The physical meaning of the holographic principle

C Fields, JF Glazebrook, A Marciano - arXiv preprint arXiv:2210.16021, 2022 - arxiv.org
We show in this pedagogical review that far from being" an apparent law of physics that
stands by itself"(R. Bousso, Rev. Mod. Phys. 74 (2002), 825-874), the holographic principle …

Separability, contextuality, and the quantum Frame Problem

C Fields, JF Glazebrook - International Journal of Theoretical Physics, 2023 - Springer
We study the relationship between assumptions of state separability and both preparation
and measurement contextuality, and the relationship of both of these to the frame problem …

Computing generalized ranks of persistence modules via unfolding to zigzag modules

TK Dey, C Xin - arXiv preprint arXiv:2403.08110, 2024 - arxiv.org
For a $ P $-indexed persistence module ${\sf M} $, the (generalized) rank of ${\sf M} $ is
defined as the rank of the limit-to-colimit map for the diagram of vector spaces of ${\sf M} …

Harder–Narasimhan filtrations of persistence modules

M Fersztand, E Jacquard, V Nanda… - Transactions of the …, 2024 - Wiley Online Library
Abstract The Harder–Narasimhan (HN) type of a quiver representation is a discrete invariant
parameterised by a real‐valued function (called a central charge) defined on the vertices of …

Multilinear hyperquiver representations

T Muller, V Nanda, A Seigal - arXiv preprint arXiv:2305.05622, 2023 - arxiv.org
We count singular vector tuples of a system of tensors assigned to the edges of a directed
hypergraph. To do so, we study the generalisation of quivers to directed hypergraphs …

[HTML][HTML] Harder-Narasimhan filtrations and zigzag persistence

M Fersztand, V Nanda, U Tillmann - Advances in Applied Mathematics, 2024 - Elsevier
We introduce a sheaf-theoretic stability condition for finite acyclic quivers. Our main result
establishes that for representations of affine type A˜ quivers, there is a precise relationship …

Quiver Laplacians and Feature Selection

O Sumray, HA Harrington, V Nanda - arXiv preprint arXiv:2404.06993, 2024 - arxiv.org
The challenge of selecting the most relevant features of a given dataset arises ubiquitously
in data analysis and dimensionality reduction. However, features found to be of high …

Sequential measurements, TQFTs, and TQNNs

C Fields, JF Glazebrook, A Marciano - arXiv preprint arXiv:2205.13184, 2022 - arxiv.org
We introduce novel methods for implementing generic quantum information within a scale-
free architecture. For a given observable system, we show how observational outcomes are …