863 research outputs found

    Feedback Vertex Sets in Tournaments

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    We study combinatorial and algorithmic questions around minimal feedback vertex sets in tournament graphs. On the combinatorial side, we derive strong upper and lower bounds on the maximum number of minimal feedback vertex sets in an n-vertex tournament. We prove that every tournament on n vertices has at most 1.6740^n minimal feedback vertex sets, and that there is an infinite family of tournaments, all having at least 1.5448^n minimal feedback vertex sets. This improves and extends the bounds of Moon (1971). On the algorithmic side, we design the first polynomial space algorithm that enumerates the minimal feedback vertex sets of a tournament with polynomial delay. The combination of our results yields the fastest known algorithm for finding a minimum size feedback vertex set in a tournament

    A reconstruction theorem for almost-commutative spectral triples

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    We propose an expansion of the definition of almost-commutative spectral triple that accommodates non-trivial fibrations and is stable under inner fluctuation of the metric, and then prove a reconstruction theorem for almost-commutative spectral triples under this definition as a simple consequence of Connes's reconstruction theorem for commutative spectral triples. Along the way, we weaken the orientability hypothesis in the reconstruction theorem for commutative spectral triples, and following Chakraborty and Mathai, prove a number of results concerning the stability of properties of spectral triples under suitable perturbation of the Dirac operator.Comment: AMS-LaTeX, 19 pp. V4: Updated version incorporating the erratum of June 2012, correcting the weak orientability axiom in the definition of commutative spectral triple, stengthening Lemma A.10 to cover the odd-dimensional case and the proof of Corollary 2.19 to accommodate the corrected weak orientability axio

    Evidence of Final-State Suppression of High-p_T Hadrons in Au + Au Collisions Using d + Au Measurements at RHIC

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    Transverse momentum spectra of charged hadrons with pT<{p_{T} <} 6 GeV/c have been measured near mid-rapidity (0.2 <η<< \eta < 1.4) by the PHOBOS experiment at RHIC in Au + Au and d + Au collisions at sNN=200GeV{\sqrt{s_{_{NN}}} = \rm {200 GeV}}. The spectra for different collision centralities are compared to p+pˉ{p + \bar{p}} collisions at the same energy. The resulting nuclear modification factor for central Au + Au collisions shows evidence of strong suppression of charged hadrons in the high-pTp_{T} region (>2{>2} GeV/c). In contrast, the d + Au nuclear modification factor exhibits no suppression of the high-pTp_{T} yields. These measurements suggest a large energy loss of the high-pTp_{T} particles in the highly interacting medium created in the central Au + Au collisions. The lack of suppression in d + Au collisions suggests that it is unlikely that initial state effects can explain the suppression in the central Au + Au collisions.Comment: 3 pages, 4 figures, International Europhysics Conference on High Energy Physics EPS (July 17th-23rd 2003) in Aachen, German

    Single Spin Asymmetry ANA_N in Polarized Proton-Proton Elastic Scattering at s=200\sqrt{s}=200 GeV

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    We report a high precision measurement of the transverse single spin asymmetry ANA_N at the center of mass energy s=200\sqrt{s}=200 GeV in elastic proton-proton scattering by the STAR experiment at RHIC. The ANA_N was measured in the four-momentum transfer squared tt range 0.003t0.0350.003 \leqslant |t| \leqslant 0.035 \GeVcSq, the region of a significant interference between the electromagnetic and hadronic scattering amplitudes. The measured values of ANA_N and its tt-dependence are consistent with a vanishing hadronic spin-flip amplitude, thus providing strong constraints on the ratio of the single spin-flip to the non-flip amplitudes. Since the hadronic amplitude is dominated by the Pomeron amplitude at this s\sqrt{s}, we conclude that this measurement addresses the question about the presence of a hadronic spin flip due to the Pomeron exchange in polarized proton-proton elastic scattering.Comment: 12 pages, 6 figure

    Longitudinal double-spin asymmetry and cross section for inclusive neutral pion production at midrapidity in polarized proton collisions at sqrt(s) = 200 GeV

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    We report a measurement of the longitudinal double-spin asymmetry A_LL and the differential cross section for inclusive Pi0 production at midrapidity in polarized proton collisions at sqrt(s) = 200 GeV. The cross section was measured over a transverse momentum range of 1 < p_T < 17 GeV/c and found to be in good agreement with a next-to-leading order perturbative QCD calculation. The longitudinal double-spin asymmetry was measured in the range of 3.7 < p_T < 11 GeV/c and excludes a maximal positive gluon polarization in the proton. The mean transverse momentum fraction of Pi0's in their parent jets was found to be around 0.7 for electromagnetically triggered events.Comment: 6 pages, 3 figures, submitted to Phys. Rev. D (RC
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