Quantum particle confined to a thin-layer volume: Non-uniform convergence toward the curved surface

We clearly refine the fundamental framework of the thin-layer quantization procedure, and further develop the procedure by taking the proper terms of degree one in $q_3$ ($q_3$ denotes the curvilinear coordinate variable perpendicular to curved surface) back into the surface quantum equation. The well-known geometric potential and kinetic term are modified by the surface thickness. Applying the developed formalism to a toroidal system obtains the modification for the kinetic term and the modified geometric potential including the influence of the surface thickness.Comment: 9 pages, 3 figure

Dynamics of domain wall in charged AdS dilaton black hole spacetime

For the $n-1$ dimensional FRW domain wall universe induced by $n$ dimensional charged dilaton black hole, its movement formula in the bulk can be rewrite as the expansion or collapsing of domain wall. By analysing, we found that in this static AdS space, the cosmologic behaviour of domain wall is particularly single. Even more surprising, it exists an anomaly that the domain wall has a motion area outside of horizon, in which it cannot be explained by our classical theory.Comment: 6 pages, 10figure

A Pyramid Scheme Model Based on "Consumption Rebate" Frauds

There are various types of pyramid schemes which have inflicted or are inflicting losses on many people in the world. We propose a pyramid scheme model which has the principal characters of many pyramid schemes appeared in recent years: promising high returns, rewarding the participants recruiting the next generation of participants, and the organizer will take all the money away when he finds the money from the new participants is not enough to pay the previous participants interest and rewards. We assume the pyramid scheme carries on in the tree network, ER random network, SW small-world network or BA scale-free network respectively, then give the analytical results of how many generations the pyramid scheme can last in these cases. We also use our model to analyse a pyramid scheme in the real world and we find the connections between participants in the pyramid scheme may constitute a SW small-world network.Comment: 17 pages, 10 figure

Sparse-View X-Ray CT Reconstruction Using ℓ1\ell_1 Prior with Learned Transform

A major challenge in X-ray computed tomography (CT) is reducing radiation dose while maintaining high quality of reconstructed images. To reduce the radiation dose, one can reduce the number of projection views (sparse-view CT); however, it becomes difficult to achieve high-quality image reconstruction as the number of projection views decreases. Researchers have applied the concept of learning sparse representations from (high-quality) CT image dataset to the sparse-view CT reconstruction. We propose a new statistical CT reconstruction model that combines penalized weighted-least squares (PWLS) and $\ell_1$ prior with learned sparsifying transform (PWLS-ST-$\ell_1$), and a corresponding efficient algorithm based on Alternating Direction Method of Multipliers (ADMM). To moderate the difficulty of tuning ADMM parameters, we propose a new ADMM parameter selection scheme based on approximated condition numbers. We interpret the proposed model by analyzing the minimum mean square error of its ($\ell_2$-norm relaxed) image update estimator. Our results with the extended cardiac-torso (XCAT) phantom data and clinical chest data show that, for sparse-view 2D fan-beam CT and 3D axial cone-beam CT, PWLS-ST-$\ell_1$ improves the quality of reconstructed images compared to the CT reconstruction methods using edge-preserving regularizer and $\ell_2$ prior with learned ST. These results also show that, for sparse-view 2D fan-beam CT, PWLS-ST-$\ell_1$ achieves comparable or better image quality and requires much shorter runtime than PWLS-DL using a learned overcomplete dictionary. Our results with clinical chest data show that, methods using the unsupervised learned prior generalize better than a state-of-the-art deep "denoising" neural network that does not use a physical imaging model.Comment: The first two authors contributed equally to this wor

Color-Magnitude Distribution of Face-on Nearby Galaxies in SDSS DR7

We have analyzed the distributions in the color-magnitude diagram (CMD) of a large sample of face-on galaxies to minimize the effect of dust extinctions on galaxy color. About 300 thousand galaxies with $log(a/b) <$ 0.2 and redshift $z < 0.2$ are selected from the SDSS DR7 catalog. Two methods are employed to investigate the distributions of galaxies in the CMD including 1-D Gaussian fitting to the distributions in individual magnitude bins and 2-D Gaussian mixture model (GMM) fitting to galaxies as a whole. We find that in the 1-D fitting only two Gaussians are not enough to fit galaxies with the excess present between the blue cloud and the red sequence. The fitting to this excess defines the centre of the green-valley in the local universe to be $(u-r)_{0.1} = -0.121M_{r,0.1}-0.061$. The fraction of blue cloud and red sequence galaxies turns over around $M_{r,0.1} \sim -20.1$ mag, corresponding to stellar mass of $3\times10^{10}M_\odot$. For the 2-D GMM fitting, a total of four Gaussians are required, one for the blue cloud, one for the red sequence and the additional two for the green valley. The fact that two Gaussians are needed to describe the distributions of galaxies in the green valley is consistent with some models that argue for two different evolutionary paths from the blue cloud to the red sequence.Comment: Accepted by ApJ, 9 pages, 8 figures, 1 tabl

A Scalable Limited Feedback Design for Network MIMO using Per-Cell Product Codebook

