arXiv research

Study spherical Fourier transform on hypergeometric type harmonic manifolds.

Injectivity of geodesic ray transform on specific Finsler manifolds proven.

Solves wave equation on non-flat harmonic manifolds using Abel transform and Fourier analysis.

In earlier papers, we introduced spherical T-duality, which relates pairs of the form $(P,H)$ consisting of an oriented $S^3$-bundle $P\rightarrow M$ and a 7-cocycle $H$ on $P$ called the 7-flux. Intuitively, the spherical T-dual is another such pair $(\hat P, \hat H)$ and spherical T-duality exchanges the 7-flux with …

Recent work by Cohen \emph{et al.} has achieved state-of-the-art results for learning spherical images in a rotation invariant way by using ideas from group representation theory and noncommutative harmonic analysis. In this paper we propose a generalization of this work that generally exhibits improved performace, but…

Convolutional Neural Networks (CNNs) have become the method of choice for learning problems involving 2D planar images. However, a number of problems of recent interest have created a demand for models that can analyze spherical images. Examples include omnidirectional vision for drones, robots, and autonomous cars, mo…

The paper derives and proves the Helgason Fourier transform for vector bundle-valued differential forms on homogeneous spaces.

A new class of harmonic Hadamard manifolds, those spaces called of hypergeometric type, is defined in terms of Gauss hypergeometric equations. Spherical Fourier transform defined on a harmonic Hadamard manifold of hypergeometric type admits an inversion formula. A characterization of harmonic Hadamard manifold being of…

Algorithm learns means of spherical Gaussian mixtures efficiently in low dimensions.

Study integral kernels on complex symmetric spaces and their Dyson Brownian Motion applications.

We prove new kinematic formulas for tensor valuations and simplify previously known Crofton formulas by using the recently developed algebraic theory of translation invariant valuations. The heart of the paper is the computation of the Alesker-Fourier transform on the large class of spherical valuations, which is achie…

New algorithm for estimating multivariate quantiles using stochastic optimal transport.

Developed a diffusion model on spherical data, addressing geometric and stochastic challenges.

New Fourier features improve high-precision approximation in large-scale problems.

Fourier PCA is Principal Component Analysis of a matrix obtained from higher order derivatives of the logarithm of the Fourier transform of a distribution.We make this method algorithmic by developing a tensor decomposition method for a pair of tensors sharing the same vectors in rank-$1$ decompositions. Our main appli…

Paper proves Fourier transform for valuations, simplifying previous work.

Efficient algorithm learns mixture models of heavy-tailed distributions.

We investigate the rigidity and asymptotic properties of quantum SU(2) representations of mapping class groups. In the spherical braid group case the trivial representation is not isolated in the family of quantum SU(2) representations. In particular, they may be used to give an explicit check that spherical braid grou…

A new algorithm computes Fourier coefficients for a specified range efficiently.

Structured CNN designed using the prior information of problems potentially improves efficiency over conventional CNNs in various tasks in solving PDEs and inverse problems in signal processing. This paper introduces BNet2, a simplified Butterfly-Net and inline with the conventional CNN. Moreover, a Fourier transform i…

Paper computes link determinants using Fourier-Hadamard transforms.

Generative model emulates climate model for 100-year forecasts.

The Fourier transform of Heegaard Floer d-invariants helps classify 3-manifolds.

X-ray transform on H-type groups solved, revealing function injectivity.

Proves conditions for Fourier transforms in rank 1 symmetric spaces.

This work improves Fourier pricing for multi-asset options using RQMC with domain transformation.

Algorithm describes Fourier transform of Stokes data at infinity.

The paper studies Fourier-Laplace transforms in polynomial OU volatility models for option pricing.

New algorithms learn sparse set functions in non-orthogonal Fourier bases.

In this paper, we study robust tensor completion by using transformed tensor singular value decomposition (SVD), which employs unitary transform matrices instead of discrete Fourier transform matrix that is used in the traditional tensor SVD. The main motivation is that a lower tubal rank tensor can be obtained by usin…

We prove that the Fourier--Laplace--Nahm transform for connections on the projective line is a hyper-Kähler isometry.

Transformers improve with Fourier integral attentions.

The paper derives statistics of multi-factor functions from their Fourier transforms.

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 $X\times Y$, 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 …

Enhances Fourier estimator performance for asynchronous event-data.

Many signals on Cartesian product graphs appear in the real world, such as digital images, sensor observation time series, and movie ratings on Netflix. These signals are "multi-dimensional" and have directional characteristics along each factor graph. However, the existing graph Fourier transform does not distinguish …

RP-GFRFT unifies fractional order and rotation control for graph signals.

Study identifies and analyzes three types of errors in learning Fourier operators.

The maximum mean discrepancy (MMD) is a recently proposed test statistic for two-sample test. Its quadratic time complexity, however, greatly hampers its availability to large-scale applications. To accelerate the MMD calculation, in this study we propose an efficient method called FastMMD. The core idea of FastMMD is …

The study establishes uncertainty principles on harmonic manifolds of rank one.

FourNet approximates financial transition densities using Fourier transforms.

The paper connects quantum $6j$-symbols to tetrahedra volumes via discrete Fourier transforms.

We introduce the spherical phylon group, a subgroup of the group of all formal diffeomorphisms of $\R^d$ that fix the origin. The invariant theory of the spherical phylon group is used to understand the invariants of the Laplace transform.

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…

Many neural speech enhancement and source separation systems operate in the time-frequency domain. Such models often benefit from making their Short-Time Fourier Transform (STFT) front-ends trainable. In current literature, these are implemented as large Discrete Fourier Transform matrices; which are prohibitively inef…

New method for optimizing risk in financial models using Fourier transforms.

Quantum Fourier Transform aids machine learning inference.