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Kleshchev's decomposition numbers and branching coefficients in the Fock space
10.1090/S0002-9947-07-04202-XTransactions of the American Mathematical Society36031179-119
Parallelotope tilings and q-decomposition numbers
We provide closed formulas for a large subset of the canonical basis vectors of the Fock space representation of Uq(slₑ). These formulas arise from parallelotopes which assemble to form polytopal complexes. The subgraphs of the Ext¹ -quivers of v-Schur algebras at complex e-th roots of unity generated by simple modules corresponding to these canonical basis vectors are given by the 1-skeletons of the polytopal complexes
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A v-analogue of Peel's theorem
We compute the v-decomposition numbers dλμ(v) for λ being a hook partition, and μ e-regular
Inter-band magnetoplasmons in mono- and bi-layer graphene
Collective excitations spectrum of Dirac electrons in mono and bilayer
graphene in the presence of a uniform magnetic field is investigated.
Analytical results for inter-Landau band plasmon spectrum within the
self-consistent-field approach are obtained. SdH type oscillations that are a
monotonic function of the magnetic field are observed in the plasmon spectrum
of both mono- and bi-layer graphene systems. The results presented are also
compared with those obtained in conventional 2DEG. The chiral nature of the
quasiparticles in mono and bilayer graphene system results in the observation
of and Berry's phase in the SdH- type oscillations in the plasmon
spectrum.Comment: 9 pages, 2 figure
Implementation of a three-quantum-bit search algorithm
We report the experimental implementation of Grover's quantum search
algorithm on a quantum computer with three quantum bits. The computer consists
of molecules of C-labeled CHFBr, in which the three weakly coupled
spin-1/2 nuclei behave as the bits and are initialized, manipulated, and read
out using magnetic resonance techniques. This quantum computation is made
possible by the introduction of two techniques which significantly reduce the
complexity of the experiment and by the surprising degree of cancellation of
systematic errors which have previously limited the total possible number of
quantum gates.Comment: Published in Applied Physics Letters, vol. 76, no. 5, 31 January
2000, p.646-648, after minor revisions. (revtex, mypsfig2.sty, 3 figures
Nuclear Magnetic Resonance Quantum Computing Using Liquid Crystal Solvents
Liquid crystals offer several advantages as solvents for molecules used for
nuclear magnetic resonance quantum computing (NMRQC). The dipolar coupling
between nuclear spins manifest in the NMR spectra of molecules oriented by a
liquid crystal permits a significant increase in clock frequency, while short
spin-lattice relaxation times permit fast recycling of algorithms, and save
time in calibration and signal-enhancement experiments. Furthermore, the use of
liquid crystal solvents offers scalability in the form of an expanded library
of spin-bearing molecules suitable for NMRQC. These ideas are demonstrated with
the successful execution of a 2-qubit Grover search using a molecule
(CHCl) oriented in a liquid crystal and a clock speed eight
times greater than in an isotropic solvent. Perhaps more importantly, five
times as many logic operations can be executed within the coherence time using
the liquid crystal solvent.Comment: Minor changes. Published in Appl. Phys. Lett. v.75, no.22, 29 Nov
1999, p.3563-356
Measuring the prevalence of regional mutation rates: an analysis of silent substitutions in mammals, fungi, and insects
BackgroundThe patterns of mutation vary both within and across genomes. It has been shown for a few mammals that mutation rates vary within the genome, while for unknown reasons, the sensu stricto yeasts have uniform rates instead. The generality of these observations has been unknown. Here we examine silent site substitutions in a more expansive set (20 mammals, 27 fungi, 4 insects) to determine why some genomes demonstrate this mosaic distribution and why others are uniform.ResultsWe applied several intragene and intergene correlation tests to measure regional substitution patterns. Assuming that silent sites are a reasonable approximation to neutrally mutating sequence, our results show that all multicellular eukaryotes exhibit mutational heterogeneity. In striking contrast, all fungi are mutationally uniform - with the exception of three Candida species: C. albicans, C. dubliniensis, and C. tropicalis. We speculate that aspects of replication timing may be responsible for distinguishing these species. Our analysis also reveals classes of genes whose silent sites behave anomalously with respect to the mutational background in many species, indicating prevalent selective pressures. Genes associated with nucleotide binding or gene regulation have consistently low silent substitution rates in every mammalian species, as well as multiple fungi. On the other hand, receptor genes repeatedly exhibit high silent substitution rates, suggesting they have been influenced by diversifying selection.ConclusionOur findings provide a framework for understanding the regional mutational properties of eukaryotes, revealing a sharp difference between fungi and multicellular species. They also elucidate common selective pressures acting on eukaryotic silent sites, with frequent evidence for both purifying and diversifying selection
Quantum Bit Regeneration
Decoherence and loss will limit the practicality of quantum cryptography and
computing unless successful error correction techniques are developed. To this
end, we have discovered a new scheme for perfectly detecting and rejecting the
error caused by loss (amplitude damping to a reservoir at T=0), based on using
a dual-rail representation of a quantum bit. This is possible because (1)
balanced loss does not perform a ``which-path'' measurement in an
interferometer, and (2) balanced quantum nondemolition measurement of the
``total'' photon number can be used to detect loss-induced quantum jumps
without disturbing the quantum coherence essential to the quantum bit. Our
results are immediately applicable to optical quantum computers using single
photonics devices.Comment: 4 pages, postscript only, figures available at
http://feynman.stanford.edu/qcom
Doubling of the bands in overdoped Bi2Sr2CaCu2O8-probable evidence for c-axis bilayer coupling
We present high resolution ARPES data of the bilayer superconductor
Bi2Sr2CaCu2O8 (Bi2212) showing a clear doubling of the near EF bands. This
splitting approaches zero along the (0,0)-(pi,pi) nodal line and is not
observed in single layer Bi2Sr2CuO6 (Bi2201), suggesting that the splitting is
due to the long sought after bilayer splitting effect. The splitting has a
magnitude of approximately 75 meV near the middle of the zone, extrapolating to
about 100 meV near the (pi,0) poin
Panle Discussion: The Impact of U.S. Trade Law Actions on Business Decisions in Taiwan
Transcript of the panel discussion on the impact of United States trade law on business decisions in Taiwan
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