In network MIMO systems, channel state information is required at the transmitter side to multiplex users in the spatial domain. Since perfect channel knowledge is difficult to obtain in practice, \emph{limited feedback} is a widely accepted solution. The {\em dynamic number of cooperating BSs} and {\em heterogeneous path loss effects} of network MIMO systems pose new challenges on limited feedback design. In this paper, we propose a scalable limited feedback design for network MIMO systems with multiple base stations, multiple users and multiple data streams for each user. We propose a {\em limited feedback framework using per-cell product codebooks}, along with a {\em low-complexity feedback indices selection algorithm}. We show that the proposed per-cell product codebook limited feedback design can asymptotically achieve the same performance as the joint-cell codebook approach. We also derive an asymptotic \emph{per-user throughput loss} due to limited feedback with per-cell product codebooks. Based on that, we show that when the number of per-user feedback-bits $B_{k}$ is $\mathcal{O}\big( Nn_{T}n_{R}\log_{2}(\rho g_{k}^{sum})\big)$, the system operates in the \emph{noise-limited} regime in which the per-user throughput is $\mathcal{O} \left( n_{R} \log_{2} \big( \frac{n_{R}\rho g_{k}^{sum}}{Nn_{T}} \big) \right)$. On the other hand, when the number of per-user feedback-bits $B_{k}$ does not scale with the \emph{system SNR} $\rho$, the system operates in the \emph{interference-limited} regime where the per-user throughput is $\mathcal{O}\left( \frac{n_{R}B_{k}}{(Nn_{T})^{2}} \right)$. Numerical results show that the proposed design is very flexible to accommodate dynamic number of cooperating BSs and achieves much better performance compared with other baselines (such as the Givens rotation approach).Comment: 11 pages, 5 figures, Accepted to the IEEE transactions on Wireless Communicatio

A Noise-Sensitivity-Analysis-Based Test Prioritization Technique for Deep Neural Networks

Deep neural networks (DNNs) have been widely used in the fields such as natural language processing, computer vision and image recognition. But several studies have been shown that deep neural networks can be easily fooled by artificial examples with some perturbations, which are widely known as adversarial examples. Adversarial examples can be used to attack deep neural networks or to improve the robustness of deep neural networks. A common way of generating adversarial examples is to first generate some noises and then add them into original examples. In practice, different examples have different noise-sensitive. To generate an effective adversarial example, it may be necessary to add a lot of noise to low noise-sensitive example, which may make the adversarial example meaningless. In this paper, we propose a noise-sensitivity-analysis-based test prioritization technique to pick out examples by their noise sensitivity. We construct an experiment to validate our approach on four image sets and two DNN models, which shows that examples are sensitive to noise and our method can effectively pick out examples by their noise sensitivity

Thermodynamics for Kodama observer in general spherically symmetric spacetimes

By following the spirit of arXiv:1003.5665, we define a new Tolman temperature of Kodama observer directly related to its acceleration. We give a generalized integral form of thermodynamics relation on virtual sphere of constant $r$ in non-static spherical symmetric spacetimes. This relation contains work term contributed by `redshift work density', `pressure density' and `gravitational work density'. We illustrate it in RN black hole, Dilaton-Maxwell-Einstein black hole and Vaidya black hole. We argue that the co-moving observers are not physically related to Kodama observers in FRW universe unless in the vacuum case. We also find that a generalized differential form of first law is difficult to be well defined, and it would not give more information than the integral form.Comment: 18 pages, typos corrected, references adde

Magnetic extraction of energy from accretion disc around a rotating black hole

An analytical expression for the disc power is derived based on an equivalent circuit in black hole (BH) magnetosphere with a mapping relation between the radial coordinate of the disc and that of unknown astrophysical load. It turns out that this disc power is comparable with two other disc powers derived in the Poynting flux and hydrodynamic regimes, respectively. In addition, the relative importance of the disc power relative to the BZ power is discussed. It is shown that the BZ power is generally dominated by the disc power except some extreme cases. Furthermore, we show that the disc power derived in our model can be well fitted with the jet power of M87.Comment: 7 pages, 5 figure

PWLS-ULTRA: An Efficient Clustering and Learning-Based Approach for Low-Dose 3D CT Image Reconstruction

The development of computed tomography (CT) image reconstruction methods that significantly reduce patient radiation exposure while maintaining high image quality is an important area of research in low-dose CT (LDCT) imaging. We propose a new penalized weighted least squares (PWLS) reconstruction method that exploits regularization based on an efficient Union of Learned TRAnsforms (PWLS-ULTRA). The union of square transforms is pre-learned from numerous image patches extracted from a dataset of CT images or volumes. The proposed PWLS-based cost function is optimized by alternating between a CT image reconstruction step, and a sparse coding and clustering step. The CT image reconstruction step is accelerated by a relaxed linearized augmented Lagrangian method with ordered-subsets that reduces the number of forward and back projections. Simulations with 2-D and 3-D axial CT scans of the extended cardiac-torso phantom and 3D helical chest and abdomen scans show that for both normal-dose and low-dose levels, the proposed method significantly improves the quality of reconstructed images compared to PWLS reconstruction with a nonadaptive edge-preserving regularizer (PWLS-EP). PWLS with regularization based on a union of learned transforms leads to better image reconstructions than using a single learned square transform. We also incorporate patch-based weights in PWLS-ULTRA that enhance image quality and help improve image resolution uniformity. The proposed approach achieves comparable or better image quality compared to learned overcomplete synthesis dictionaries, but importantly, is much faster (computationally more efficient).Comment: Accepted to IEEE Transaction on Medical Imagin