arXiv subjects
Publications and source records attributed to Ryoma Kobayashi.
We give two small generating sets for the subgroup of the mapping class group of a non-orientable closed surface which is generated by Dehn twists and acts trivially on the $\mathbb{Z}_2$ coefficient first homology group of the surface.
Rationale and Objectives: Computer-aided detection systems for chest radiographs are widely used, and concurrent reader displays, such as bounding-box (BB) highlights, may influence the reading process. This pilot study used eye tracking to conduct a preliminary experiment to quantify which aspects of visual search were affected. Materials and Methods: We sampled 180 chest radiographs from the VinDR-CXR dataset: 120 with solitary pulmonary nodules or masses and 60 without. The BBs were configured to yield an overall display sensitivity and specificity of 80%. Three radiologists (with 11, 5, and 1 years of experience, respectively) interpreted each case twice - once with BBs visible and once without - after a washout of >= 2 weeks. Eye movements were recorded using an EyeTech VT3 Mini. Metrics included interpretation time, time to first fixation on the lesion, lesion dwell time, total gaze-path length, and lung-field coverage ratio. Outcomes were modeled using a linear mixed model, with reading condition as a fixed effect and case and reader as random intercepts. The primary analysis was restricted to true positives (n=96). Results: Concurrent BB display prolonged interpretation time by 4.9 s (p<0.001) and increased lesion dwell time by 1.3 s (p<0.001). Total gaze-path length increased by 2,076 pixels (p<0.001), and lung-field coverage ratio increased by 10.5% (p<0.001). Time to first fixation on the lesion was reduced by 1.3 s (p<0.001). Conclusion: Eye tracking captured measurable alterations in search behavior associated with concurrent BB displays during chest radiograph interpretation. These findings support the feasibility of this approach and highlight the need for larger studies to confirm effects and explore implications across modalities and clinical contexts.
Let $N_{g,n}$ be a genus $g$ compact non-orientable surface with $n$ boundaries. We explain about relations on the level $d$ mapping class group $\mathcal{M}_d(N_{g,0})$ of $N_{g,0}$ and the level $d$ principal congruence subgroup $Γ_d(g-1)$ of $\mathrm{SL}(g-1;\mathbb{Z})$. As applications, we give a normal generating set of $\mathcal{M}_d(N_{g,n})$ for $g\ge4$ and $n\ge0$, and finite generating sets of $\mathcal{M}_d(N_{g,n})$ for some $d$, any $g\ge4$ and $n\ge0$.
Omori and the author have given an infinite presentation for the mapping class group of a compact non-orientable surface. In this paper, we give more simple infinite presentations for this group.
The abelianization of the level $d$ principal congruence subgroup $Γ_d(n)$ of $\textrm{SL}(n;\mathbb{Z})$ was determined by Lee-Szczarba. By this result and a result of Tits, we can obtain a minimal generating set for $Γ_d(n)$. In this paper, we give a minimal generating set for $Γ_d(n)$ and determine the abelianization of $Γ_d(n)$, without using the results of Tits and Lee-Szczarba. Moreover, we give three theorems about $Γ_d(n)$.
A finite presentation for the subgroup of the mapping class group of a compact non-orientable surface generated by all Dehn twists was given by Stukow. In this paper, we give an infinite presentation for this group, mainly using the presentation given by Stukow and Birman exact sequences on mapping class groups of non-orientable surfaces.
The level $2$ mapping class group of an orientable closed surface can be generated by squares of Dehn twists about non-separating curves. On the other hand, the level $2$ mapping class group $\mathcal{M}_2(N_g)$ of a non-orientable closed surface $N_g$ can not be generated by only Dehn twists, and so it can not be generated by squares of Dehn twists about non-separating curves. In this paper, we prove that the Dehn twist subgroup of $\mathcal{M}_2(N_g)$ can not be generated by squares of Dehn twists about non-separating curves either. As an application, we give a finite generating set for the subgroup of $\mathcal{M}_2(N_g)$ generated by Dehn twist about separating curves and squares of Dehn twists about non-separating curves. Moreover, we examine about actions on non-separating simple closed curves of $N_g$ by $\mathcal{M}_2(N_g)$.
For any finite type connected surface $S$, we give an infinite presentation of the fundamental group $π_1(S,\ast)$ of $S$ based at an interior point $\ast\in{S}$ whose generators are represented by simple loops. When $S$ is non-orientable, we also give an infinite presentation of the subgroup of $π_1(S,\ast)$ generated by elements which are represented by simple loops whose regular neighborhoods are annuli.
