On Capacity Optimality of OAMP: Beyond IID Sensing Matrices and Gaussian Signaling

This paper investigates a large unitarily invariant system (LUIS) involving a unitarily invariant sensing matrix, an arbitrarily fixed signal distribution, and forward error control (FEC) coding. A universal Gram-Schmidt orthogonalization is considered for the construction of orthogonal approximate message passing (OAMP), which renders the results applicable to general prototypes without the differentiability restriction. For OAMP with Lipschitz continuous local estimators, we develop two variational single-input-single-output transfer functions, based on which we analyze the achievable rate of OAMP. Furthermore, when the state evolution of OAMP has a unique fixed point, we reveal that OAMP reaches the constrained capacity predicted by the replica method of the LUIS with an arbitrary signal distribution based on matched FEC coding. The replica method is rigorous for LUIS with Gaussian signaling and for certain sub-classes of LUIS with arbitrary signal distributions. Several area properties are established based on the variational transfer functions of OAMP. Meanwhile, we elaborate a replica constrained capacity-achieving coding principle for LUIS, based on which irregular low-density parity-check (LDPC) codes are optimized for binary signaling in the simulation results. We show that OAMP with the optimized codes has significant performance improvement over the un-optimized ones and the well-known Turbo linear MMSE algorithm. For quadrature phase-shift keying (QPSK) modulation, replica constrained capacity-approaching bit error rate (BER) performances are observed under various channel conditions.Comment: Single column, 34 pages, 9 figure

Limits of single-photon storage in a single Λ\Lambda-type atom

We theoretically investigate the limits of single-photon storage in a single $\Lambda$-type atom, specifically the trade-off between storage efficiency and storage speed. We show that a control field can accelerate the storage process without degrading efficiency too much. However, the storage speed is ultimately limited by the total decay rate of the involved excited state. For a single-photon pulse propagating in a regular one-dimensional waveguide, the storage efficiency has an upper limit of $50 \%$. Perfect single-photon storage can be achieved by using a chiral waveguide or the Sagnac interferometry. By comparing the storage efficiencies of Fock-state and coherent-state pulses, we reveal the influence of quantum statistics of light on photon storage at the single-photon level.Comment: 10 pages and 10 figure

Postoperative influences of the torsional phacoemulsification on foveal thickness and corneal edema

AIM: To report the influences onfoveal thickness and corneal edema after torsional phacoemulsification.<p>METHODS: Totally 52 patients(52 eyes)with age-related cataract were randomly assigned to phacoemulsification using torsional mode(26 eyes)or conventional ultrasound mode(26 eyes). The foveal thickness examined by optical coherence tomography(OCT)after surgery at 1, 4 and 12wk and corneal edema was examined by slit lamp after surgery at 1d.<p>RESULTS: The postoperative averagefoveal thickness datas of the two groups, comparing with corresponding preoperative datas, were significantly augmented at 1, 4 and 12wk(<i>P</i><0.05); the difference of foveal thickness was obviously augmented at 1wk postoperatively(<i>P</i><0.05), was no obvious differences at 4 and 12wk(<i>P</i>>0.05). The effects of corneal edema in torsional group were slighter(<i>P</i><0.05). <p>CONCLUSION: The postoperative influences onfoveal thickness and corneal edema with torsional mode are slighter than that with ultrasound mode, and the postoperative reactions with torsional mode are efficiently reduced

A systematic study on the binding energy of Λ\Lambda hypernuclei

In this paper, we calculated the binding energy per baryon of the $\Lambda$ hypernuclei systemically, using the relativistic mean field theory (RMF) in a statistic frame. Some resemble properties are found among most of the hypernuclei found in experiments. The data show that a $\Lambda$ hypernucleus will be more stable, if it is composed of a $\Lambda$ hyperon adding to a stable normal nuclear core, or a $\Lambda$ hyperon replacing a neutron in a stable normal nuclear core. According to our calculations, existences of some new $\Lambda$ hypernuclei are predicted under the frame of RMF.Comment: 8 pages, 6 figures, 3 table

Attenuation of transcriptional bursting in mRNA transport

Due to the stochastic nature of biochemical processes, the copy number of any given type of molecule inside a living cell often exhibits large temporal fluctuations. Here, we develop analytic methods to investigate how the noise arising from a bursting input is reshaped by a transport reaction which is either linear or of the Michaelis-Menten type. A slow transport rate smoothes out fluctuations at the output end and minimizes the impact of bursting on the downstream cellular activities. In the context of gene expression in eukaryotic cells, our results indicate that transcriptional bursting can be substantially attenuated by the transport of mRNA from nucleus to cytoplasm. Saturation of the transport mediators or nuclear pores contributes further to the noise reduction. We suggest that the mRNA transport should be taken into account in the interpretation of relevant experimental data on transcriptional bursting.Comment: 18 pages, 3 figure

4-Fluoro-2-[(E)-2-pyridyliminomethyl]phenol

In the title compound, C12H9FN2O, the dihedral angle between the benzene ring and the pyridine ring is 4.35 (16)°. The mol­ecular conformation is stabilized by an intra­molecular O—H⋯N hydrogen bond