A General SU(2) Formulation for Quantum Searching with Certainty

A general quantum search algorithm with arbitrary unitary transformations and an arbitrary initial state is considered in this work. To serach a marked state with certainty, we have derived, using an SU(2) representation: (1) the matching condition relating the phase rotations in the algorithm, (2) a concise formula for evaluating the required number of iterations for the search, and (3) the final state after the search, with a phase angle in its amplitude of unity modulus. Moreover, the optimal choices and modifications of the phase angles in the Grover kernel is also studied.Comment: 8 pages, 2 figure

High-Pressure Induced Structural Phase Transition in CaCrO4: Evidence from Raman Scattering Studies

Raman spectroscopic studies have been carried out on CaCrO4 under pressure up to 26GPa at ambient temperature. The Raman spectra showed CaCrO4 experienced a continuous structural phase transition started at near 6GPa, and finished at about 10GPa. It is found that the high-pressure phase could be quenched to ambient conditions. Pressure dependence of the Raman peaks suggested there existed four pressure regions related to different structural characters. We discussed these characters and inferred that the nonreversible structural transition in CaCrO4, most likely was from a zircon-type (I41/amd) ambient phase to a scheelite-type high pressure structure (I41/a).Comment: submitte

Cloning and molecular characterization of TaAGO1, a member of argonaute gene family in wheat (Triticum aestivum L.)

Argonaute (AGO) proteins play important roles in RNA silencing processes through formation of complexes with the mature microRNAs. In this study, a wheat AGO gene referred to TaAGO1, which shares high similarities to AtAGO1 in Arabidopsis and OsAGO1 in rice, was characterized. As a cDNA full length of 3747 bp, TaAGO1 encodes a 1099-aa polypeptide with a molecular weight of 122 kD and an isoelectric point (pI) of 9.52. Subcellular prediction analysis suggests that TaAGO1 is to target onto the cytoplasm after endoplasmic reticulum (ER) sorted. Similar to AtAGO1 and OsAGO1, TaAGO1 contains PIWI and DDH, two conserved domains in AGOs. Phylogenetic analysis indicated that TaAGO1 was possibly derived from different progenitors with its homologous across diverse plant species. The transcripts of TaAGO1 were significantly regulated by the stresses of phosphorus deprivation and dehydration, and exogenous treatment of abscisic acid (ABA), suggesting that this wheat AGO member also exerts roles on mediating above signaling transductions. Southern blotting analysis revealed that genome AA, SS, and DD, three diploids composing of the hexaploid wheat, all harbored two copies of TaAGO1. Down-regulation of TaAGO1 in wheat led to conspicuously phenotypic alterations of the young plantlets, with a variety of abnormal growth features. Taking the results in this study together, it was implicated that TaAGO1 exists as a subset of copies in wheat and plays critical roles on silencing of appropriate target genes via regulation of TaAGO1-MiRNAs complex formation.Key words: Wheat (Triticum aestivum L.), argonaute (AGO) gene 1, cloning, molecular characterization, antisense expression

Reconstruction of 2D Al Ti on TiB in an aluminium melt

It has been widely considered that Al Ti is involved in the aluminium nucleation on TiB , although the mechanism has not been fully understood. In this paper molecular dynamics has been conducted to investigate this phenomenon at an atomistic scale. It was found that a two-dimensional Al Ti layer may remain on TiB above the aluminium liquidus. In addition, the results showed that this 2D Al Ti undergoes interface reconstruction by forming a triangular pattern. This triangular pattern consists of different alternative stacking sequences. The transition region between the triangles forms an area of strain concentration. By means of this mechanism, this interfacial Al Ti layer stabilizes itself by localizing the large misfit strain between TiB and Al Ti This reconstruction is similar to the hdp-fcc interface reconstruction in other systems which has been observed experimentally.EPSR

A General Phase Matching Condition for Quantum Searching Algorithm

A general consideration on the phase rotations in quantum searching algorithm is taken in this work. As four phase rotations on the initial state, the marked states, and the states orthogonal to them are taken account, we deduce a phase matching condition for a successful search. The optimal options for these phase are obtained consequently.Comment: 3 pages, 3 figure

Density Matrix in Quantum Mechanics and Distinctness of Ensembles Having the Same Compressed Density Matrix

