A Sawtooth Permanent Magnetic Lattice for Ultracold Atoms and BECs

We propose a new permanent magnetic lattice for creating periodic arrays of Ioffe-Pritchard permanent magnetic microtraps for holding and controlling ultracold atoms and Bose-Einstein condensates (BECs). Lattice can be designed on thin layer of magnetic films such as $Tb_6$$Gd_10$$Fe_{80}$$Co_4$. In details, we investigate single layer and two crossed layers of sawtooth magnetic patterns with thicknesses of 50 and 500nm respectively with a periodicity of 1$\mu$m. Trap depth and frequencies can be changed via an applied bias field to handle tunneling rates between lattice sites. We present analytical expressions and using numerical calculations show that this lattice has non-zero potential minima to avoid majorana spin flips. One advantage of this lattice over previous ones is that it is easier to manufacture.Comment: 8 pages, 6 figure

Image quality assessment based on harmonics gain/loss information

We present an objective reduced-reference image quality assessment method based on harmonic gain/loss information through a discriminative analysis of local harmonic strength (LHS). The LHS is computed from the gradient of images, and its value represents a relative degree of the appearance of blockiness on images when it is related to energy gain within an image. Furthermore, comparison between local harmonic strength values from an original, distortion-free image and a degraded, processed, or compressed version of the image shows that the LHS can also be used to indicate other types of degradations, such as blurriness that corresponds with energy loss. Our simulations show that we can develop a single metric based on this gain/loss information and use it to rate the quality of images encoded by various encoders such as DCT-based JPEG, wavelet-based JPEG 2000, or various processed images. We show that our method can overcome some limitations of the traditional PSNR

More on energy and Randic energy of specific graphs

Let $G$ be a simple graph of order $n$. The energy $E(G)$ of the graph $G$ is the sum of the absolute values of the eigenvalues of $G$. The Randi\'{c} matrix of $G$, denoted by $R(G)$, is defined as the $n\times n$ matrix whose $(i,j)$-entry is $(d_id_j)^{\frac{-1}{2}}$ if $v_i$ and $v_j$ are adjacent and $0$ for another cases. The Randi\'{c} energy $RE$ of $G$ is the sum of absolute values of the eigenvalues of $R(G)$. In this paper we compute the energy and Randi\'{c} energy for certain graphs. Also we propose a conjecture on Randi\'c energy.Comment: 14 page