Statistical stability in time reversal

When a signal is emitted from a source, recorded by an array of transducers, time reversed and re-emitted into the medium, it will refocus approximately on the source location. We analyze the refocusing resolution in a high frequency, remote sensing regime, and show that, because of multiple scattering, in an inhomogeneous or random medium it can improve beyond the diffraction limit. We also show that the back-propagated signal from a spatially localized narrow-band source is self-averaging, or statistically stable, and relate this to the self-averaging properties of functionals of the Wigner distribution in phase space. Time reversal from spatially distributed sources is self-averaging only for broad-band signals. The array of transducers operates in a remote-sensing regime so we analyze time reversal with the parabolic or paraxial wave equation

Time Reversal Communication in Rayleigh-Fading Broadcast Channels with Pinholes

The paper presents an analysis of the time reversal in independent-multipath Rayleigh-fading channels with $N$ inputs (transmitters) and $M$ outputs (receivers). The main issues addressed are the condition of statistical stability, the rate of information transfer and the effect of pinholes. The stability condition is proved to be $MC\ll N_{\rm eff}B$ for broadband channels and $M\ll N_{\rm eff}$ for narrowband channels where $C$ is the symbol rate, $B$ is the bandwidth and $N_{\rm eff}$ is the {\em effective} number (maybe less than 1) of transmitters. It is shown that when the number of screens, $n-1$, is relatively low compared to the logarithm of numbers of pinholes $N_{\rm eff}$ is given by the {\em harmonic} (or {\em inverse}) {\em sum} of the number of transmitters and the numbers of pinholes at all screens. The novel idea of the effective number of time reversal array (TRA) elements is introduced to derive the stability condition and estimate the channel capacity in the presence of multi-screen pinholes. The information rate, under the constraints of the noise power $\nu$ per unit frequency and the average total power $P$, attains the supremum $P/\nu$ in the regime $M\wedge N_{\rm eff}\gg P/(\nu B)$. In particular, when $N_{\rm eff}\gg M\gg P/(B\nu)$ the optimal information rate can be achieved with statistically stable, sharply focused signals.Comment: Corrected typos and minor change of conten

Early redox activities modulate Xenopus tail regeneration.

Redox state sustained by reactive oxygen species (ROS) is crucial for regeneration; however, the interplay between oxygen (O2), ROS and hypoxia-inducible factors (HIF) remains elusive. Here we observe, using an optic-based probe (optrode), an elevated and steady O2 influx immediately upon amputation. The spatiotemporal O2 influx profile correlates with the regeneration of Xenopus laevis tadpole tails. Inhibition of ROS production but not ROS scavenging decreases O2 influx. Inhibition of HIF-1α impairs regeneration and stabilization of HIF-1α induces regeneration in the refractory period. In the regeneration bud, hypoxia correlates with O2 influx, ROS production, and HIF-1α stabilization that modulate regeneration. Further analyses reveal that heat shock protein 90 is a putative downstream target of HIF-1α while electric current reversal is a de facto downstream target of HIF-1α. Collectively, the results show a mechanism for regeneration via the orchestration of O2 influx, ROS production, and HIF-1α stabilization

Source localization in random acoustic waveguides

Mode coupling due to scattering by weak random inhomogeneities in waveguides leads to loss of coherence of wave fields at long distances of propagation. This in turn leads to serious deterioration of coherent source localization methods, such as matched field. We study with analysis and numerical simulations how such deterioration occurs and introduce a novel incoherent approach for long range source localization in random waveguides. It is based on a special form of transport theory for the incoherent fluctuations of the wave field. We study theoretically the statistical stability of the method and illustrate its performance with numerical simulations. We also show how it can be used to estimate the correlation function of the random fluctuations of the wave speed