arXiv subjects

Kan Shota

Publications and source records attributed to Kan Shota.

3 recordsLinked to original sources

arXiv2026

Fast Enumeration of Minimal Removable Sets in Monotone Systems with Application to Core Collapse Analysis

In network vulnerability analysis, it is crucial to evaluate the robustness of $k$-cores against vertex removals. A $k$-core is often fragile since removing a few vertices can trigger a large reduction in the core size, a phenomenon known as core collapse. In this paper, we study the problem of enumerating all minimal removable sets (MinRSs) of a given $k$-core, where a MinRS is a minimal nonempty set of vertices whose removal results in a smaller $k$-core graph. We consider this problem within a general mathematical framework based on monotone systems. We show that, for a monotone system that is given with an underlying graph $G=(V,E)$, all MinRSs of a solution can be enumerated in $O((n+m)n\tau_\omega)$ time, where $n=|V|$, $m=|E|$ and $\tau_\omega$ denotes the computation time of evaluating the monotone function of the system. Furthermore, if the system satisfies the newly defined in-dominating seed property, the complexity drops to $O((n+m) \log n \cdot \tau_\omega)$ time. We prove that standard $k$-cores in undirected graphs satisfy this property, enabling MinRS enumeration in $O((n+m)\log n)$ time, a significant improvement over the baseline. We also extend our framework to enumerate all solutions in a given monotone system. This yields an $O((n+m)\log n)$-delay algorithm for all $k$-core subgraphs, outperforming an algorithm given by [Boley et al., Theoretical Computer Science, 2010]. Our framework is applicable to various $k$-core extensions, including weighted $k$-cores, multi-layer $\boldsymbol{k}$-cores, and $(k,\ell)$-cores.

cs.DS↗

arXiv2024

Systematic evaluation of the isolated effect of tissue environment on the transcriptome using a single-cell RNA-seq atlas dataset

Background: Understanding cellular diversity throughout the body is essential for elucidating the complex functions of biological systems. Recently, large-scale single-cell omics datasets, known as omics atlases, have become available. These atlases encompass data from diverse tissues and cell-types, providing insights into the landscape of cell-type-specific gene expression. However, the isolated effect of the tissue environment has not been thoroughly investigated. Evaluating this isolated effect is challenging due to statistical confounding with cell-type effects, arising from significant biases in the combinations of tissues and cell-types within the body. Results: This study introduces a novel data analysis framework, named the Combinatorial Sub-dataset Extraction for Confounding Reduction (COSER), which addresses statistical confounding by using graph theory to enumerate appropriate sub-datasets. COSER enables the assessment of isolated effects of discrete variables in single cells. Applying COSER to the Tabula Muris Senis single-cell transcriptome atlas, we characterized the isolated impact of tissue environments. Our findings demonstrate that some of genes are markedly affected by the tissue environment, particularly in modulating intercellular diversity in immune responses and their age-related changes. Conclusion: COSER provides a robust, general-purpose framework for evaluating the isolated effects of discrete variables from large-scale data mining. This approach reveals critical insights into the interplay between tissue environments and gene expression.

q-bio.GN↗

arXiv2024

SSD Set System, Graph Decomposition and Hamiltonian Cycle

In this paper, we first study what we call Superset-Subset-Disjoint (SSD) set system. Based on properties of SSD set system, we derive the following (I) to (IV): (I) For a nonnegative integer $k$ and a graph $G=(V,E)$ with $|V|\ge2$, let $X_1,X_2,\dots,X_q\subsetneq V$ denote all maximal proper subsets of $V$ that induce $k$-edge-connected subgraphs. Then at least one of (a) and (b) holds: (a) $\{X_1,X_2,\dots,X_q\}$ is a partition of $V$; and (b) $V\setminus X_1, V\setminus X_2,\dots,V\setminus X_q$ are pairwise disjoint. (II) For $k=1$ and a strongly-connected digraph $G$, whether $V$ is in (a) and/or (b) can be decided in $O(n+m)$ time and we can generate all such $X_1,X_2,\dots,X_q$ in $O(n+m+|X_1|+|X_2|+\dots+|X_q|)$ time, where $n=|V|$ and $m=|E|$. (III) For a digraph $G$, we can enumerate in linear delay all vertex subsets of $V$ that induce strongly-connected subgraphs. (IV) A digraph is Hamiltonian if there is a spanning subgraph that is strongly-connected and in the case (a).

cs.DS↗