541 research outputs found

    Cutoff for the Ising model on the lattice

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    Introduced in 1963, Glauber dynamics is one of the most practiced and extensively studied methods for sampling the Ising model on lattices. It is well known that at high temperatures, the time it takes this chain to mix in L1L^1 on a system of size nn is O(logn)O(\log n). Whether in this regime there is cutoff, i.e. a sharp transition in the L1L^1-convergence to equilibrium, is a fundamental open problem: If so, as conjectured by Peres, it would imply that mixing occurs abruptly at (c+o(1))logn(c+o(1))\log n for some fixed c>0c>0, thus providing a rigorous stopping rule for this MCMC sampler. However, obtaining the precise asymptotics of the mixing and proving cutoff can be extremely challenging even for fairly simple Markov chains. Already for the one-dimensional Ising model, showing cutoff is a longstanding open problem. We settle the above by establishing cutoff and its location at the high temperature regime of the Ising model on the lattice with periodic boundary conditions. Our results hold for any dimension and at any temperature where there is strong spatial mixing: For Z2\Z^2 this carries all the way to the critical temperature. Specifically, for fixed d1d\geq 1, the continuous-time Glauber dynamics for the Ising model on (Z/nZ)d(\Z/n\Z)^d with periodic boundary conditions has cutoff at (d/2λ)logn(d/2\lambda_\infty)\log n, where λ\lambda_\infty is the spectral gap of the dynamics on the infinite-volume lattice. To our knowledge, this is the first time where cutoff is shown for a Markov chain where even understanding its stationary distribution is limited. The proof hinges on a new technique for translating L1L^1 to L2L^2 mixing which enables the application of log-Sobolev inequalities. The technique is general and carries to other monotone and anti-monotone spin-systems.Comment: 34 pages, 3 figure

    A scalable quantum computer with an ultranarrow optical transition of ultracold neutral atoms in an optical lattice

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    We propose a new quantum-computing scheme using ultracold neutral ytterbium atoms in an optical lattice. The nuclear Zeeman sublevels define a qubit. This choice avoids the natural phase evolution due to the magnetic dipole interaction between qubits. The Zeeman sublevels with large magnetic moments in the long-lived metastable state are also exploited to address individual atoms and to construct a controlled-multiqubit gate. Estimated parameters required for this scheme show that this proposal is scalable and experimentally feasible.Comment: 6 pages, 6 figure

    Probing the high momentum component of the deuteron at high Q^2

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    The d(e,e'p) cross section at a momentum transfer of 3.5 (GeV/c)^2 was measured over a kinematical range that made it possible to study this reaction for a set of fixed missing momenta as a function of the neutron recoil angle theta_nq and to extract missing momentum distributions for fixed values of theta_nq up to 0.55 GeV/c. In the region of 35 (deg) <= theta_nq <= 45 (deg) recent calculations, which predict that final state interactions are small, agree reasonably well with the experimental data. Therefore these experimental reduced cross sections provide direct access to the high momentum component of the deuteron momentum distribution in exclusive deuteron electro-disintegration.Comment: 5 pages, 2 figure

    Exclusive Neutral Pion Electroproduction in the Deeply Virtual Regime

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    We present measurements of the ep->ep pi^0 cross section extracted at two values of four-momentum transfer Q^2=1.9 GeV^2 and Q^2=2.3 GeV^2 at Jefferson Lab Hall A. The kinematic range allows to study the evolution of the extracted hadronic tensor as a function of Q^2 and W. Results will be confronted with Regge inspired calculations and GPD predictions. An intepretation of our data within the framework of semi-inclusive deep inelastic scattering has also been attempted

    The prognostic significance of low-frequency somatic mutations in metastatic cutaneous melanoma

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    Background: Little is known about the prognostic significance of somatically mutated genes in metastatic melanoma (MM). We have employed a combined clinical and bioinformatics approach on tumor samples from cutaneous melanoma (SKCM) as part of The Cancer Genome Atlas project (TCGA) to identify mutated genes with potential clinical relevance. Methods: After limiting our DNA sequencing analysis to MM samples (n = 356) and to the CANCER CENSUS gene list, we filtered out mutations with low functional significance (snpEFF). We performed Cox analysis on 53 genes that were mutated in ≥3% of samples, and had ≥50% difference in incidence of mutations in deceased subjects versus alive subjects. Results: Four genes were potentially prognostic [RAC1, FGFR1, CARD11, CIITA; false discovery rate (FDR) 75% of the samples that exhibited corresponding DNA mutations. The low frequency, UV signature type and RNA expression of the 22 genes in MM samples were confirmed in a separate multi-institution validation cohort (n = 413). An underpowered analysis within a subset of this validation cohort with available patient follow-up (n = 224) showed that somatic mutations in SPEN and RAC1 reached borderline prognostic significance [log-rank favorable (p = 0.09) and adverse (p = 0.07), respectively]. Somatic mutations in SPEN, and to a lesser extent RAC1, were not associated with definite gene copy number or RNA expression alterations. High (>2+) nuclear plus cytoplasmic expression intensity for SPEN was associated with longer melanoma-specific overall survival (OS) compared to lower (≤ 2+) nuclear intensity (p = 0.048). We conclude that expressed somatic mutations in infrequently mutated genes beyond the well-characterized ones (e.g., BRAF, RAS, CDKN2A, PTEN, TP53), such as RAC1 and SPEN, may have prognostic significance in MM

    Search for supersymmetry with a dominant R-parity violating LQDbar couplings in e+e- collisions at centre-of-mass energies of 130GeV to 172 GeV

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    A search for pair-production of supersymmetric particles under the assumption that R-parity is violated via a dominant LQDbar coupling has been performed using the data collected by ALEPH at centre-of-mass energies of 130-172 GeV. The observed candidate events in the data are in agreement with the Standard Model expectation. This result is translated into lower limits on the masses of charginos, neutralinos, sleptons, sneutrinos and squarks. For instance, for m_0=500 GeV/c^2 and tan(beta)=sqrt(2) charginos with masses smaller than 81 GeV/c^2 and neutralinos with masses smaller than 29 GeV/c^2 are excluded at the 95% confidence level for any generation structure of the LQDbar coupling.Comment: 32 pages, 30 figure

    Search for Neutrinoless tau Decays Involving the K_S^0 Meson

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    We have searched for lepton flavor violating decays of the tau lepton with one or two KS0 mesons in the final state. The data used in the search were collected with the CLEO II and II.V detectors at the Cornell Electron Storage Ring (CESR) and correspond to an integrated luminosity of 13.9 fb^-1 at the Upsilon(4S) resonance. No evidence for signals were found, therefore we have set 90% confidence level (C.L.) upper limits on the branching fractions B(tau -> e KS0) mu KS0) e 2KS0) < 2.2e-6, and B(tau -> mu 2KS0) < 3.4e-6. These represent significantly improved upper limits on the two-body decays and first upper limits on the three-body decays.Comment: 9 pages postscript, also available through http://w4.lns.cornell.edu/public/CLNS, submitted to PRD Rapid Communication
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