Emergence of power laws with different power-law exponents from reversal quasi-symmetry and Gibrat’s law

To explore the emergence of power laws in social and economic phenomena, the authors discuss the mechanism whereby reversal quasi-symmetry and Gibrat’s law lead to power laws with different powerlaw exponents. Reversal quasi-symmetry is invariance under the exchange of variables in the joint PDF (probability density function). Gibrat’s law means that the conditional PDF of the exchange rate of variables does not depend on the initial value. By employing empirical worldwide data for firm size, from categories such as plant assets K, the number of employees L, and sales Y in the same year, reversal quasi-symmetry, Gibrat’s laws, and power-law distributions were observed. We note that relations between power-law exponents and the parameter of reversal quasi-symmetry in the same year were first confirmed. Reversal quasi-symmetry not only of two variables but also of three variables was considered. The authors claim the following. There is a plane in 3-dimensional space (log K, log L, log Y ) with respect to which the joint PDF PJ (K,L, Y ) is invariant under the exchange of variables. The plane accurately fits empirical data (K,L, Y ) that follow power-law distributions. This plane is known as the Cobb-Douglas production function, Y = AKαLβ which is frequently hypothesized in economics.

The DNA methyltransferase Dnmt1 directly interacts with the SET and RING finger-associated (SRA) domain of the multifunctional protein Uhrf1 to facilitate accession of the catalytic center to hemi-methylated DNA

This research was originally published in Journal of Biological Chemistry. Ahmet Can Berkyurek, Isao Suetake, Kyohei Arita, Kohei Takeshita, Atsushi Nakagawa, Masahiro Shirakawa and Shoji Tajima. The DNA methyltransferase Dnmt1 directly interacts with the SET and RING finger-associated (SRA) domain of the multifunctional protein Uhrf1 to facilitate accession of the catalytic center to hemi-methylated DNA. Journal of Biological Chemistry. 2014; 289, 379-386. © the American Society for Biochemistry and Molecular Biology

Deoxyfluorination of alcohols using N,N-diethyl-α,α-difluoro-(m-methylbenzyl)amine

Deoxyfluorination of alcohols was carried out using N,N-diethyl-α,α-difluoro-(m-methylbenzyl)amine (DFMBA). Primary alcohols were effectively converted to fluorides under microwave irradiation or conventional heating. Deoxyfluorination of an anomeric hydroxy group in sugars by DFMBA proceeded at below room temperature and glycosyl fluorides could be obtained in good yields. The deoxyfluorination reaction chemoselectively proceeded and various protecting groups on the sugar can survive under the reaction conditions

Selective synthesis of fluorinated carbohydrates using N,N-diethyl-α,α-difluoro-(m-methylbenzyl)amine

Deoxyfluorination of a hydroxy group in rbohydrates was carried out using N,N-diethyl-α,α-difluoro-(m-methylbenzyl)amine. A primary hydroxy group in carbohydrates was effectively converted to the corresponding fluoride under micro-wave irradiation or at 100°C. Deoxyfluorination of hydroxy groups at the anomeric position proceeded at below room temperature, and glycosyl fluorides could be obtained in good yields. The reaction chemoselectively proceeded, and various protecting groups of carbohydrates can survive under the reaction conditions