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Hiroki Kodama

Publications and source records attributed to Hiroki Kodama.

12 recordsLinked to original sources
arXiv2026

Distinguishing regular polygons, cycle graphs, and circular metric spaces by the distance multiset and magnitude

We investigate how effectively finite metric spaces can be distinguished by distance-based invariants. As model spaces, we consider regular polygons, cycle graphs, and their generalization, circular metric spaces, and as invariants we consider the distance multiset, magnitude, and magnitude homology. We construct explicit families of homometric but non-congruent circular metric spaces, and in many even cases these examples also have the same magnitude as the original space. We prove that regular polygons are determined by the distance multiset among planar metric spaces, but not in general. We also determine, for several values of $n$, whether regular $n$-gons and $n$-cycle graphs are determined by magnitude.

math.MG↗
arXiv2026

Structural Oscillatority Criterion of Boolean Networks

Azuma et al. showed that a cactus-expandable Boolean network $Σ$ is structurally oscillatory if all the simple cycles of $Σ$ contain an odd number of inhibiting edges. We show that we do not need the cactus-expandable condition. Namely, a strongly connected Boolean network $Σ$ is structurally oscillatory if and only if all the simple cycles of $Σ$ contain an odd number of inhibiting edges. Additionally, we provide a characterization of a structurally oscillatory Boolean network for the general case.

math.CO↗
arXiv2026

Characterization of cactus-expandable digraphs via doubly bidirectionally connected pairs

Azuma et al.\ showed that a strongly connected digraph without a doubly bidirectionally connected pair is cactus-expandable. We prove the converse: if a digraph has a doubly bidirectionally connected pair, then no expansion of it is a cactus digraph. Combined with the theorem of Azuma et al., this yields a characterization of strongly connected cactus-expandable digraphs.

math.CO↗
arXiv2026

Lefschetz fibrations on the Milnor fibers of cusp and simple elliptic singularities

We show that the total space of the Milnor fibration associated with any cusp or simple elliptic singularity in complex three variables admits an $S^1$-parametric genus-one Lefschetz fibration structure over the $2$-disk. As a consequence, we demonstrate that the Lawson type foliations on $S^5$ associated with such singularities can be regarded as the pullback of the Reeb foliation on $S^3$. This enables us to provide an alternative proof of a previous result by the third author, which states that every Lawson type foliation admits a leafwise symplectic structure. Also we see that a pair of such Milnor fibers can be glued together along boundary into a closed oriented 4-manifold exactly when the pair corresponds to one of the ten extended strange duality pairs among the cusp singularities. This gluing is compatible with the Lefschetz fibrations and the resultant 4-manifold is diffeomrphic to a K3 surface.

math.GT↗
arXiv2024

Relative simplicity of the universal coverings of transformation groups and Tsuboi's metric

Many transformation groups on manifolds are simple, but their universal coverings are not. In the present paper, we study the concept of relatively simple group, that is, a group with the maximum proper normal subgroup. We show that many examples of universal coverings of transformation groups are relatively simple, including the universal covering $\widetilde{\mathrm{Ham}}(M,ω)$ of the group of Hamiltonian diffeomorphisms of a closed symplectic manifold $(M,ω)$. Tsuboi constructed a metric space $\mathcal{M}(G)$ for a simple group $G$. We generalize his construction to relatively simple groups, and study their large scale geometric structure. In particular, Tsuboi's metric space of $\widetilde{\mathrm{Ham}}(M, ω)$ is not quasi-isometric to the half line for every closed symplectic manifold $(M,ω)$.

math.GR↗
arXiv2022

A mathematical model of network elastoplasticity

We introduce a mathematical model, based on networks, for the elasticity and plasticity of materials. We define the tension tensor for a periodic graph in a Euclidean space, and we show that the tension tensor expresses elasticity under deformation. Plasticity is induced by local moves on a graph. The graph is described in terms of the weights of edges, and we discuss how these weights affect the plasticity.

math.DG↗
arXiv2018

Derivatives of flat functions

We remark that there is no smooth function $f(x)$ on $[0, 1]$ which is flat at $0$ such that the derivative $f^{(n)}$ of any order $n\geq 0$ is positive on $(0,1]$. Moreover, the number of zeros of the $n$-th derivative $f^{(n)}$ grows to the infinity and the zeros accumulate to $0$ when $n \to \infty$.

math.GM↗
arXiv2014

Higher weight Gel'fand-Kalinin-Fuks classes of formal Hamiltonian vector fields of symplectic R^2

In "The Gel'fand-Kalinin-Fuks class and characteristic classes of transversely symplectic foliations", arXiv:0910.3414, (October 2009) by D.Kotschick and S.Morita, the relative Gel'fand-Kalinin-Fuks cohomology groups of the formal Hamiltonian vector fields without constant vector fields on 2n-plane were characterized by two parameters, one is degree and the other is weight. And they obtained those cohomology groups of the 2-plane while their weight <= 10. In this paper, for those cohomology groups of the 2-plane, we succeeded in determining the dimension of cochain complexes by Sp(2,R)-representation theory for their weight even less than 50, thus, we manipulate the Euler characteristic numbers. We also decide our relative Gel'fand-Kalinin-Fuks cohomology groups until whose weight < 20 by getting a concrete matrix representation of the coboundary operator.

math.SG↗
arXiv2011

On non-uniformly simple groups

Suppose $G$ is a simple group. For any nontrivial elements $g$ and $h$, $g$ can be written as a finite product of conjugates of $h$ or the inverse of $h$. G is called uniformly simple if the length of such an expression is uniformly bounded. We show that the infinite alternating group is non-uniformly simple and evaluate how the length of such an expression is unbounded.

math.GR↗