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Clayton Suguio Hida

Publications and source records attributed to Clayton Suguio Hida.

6 recordsLinked to original sources
arXiv2026

Plasticity in graph metric spaces and their hyperspaces

A metric space is plastic if every bijective nonexpansive self-map is an isometry. We prove that the hyperspace of nonempty compact subsets of every connected, locally finite, regular graph, equipped with the Hausdorff metric associated with the path metric, is plastic. The proof identifies the sets with smallest unit balls as the nonempty subsets of adjacent-twin classes and shows that every nonexpansive bijection induces an automorphism of the quotient graph preserving the sizes of these classes. Singletons are preserved when there are no adjacent twins, but need not be preserved in general. We also prove that $\mathcal{K}(K\times G)$ is plastic for every compact connected metric space $K$ and every connected, locally finite, regular graph $G$, with the supremum metric on the product, and give a more general criterion for such products. Further results include a plastic metric space whose hyperspace is not plastic, plasticity of every tree, and plasticity of the hyperspace of a connected, locally finite graph with only finitely many vertices of minimum degree.

math.GN↗
arXiv2026

Class Imbalance and Batch Effects in LLM-Based Screening for Systematic Reviews

This study analyses LLMs in imbalanced binary classification, using study screening in systematic reviews as the application domain. An experiment was conducted in five reviews, comparing individual and batch processing, with and without prevalence metadata. The results indicate a limited influence of the prevalence metadata, with no evidence that it improves performance. In contrast, batch processing produced larger behavioral changes that varied according to the prevalence of the class. The aggregate and item-level analyses did not always coincide. Therefore, batch processing should be evaluated not only in terms of cost, but also in relation to its effects on decision-making behavior.

cs.CL↗
arXiv2023

C*-convexity and C*-Polyhedron

A polyhedron in a Banach space is a family of points $\mathcal{X}$ such that for every $x\in \mathcal{X}$, there is a closed convex set $C$ such that $a\notin C$ and $\mathcal{X}\setminus\{x\}\subset C$. In this article, we consider the notion of C*-convexity and introduce the notion of a C*-polyhedron, which is a noncommutative version of the notion of polyhedrons. We investigate the largest size of a C*-polyhedron in some classical C*-algebras.

math.OA↗
arXiv2020

Uncountable almost irredundant sets in nonseparable C*-algebras

In this article, we consider the notion of almost irredundant sets: A subset $\mathcal{X}$ of a C*-algebra $\mathcal{A}$ is called almost irredundant if and only if for every $a\in \mathcal{X}$, the element $a$ does not belong to the norm-closure of $$\{\sum_{i=1}^n λ_i \prod_{j=1}^{n_i}a_{i,j}: \textrm{ where } a_{i,j} \in \mathcal{X}\setminus\{a\} \textrm{ and} \sum |λ_i|\leq 1\}.$$ Since every almost irrredundant set is in particular a discrete set, it follows that the density of $\mathcal{A}$ is an upper bound for the size of almost irredundant sets. We prove that under the Proper Forcing Axiom (PFA), there is an uncountable almost irredundant set in every C*-algebra with an uncountable increasing sequence of ideals. In particular, assuming PFA, every nonseparable scattered C*-algebra admits an uncountable almost irredundant set.

math.OA↗
arXiv2018

Large irredundant sets in operator algebras

A subset $\mathcal X$ of a C*-algebra $\mathcal A$ is called irredundant if no $A\in \mathcal X$ belongs to the C*-subalgebra of $\mathcal A$ generated by $\mathcal X\setminus \{A\}$. Separable C*-algebras cannot have uncountable irredundant sets and all members of many classes of nonseparable C*-algebras, e.g., infinite dimensional von Neumann algebras have irredundant sets of cardinality continuum. There exists a considerable literature showing that the question whether every AF commutative nonseparable C*-algebra has an uncountable irredundant set is sensitive to additional set-theoretic axioms and we investigate here the noncommutative case. Assuming $\diamondsuit$ (an additional axiom stronger than the continuum hypothesis) we prove that there is an AF C*-subalgebra of $\mathcal B(\ell_2)$ of density $2^ω=ω_1$ with no nonseparable commutative C*-subalgebra and with no uncountable irredundant set. On the other hand we also prove that it is consistent that every discrete collection of operators in $\mathcal B(\ell_2)$ of cardinality continuum contains an irredundant subcollection of cardinality continuum. Other partial results and more open problems are presented.

math.OA↗
arXiv2016

Two Cardinal Inequalities about Bidiscrete Systems

We consider the cardinal invariant $bd$ defined by M. Džamonja and I. Juhász concerning bidiscrete systems. Using the relation between bidiscrete systems and irredundance for a compact Hausdorff space $K$, we prove that ${w(K)\leq bd(K)\cdot hL(K)^+}$, generalizing a result of S. Todorcevic concerning the irredundance in Boolean algebras and we prove that for every maximal irredundant family $\mathcal{F}\subset C(K)$, there is a $π$-base $\mathcal{B}$ for $K$ with $|\mathcal{F}|=|\mathcal{B}|$, a result analogous to the McKenzie Theorem for Boolean algebras in the context of compact spaces. In particular, it is a consequence of the latter result that $π(K)\leq bd(K)$ for every compact Hausdorff space $K$. From the relation between bidiscrete systems and biorthogonal systems, we obtain some results about biorthogonal systems in Banach spaces of the form $C(K)$.

math.FA↗