For a compact surface $S$, let $\mathcal{I}(S)$ denote the Torelli group of $S$. For a compact orientable surface $Σ$, $\mathcal{I}(Σ)$ is generated by BSCC maps and BP maps. For a non-orientable closed surface $N$, $\mathcal{I}(N)$ is generated by BSCC maps and BP maps. In this paper, we give an explicit normal generating set for $\mathcal{I}(N_g^b)$, where $N_g^b$ is a genus-$g$ compact non-orientable surface with $b$ boundary components for $g\geq4$ and $b\geq1$.
Learning from Label Proportions (LLP) is a weakly supervised learning method that aims to perform instance classification from training data consisting of pairs of bags containing multiple instances and the class label proportions within the bags. Previous studies on multiclass LLP can be divided into two categories according to the learning task: per-instance label classification and per-bag label proportion estimation. However, these methods often results in high variance estimates of the risk when applied to complex models, or lack statistical learning theory arguments. To address this issue, we propose new learning methods based on statistical learning theory for both per-instance and per-bag policies. We demonstrate that the proposed methods are respectively risk-consistent and classifier-consistent in an instance-wise manner, and analyze the estimation error bounds. Additionally, we present a heuristic approximation method that utilizes an existing method for regressing label proportions to reduce the computational complexity of the proposed methods. Through benchmark experiments, we demonstrated the effectiveness of the proposed methods.
We construct two types of non-holomorphic Lefschetz fibrations over $S^2$ with $(-1)$-sections ---hence, they are fiber sum indecomposable--- by giving the corresponding positive relators. One type of the two does not satisfy the slope inequality (a necessary condition for a fibration to be holomorphic) and has a simply-connected total space, and the other has a total space that cannot admit any complex structure in the first place. These give an alternative existence proof for non-holomorphic Lefschetz pencils without Donaldson's theorem.
We give an infinite presentation for the mapping class group of a non-orientable surface with boundary components. The presentation is a generalization of the presentation given by the second author [15].
We obtain a finite generating set for the level 2 twist subgroup of the mapping class group of a closed non-orientable surface. The generating set consists of crosscap pushing maps along non-separating two-sided simple loops and squares of Dehn twists along non-separating two-sided simple closed curves. We also prove that the level 2 twist subgroup is normally generated in the mapping class group by a crosscap pushing map along a non-separating two-sided simple loop for genus $g\geq 5$ and $g=3$. As an application, we calculate the first homology group of the level 2 twist subgroup for genus $g\geq 5$ and $g=3$.
For a closed surface $S$, its Torelli group $\mathcal{I}(S)$ is the subgroup of the mapping class group of $S$ consisting of elements acting trivially on $H_1(S;\mathbb{Z})$. When $S$ is orientable, a generating set for $\mathcal{I}(S)$ is known. In this paper, we give a normal generating set of $\mathcal{I}(N_g)$ for $g\geq4$, where $N_g$ is a genus-$g$ non-orientable closed surface.
Let $\operatorname{Aut}(H_1(N_g;\mathbb Z_2),\cdot )$ be the group of automorphisms on the first homology group with $\mathbb Z_2$ coefficient of a closed non-orientable surface $N_g$ preserving the mod $2$ intersection form. In this paper, we obtain a finite presentation for $\operatorname{Aut}(H_1(N_g;\mathbb Z_2),\cdot )$. As applications we calculate the first homology group and the second homology group of $\operatorname{Aut}(H_1(N_g;\mathbb Z_2),\cdot )$.
It is known that the level $2$ principal congruence subgroup of $GL(n;\mathbb{Z})$ has a finite generating set. In this paper, we give a finite presentation of the level $2$ principal congruence subgroup of $GL(n;\mathbb{Z})$.
In this paper, given a finitely presented group $Γ$, we provide the explicit monodromy of a Lefschetz fibration with $(-1)$-sections whose total space has fundamental group $Γ$ by applying "twisted substitutions" to that of the Lefschetz fibration constructed by Cadavid and independently Korkmaz. Consequently, we obtain an upper bound for the minimum $g$ such that there exists a genus-$g$ Lefschetz pencil on a smooth 4-manifold whose fundamental group is isomorphic to $Γ$.
It is known that every finitely presented group is the fundamental group of the total space of a Lefschetz fibration. In this paper, we give another proof which improves the result of Korkmaz. In addition, Korkmaz defined the genus of a finitely presented group. We also evaluate upper bounds for genera of some finitely presented groups.