Random Unitaries Give Quantum Expanders

We show that randomly choosing the matrices in a completely positive map from the unitary group gives a quantum expander. We consider Hermitian and non-Hermitian cases, and we provide asymptotically tight bounds in the Hermitian case on the typical value of the second largest eigenvalue. The key idea is the use of Schwinger-Dyson equations from lattice gauge theory to efficiently compute averages over the unitary group.Comment: 14 pages, 1 figur

Information capacity of optical fiber channels with zero average dispersion

We study the statistics of optical data transmission in a noisy nonlinear fiber channel with a weak dispersion management and zero average dispersion. Applying path integral methods we have found exactly the probability density functions of channel output both for a non-linear noisy channel and for a linear channel with additive and multiplicative noise. We have obtained analytically a lower bound estimate for the Shannon capacity of considered nonlinear fiber channel.Comment: 4 pages, subbmited to Phys. Rev. Let

Spatiotemporal Response of Crystals in X-ray Bragg Diffraction

The spatiotemporal response of crystals in x-ray Bragg diffraction resulting from excitation by an ultra-short, laterally confined x-ray pulse is studied theoretically. The theory presents an extension of the analysis in symmetric reflection geometry [1] to the generic case, which includes Bragg diffraction both in reflection (Bragg) and transmission (Laue) asymmetric scattering geometries. The spatiotemporal response is presented as a product of a crystal-intrinsic plane wave spatiotemporal response function and an envelope function defined by the crystal-independent transverse profile of the incident beam and the scattering geometry. The diffracted wavefields exhibit amplitude modulation perpendicular to the propagation direction due to both angular dispersion and the dispersion due to Bragg's law. The characteristic measure of the spatiotemporal response is expressed in terms of a few parameters: the extinction length, crystal thickness, Bragg angle, asymmetry angle, and the speed of light. Applications to self-seeding of hard x-ray free electron lasers are discussed, with particular emphasis on the relative advantages of using either the Bragg or Laue scattering geometries. Intensity front inclination in asymmetric diffraction can be used to make snapshots of ultra-fast processes with femtosecond resolution

Time dependence of Bragg forward scattering and self-seeding of hard x-ray free-electron lasers

Free-electron lasers (FELs) can now generate temporally short, high power x-ray pulses of unprecedented brightness, even though their longitudinal coherence is relatively poor. The longitudinal coherence can be potentially improved by employing narrow bandwidth x-ray crystal optics, in which case one must also understand how the crystal affects the field profile in time and space. We frame the dynamical theory of x-ray diffraction as a set of coupled waves in order to derive analytic expressions for the spatiotemporal response of Bragg scattering from temporally short incident pulses. We compute the profiles of both the reflected and forward scattered x-ray pulses, showing that the time delay of the wave $\tau$ is linked to its transverse spatial shift $\Delta x$ through the simple relationship $\Delta x = c\tau \cot\theta$, where $\theta$ is the grazing angle of incidence to the diffracting planes. Finally, we apply our findings to obtain an analytic description of Bragg forward scattering relevant to monochromatically seed hard x-ray FELs.Comment: 11 pages, 6 figure

Ultimate Precision of Adaptive Noise Estimation

We consider the estimation of noise parameters in a quantum channel, assuming the most general strategy allowed by quantum mechanics. This is based on the exploitation of unlimited entanglement and arbitrary quantum operations, so that the channel inputs may be interactively updated. In this general scenario, we draw a novel connection between quantum metrology and teleportation. In fact, for any teleportation-covariant channel (e.g., Pauli, erasure, or Gaussian channel), we find that adaptive noise estimation cannot beat the standard quantum limit, with the quantum Fisher information being determined by the channel’s Choi matrix. As an example, we establish the ultimate precision for estimating excess noise in a thermal-loss channel, which is crucial for quantum cryptography. Because our general methodology applies to any functional that is monotonic under trace-preserving maps, it can be applied to simplify other adaptive protocols, including those for quantum channel discrimination. Setting the ultimate limits for noise estimation and discrimination paves the way for exploring the boundaries of quantum sensing, imaging, and tomography

Survivin a radiogenetic promoter for glioblastoma viral gene therapy independently from CArG motifs