We clarify different definitions of the density matrix by proposing the use of different names, the full density matrix for a single-closed quantum system, the compressed density matrix for the averaged single molecule state from an ensemble of molecules, and the reduced density matrix for a part of an entangled quantum system, respectively. We show that ensembles with the same compressed density matrix can be physically distinguished by observing fluctuations of various observables. This is in contrast to a general belief that ensembles with the same compressed density matrix are identical. Explicit expression for the fluctuation of an observable in a specified ensemble is given. We have discussed the nature of nuclear magnetic resonance quantum computing. We show that the conclusion that there is no quantum entanglement in the current nuclear magnetic resonance quantum computing experiment is based on the unjustified belief that ensembles having the same compressed density matrix are identical physically. Related issues in quantum communication are also discussed.Comment: 26 pages. To appear in Foundations of Physics, 36 (8), 200

Complex sequencing rules of birdsong can be explained by simple hidden Markov processes

Complex sequencing rules observed in birdsongs provide an opportunity to investigate the neural mechanism for generating complex sequential behaviors. To relate the findings from studying birdsongs to other sequential behaviors, it is crucial to characterize the statistical properties of the sequencing rules in birdsongs. However, the properties of the sequencing rules in birdsongs have not yet been fully addressed. In this study, we investigate the statistical propertiesof the complex birdsong of the Bengalese finch (Lonchura striata var. domestica). Based on manual-annotated syllable sequences, we first show that there are significant higher-order context dependencies in Bengalese finch songs, that is, which syllable appears next depends on more than one previous syllable. This property is shared with other complex sequential behaviors. We then analyze acoustic features of the song and show that higher-order context dependencies can be explained using first-order hidden state transition dynamics with redundant hidden states. This model corresponds to hidden Markov models (HMMs), well known statistical models with a large range of application for time series modeling. The song annotation with these models with first-order hidden state dynamics agreed well with manual annotation, the score was comparable to that of a second-order HMM, and surpassed the zeroth-order model (the Gaussian mixture model (GMM)), which does not use context information. Our results imply that the hierarchical representation with hidden state dynamics may underlie the neural implementation for generating complex sequences with higher-order dependencies

Resonance-free Region in scattering by a strictly convex obstacle

We prove the existence of a resonance free region in scattering by a strictly convex obstacle with the Robin boundary condition. More precisely, we show that the scattering resonances lie below a cubic curve which is the same as in the case of the Neumann boundary condition. This generalizes earlier results on cubic poles free regions obtained for the Dirichlet boundary condition.Comment: 29 pages, 2 figure

Extraction of the Nuetron Electric Form Factor from Measurements of Inclusive Double Spin Asymmetries

Background: Measurements of the neutron charge form factor, GnE , are challenging because the neutron has no net charge. In addition, measurements of the neutron form factors must use nuclear targets which require accurately accounting for nuclear effects. Extracting GnE with different targets and techniques provides an important test of our handling of these effects. Purpose: The goal of the measurement was to use an inclusive asymmetry measurement technique to extract the neutron charge form factor at a four-momentum transfer of 1(GeV/c)2 . This technique has very different systematic uncertainties than traditional exclusive measurements and thus serves as an independent check of whether nuclear effects have been taken into account correctly. Method: The inclusive quasielastic reaction 3→He(→e,e′) was measured at Jefferson Laboratory. The neutron electric form factor, GnE , was extracted at Q2=0.98(GeV/c)2 from ratios of electron-polarization asymmetries measured for two orthogonal target spin orientations. This Q2 is high enough that the sensitivity to GnE is not overwhelmed by the neutron magnetic contribution, and yet low enough that explicit neutron detection is not required to suppress pion production. Results: The neutron electric form factor, GnE , was determined to be 0.0414 ± 0.0077 (stat) ± 0.0022 (syst) , providing the first high-precision inclusive extraction of the neutron\u27s charge form factor. Conclusions: The use of the inclusive quasielastic 3→He(→e,e′) with a four-momentum transfer near 1(GeV/c)2 has been used to provide a unique measurement of GnE . This new result provides a systematically independent validation of the exclusive extraction technique results and implies that the nuclear corrections are understood. This is contrary to the proton form factor where asymmetry and differential cross section measurements have been shown to have large systematic differences