Arithmetic purity of strong approximation for homogeneous spaces

We prove that any open subset $U$ of a semi-simple simply connected quasi-split linear algebraic group $G$ with ${codim} (G\setminus U, G)\geq 2$ over a number field satisfies strong approximation by establishing a fibration of $G$ over a toric variety. We also prove a similar result of strong approximation with Brauer-Manin obstruction for a partial equivariant smooth compactification of a homogeneous space where all invertible functions are constant and the semi-simple part of the linear algebraic group is quasi-split. Some semi-abelian varieties of any given dimension where the complements of a rational point do not satisfy strong approximation with Brauer-Manin obstruction are given

Signal Transduction Pathways in the Pentameric Ligand-Gated Ion Channels

The mechanisms of allosteric action within pentameric ligand-gated ion channels (pLGICs) remain to be determined. Using crystallography, site-directed mutagenesis, and two-electrode voltage clamp measurements, we identified two functionally relevant sites in the extracellular (EC) domain of the bacterial pLGIC from Gloeobacter violaceus (GLIC). One site is at the C-loop region, where the NQN mutation (D91N, E177Q, and D178N) eliminated inter-subunit salt bridges in the open-channel GLIC structure and thereby shifted the channel activation to a higher agonist concentration. The other site is below the C-loop, where binding of the anesthetic ketamine inhibited GLIC currents in a concentration dependent manner. To understand how a perturbation signal in the EC domain, either resulting from the NQN mutation or ketamine binding, is transduced to the channel gate, we have used the Perturbation-based Markovian Transmission (PMT) model to determine dynamic responses of the GLIC channel and signaling pathways upon initial perturbations in the EC domain of GLIC. Despite the existence of many possible routes for the initial perturbation signal to reach the channel gate, the PMT model in combination with Yen's algorithm revealed that perturbation signals with the highest probability flow travel either via the β1-β2 loop or through pre-TM1. The β1-β2 loop occurs in either intra- or inter-subunit pathways, while pre-TM1 occurs exclusively in inter-subunit pathways. Residues involved in both types of pathways are well supported by previous experimental data on nAChR. The direct coupling between pre-TM1 and TM2 of the adjacent subunit adds new insight into the allosteric signaling mechanism in pLGICs. © 2013 Mowrey et al

Liquid rocket combustor computer code development

The Advanced Rocket Injector/Combustor Code (ARICC) that has been developed to model the complete chemical/fluid/thermal processes occurring inside rocket combustion chambers are highlighted. The code, derived from the CONCHAS-SPRAY code originally developed at Los Alamos National Laboratory incorporates powerful features such as the ability to model complex injector combustion chamber geometries, Lagrangian tracking of droplets, full chemical equilibrium and kinetic reactions for multiple species, a fractional volume of fluid (VOF) description of liquid jet injection in addition to the gaseous phase fluid dynamics, and turbulent mass, energy, and momentum transport. Atomization and droplet dynamic models from earlier generation codes are transplated into the present code. Currently, ARICC is specialized for liquid oxygen/hydrogen propellants, although other fuel/oxidizer pairs can be easily substituted

Optical Resonator Analog of a Two-Dimensional Topological Insulator

A lattice of optical ring resonators can exhibit a topological insulator phase, with the role of spin played by the direction of propagation of light within each ring. Unlike the system studied by Hafezi et al., topological protection is achieved without fine-tuning the inter-resonator couplings, which are given the same periodicity as the underlying lattice. The topological insulator phase occurs for strong couplings, when the tight-binding method is inapplicable. Using the transfer matrix method, we derive the bandstructure and phase diagram, and demonstrate the existence of robust edge states. When gain and loss are introduced, the system functions as a diode for coupled resonator modes.Comment: 10 pages, 9 figure

Mathematical problems for complex networks

Copyright @ 2012 Zidong Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This article is made available through the Brunel Open Access Publishing Fund.Complex networks do exist in our lives. The brain is a neural network. The global economy is a network of national economies. Computer viruses routinely spread through the Internet. Food-webs, ecosystems, and metabolic pathways can be represented by networks. Energy is distributed through transportation networks in living organisms, man-made infrastructures, and other physical systems. Dynamic behaviors of complex networks, such as stability, periodic oscillation, bifurcation, or even chaos, are ubiquitous in the real world and often reconfigurable. Networks have been studied in the context of dynamical systems in a range of disciplines. However, until recently there has been relatively little work that treats dynamics as a function of network structure, where the states of both the nodes and the edges can change, and the topology of the network itself often evolves in time. Some major problems have not been fully investigated, such as the behavior of stability, synchronization and chaos control for complex networks, as well as their applications in, for example, communication and bioinformatics