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

ELT requirements for future observations of the Intergalactic Medium

We summarise the science cases for an ELT that were presented in the parallel session on the intergalactic medium, and the open discussion that followed the formal presentations. Observations of the IGM with an ELT provides tremendous potential for dramatic improvements in current programmes in a very wide variety of subjects. These range from fundamental physics (expansion of the Universe, nature of the dark matter, variation of physical constants), cosmology (geometry of the Universe, large-scale structure), reionisation (ionisation state of the IGM at high redshift>6, to more traditional astronomy, such as the interactions between galaxies and the IGM (metal enrichment, galactic winds and other forms of feedback), and the study of the interstellar medium in high redshift galaxies through molecules. The requirements on ELTs and their instruments for fulfilling this potential are discussed.Comment: proceedings IAU 232 "Extremely Large Telescopes", eds Whitelock, Leibundgut and Dennefeld, comments welcom

Optimal Stabilization using Lyapunov Measures

Numerical solutions for the optimal feedback stabilization of discrete time dynamical systems is the focus of this paper. Set-theoretic notion of almost everywhere stability introduced by the Lyapunov measure, weaker than conventional Lyapunov function-based stabilization methods, is used for optimal stabilization. The linear Perron-Frobenius transfer operator is used to pose the optimal stabilization problem as an infinite dimensional linear program. Set-oriented numerical methods are used to obtain the finite dimensional approximation of the linear program. We provide conditions for the existence of stabilizing feedback controls and show the optimal stabilizing feedback control can be obtained as a solution of a finite dimensional linear program. The approach is demonstrated on stabilization of period two orbit in a controlled standard map

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