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

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 $\pi$ and $2\pi$ 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 $^{13}$C-labeled CHFBr$_2$, 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 ($^{13}$C$^{1}$HCl$_3$) 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