi-dimensional frequency domain.
result Solves multi-valuedness of spectra and enables directional frequency analysis.
The paper proposes a novel method for optimizing bounded functions using Fourier series and Ricci flow.
problem Optimizing bounded functions using Fourier series and Ricci flow.
method Approximating the initial manifold using Fourier series and center/boundary sampling. Iteratively evolving the manifold using geodesic hyper-spheres and inverse Ricci flow.
result The method allows for the optimization of high curvature regions and achieves potential global optima.
Algorithm describes Fourier transform of Stokes data at infinity.
problem Understanding the Fourier transform of Stokes data at infinity.
method Topological description and algorithmic approach using recent results and language of Stokes local systems.
result Explicit isomorphisms between wild character varieties are induced.
The paper studies Fourier-Laplace transforms in polynomial OU volatility models for option pricing.
problem Calibrating and pricing options in polynomial Ornstein-Uhlenbeck volatility models.
method Analyzes Fourier-Laplace transforms, connects to Riccati equations, and develops numerical schemes.
result Establishes existence and solution for Riccati equations and provides efficient numerical methods.
New algorithms learn sparse set functions in non-orthogonal Fourier bases.
problem Learning sparse set functions in non-orthogonal Fourier bases.
method Novel algorithms using non-orthogonal Fourier transforms.
result At most nk−klog2k+k queries for k non-zero Fourier coefficients. A new sampling strategy for random Fourier features reduces computation time and improves prediction performance.
problem Efficient generation of random Fourier features for kernel approximation.
method Surrogate leverage weighted sampling guided by kernel alignment, avoiding matrix inversion.
result Time complexity reduced from O(ns^2+s^3) to O(ns^2), comparable or slightly better prediction performance.
Transformers improve with Fourier integral attentions.
problem Inefficiency of dot-product attention in capturing feature dependencies.
method Interpreted attention as kernel regression, proposed FourierFormer with generalized Fourier integral kernels.
result FourierFormer achieves better accuracy and reduces redundancy.
The paper derives statistics of multi-factor functions from their Fourier transforms.
problem Deriving statistics of multi-factor functions from Fourier transforms.
method Developed an m-Coefficient/Index Annihilation Theorem to analyze the moments of a function from its Fourier transform.
result The mth moment of a function becomes a series of terms, each with precisely m Fourier coefficients, and the indices sum to zero.
We prove that the Fourier--Laplace--Nahm transform for connections on the projective line is a hyper-Kähler isometry.
Study spherical Fourier transform on hypergeometric type harmonic manifolds.
problem Spherical Fourier transform on harmonic Hadamard manifolds.
method Representation of spherical functions by Gauss hypergeometric functions.
result Inversion formula, convolution rule, and Plancherel theorem are derived.
Efficient trainable front-end for neural speech enhancement.
problem Inefficient STFT front-ends in neural speech enhancement models.
method Butterfly mechanism for Fast Fourier Transform, trainable STFT window.
result Accuracy and efficiency improvements for low-compute systems.
New method uses Fourier transform as prior for kernel approximation.
problem Approximating kernel functions efficiently.
method Pseudo-Bayesian learning with kernel Fourier transform as prior.
result Derived generalization bounds optimized by pseudo-posterior.
Paper improves tensor completion using unitary transforms.
problem Robust tensor completion for various datasets.
method Transformed tensor SVD with unitary matrices.
result Recovered images have better PSNR than traditional methods.
In this paper we prove a new inversion theorem and a refinement of an old support theorem for two Radon transforms on a symmetric space. Included are some new identities for the Abel transform and some results about the Fourier transform from a joint work with Rawat, Sengupta and Sitaram.
Given two compact hyperkähler surfaces X and Y and a holomorphic vector bundle Q on X×Y, which is a generalized instanton, one can define a Fourier-Mukai transform, which, under suitable assumptions, maps vector bundles on X to vector bundles on Y. If X and Y are dual complex tori, this transform …
Abstract: Analogs of Hilbert-Chow morphism for generalized discriminants.
problem No specific problem stated in the abstract.
method No specific method stated in the abstract.
result No specific key result stated in the abstract.
New algorithm for 2D SWDFT reduces redundant calculations.
problem Redundant calculations in overlapping windows for 2D SWDFT.
method Tree data structure based on Cooley-Tukey FFT for efficient computation.
result Our algorithm reduces operations to O(N0N1n0n1). Enhances Fourier estimator performance for asynchronous event-data.
problem Improving correlation and covariance estimation on event-data.
method Implement and test NUFFT methods with different averaging kernels.
result Demonstrates improved performance and relationship between averaging scales.
New Fourier transform method handles missing data and asynchronous observations.
problem Volatility inference with missing or asynchronous data.
method Spectral framework using Fourier transforms.
result Consistent volatility functional estimation with limit distributions.
A Fourier transform approach optimizes clustering algorithms.
problem Optimizing clustering algorithms for accuracy and reliability.
method Fourier transform and Gaussian filtering to smooth density functions, detecting peaks as cluster centroids.
result Remarkable accuracy in finding cluster centroids, overcoming initialization problems.
