Výsledky vyhledávání - "MCINNIS, IAN"

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Autor: Cheng, Jeffrey, McInnis, Ian Malcolm Johnson, Yee, Matthew

We study the inertia of distance matrices of weighted graphs. Our novel congruence-based proof of the inertia of weighted trees extends to a proof for the inertia of weighted unicyclic graphs whose cycle is a triangle. Partial results are given on th

Externí odkaz: http://arxiv.org/abs/2304.13020

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Isometric embedding and spectral constraints for weighted graph metrics

Autor: Cheng, Jeffrey, McInnis, Ian Malcolm Johnson, Yee, Matthew

A weighted graph $\phi G$ encodes a finite metric space $D_{\phi G}$. When is $D$ totally decomposable? When does it embed in $\ell_1$ space? When does its representing matrix have $\leq 1$ positive eigenvalue? We give useful lemmata and prove that t

Externí odkaz: http://arxiv.org/abs/2304.13018

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Characterizing and generalizing cycle completable graphs

Autor: Chudnovsky, Maria, McInnis, Ian Malcolm Johnson

The family of cycle completable graphs has several cryptomorphic descriptions, the equivalence of which has heretofore been proven by a laborious implication-cycle that detours through a motivating matrix completion problem. We give a concise proof,

Externí odkaz: http://arxiv.org/abs/2304.09335

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Bicategories, Biequivalence, and Bi-Interpretability

Autor: D'Arienzo, Anthony, Pagano, Vinny, McInnis, Ian M. J.

We make explicit the correspondence between syntax and syntactic categories for coherent first-order logic, providing a categorical characterization of bi-interpretability. This is done by creating a biequivalence between a bicategory of coherent the

Externí odkaz: http://arxiv.org/abs/2011.14056

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