A Mixture Model of Truncated Zeta Distributions with Applications to Scientific Collaboration Networks

The degree distribution has attracted considerable attention from network scientists in the last few decades to have knowledge of the topological structure of networks. It is widely acknowledged that many real networks have power-law degree distributions. However, the deviation from such a behavior often appears when the range of degrees is small. Even worse, the conventional employment of the continuous power-law distribution usually causes an inaccurate inference as the degree should be discrete-valued. To remedy these obstacles, we propose a finite mixture model of truncated zeta distributions for a broad range of degrees that disobeys a power-law behavior in the range of small degrees while maintaining the scale-free behavior. The maximum likelihood algorithm alongside the model selection method is presented to estimate model parameters and the number of mixture components. The validity of the suggested algorithm is evidenced by Monte Carlo simulations. We apply our method to five disciplines of scientific collaboration networks with remarkable interpretations. The proposed model outperforms the other alternatives in terms of the goodness-of-fit.     

Ruthenium‐Catalyzed Alkylation of Indoles with Tertiary Amines by Oxidation of a sp3 C?H Bond and Lewis Acid Catalysis

Ruthenium porphyrins (particularly [Ru(2,6‐Cl₂tpp)CO]; tpp=tetraphenylporphinato) and RuCl₃ can act as oxidation and/or Lewis acid catalysts for direct C‐3 alkylation of indoles, giving the desired products in high yields (up to 82 % based on 60–95 % substrate conversions). These ruthenium compounds catalyze oxidative coupling reactions of a wide variety of anilines and indoles bearing electron‐withdrawing or electron‐donating substituents with high regioselectivity when using tBuOOH as an oxidant, resulting in the alkylation of N‐arylindoles to 3‐{[(N‐aryl‐N‐alkyl)amino]methyl}indoles (yield: up to 82 %, conversion: up to 95 %) and the alkylation of N‐alkyl or N‐H indoles to 3‐[p‐(dialkylamino)benzyl]indoles (yield: up to 73 %, conversion: up to 92 %). A tentative reaction mechanism involving two pathways is proposed: an iminium ion intermediate may be generated by oxidation of an sp³ C? H bond of the alkylated aniline by an oxoruthenium species; this iminium ion could then either be trapped by an N‐arylindole (pathway A) or converted to formaldehyde, allowing a subsequent three‐component coupling reaction of the in situ generated formaldehyde with an N‐alkylindole and an aniline in the presence of a Lewis acid catalyst (pathway B). The results of deuterium‐labeling experiments are consistent with the alkylation of N‐alkylindoles via pathway B. The relative reaction rates of [Ru(2,6‐Cl₂tpp)CO]‐catalyzed oxidative coupling reactions of 4‐X‐substituted N,N‐dimethylanilines with N‐phenylindole (using tBuOOH as oxidant), determined through competition experiments, correlate linearly with the substituent constants σ (R²=0.989), giving a ρ value of ?1.09. This ρ value and the magnitudes of the intra‐ and intermolecular deuterium isotope effects (k_H/k_D) suggest that electron transfer most likely occurs during the initial stage of the oxidation of 4‐X‐substituted N,N‐dimethylanilines. Ruthenium‐catalyzed three‐component reaction of N‐alkyl/N‐H indoles, paraformaldehyde, and anilines gave 3‐[p‐(dialkylamino)benzyl]indoles in up to 82 % yield (conversion: up to 95 %).     

Perturbation analysis of finitely clad optical waveguides and couplers

In calculating the modal characteristics of a finitely clad optical waveguide, if the wavelength is much shorter than the core of the waveguide, then the cladding of the waveguide can be assumed to be infinite. On the other hand, if the wavelength is much longer than the core, the core can be ignored. These two approximations, although simple and accurate in the two respective extreme cases, do not provide adequate information in the transition region, where many tapered devices are operated. To overcome this a novel perturbation method is devised, in which these two approximations are combined in such a way that a result that is accurate in all cases can be obtained. Analytical expressions based on this method for describing the dispersion characteristics of finitely clad slab waveguides and circular step-index fibres are derived and compared with other conventional approximations. The combined use of this method and the coupled-mode theory for the analysis of optical couplers is also described.     

Hilbert空间中非扩张映象的最近的公共不动点的逼近问题

本文在Hilbert空间的框架下,研究无限族非扩张映象T_1,T_2,…的迭代程序x_n+1=λ_(n+1)y+(1-λ_(n+1))T_(n+1)x_n的收敛性问题．在适当的条件下,证明了该迭代序列收敛于这一非扩张映象族的最近的公共不动点．其结果改进和推广了引文中相应的结果．     

由数列定义的函数

We construct real valued functions from infinite sequences. We also consider some properties of such functions and null sequences.     

Bacteria-based AND logic gate: a decision-making and self-powered biosensor

We developed a bacteria-based AND logic gate using a Pseudomonas aeruginosa lasI/rhlI double mutant with two quorum-sensing signaling molecules as the input signals. We showed a distinct electrical output signal, despite the complexity and continuous regulation of metabolic reactions of living cells.     

A versatile palladium catalyst system for Suzuki-Miyaura coupling of alkenyl tosylates and mesylates

A general and effective palladium system for Suzuki-Miyaura coupling of alkenyl electrophiles under mild reaction conditions is reported. With the Pd(OAc)(2)/CM-phos system, a variety of alkenyl tosylates are coupled well with ArB(OH)(2). Moreover, the first successful examples of using alkenyl mesylates in alkenylation are also described.