On the probability of undetected error for the maximum distance separable codes

The performance of maximum-distance-separable codes with symbols from GF(1) when they are used for pure error detection or for simultaneous error correction and detection is investigated. These codes are good for symbol error detection. Their probability of undetected error is upper bounded by q to the -r and decreases monotonically as the symbol error probability epsilon decreases from (q-1)/q to 0, where r is the number of parity-check symbols of a code

Coding for reliable satellite communications

This research project was set up to study various kinds of coding techniques for error control in satellite and space communications for NASA Goddard Space Flight Center. During the project period, researchers investigated the following areas: (1) decoding of Reed-Solomon codes in terms of dual basis; (2) concatenated and cascaded error control coding schemes for satellite and space communications; (3) use of hybrid coding schemes (error correction and detection incorporated with retransmission) to improve system reliability and throughput in satellite communications; (4) good codes for simultaneous error correction and error detection, and (5) error control techniques for ring and star networks

Ricci-flat graphs with girth at least five

A graph is called Ricci-flat if its Ricci-curvatures vanish on all edges. Here we use the definition of Ricci-cruvature on graphs given in [Lin-Lu-Yau, Tohoku Math., 2011], which is a variation of [Ollivier, J. Funct. Math., 2009]. In this paper, we classified all Ricci-flat connected graphs with girth at least five: they are the infinite path, cycle $C_n$ ($n\geq 6$), the dodecahedral graph, the Petersen graph, and the half-dodecahedral graph. We also construct many Ricci-flat graphs with girth 3 or 4 by using the root systems of simple Lie algebras.Comment: 14 pages, 15 figure

Diquarks, Pentaquarks and Dibaryons

We explore the connection between pentaquarks and dibaryons composed of three diquarks in the framework of the diquark model. With the available experimental data on H dibaryon, we estimate the Pauli blocking and annihilation effects and constrain the $P=-$ pentaquark $SU(3)_F$ singlet mass. Using the $\Theta^+$ pentaquark mass, we estimate $P=-$ dibaryon mass

Recovering Dense Tissue Multispectral Signal from in vivo RGB Images

Hyperspectral/multispectral imaging (HSI/MSI) contains rich information clinical applications, such as 1) narrow band imaging for vascular visualisation; 2) oxygen saturation for intraoperative perfusion monitoring and clinical decision making [1]; 3) tissue classification and identification of pathology [2]. The current systems which provide pixel-level HSI/MSI signal can be generally divided into two types: spatial scanning and spectral scanning. However, the trade-off between spatial/spectral resolution, the acquisition time, and the hardware complexity hampers implementation in real-world applications, especially intra-operatively. Acquiring high resolution images in real-time is important for HSI/MSI in intra-operative imaging, to alleviate the side effect caused by breathing, heartbeat, and other sources of motion. Therefore, we developed an algorithm to recover a pixel-level MSI stack using only the captured snapshot RGB images from a normal camera. We refer to this technique as "super-spectral-resolution". The proposed method enables recovery of pixel-level-dense MSI signals with 24 spectral bands at ~11 frames per second (FPS) on a GPU. Multispectral data captured from porcine bowel and sheep/rabbit uteri in vivo has been used for training, and the algorithm has been validated using unseen in vivo animal experiments.Comment: accepted by Hamlyn Symposium 201