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A classical result in Morse theory is the determination of the homotopy type of the loop space of a manifold. In this paper, we study this result through the lens of discrete Morse theory. This requires a suitable simplicial model for the loop space.

Externí odkaz: http://arxiv.org/abs/2407.12156

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Discrete Morse theory for open complexes

Autor: Knudson, Kevin P., Scoville, Nicholas A.

We develop a discrete Morse theory for open simplicial complexes $K=X\setminus T$ where $X$ is a simplicial complex and $T$ a subcomplex of $X$. A discrete Morse function $f$ on $K$ gives rise to a discrete Morse function on the order complex $S_K$ o

Externí odkaz: http://arxiv.org/abs/2402.12116

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Bounds on Kemeny's constant of a graph and the Nordhaus-Gaddum problem

Autor: Kim, Sooyeong, Madras, Neal, Chan, Ada, Kempton, Mark, Kirkland, Stephen, Knudson, Adam

We study Nordhaus-Gaddum problems for Kemeny's constant $\mathcal{K}(G)$ of a connected graph $G$. We prove bounds on $\min\{\mathcal{K}(G),\mathcal{K}(\overline{G})\}$ and the product $\mathcal{K}(G)\mathcal{K}(\overline{G})$ for various families of

Externí odkaz: http://arxiv.org/abs/2309.05171

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Kemeny's constant and enumerating Braess edges in trees

Autor: Jang, Jihyeug, Kempton, Mark, Kim, Sooyeong, Knudson, Adam, Madras, Neal, Song, Minho

We study the problem of enumerating Braess edges for Kemeny's constant in trees. We obtain bounds and asympotic results for the number of Braess edges in some families of trees.

Externí odkaz: http://arxiv.org/abs/2309.02977

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A Nordhaus-Gaddum type problem for the normalized Laplacian spectrum and graph Cheeger constant

Autor: Faught, J. Nolan, Kempton, Mark, Knudson, Adam

For a graph $G$ on $n$ vertices with normalized Laplacian eigenvalues $0 = \lambda_1(G) \leq \lambda_2(G) \leq \cdots \leq \lambda_n(G)$ and graph complement $G^c$, we prove that \begin{equation*} \max\{\lambda_2(G),\lambda_2(G^c)\}\geq \frac{2}{n^2}

Externí odkaz: http://arxiv.org/abs/2304.01979

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Akademický článek

Gathering information on maternal immunization readiness in Bangladesh, Ghana, Kenya, Mozambique, and Nepal: Applying a WHO checklist

Autor: Ranju Baral, Sophia Knudson, Iracema Barros, Patience Cofie, Patience Dapaah, Sadaf Khan, Sandeep Kumar, Kamran Mehedi, Lauren Newhouse, Elkanah Otiang, Rosemond Owusu, Clint Pecenka, Melanie Picolo, Judite Pinto, Diana Quelhas, Satyabrata Routray, Surendra Uranw, Jessica A. Fleming

Publikováno v: Human Vaccines & Immunotherapeutics, Vol 20, Iss 1 (2024)

New respiratory syncytial virus (RSV) maternal vaccines have begun roll out in some countries, with efforts in progress to broaden access worldwide and shorten the timeline to access for low- and middle-income countries (LMICs). Prior to new maternal

Externí odkaz: https://doaj.org/article/2b7295e3be1c400eb96a342eea464ee2