Results 191 to 200 of about 5,183 (263)
Frequency‐dependent contraction rates for the Bayesian method to the inverse source problem
Transactions of the London Mathematical Society, Volume 13, Issue 1, December 2026.Abstract This paper addresses an inverse source problem for acoustic waves in a range of frequencies. Our study has two main goals. First, although the problem is severely ill‐posed with a logarithmic stability estimate, we demonstrate, through careful analysis of the forward map's singular values, that increasing the frequency range enhances stability,
Pu‐Zhao Kow, Jenn‐Nan Wang
wiley +1 more source
Generalizable, sequence-invariant deep learning image reconstruction for subspace-constrained quantitative MRI. [PDF]
Magn Reson MedHu Z +6 more
europepmc +1 more source
Stochastic Gradient Descent in High Dimensions for Multi‐Spiked Tensor PCA
Communications on Pure and Applied Mathematics, Volume 79, Issue 10, Page 2291-2369, October 2026.ABSTRACT We study the high‐dimensional dynamics of online stochastic gradient descent (SGD) for the multi‐spiked tensor model. This multi‐index model arises from the tensor principal component analysis (PCA) problem with multiple spikes, where the goal is to estimate the unknown signal vectors within the N$N$‐dimensional unit sphere through maximum ...
Gérard Ben Arous +2 more
wiley +1 more source
Globalizing manifold-based reduced models for equations and data. [PDF]
Nat CommunKaszás B, Haller G.
europepmc +1 more source
Magnetic Resonance in Medicine, Volume 96, Issue 4, Page 1956-1971, October 2026.ABSTRACT Aims Purpose: Dictionary matching is a standard tool in quantitative MRI (qMRI), but typically lacks uncertainty quantification (UQ). This is critical when advanced reconstructions (e.g., compressed sensing, deep learning) introduce complex‐valued, spatially varying, and temporally correlated noise that violates standard assumptions of ...
Brian Toner +7 more
wiley +1 more source
Robust Heteroclinic Cycles in Pluridimensions. [PDF]
J Nonlinear SciCastro SBSD, Rucklidge AM.
europepmc +1 more source
A Comparison of Tissue Property Values Estimated Using Conventional Cardiac MRF and MT‐Cardiac MRF
Magnetic Resonance in Medicine, Volume 96, Issue 4, Page 1806-1813, October 2026.ABSTRACT Purpose To evaluate the impact of explicitly modeling Magnetization Transfer (MT) during reconstruction of cardiac Magnetic Resonance Fingerprinting (cMRF) maps on T1 and T2 quantification. Methods cMRF data were reconstructed using two dictionaries: a conventional cMRF dictionary that ignores MT processes, and an MT‐cMRF dictionary modeling ...
Sydney Kaplan +7 more
wiley +1 more source
Multidimensional Gene Space as an Approach for Analyzing the Organization of Genomes. [PDF]
Int J Mol SciZaytsev K, Bogatyreva N, Fedorov A.
europepmc +1 more source
Communications on Pure and Applied Mathematics, Volume 79, Issue 9, Page 2107-2157, September 2026.ABSTRACT The leading‐order asymptotic behavior of the solution of the Cauchy initial‐value problem for the Benjamin–Ono equation in L2(R)$L^2(\mathbb {R})$ is obtained explicitly for generic rational initial data u0$u_0$. An explicit asymptotic wave profile uZD(t,x;ε)$u^\mathrm{ZD}(t,x;\epsilon)$ is given, in terms of the branches of the multivalued ...
Elliot Blackstone +3 more
wiley +1 more source
Cognitive near-singularity: a possibility theorem and a witness-based protocol with a corpus case study. [PDF]
Front Artif IntellWilliams AE.
europepmc +1 more source