The congruence subgroup problem

This is a short survey of the progress on the congruence subgroup problem since the sixties when the first major results on the integral unimodular groups appeared. It is aimed at the non-specialists and avoids technical details.Comment: 10 page

He II optical depth and UV escape fraction of galaxies

We study the effect of H I ionizing photons escaping from high-redshift (high-z) galaxies have on the He II ionizing ultraviolet background (UVB) radiation. While these photons do not directly interact with He II ions, we show that they play an important role, through radiative transport, in modifying the shape of He II ionizing part of UVB spectrum. Within the observed range of UV escape from galaxies, we show that the rapid increase in He II Lyman alpha effective optical depth at z~2.7 can naturally be explained by radiative transport effects. Therefore, the relationship between a well measured He II Lyman alpha effective optical depth and the redshift in the post-He II reionization era can be used to place additional constraints on the redshift evolution of UV escape from high-z galaxies. Our study also suggests that the escape fraction of H I ionizing photons from galaxies has an important role in the fluctuations of the He II ionizing UVB.Comment: Published in MNRAS Letters, replacement of a figure and minor text changes corresponding to published versio

Decrease in gyrase A protein expression in _E. coli_ cells inhibited by antisense ribozymes

RNase P complexed with external guide sequence (EGS) represents a novel nucleic-acid-based gene interference approach to modulate gene expression. Nucleic acid-based gene interference technologies represent promising strategies for specific inhibition of mRNA sequences of choice. Recently, small interfering RNAs have been implicated in inducing endogenous RNase of the RNA-induced silencing complex in the RNA interference pathway to inhibit gene expression and growth of several human viruses. We report down regulation of protein expression of _E. coli_ gyrase A, an essential gene for DNA supercoiling and antibiotic susceptibility in BL21 (DE3) strain of _E. coli_, using Ribonuclease P based external guide sequence (EGS) technique. EGS directed against gyrase A gene that was cloned into pUC vector, which contains the ampicillin (Amp) resistance gene. The recombinant plasmid pT7EGyrA was transformed into BL21 (DE3) and inductions were performed using IPTG. Western blot was done to investigate the downregulation of gyrase A protein. The results showed a significant decrease of gyrase A suggesting the utility of EGS RNAs in gene therapy applications, by inhibiting the expression of essential proteins

A topological realization of the congruence subgroup Kernel A

A number of years ago, Kumar Murty pointed out to me that the computation of the fundamental group of a Hilbert modular surface ([7],IV,${\S}$6), and the computation of the congruence subgroup kernel of SL(2) ([6]) were surprisingly similar. We puzzled over this, in particular over the role of elementary matrices in both computations. We formulated a very general result on the fundamental group of a Satake compactification of a locally symmetric space. This lead to our joint paper [1] with Lizhen Ji and Les Saper on these fundamental groups. Although the results in it were intriguingly similar to the corresponding calculations of the congruence subgroup kernel of the underlying algebraic group in [5], we were not able to demonstrate a direct connection (cf. [1], ${\S}$7). The purpose of this note is to explain such a connection. A covering space is constructed from inverse limits of reductive Borel-Serre compactifications. The congruence subgroup kernel then appears as the group of deck transformations of this covering. The key to this is the computation of the fundamental group in [1]