A Hybrid Quantum Encoding Algorithm of Vector Quantization for Image Compression

Many classical encoding algorithms of Vector Quantization (VQ) of image compression that can obtain global optimal solution have computational complexity O(N). A pure quantum VQ encoding algorithm with probability of success near 100% has been proposed, that performs operations 45sqrt(N) times approximately. In this paper, a hybrid quantum VQ encoding algorithm between classical method and quantum algorithm is presented. The number of its operations is less than sqrt(N) for most images, and it is more efficient than the pure quantum algorithm. Key Words: Vector Quantization, Grover's Algorithm, Image Compression, Quantum AlgorithmComment: Modify on June 21. 10pages, 3 figure

Pairs of Noncrossing Free Dyck Paths and Noncrossing Partitions

Using the bijection between partitions and vacillating tableaux, we establish a correspondence between pairs of noncrossing free Dyck paths of length $2n$ and noncrossing partitions of $[2n+1]$ with $n+1$ blocks. In terms of the number of up steps at odd positions, we find a characterization of Dyck paths constructed from pairs of noncrossing free Dyck paths by using the Labelle merging algorithm.Comment: 9 pages, 5 figures, revised version, to appear in Discrete Mathematic

ABJ Quadrality

We study physical consequences of adding orientifolds to the ABJ triality, which is among 3d N=6 superconformal Chern-Simons theory known as ABJ theory, type IIA string in AdS_4 x CP^3 and N=6 supersymmetric (SUSY) Vasiliev higher spin theory in AdS_4. After adding the orientifolds, it is known that the gauge group of the ABJ theory becomes O(N_1)xUSp(2N_2) while the background of the string theory is replaced by AdS_4 x CP^3/Z_2, and the supersymmetries in the both theories reduce to N=5. We propose that adding the orientifolds to the N=6 Vasiliev theory leads to N=5 SUSY Vasiliev theory. It turns out that the N=5 case is more involved because there are two formulations of the N=5 Vasiliev theory with either O or USp internal symmetry. We show that the two N=5 Vasiliev theories can be understood as certain projections of the N=6 Vasiliev theory, which we identify with the orientifold projections in the Vasiliev theory. We conjecture that the O(N_1)xUSp(2N_2) ABJ theory has the two vector model like limits: N_2 >> N_1 and N_1 >> N_2 which correspond to the semi-classical N=5 Vasiliev theories with O(N_1) and USp(2N_2) internal symmetries respectively. These correspondences together with the standard AdS/CFT correspondence comprise the ABJ quadrality among the N=5 ABJ theory, string/M-theory and two N=5 Vasliev theories. We provide a precise holographic dictionary for the correspondences by comparing correlation functions of stress tensor and flavor currents. Our conjecture is supported by various evidence such as agreements of the spectra, one-loop free energies and SUSY enhancement on the both sides. We also predict the leading free energy of the N=5 Vasiliev theory from the CFT side. As a byproduct, we give a derivation of the relation between the parity violating phase in the N=6 Vasiliev theory and the parameters in the N=6 ABJ theory, which was conjectured in arXiv:1207.4485

Condition monitoring of an advanced gas-cooled nuclear reactor core

A critical component of an advanced gas-cooled reactor station is the graphite core. As a station ages, the graphite bricks that comprise the core can distort and may eventually crack. Since the core cannot be replaced, the core integrity ultimately determines the station life. Monitoring these distortions is usually restricted to the routine outages, which occur every few years, as this is the only time that the reactor core can be accessed by external sensing equipment. This paper presents a monitoring module based on model-based techniques using measurements obtained during the refuelling process. A fault detection and isolation filter based on unknown input observer techniques is developed. The role of this filter is to estimate the friction force produced by the interaction between the wall of the fuel channel and the fuel assembly supporting brushes. This allows an estimate to be made of the shape of the graphite bricks that comprise the core and, therefore, to monitor any distortion on them

Are spectroscopic factors from transfer reactions consistent with asymptotic normalisation coefficients?

It is extremely important to devise a reliable method to extract spectroscopic factors from transfer cross sections. We analyse the standard DWBA procedure and combine it with the asymptotic normalisation coefficient, extracted from an independent data set. We find that the single particle parameters used in the past generate inconsistent asymptotic normalization coefficients. In order to obtain a consistent spectroscopic factor, non-standard parameters for the single particle overlap functions can be used but, as a consequence, often reduced spectroscopic strengths emerge. Different choices of optical potentials and higher order effects in the reaction model are also studied. Our test cases consist of: $^{14}$C(d,p)$^{15}$C(g.s.) at $E_d^{lab}=14$ MeV, $^{16}$O(d,p)$^{17}$O(g.s.) at $E_d^{lab}=15$ MeV and $^{40}$Ca(d,p)$^{41}$Ca(g.s.) at $E_d^{lab}=11$ MeV. We underline the importance of performing experiments specifically designed to extract ANCs for these systems.Comment: 15 pages, 12 figures, Phys. Rev. C (in press