726 research outputs found

    Experimental Study of the Shortest Reset Word of Random Automata

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    In this paper we describe an approach to finding the shortest reset word of a finite synchronizing automaton by using a SAT solver. We use this approach to perform an experimental study of the length of the shortest reset word of a finite synchronizing automaton. The largest automata we considered had 100 states. The results of the experiments allow us to formulate a hypothesis that the length of the shortest reset word of a random finite automaton with nn states and 2 input letters with high probability is sublinear with respect to nn and can be estimated as $1.95 n^{0.55}.

    Quantum magneto-optics of graphite family

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    The optical conductivity of graphene, bilayer graphene, and graphite in quantizing magnetic fields is studied. Both dynamical conductivities, longitudinal and Hall's, are analytically evaluated. The conductivity peaks are explained in terms of electron transitions. We have shown that trigonal warping can be considered within the perturbation theory for strong magnetic fields larger than 1 T and in the semiclassical approach for weak fields when the Fermi energy is much larger than the cyclotron frequency. The main optical transitions obey the selection rule with \Deltan = 1 for the Landau number n, however the \Deltan = 2 transitions due to the trigonal warping are also possible. The Faraday/Kerr rotation and light transmission/reflection in the quantizing magnetic fields are calculated. Parameters of the Slonczewski-Weiss-McClure model are used in the fit taking into account the previous dHvA measurements and correcting some of them for the case of strong magnetic fields.Comment: 28 pages, 12 figures. arXiv admin note: text overlap with arXiv:1106.340

    Inclusive Dielectron Cross Sections in p+p and p+d Interactions at Beam Energies from 1.04 to 4.88 GeV

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    Measurements of dielectron production in p+p and p+d collisions with beam kinetic energies from 1.04 to 4.88 GeV are presented. The differential cross section is presented as a function of invariant pair mass, transverse momentum, and rapidity. The shapes of the mass spectra and their evolution with beam energy provide information about the relative importance of the various dielectron production mechanisms in this energy regime. The p+d to p+p ratio of the dielectron yield is also presented as a function of invariant pair mass, transverse momentum, and rapidity. The shapes of the transverse momentum and rapidity spectra from the p+d and p+p systems are found to be similar to one another for each of the beam energies studied. The beam energy dependence of the integrated cross sections is also presented.Comment: 15 pages and 16 figure

    Baryon Stopping and Charged Particle Distributions in Central Pb+Pb Collisions at 158 GeV per Nucleon

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    Net proton and negative hadron spectra for central \PbPb collisions at 158 GeV per nucleon at the CERN SPS were measured and compared to spectra from lighter systems. Net baryon distributions were derived from those of net protons, utilizing model calculations of isospin contributions as well as data and model calculations of strange baryon distributions. Stopping (rapidity shift with respect to the beam) and mean transverse momentum \meanpt of net baryons increase with system size. The rapidity density of negative hadrons scales with the number of participant nucleons for nuclear collisions, whereas their \meanpt is independent of system size. The \meanpt dependence upon particle mass and system size is consistent with larger transverse flow velocity at midrapidity for \PbPb compared to \SS central collisions.Comment: This version accepted for publication in PRL. 4 pages, 3 figures. Typos corrected, some paragraphs expanded in response to referee comments, to better explain details of analysi

    Two-proton correlations from 158 AGeV Pb+Pb central collisions

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    The two-proton correlation function at midrapidity from Pb+Pb central collisions at 158 AGeV has been measured by the NA49 experiment. The results are compared to model predictions from static thermal Gaussian proton source distributions and transport models RQMD and VENUS. An effective proton source size is determined by minimizing CHI-square/ndf between the correlation functions of the data and those calculated for the Gaussian sources, yielding 3.85 +-0.15(stat.) +0.60-0.25(syst.) fm. Both the RQMD and the VENUS model are consistent with the data within the error in the correlation peak region.Comment: RevTeX style, 6 pages, 4 figures, 1 table. More discussion are added about the structure on the tail of the correlation function. The systematic error is revised. To appear in Phys. Lett.

    Many private mutations originate from the first few divisions of a human colorectal adenoma.

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    Intratumoural mutational heterogeneity (ITH) or the presence of different private mutations in different parts of the same tumour is commonly observed in human tumours. The mechanisms generating such ITH are uncertain. Here we find that ITH can be remarkably well structured by measuring point mutations, chromosome copy numbers, and DNA passenger methylation from opposite sides and individual glands of a 6 cm human colorectal adenoma. ITH was present between tumour sides and individual glands, but the private mutations were side-specific and subdivided the adenoma into two major subclones. Furthermore, ITH disappeared within individual glands because the glands were clonal populations composed of cells with identical mutant genotypes. Despite mutation clonality, the glands were relatively old, diverse populations when their individual cells were compared for passenger methylation and by FISH. These observations can be organized into an expanding star-like ancestral tree with co-clonal expansion, where many private mutations and multiple related clones arise during the first few divisions. As a consequence, most detectable mutational ITH in the final tumour originates from the first few divisions. Much of the early history of a tumour, especially the first few divisions, may be embedded within the detectable ITH of tumour genomes

    Event-by-event fluctuations of the kaon to pion ratio in central Pb+Pb collisions at 158 GeV per Nucleon

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    We present the first measurement of fluctuations from event to event in the production of strange particles in collisions of heavy nuclei. The ratio of charged kaons to charged pions is determined for individual central Pb+Pb collisions. After accounting for the fluctuations due to detector resolution and finite number statistics we derive an upper limit on genuine non-statistical fluctuations, perhaps related to a first or second order QCD phase transition. Such fluctuations are shown to be very small.Comment: 4 pages, 2 figure

    Event-by-event fluctuations of average transverse momentum in central Pb+Pb collisions at 158 GeV per nucleon

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    We present first data on event-by-event fluctuations in the average transverse momentum of charged particles produced in Pb+Pb collisions at the CERN SPS. This measurement provides previously unavailable information allowing sensitive tests of microscopic and thermodynamic collision models and to search for fluctuations expected to occur in the vicinity of the predicted QCD phase transition. We find that the observed variance of the event-by-event average transverse momentum is consistent with independent particle production modified by the known two-particle correlations due to quantum statistics and final state interactions and folded with the resolution of the NA49 apparatus. For two specific models of non-statistical fluctuations in transverse momentum limits are derived in terms of fluctuation amplitude. We show that a significant part of the parameter space for a model of isospin fluctuations predicted as a consequence of chiral symmetry restoration in a non-equilibrium scenario is excluded by our measurement.Comment: 6 pages, 2 figures, submitted to Phys. Lett.
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