RP-GFRFT unifies fractional order and rotation control for graph signals.
problem Lack of rotation-based spectral control in GFRFT and zero-angle degeneracy in AGFT.
method Rotation-parameterized graph fractional Fourier transform (RP-GFRFT) with degeneracy preserving rotation matrix.
result RP-GFRFT improves spectral filtering performance over existing methods.
The paper derives and proves the Helgason Fourier transform for vector bundle-valued differential forms on homogeneous spaces.
problem Deriving the Helgason Fourier transform for vector bundle-valued differential forms on homogeneous spaces.
method Employing the perspective of the functional equation satisfied by the classical Fourier transform, the paper derives the Helgason Fourier transform map and proves its properties.
result The Fourier transform is explicitly given and proven to be a map from vector bundle-valued differential forms to another vector bundle-valued differential form on the product space.
Study identifies and analyzes three types of errors in learning Fourier operators.
problem Statistical, discretization, and truncation errors in learning Fourier operators.
method Analysis of a Discrete Fourier Transform (DFT) based least squares estimator.
result Established upper and lower bounds on statistical, discretization, and truncation errors.
New MCMC method tackles heavy tailed distributions using Fourier transforms.
problem Challenges in sampling from heavy tailed distributions using MCMC.
method Proposes Fourier transform MCMC to sample from densities with known Fourier transforms.
result Shows geometric ergodicity of the resulting Markov chain for heavy tailed distributions.
FourNet approximates financial transition densities using Fourier transforms.
problem Approximating transition densities in finance with high accuracy.
method FourNet is a novel FFNN with Gaussian activation, learning from characteristic functions.
result FourNet can approximate transition densities arbitrarily well with finite neurons.
The study establishes uncertainty principles on harmonic manifolds of rank one.
problem Developing uncertainty principles for harmonic manifolds of rank one.
method Derivation of various uncertainty principles including Heisenberg, Morgen, Schrödinger, and Hömanders principles.
result Generalization of Hausdorff-Young inequality to harmonic manifolds of rank one.
The paper connects quantum 6j-symbols to tetrahedra volumes via discrete Fourier transforms.
problem Understanding the asymptotic behavior of quantum 6j-symbols and their relation to 3-manifold invariants. method Proposing and proving a conjecture linking discrete Fourier transforms of quantum 6j-symbols to the volumes of deeply truncated tetrahedra. result Supporting evidence for the conjecture in specific cases, with numerical calculations for larger dihedral angles.
GWNN uses graph wavelets for efficient graph CNNs.
problem Spectral graph CNNs' high computational cost and lack of interpretability.
method Graph wavelet transform for efficient graph convolution.
result GWNN significantly outperforms spectral graph CNNs.
Computing accurate estimates of the Fourier transform of analog signals from discrete data points is important in many fields of science and engineering. The conventional approach of performing the discrete Fourier transform of the data implicitly assumes periodicity and bandlimitedness of the signal. In this paper, we…
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.
Quantum Fourier Transform aids machine learning inference.
problem Generalizing from finite data samples to ground truth.
method Inspired by quantum algorithms, uses Quantum Fourier Transform to expose invariant subspace for data comparison.
result Proposes a concrete implementation for machine learning applications leveraging symmetries.
The aim of this article is to provide a systematic analysis of the conditions such that Fourier transform valuation formulas are valid in a general framework; i.e. when the option has an arbitrary payoff function and depends on the path of the asset price process. An interplay between the conditions on the payoff funct…
Injective X-ray transform on Heisenberg group for regular functions.
problem Injectivity of X-ray transform on sub-Riemannian manifolds.
method Group Fourier Transform and analysis of taming metrics.
result Sufficiently regular functions on Heisenberg group are determined by their line integrals.
Study light ray transform on Lorentzian manifolds without conjugate points.
problem Recovering spacelike singularities from weighted light ray transforms.
method Fourier Integral Operator analysis and filtered back-projection.
result Recovery of spacelike singularities from weighted light ray transforms without conjugate points.
Paper proves bijection of periodic instantons to singular monopoles.
problem Establishing bijection between spatially periodic instantons and singular monopoles.
method Uses Nahm transform and Fourier-Mukai transform, intertwining with Kobayashi-Hitchin correspondences.
result Nahm transform is a bijection as suggested by heuristic.
New algorithm defends against adversarial examples in image classification.
problem Defending against adversarial examples in image classification.
method Approximates Discrete Fourier transform of sparse signals corrupted by L0 noise. result Successfully defends against L0 adversaries in image classification. New bounds for learning polynomial surrogates with L∞ guarantees.
problem Learning polynomial surrogates for bounded binary functions with L∞ error guarantees. method Characterized minimax sample complexity for two classes of polynomials under subgaussian noise.
result Sample complexity rates differ from noiseless case, scaling as nd+1 for degree d polynomials and ns2 for sparse polynomials.