Track D Social Science, Human Rights and Political Science

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/138414/1/jia218442.pd

Interval Edge-Colorings of Cartesian Products of Graphs I

A proper edge-coloring of a graph $G$ with colors $1, . . ., t$ is an interval $t$-coloring if all colors are used and the colors of edges incident to each vertex of $G$ form an interval of integers. A graph $G$ is interval colorable if it has an interval $t$-coloring for some positive integer $t$. Let $\mathfrak{N}$ be the set of all interval colorable graphs. For a graph $G \in \mathfrak{N}$, the least and the greatest values of $t$ for which $G$ has an interval $t$-coloring are denoted by $w(G)$ and $W(G)$, respectively. In this paper we first show that if $G$ is an $r$-regular graph and $G \in \mathfrak{N}$, then $W(G \square P_m) \geq W(G) + W(P_m) + (m − 1)r$ $(m \in \mathbb{N})$ and $W(G \square C_{2n}) \geq W(G) +W(C_{2n}) + nr$ $(n \geq 2)$. Next, we investigate interval edge-colorings of grids, cylinders and tori. In particular, we prove that if $G \square H$ is planar and both factors have at least 3 vertices, then $G \square H \in \mathfrak{N}$ and $w(G \square H) leq 6$. Finally, we confirm the first author’s conjecture on the $n$-dimensional cube $Q_n$ and show that $Q_n$ has an interval $t$-coloring if and only if $n \leq t \leq \frac{n(n+1)}{2}$

Improving VAE based molecular representations for compound property prediction

Collecting labeled data for many important tasks in chemoinformatics is time consuming and requires expensive experiments. In recent years, machine learning has been used to learn rich representations of molecules using large scale unlabeled molecular datasets and transfer the knowledge to solve the more challenging tasks with limited datasets. Variational autoencoders are one of the tools that have been proposed to perform the transfer for both chemical property prediction and molecular generation tasks. In this work we propose a simple method to improve chemical property prediction performance of machine learning models by incorporating additional information on correlated molecular descriptors in the representations learned by variational autoencoders. We verify the method on three property prediction asks. We explore the impact of the number of incorporated descriptors, correlation between the descriptors and the target properties, sizes of the datasets etc. Finally, we show the relation between the performance of property prediction models and the distance between property prediction dataset and the larger unlabeled dataset in the representation space