Afternoon Sessions: 2:00-3:20 pm

1. Hayden Pecoraro: hpecora1@uncc.edu (in-person)

Title: A Construction of a Special Frechet-Urysohn Space

2. Xingnan Zhang: xzhang42@uncc.edu 

Title: Representation and Simulation of Multivariate Dickman Distributions and Vervaat Perpetuities

3. Phuong Hoang: phoang3@uncc.edu

Title: Introduction to the optimal reversible transition couplings for random walk on graphs

4. Su Xu sxu10@uncc.edu (in-person)

Title: Robustness and Resilience of Deconvolution Methods for Bulk Tissue RNAseq Data 

1 Title: A Construction of a Special Fr\'{e}chet-Urysohn Space

Abstract: Set-theoretic topology is concerned with the construction of examples of topological spaces satisfying combinations of interesting properties relative to various strengthenings of the standard ZFC axioms. In this work, we consider two selection principles modifying the standard notion of topological separability, called H-separability and mH-separability, originally introduced in work of Bella, Bonanzinga, and Matveev. The question of whether mH- and H-separability can be made distinguishable was recently answered in the positive by Bardyla, Maesano, and Zdomskyy under the small cardinal assumption p = c. We extend this consistency result by constructing two additional examples of topological spaces distinguishing these properties. The first under the assumption that either b = c or p = b and the second simply in ZFC. The constructions proceed via transfinite recursion of length b on the topology of the space.

2. Title: Representation and Simulation of Multivariate Dickman Distributions and Vervaat Perpetuities

Abstract: A multivariate extension of the Dickman distribution was recently introduced, but very few properties have been studied. We derive three representations and simulations of the multivariate Dickman random variable tailored for different scenarios. Simulation results are also presented.

3. Title: Introduction to the optimal reversible transition couplings for random walks on graphs

Abstract:  This talk is based on recent joint work with K. McGoff and X. Li. Motivated by the problem of graph alignment, we develop a new type of optimal transport problem for weighted random walks on undirected graphs. In the talk, I will discuss the formulation of the problem, as well as its fundamental properties as an optimization problem, and how it can be used to solve the graph isomorphism problem.

4. Title: Robustness and Resilience of Deconvolution Methods for Bulk Tissue RNAseq Data 

Abstract: The goal of this study is to benchmark the robustness and resilience of four selected deconvolution methods, two reference-based and two reference-free, for bulk tissue RNA sequencing data. We simulate pseudo bulk tissue RNA sequencing data under scenarios where the basic assumptions of the methods are violated for the robustness evaluation. The resilience of these methods are evaluated by shifting the distribution of single cell profiles when generating the pseudo bulk tissue RNAseq data. Four single cell RNA (scRNA) sequencing datasets from different tissues types are used in the simulations. We compare the estimated cell proportions with the ground truth based on Pearson correlation coefficient, root mean squared deviation and mean absolute deviation. Our simulation results show that reference-based methods are more robust than reference free deconvolution methods when reliable reference scRNA sequencing data are used. While, reference-free methods show merits when there is no appropriate scRNA reference data can be used.