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
Robustness of Topological Phases on Aperiodic Lattices. [PDF]
Math Phys Anal GeomLi Y.
europepmc +1 more source
Analysis of Eigenvalue Clustering Leads to Optimal Scaling in Numerical Radiative Transfer
Numerical Linear Algebra with Applications, Volume 33, Issue 5, October 2026.ABSTRACT We consider a multidimensional polychromatic radiative transfer (RT) problem, accounting for scattering processes in a general form, that is, anisotropic (dipole) scattering with partial frequency redistribution. Given a discrete ordinates (SN$$ {S}_N $$) discretization, we report the corresponding matrix structures, depending on the model and
Pietro Benedusi +3 more
wiley +1 more source
Canonicalizing Zeta Generators: Genus Zero and Genus One. [PDF]
Commun Math PhysDorigoni D +7 more
europepmc +1 more source
Domain‐Knowledge‑Guided Rule Extraction for Governing Nepheline Amount in High‑Level Waste Glasses
International Journal of Applied Glass Science, Volume 17, Issue 4, October 2026.ABSTRACT Nepheline crystallization during canister centerline cooling is one of the most constraining factors limiting waste loading in high‐level waste (HLW) borosilicate glasses. Existing predictive models treat nepheline formation as a binary outcome, yet durability degradation depends continuously on nepheline fraction.
Irmak Sargin
wiley +1 more source
Adjoint <i>L</i>-functions, congruence ideals, and Selmer groups over GL n. [PDF]
Res Number TheoryFong HL.
europepmc +1 more source
Solving Stochastic Climate‐Economy Models: A Deep Least‐Squares Monte Carlo Approach
Mathematical Finance, Volume 36, Issue 4, Page 751-770, October 2026.ABSTRACT Stochastic versions of recursive integrated climate‐economy assessment models are essential for studying and quantifying policy decisions under uncertainty. However, as the number of state variables and stochastic shocks increases, solving these models via deterministic grid‐based dynamic programming (e.g., value‐function iteration/projection ...
Aleksandar Arandjelović +4 more
wiley +1 more source
Thermodynamics à la Souriau on Kähler Non-Compact Symmetric Spaces for Cartan Neural Networks. [PDF]
Entropy (Basel)Fré PG, Sorin AS, Trigiante M.
europepmc +1 more source
Abelian number fields with frobenian conditions
Mathematika, Volume 72, Issue 4, October 2026.Abstract We study the distribution of abelian number fields with frobenian conditions imposed on the conductor. In particular, we find an asymptotic for the number of abelian field extensions of a number field k$k$ whose conductor is the sum of two squares. We also discuss an application of the Brauer group of stacks to quadratic number fields.
Julie Tavernier
wiley +1 more source
Quadratic Subproduct Systems, Free Products, and Their C*-Algebras. [PDF]
Integr Equ Oper TheoryArici F, Ge Y.
europepmc +1 more source