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Check out my new “Media Literacy Roundup: 2 August 2025” newsletter on SubStack!
https://open.substack.com/pub/wfryer/p/media-literacy-roundup-2-august-2025?r=d4phj&utm_campaign=post&u…

Media Literacy Roundup: 2 August 2025
Media, Links and Reflections from Wes Fryer

Discrete Spectrum and Spectral Rigidity of a Second-Order Geometric Deformation Operator
Anton Alexa
https://arxiv.org/abs/2507.01440 https://

Discrete Spectrum and Spectral Rigidity of a Second-Order Geometric Deformation Operator
We analyze the spectral properties of a self-adjoint second-order differential operator $\hat{C}$, defined on the Hilbert space $L^2([-v_c, v_c])$ with Dirichlet boundary conditions. We derive the discrete spectrum $\{C_n\}$, prove the completeness of the associated eigenfunctions, and establish orthogonality and normalization relations. The analysis follows the classical Sturm--Liouville framework and confirms that the deformation modes $C_n$ form a spectral basis on the compact interval. We f…

This https://arxiv.org/abs/2505.17370 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

FRIREN: Beyond Trajectories -- A Spectral Lens on Time
Long-term time-series forecasting (LTSF) models are often presented as general-purpose solutions that can be applied across domains, implicitly assuming that all data is pointwise predictable. Using chaotic systems such as Lorenz-63 as a case study, we argue that geometric structure - not pointwise prediction - is the right abstraction for a dynamic-agnostic foundational model. Minimizing the Wasserstein-2 distance (W2), which captures geometric changes, and providing a spectral view of dynamic…

Some geometric and spectral aspects of restriction problems
Hajer Bahouri, Veronique Fischer
https://arxiv.org/abs/2507.00204 https://

Some geometric and spectral aspects of restriction problems
This texts commemorates the memory of Haim Brezis and explores some aspects of the restriction problem, particularly its connections to spectral and geometric analysis. Our choice of subject is motivated by Brezis' significant contributions to various domains related to this problem, including harmonic analysis, partial differential equations, spectral theory, representation theory, number theory, and many others.

Geometric Littlewood-Offord problems via lattice point counting
Alexandr Grebennikov, Matthew Kwan
https://arxiv.org/abs/2505.24699 https://

Geometric Littlewood-Offord problems via lattice point counting
Consider nonzero vectors $a_{1},\dots,a_{n}\in\mathbb{C}^{k}$, independent Rademacher random variables $ξ_{1},\dots,ξ_{n}$, and a set $S\subseteq\mathbb{C}^{k}$. What upper bounds can we prove on the probability that the random sum $ξ_{1}a_{1}+\dots+ξ_{n}a_{n}$ lies in $S$? We develop a general framework that allows us to reduce problems of this type to counting lattice points in $S$. We apply this framework with known results from diophantine geometry to prove various bounds when $S$ is a …

Information Geometry on the $\ell^2$-Simplex via the $q$-Root Transform
Levin Maier
https://arxiv.org/abs/2506.00485 https://arxiv.or…

Information Geometry on the $\ell^2$-Simplex via the $q$-Root Transform
In this paper, we introduce \emph{$\ell^p$-information geometry}, an infinite dimensional framework that shares key features with the geometry of the space of probability densities \( \mathrm{Dens}(M) \) on a closed manifold, while also incorporating aspects of measure-valued information geometry. We define the \emph{$\ell^2$-probability simplex} with a noncanonical differentiable structure induced via the \emph{$q$-root transform} from an open subset of the $\ell^p$-sphere. This structure rend…

Moduli space of Conformal Field Theories and non-commutative Riemannian geometry
Yan Soibelman
https://arxiv.org/abs/2506.00896 https://

Moduli space of Conformal Field Theories and non-commutative Riemannian geometry
We discuss the analogy between collapsing Conformal Field Theories and measured Gromov-Hausdorff limit of Riemannian manifolds with non-negative Ricci curvature. Motivated by this analogy we propose the notion of non-commutative (``quantum") Riemannian d-geometry. We explain how this structure is related to Connes's spectral triples in the case d=1. In the Appendix based on the unpublished joint work with Maxim Kontsevich we discuss deformation theory of Quantum Field Theories as well as an app…

Nematic ordering in active fluids driven by substrate deformations: Mechanisms and patterning regimes
Varun Venkatesh, Amin Doostmohammadi
https://arxiv.org/abs/2505.24639

Nematic ordering in active fluids driven by substrate deformations: Mechanisms and patterning regimes
The interplay between active matter and its environment is central to understanding emergent behavior in biological and synthetic systems. Here, we show that coupling active nematic flows to small-amplitude deformations of a compliant substrate can fundamentally reorganize the system's dynamics. Using a model that combines active nematohydrodynamics with substrate mechanics, we find that contractile active nematics-normally disordered in flat geometries-undergo a sharp transition to long-range …

This https://arxiv.org/abs/2502.17570 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

Effects of spacetime geometry on neutrino oscillation inside a Core-Collapse Supernova
Neutrinos are excellent probes of the inner structures of supernovas. However, an understanding of their dynamics remains incomplete, which is crucial for properly interpreting the detector data. The huge matter density inside a core collapse supernova affects the self-coupling of the neutrinos through a geometrical four-fermion interaction induced by spacetime torsion generated by the fermions themselves. For normal mass hierarchy, the effect is negligible; for inverted mass hierarchy however,…

AFIRE: Accurate and Fast Image Reconstruction Algorithm for Geometric-inconsistency Multispectral CT
Yu Gao, Chong Chen
https://arxiv.org/abs/2505.24793 ht…

AFIRE: Accurate and Fast Image Reconstruction Algorithm for Geometric-inconsistency Multispectral CT
For nonlinear multispectral computed tomography (CT), accurate and fast image reconstruction is challenging when the scanning geometries under different X-ray energy spectra are inconsistent or mismatched. Motivated by this, we propose an accurate and fast algorithm named AFIRE to address such problem in the case of mildly full scan. We discover that the derivative operator (gradient) of the involved nonlinear mapping at some special points, for example, at zero, can be represented as a composi…