Kengo Kawamura

The purpose of this paper is to introduce an enriched presentation, called a shade quandle presentation, containing information that can be used to normalize Alexander type invariants. We also introduce transformations on shade quandle presentations and show that two shade quandle presentations of an oriented link are related by the transformations. We see that the transformations are finer than the strong Tietze transformations to normalize Alexander type invariants.

This study examines the educational effect of the Academic Support Center at Kogakuin University. Following the initial assessment, it was suggested that group bias had led to an underestimation of the Center's true impact. To address this issue, the authors applied the theory of causal inference. By using T-learner, the conditional average treatment effect (CATE) of the Center's face-to-face (F2F) personal assistance program was evaluated. Extending T-learner, the authors produced a new CATE function that depends on the number of treatments (F2F sessions) and used the estimated function to predict the CATE performance of F2F assistance.

We introduce the notion of bicolored diagrams which are closely related to the region crossing changes. Moreover, we refine Cheng’s results on the region crossing changes and propose a certain way to calculate the Arf invariant of a proper link using a bicolored diagram.