Translation and Rotation Invariant Multiscale Image Registration

The most recent research involved registering images in the presence of translations and rotations using one iteration of the redundant discrete wavelet transform. We extend this work by creating a new multiscale transform to register two images with translation or rotation differences, independent of scale differences between the images. Our two-dimensional multiscale transform uses an innovative combination of lowpass filtering and the continuous wavelet transform to mimic the two-dimensional redundant discrete wavelet transform. This allows us to obtain multiple subbands at various scales while maintaining the desirable properties of the redundant discrete wavelet transform. Whereas the discrete wavelet transform produces results only at dyadic scales, our new multiscale transform produces data at all integer scales. This added flexibility improves registration accuracy without greatly increasing computational complexity and permits accurate registration even in the presence of scale differences

Nonconventional odd denominator fractional quantum Hall states in the second Landau level

We report the observation of a new fractional quantum Hall state in the second Landau level of a two-dimensional electron gas at the Landau level filling factor $\nu=2+6/13$. We find that the model of noninteracting composite fermions can explain the magnitude of gaps of the prominent 2+1/3 and 2+2/3 states. The same model fails, however, to account for the gaps of the 2+2/5 and the newly observed 2+6/13 states suggesting that these two states are of exotic origin.omposite fermion model. However, the weaker 2+2/5 and 2+6/13 states deviate significantly suggesting that these states are of exotic origin

Electron Scattering in AlGaN/GaN Structures

We present data on mobility lifetime, $\tau_t$, quantum lifetime, $\tau_q$, and cyclotron resonance lifetime, $\tau_{CR}$, of a sequence of high-mobility two-dimensional electron gases in the AlGaN/GaN system, covering a density range of $\sim1-4.5\times10^{12}$cm$^{-2}$. We observe a large discrepancy between $\tau_q$ and $\tau_{CR}$ ($\tau_q\sim\tau_{CR}$/6) and explain it as the result of density fluctuations of only a few percent. Therefore, only $\tau_{CR}$ --and not $\tau_q$ -- is a reliable measure of the time between electron scattering events in these specimens. The ratio $\tau_t / \tau_{CR}$ increases with increasing density in this series of samples, but scattering over this density range remains predominantly in the large-angle scattering regime

Evidence for the Collective Nature of the Reentrant Integer Quantum Hall States of the Second Landau Level

We report an unexpected sharp peak in the temperature dependence of the magnetoresistance of the reentrant integer quantum Hall states in the second Landau level. This peak defines the onset temperature of these states. We find that in different spin branches the onset temperatures of the reentrant states scale with the Coulomb energy. This scaling provides direct evidence that Coulomb interactions play an important role in the formation of these reentrant states evincing their collective nature

Particle-hole Asymmetry of Fractional Quantum Hall States in the Second Landau Level of a Two-dimensional Hole System

We report the first unambiguous observation of a fractional quantum Hall state in the Landau level of a two-dimensional hole sample at the filling factor $\nu=8/3$. We identified this state by a quantized Hall resistance and an activated temperature dependence of the longitudinal resistance and found an energy gap of 40 mK. To our surprise the particle-hole conjugate state at filling factor $\nu=7/3$ in our sample does not develop down to 6.9 mK. This observation is contrary to that in electron samples in which the 7/3 state is typically more stable than the 8/3 state. We present evidence that the asymmetry between the 7/3 and 8/3 states in our hole sample is due to Landau level mixing