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

Effects of vesicular-arbuscular mycorrhiza on 14C and 15N distribution in nodulated fababeans

Includes bibliographical references (pages 249-250).A two-compartment growth chamber in which the aboveground plant materials were exposed to 14CO2 and the belowground portion was exposed to 15N2 under normal atmospheric pressure was designed for carbon and nitrogen transfer studies. Vicia faba infected with vesicular-arbuscular fungus Glomus mossae and non-mycorrhizal plants fixed similar quantities of N2 at an age of 6½ wk. Approximately 0.10 mg N was fixed ∙ g−1 dry plant materials ∙ day−1 and 40 mg C • g−1 dry matter day−1 were synthesized by mycorrhizal and non-mycorrhizal fababeans during 48 h exposure to 14CO2 at 6½ wk with no apparent difference in yield of dry matter. The non-mycorrhizal plants transferred 37% of the fixed 14C beneath ground. The mycorrhizal ones transferred 47% of the fixed 14C beneath ground. Most of the difference could be accounted for in the belowground respiration. The 14CO2 produced by root-microbial systems of the mycorrhizal fababeans was twice as great as that of the nonmycorrhizal; both contained active rhizobium

Uniform polynomial rates of convergence for a class of L\'evy-driven controlled SDEs arising in multiclass many-server queues

We study the ergodic properties of a class of controlled stochastic differential equations (SDEs) driven by $\alpha$-stable processes which arise as the limiting equations of multiclass queueing models in the Halfin-Whitt regime that have heavy-tailed arrival processes. When the safety staffing parameter is positive, we show that the SDEs are uniformly ergodic and enjoy a polynomial rate of convergence to the invariant probability measure in total variation, which is uniform over all stationary Markov controls resulting in a locally Lipschitz continuous drift. We also derive a matching lower bound on the rate of convergence (under no abandonment). On the other hand, when all abandonment rates are positive, we show that the SDEs are exponentially ergodic uniformly over the above-mentioned class of controls. Analogous results are obtained for L\'evy-driven SDEs arising from multiclass many-server queues under asymptotically negligible service interruptions. For these equations, we show that the aforementioned ergodic properties are uniform over all stationary Markov controls. We also extend a key functional central limit theorem concerning diffusion approximations so as to make it applicable to the models studied here

Investigation of Settlements of a Trunk Road Embankment in Hong Kong

A 25 m high fill embankment was constructed as part of a Trunk Road scheme in Hong Kong. In June 1985, large settlements of the order of 250 mm were observed in the embankment. This was followed by a local slippage of surface material from the downstream slope face. To meet the schedule for opening the trunk road in late September, a number of emergency measures costing about HK$1 M (US$0.13 M) were implemented to stabilize the embankment. An investigation was subsequently carried out to assess the cause of the movement and the long term stability of the embankment. This paper summarizes the sequence of events leading to the settlements and outlines the investigation carried out. The proposed hydrocompaction mechanism and the effects of grouting on the embankment are discussed

A Trouble with Ho\v{r}ava-Lifshitz Gravity

We study the structure of the phase space in Ho\v{r}ava-Lifshitz theory. With the constraints derived from the action, the phase space is described by five fields, thus there is a lack of canonical structure. The Poisson brackets of the Hamiltonian density do not form a closed structure, resulting in many new constraints. Taking these new constraints into account, it appears that there is no degree of freedom left, or the phase space is reduced to one with an odd number of fields.Comment: 12 pages, some discussions, comments and references added, JHEP styl