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Research Paper#Quantum Information Theory, Entanglement, Singular Value Decomposition🔬 ResearchAnalyzed: Jan 3, 2026 16:17

Generalized Entanglement Entropies via Unit-Invariant SVD

Published:Dec 28, 2025 16:51
1 min read
ArXiv

Analysis

This paper introduces novel generalizations of entanglement entropy using Unit-Invariant Singular Value Decomposition (UISVD). These new measures are designed to be invariant under scale transformations, making them suitable for scenarios where standard entanglement entropy might be problematic, such as in non-Hermitian systems or when input and output spaces have different dimensions. The authors demonstrate the utility of UISVD-based entropies in various physical contexts, including Biorthogonal Quantum Mechanics, random matrices, and Chern-Simons theory, highlighting their stability and physical relevance.
Reference

“The UISVD yields stable, physically meaningful entropic spectra that are invariant under rescalings and normalisations.”

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Research Paper#Graph Theory, Network Analysis, Signal Processing🔬 ResearchAnalyzed: Jan 4, 2026 00:07

Harmonic Analysis for Directed Networks

Published:Dec 25, 2025 19:36
1 min read
ArXiv

Analysis

This paper addresses the challenges of analyzing diffusion processes on directed networks, where the standard tools of spectral graph theory (which rely on symmetry) are not directly applicable. It introduces a Biorthogonal Graph Fourier Transform (BGFT) using biorthogonal eigenvectors to handle the non-self-adjoint nature of the Markov transition operator in directed graphs. The paper's significance lies in providing a framework for understanding stability and signal processing in these complex systems, going beyond the limitations of traditional methods.
Reference

“The paper introduces a Biorthogonal Graph Fourier Transform (BGFT) adapted to directed diffusion.”

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Research#Networks🔬 ResearchAnalyzed: Jan 10, 2026 11:05

Harmonic Analysis Framework for Directed Networks: A New Approach

Published:Dec 15, 2025 16:41
1 min read
ArXiv

Analysis

This research explores a novel framework for analyzing directed networks, a significant area in graph theory and network science. The biorthogonal Laplacian framework offers a potentially powerful new tool for understanding complex network structures and dynamics.
Reference

“The article proposes a 'Biorthogonal Laplacian Framework for Non-Normal Graphs'.”

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