CT Image Reconstruction by Spatial-Radon Domain Data-Driven Tight Frame Regularization

This paper proposes a spatial-Radon domain CT image reconstruction model based on data-driven tight frames (SRD-DDTF). The proposed SRD-DDTF model combines the idea of joint image and Radon domain inpainting model of \cite{Dong2013X} and that of the data-driven tight frames for image denoising \cite{cai2014data}. It is different from existing models in that both CT image and its corresponding high quality projection image are reconstructed simultaneously using sparsity priors by tight frames that are adaptively learned from the data to provide optimal sparse approximations. An alternative minimization algorithm is designed to solve the proposed model which is nonsmooth and nonconvex. Convergence analysis of the algorithm is provided. Numerical experiments showed that the SRD-DDTF model is superior to the model by \cite{Dong2013X} especially in recovering some subtle structures in the images

Shot noise of spin current and spin transfer torque

We report the theoretical investigation of noise spectrum of spin current and spin transfer torque for non-colinear spin polarized transport in a spin-valve device which consists of normal scattering region connected by two ferromagnetic electrodes. Our theory was developed using non-equilibrium Green's function method and general non-linear $S^\sigma-V$ and $S^\tau-V$ relations were derived as a function of angle $\theta$ between magnetization of two leads. We have applied our theory to a quantum dot system with a resonant level coupled with two ferromagnetic electrodes. It was found that for the MNM system, the auto-correlation of spin current is enough to characterize the fluctuation of spin current. For a system with three ferromagnetic layers, however, both auto-correlation and cross-correlation of spin current are needed to characterize the noise spectrum of spin current. Furthermore, the spin transfer torque and the torque noise were studied for the MNM system. For a quantum dot with a resonant level, the derivative of spin torque with respect to bias voltage is proportional to $\sin\theta$ when the system is far away from the resonance. When the system is near the resonance, the spin transfer torque becomes non-sinusoidal function of $\theta$. The derivative of noise spectrum of spin transfer torque with respect to the bias voltage $N_\tau$ behaves differently when the system is near or far away from the resonance. Specifically, the differential shot noise of spin transfer torque $N_\tau$ is a concave function of $\theta$ near the resonance while it becomes convex function of $\theta$ far away from resonance. For certain bias voltages, the period $N_\tau(\theta)$ becomes $\pi$ instead of $2\pi$. For small $\theta$, it was found that the differential shot noise of spin transfer torque is very sensitive to the bias voltage and the other system parameters.Comment: 15pages, 6figure

On Beltrami Model of de Sitter Spacetime

Based on some important properties of $dS$ space, we present a Beltrami model ${\cal B}_\Lambda$ that may shed light on the observable puzzle of $dS$ space and the paradox between the special relativity principle and cosmological principle. In ${\cal B}_\Lambda$, there are inertial-type coordinates and inertial-type observers. Thus, the classical observables can be defined for test particles and light signals. In addition, by choosing the definition of simultaneity the Beltrami metric is transformed to the Robertson-Walker-like metric. It is of positive spatial curvature of order $\Lambda$. This is more or less indicated already by the CMB power spectrum from WMAP and should be further confirmed by its data in large scale.Comment: 4 page

New universal gates for topological quantum computation with Fibonacci-ε\boldsymbol{\varepsilon} composite Majorana edge modes on topological superconductor multilayers

We propose a new design of universal topological quantum computer device through a hybrid of the 1-, 2- and 7-layers of chiral topological superconductor ($\chi$TSC) thin films. Based on the $SO(7)_1/(G_2)_1$ coset construction, strongly correlated Majorana fermion edge modes on the 7-layers of $\chi$TSC are factorized into the composite of the Fibonacci $\tau$-anyon and $\varepsilon$-anyon modes in the tricritical Ising model. Furthermore, the deconfinement of $\tau$ and $\varepsilon$ via the interacting potential gives the braiding of either $\tau$ or $\varepsilon$. Topological phase gates are assembled by the braidings. With these topological phase gates, we find a set of fully topological universal gates for the $(\tau,\varepsilon)$ composite Majorana-Ising-type quantum computation. Because the Hilbert space still possesses a tensor product structure of quibts and is characterized by the fermion parities, encoding quantum information in this machine is more efficient and substantial than that with Fibonacci anyons. The computation results is easier to be read out by electric signals, so are the initial data inputted.Comment: 6 pages, 3 figues, revised versio

Snyder's Model -- de Sitter Special Relativity Duality and de Sitter Gravity

Between Snyder's quantized space-time model in de Sitter space of momenta and the \dS special relativity on \dS-spacetime of radius $R$ with Beltrami coordinates, there is a one-to-one dual correspondence supported by a minimum uncertainty-like argument. Together with Planck length $\ell_P$, $R\simeq (3/\Lambda)^{1/2}$ should be a fundamental constant. They lead to a dimensionless constant $g{\sim\ell_PR^{-1}}=(G\hbar c^{-3}\Lambda/3)^{1/2}\sim 10^{-61}$. These indicate that physics at these two scales should be dual to each other and there is in-between gravity of local \dS-invariance characterized by $g$. A simple model of \dS-gravity with a gauge-like action on umbilical manifolds may show these characters. It can pass the observation tests and support the duality.Comment: 32 page