Approximating a class of combinatorial problems with rational objective function

In the late seventies, Megiddo proposed a way to use an algorithm for the problem of minimizing a linear function a ₀ + a ₁ x ₁ + . . . + a _n x _n subject to certain constraints to solve the problem of minimizing a rational function of the form (a ₀ + a ₁ x ₁ + . . . + a _n x _n )/(b ₀ + b ₁ x ₁ + . . . + b _n x _n ) subject to the same set of constraints, assuming that the denominator is always positive. Using a rather strong assumption, Hashizume et al. extended Megiddo’s result to include approximation algorithms. Their assumption essentially asks for the existence of good approximation algorithms for optimization problems with possibly negative coefficients in the (linear) objective function, which is rather unusual for most combinatorial problems. In this paper, we present an alternative extension of Megiddo’s result for approximations that avoids this issue and applies to a large class of optimization problems. Specifically, we show that, if there is an α-approximation for the problem of minimizing a nonnegative linear function subject to constraints satisfying a certain increasing property then there is an α-approximation (1/α-approximation) for the problem of minimizing (maximizing) a nonnegative rational function subject to the same constraints. Our framework applies to covering problems and network design problems, among others.     

Association between Social Frailty and Sleep Quality among Community-dwelling Older Adults: A Cross-sectional Study

Objective: We examined the association between social frailty and subjective sleep quality among community-dwelling adults. Methods: This cross-sectional study recruited Japanese adults over the age of 60 years from health check-ups held in a public townhall in a suburban area between 2018 and 2019. Social frailty was evaluated using five criteria (living alone, not visiting friends sometimes, going out less frequently than the last year, not feeling helpful to friends or family, and not talking to someone every day) and categorized into three groups: non-frailty, pre-frailty, and frailty. Sleep quality was assessed according to the Pittsburgh Sleep Quality Index (PSQI) by giving participants a self-reported questionnaire. We performed multivariable linear regression analysis, denoting social frailty as an independent variable, and the global PSQI score as a dependent variable. Results: Data from 300 older adults were analyzed, 51.0% of whom were female. The participants'' mean age was 73.0 years (standard deviation = 5.8). Multivariable analysis revealed the notable association between social frailty and a high global PSQI score (compared with non-frailty, frailty: β = 0.94, 95% CI = 0.08 to 1.80, p = 0.033). Of the five determiners of social frailty, not talking with someone every day was especially associated with a high global PSQI score (β = 1.57, 95% CI = 0.49 to 2.66, p = 0.005). Conclusion: The present study suggests that social frailty is associated with poor sleep quality among community-dwelling older adults. Our findings indicate the importance of social frailty on sleep quality among older adults.     

Theoretical study of lanthanide-based in vivo luminescent probes for detecting hydrogen peroxide

The 4f-4f emissions from lanthanide trication (Ln³⁺) complexes are widely used in bioimaging probes. The emission intensity from Ln³⁺ depends on the surroundings, and thus, the design of appropriate photo-antenna ligands is indispensable. In this study, we focus on two probes for detecting hydrogen peroxide, for which emission intensities from Tb³⁺ are enhanced chemo-selectively by the H₂O₂-mediated oxidation of ligands. To understand the mechanism, the Gibbs free energy profiles of the ground and excited states related to emission and quenching are computed by combining our approximation—called the energy shift method—and density functional theory. The different emission intensities are mainly attributed to different activation barriers for excitation energy transfer from the ligand-centered triplet (T1) to the Tb³⁺-centered excited state. Additionally, quenching from T1 to the ground state via intersystem crossing was inhibited by intramolecular hydrogen bonds only in the highly emissive Tb³⁺ complexes. © 2018 Wiley Periodicals, Inc.     

Direct Estimation of the Surface Location of Immobilized Functional Groups for Concerted Catalysis Using a Probe Molecule

The location of active sites during concerted catalysis by a metal complex and tertiary amine on a SiO₂ surface is discussed based on the interaction between the functionalized SiO₂ surface and a probe molecule, p‐formyl phenylboronic acid. The interactions of the probe molecule with the surface functionalities, diamine ligand, and tertiary amine, were analyzed by FT‐IR and solid‐state ¹³C and ¹¹B MAS NMR. For the catalyst exhibiting high 1,4‐addition activity, the diamine ligand and tertiary amine base exist in closer proximity than in the catalyst with low activity.     

Preparation of apatite-type-silicate-supported precious metal catalysts for selective catalytic reduction of NOx

Apatite-type silicate supported precious metal catalysts were prepared and investigated for their catalytic activity in selective catalytic NO reduction. Single-phase La_9.33Si₆O₂₆ and La_8.33ASi₆O_25.5 (A=Ca, Sr, Ba) were obtained by a sol-gel method. Pd/La_9.33Si₆O₂₆ catalyst exhibited high activity for oxidation of C₃H₆, comparable to Pd/Al₂O₃ catalyst, although the specific surface area of La_9.33Si₆O₂₆ was lower than that of Al₂O₃. In addition, Pt/La_9.33Si₆O₂₆ catalyst exhibited higher activity for selective catalytic reduction of NO than Pt/Al₂O₃ catalyst. Substitution of Ba²⁺ for La³⁺ of La_9.33Si₆O₂₆ led to increased catalytic activity at low temperature.     

Turn-on fluorescence sensing of nucleoside polyphosphates using a xanthene-based Zn(II) complex chemosensor

Fluorescence sensing with small molecular chemosensors is a versatile technique for elucidation of function of various biological substances. We now report a new fluorescent chemosensor for nucleoside polyphosphates such as ATP using metal-anion coordination chemistry. The chemosensor 1-2Zn(II) is comprised of the two sites of 2,2'-dipicolylamine (Dpa)-Zn(II) as the binding motifs and xanthene as a fluorescent sensing unit for nucleoside polyphosphates. The chemosensor 1-2Zn(II) selectively senses nucleoside polyphosphates with a large fluorescence enhancement (F/F(o) > 15) and strong binding affinity (K(app) approximately = 1 x 10(6) M(-1)), whereas no detectable fluorescence change was induced by monophosphate species and various other anions. The 'turn-on,' fluorescence of 1-2Zn(II) is based on a new mechanism, which involves the binding-induced recovery of the conjugated form of the xanthene ring from its nonfluorescent deconjugated state which was formed by an unprecedented nucleophilic attack of zinc-bound water. The selective and highly sensitive ability of 1-2Zn(II) to detect nucleoside polyphosphates enables its bioanalytical applications in fluorescence visualization of ATP particulate stores in living cells, demonstrating the potential utility of 1-2Zn(II).     

Pyridylazulenes: synthesis, color changes, and structure of the colored product

A facile method for the synthesis of 1- and 2-pyridylazulenes, and of 1,3-dipyridylazulenes, is described. Color and spectral changes of these pyridylazulenes upon the addition of either acid or metal ions were investigated in detail. The color changed from blue to red upon the addition of trifluoroacetic acid or soft metal ions, depending on the substitution patterns of the pyridyl group on the azulene skeleton. The structures of the protonated or coordinated products were examined on the basis of the spectral data. It was found that the protonation or coordination of metal ions occurred on the nitrogen atom of the pyridine ring, but not on the carbon atom of azulene ring. The transition intervals of several pyridylazulenes for use as pH indicators were also determined.     

Synthesis of helicenes utilizing palladium-catalyzed double C-H arylation reaction

[5]- and [6]helicenes were synthesized in moderate to good yields from Z,Z-bis(bromostilbene)s by palladium-catalyzed double C-H arylation reaction. This method can be applied to the syntheses of helicenes possessing electron-deficient substituents.