arXiv subjects

Kengo Kawamura

Publications and source records attributed to Kengo Kawamura.

4 recordsLinked to original sources

arXiv2024

Educational Effects in Mathematics: Conditional Average Treatment Effect depending on the Number of Treatments

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.

stat.ME↗

arXiv2016

Ribbon-clasp surface-links and normal forms of singular surface-links

We introduce the notion of a ribbon-clasp surface-link, which is a generalization of a ribbon surface-link. We generalize the notion of a normal form on embedded surface-links to the case of immersed surface-links and prove that any (immersed) surface-link can be described in a normal form. It is known that an embedded surface-link is a ribbon surface-link if and only if it can be described in a symmetric normal form. We prove that an (immersed) surface-link is a ribbon-clasp surface-link if and only if it can be described in a symmetric normal form. We also introduce the notion of a ribbon-clasp normal form, which is a simpler version of a symmetric normal form.

math.GT↗

arXiv2015

Independence of Roseman moves including triple points

Roseman moves are seven types of local modification for surface-link diagrams in $3$-space which generate ambient isotopies of surface-links in $4$-space. In this paper, we focus on Roseman moves involving triple points, one of which is the famous tetrahedral move, and discuss their independence. For each diagram of any surface-link, we construct a new diagram of the same surface-link such that any sequence of Roseman moves between them must contain moves involving triple points (and the numbers of triple points of the two diagrams are the same). Moreover, we can find a pair of two diagrams of an $S^2$-knot such that any sequence of Roseman moves between them must involve at least one tetrahedral move.

math.GT↗

arXiv2014

An infinite family of prime knots with a certain property for the clasp number

The clasp number $c(K)$ of a knot $K$ is the minimum number of clasp singularities among all clasp disks bounded by $K$. It is known that the genus $g(K)$ and the unknotting number $u(K)$ are lower bounds of the clasp number, that is, $\max\{g(K),u(K)\} \leq c(K)$. Then it is natural to ask whether there exists a knot $K$ such that $\max\{g(K),u(K)\}<c(K)$. In this paper, we prove that there exists an infinite family of prime knots such that the question above is affirmative.

math.GT↗