A sulfobetaine copolymer (1) carrying a photochromic spiropyran residue was synthesized, which reversibly isomerized between the closed and open forms in pure water and in saline by irradiation with visible light. The thermodynamic stability of the open form of the spiropyran methacrylate (SPMA) units of compound 1 was reduced upon increasing NaCl concentration. In addition, photo-reversible and selective Cu 2+ complexation in saline solution ([NaCl] ¼ 1.0 wt%) was achieved using compound 1 with metal ions (Cu 2+ , Zn 2+ , Ni 2+ , or Co 2+ ). Covalently cross-linked compound 1 showed selective Cu 2+ adsorption in pure water. In contrast, the other metal ions were increasingly adsorbed as NaCl concentration increased, resulting in lower selectivity of Cu 2+ ion adsorption with 1, e.g., the ratios of adsorption of Cu 2+ , Zn 2+ , Ni 2+ , and Co 2+ with 1 in 10 wt% saline were 73, 20, 10, and 3%, respectively, while only Cu 2+ adsorption was observed in a solution of 1.0 wt% NaCl. Because the stability of the open form of the SPMA units and the metal complexation of 1 were influenced by NaCl concentration, the electrostatically cross-linked networks of the zwitterionic sulfobetaine units of 1 may be loosened by NaCl addition, resulting in easy entry of metal ions into the network. The order of metal complexation among the four metals corresponded to the Irving-Williams series. Hydrogen-bonded networks of water molecules also may contribute to the relatively ineffective selective adsorption of Cu 2+ ions by 1 compared to the electrically neutral spiropyran-carrying copolymer of N-isopropylacrylamide, 2.

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In the MINMAX SET COVER RECONFIGURATION problem, given a set system F over a universe and its two covers C start and C goal of size k, we wish to transform C start into C goal by repeatedly adding or removing a single set of F while covering the universe in any intermediate state. Then, the objective is to minimize the maximize size of any intermediate cover during transformation. We prove that MINMAX SET COVER RECONFIGURATION and MINMAX DOMINATING SET RECONFIGURATION are PSPACEhard to approximate within a factor of 2 − 1 polyloglog N , where N is the size of the universe and the number of vertices in a graph, respectively, improving upon Ohsaka (SODA 2024) [Ohs24] and Karthik C. S. and Manurangsi (2023) [KM23]. This is the first result that exhibits a sharp threshold for the approximation factor of any reconfiguration problem because both problems admit a 2-factor approximation algorithm as per Ito, Demaine, Harvey, Papadimitriou, Sideri, Uehara, and Uno (Theor. Comput. Sci., 2011) [IDHPSUU11]. Our proof is based on a reconfiguration analogue of the FGLSS reduction [FGLSS96] from Probabilistically Checkable Reconfiguration Proofs of Hirahara and Ohsaka (2024) [HO24]. We also prove that for any constant ε ∈ (0, 1), MINMAX HYPERGRAPH VERTEX COVER RECONFIGURATION on poly(ε −1 )-uniform hypergraphs is PSPACE-hard to approximate within a factor of 2 − ε.

In this study, I clarify the spatial structure of Hachioji City, Tokyo by analyzing the town units. As for the spatial structure of Hachioji City, areas with many tertiary industry workers are distributed along the transportation network, and there are areas with many non-tertiary industry workers outside of them. Areas with many tertiary industry workers include areas with an extremely large number of white-collar workers around bases that are characterized as business centers. In addition, areas with many gray-collar workers exist in the vicinity of them. There are few people engaged in the tertiary industry in the outer area, and areas where the declining population, declining birthrate and aging population are becoming more serious.