BACKGROUND: Radiogenetic therapy is a novel approach in the treatment of cancer, which employs genetic modification to alter the sensitivity of tumor cells to the effect of applied radiation. AIM: To select a potent radiation inducible promoter in the context of brain tumors and to investigate if CArG radio responsive motifs or other elements in the promoter nucleotide sequences can correlate to its response to radiation. METHODS: To select initial candidates for promoter inducible elements, the levels of mRNA expression of six different promoters were assessed using Quantitative RTPCR in D54 MG cells before and after radiation exposure. Recombinant Ad/reporter genes driven by five different promoters; CMV, VEGF, FLT-1, DR5 and survivin were constructed. Glioma cell lines were infected with different multiplicity of infection of the (promoter) Ad or CMV Ad. Cells were then exposed to a range of radiation (0–12 Gy) at single fraction. Fluorescent microscopy, Luc assay and X-gal staining was used to detect the level of expression of related genes. Different glioma cell lines and normal astrocytes were infected with Ad survivin and exposed to radiation. The promoters were analyzed for presence of CArG radio-responsive motifs and CCAAT box consensus using NCBI blast bioinformatics software. RESULTS: Radiotherapy increases the expression of gene expression by 1.25–2.5 fold in different promoters other than survivin after 2 h of radiation. RNA analysis was done and has shown an increase in copy number of tenfold for survivin. Most importantly cells treated with RT and Ad Luc driven by survivin promoter showed a fivefold increase in expression after 2 Gy of radiation in comparison to non-irradiated cells. Presence or absence of CArG motifs did not correlate with promoter response to radiation. Survivin with the best response to radiation had the lowest number of CCAAT box. CONCLUSION: Survivin is a selective potent radiation inducible promoter for glioblastoma viral gene therapy and this response to radiation could be independent of CArG motifs

A stochastic network with mobile users in heavy traffic

We consider a stochastic network with mobile users in a heavy-traffic regime. We derive the scaling limit of the multi-dimensional queue length process and prove a form of spatial state space collapse. The proof exploits a recent result by Lambert and Simatos which provides a general principle to establish scaling limits of regenerative processes based on the convergence of their excursions. We also prove weak convergence of the sequences of stationary joint queue length distributions and stationary sojourn times.Comment: Final version accepted for publication in Queueing Systems, Theory and Application

A novel Doppler backscattering (DBS) system to simultaneously monitor radio frequency plasma fluctuations and low frequency turbulence

A novel quadrature Doppler Backscattering (DBS) system has been developed and optimized for the E-band (60-90GHz) frequency range using either O-mode or X-mode polarization in DIII-D plasmas. In general, DBS measures the amplitude of density fluctuations and their velocity in the lab frame. The system can simultaneously monitor both low-frequency turbulence (f < 10MHz) and radiofrequency plasma density fluctuations over a selectable frequency range (20-500 MHz). Detection of high-frequency fluctuations has been demonstrated for low harmonics of the ion cyclotron frequency (e.g., 2fci~23MHz) and externally driven high-frequency helicon waves (f = 476MHz) using an adjustable frequency down conversion system. Importantly, this extends the application of DBS to a high-frequency spectral domain while maintaining important turbulence and flow measurement capabilities. This unique system has low phase noise, good temporal resolution (sub-millisecond) and excellent wavenumber coverage (k_{\theta} ~ 1-20cm^{-1} and k_r ~ 20-30cm^{-1}). As a demonstration, localized internal DIII-D plasma measurements are presented from turbulence (f = 20MHz) as well as fluctuations around 476MHz driven by an external high-power 476 MHz helicon wave antenna. In the future, helicon measurements will be used to validate GENRAY and AORSA modeling tools for prediction of helicon wave propagation, absorption and current drive location for the newly installed helicon current drive system on DIII-D.Comment: 13 pages, 14 figs, journal pape

On directed information theory and Granger causality graphs

Directed information theory deals with communication channels with feedback. When applied to networks, a natural extension based on causal conditioning is needed. We show here that measures built from directed information theory in networks can be used to assess Granger causality graphs of stochastic processes. We show that directed information theory includes measures such as the transfer entropy, and that it is the adequate information theoretic framework needed for neuroscience applications, such as connectivity inference problems.Comment: accepted for publications, Journal of Computational Neuroscienc

Predictability in the large: an extension of the concept of Lyapunov exponent

We investigate the predictability problem in dynamical systems with many degrees of freedom and a wide spectrum of temporal scales. In particular, we study the case of $3D$ turbulence at high Reynolds numbers by introducing a finite-size Lyapunov exponent which measures the growth rate of finite-size perturbations. For sufficiently small perturbations this quantity coincides with the usual Lyapunov exponent. When the perturbation is still small compared to large-scale fluctuations, but large compared to fluctuations at the smallest dynamically active scales, the finite-size Lyapunov exponent is inversely proportional to the square of the perturbation size. Our results are supported by numerical experiments on shell models. We find that intermittency corrections do not change the scaling law of predictability. We also discuss the relation between finite-size Lyapunov exponent and information entropy.Comment: 4 pages, 2 Postscript figures (included), RevTeX 3.0, files packed with uufile