Optical phonon scattering and theory of magneto-polarons in a quantum cascade laser in a strong magnetic field

We report a theoretical study of the carrier relaxation in a quantum cascade laser (QCL) subjected to a strong magnetic field. Both the alloy (GaInAs) disorder effects and the Frohlich interaction are taken into account when the electron energy differences are tuned to the longitudinal optical (LO) phonon energy. In the weak electron-phonon coupling regime, a Fermi's golden rule computation of LO phonon scattering rates shows a very fast non-radiative relaxation channel for the alloy broadened Landau levels (LL's). In the strong electron-phonon coupling regime, we use a magneto-polaron formalism and compute the electron survival probabilities in the upper LL's with including increasing numbers of LO phonon modes for a large number of alloy disorder configurations. Our results predict a nonexponential decay of the upper level population once electrons are injected in this state.Comment: 10 pages, 23 figure

Bistability of an In Vitro Synthetic Autoregulatory Switch

The construction of synthetic biochemical circuits is an essential step for developing quantitative understanding of information processing in natural organisms. Here, we report construction and analysis of an in vitro circuit with positive autoregulation that consists of just four synthetic DNA strands and three enzymes, bacteriophage T7 RNA polymerase, Escherichia coli ribonuclease (RNase) H, and RNase R. The modularity of the DNA switch template allowed a rational design of a synthetic DNA switch regulated by its RNA output acting as a transcription activator. We verified that the thermodynamic and kinetic constraints dictated by the sequence design criteria were enough to experimentally achieve the intended dynamics: a transcription activator configured to regulate its own production. Although only RNase H is necessary to achieve bistability of switch states, RNase R is necessary to maintain stable RNA signal levels and to control incomplete degradation products. A simple mathematical model was used to fit ensemble parameters for the training set of experimental results and was then directly applied to predict time-courses of switch dynamics and sensitivity to parameter variations with reasonable agreement. The positive autoregulation switches can be used to provide constant input signals and store outputs of biochemical networks and are potentially useful for chemical control applications

Hamming Compressed Sensing

Compressed sensing (CS) and 1-bit CS cannot directly recover quantized signals and require time consuming recovery. In this paper, we introduce \textit{Hamming compressed sensing} (HCS) that directly recovers a k-bit quantized signal of dimensional $n$ from its 1-bit measurements via invoking $n$ times of Kullback-Leibler divergence based nearest neighbor search. Compared with CS and 1-bit CS, HCS allows the signal to be dense, takes considerably less (linear) recovery time and requires substantially less measurements ($\mathcal O(\log n)$). Moreover, HCS recovery can accelerate the subsequent 1-bit CS dequantizer. We study a quantized recovery error bound of HCS for general signals and "HCS+dequantizer" recovery error bound for sparse signals. Extensive numerical simulations verify the appealing accuracy, robustness, efficiency and consistency of HCS.Comment: 33 pages, 8 figure