74 research outputs found
Worst case and probabilistic analysis of the 2-Opt algorithm for the TSP
2-Opt is probably the most basic local search heuristic for the TSP. This heuristic achieves amazingly good results on âreal worldâ Euclidean instances both with respect to running time and approximation ratio. There are numerous experimental studies on the performance of 2-Opt. However, the theoretical knowledge about this heuristic is still very limited. Not even its worst case running time on 2-dimensional Euclidean instances was known so far. We clarify this issue by presenting, for every pâN , a family of L p instances on which 2-Opt can take an exponential number of steps.
Previous probabilistic analyses were restricted to instances in which n points are placed uniformly at random in the unit square [0,1]2, where it was shown that the expected number of steps is bounded by O~(n10) for Euclidean instances. We consider a more advanced model of probabilistic instances in which the points can be placed independently according to general distributions on [0,1] d , for an arbitrary dâ„2. In particular, we allow different distributions for different points. We study the expected number of local improvements in terms of the number n of points and the maximal density Ï of the probability distributions. We show an upper bound on the expected length of any 2-Opt improvement path of O~(n4+1/3â
Ï8/3) . When starting with an initial tour computed by an insertion heuristic, the upper bound on the expected number of steps improves even to O~(n4+1/3â1/dâ
Ï8/3) . If the distances are measured according to the Manhattan metric, then the expected number of steps is bounded by O~(n4â1/dâ
Ï) . In addition, we prove an upper bound of O(Ïâd) on the expected approximation factor with respect to all L p metrics.
Let us remark that our probabilistic analysis covers as special cases the uniform input model with Ï=1 and a smoothed analysis with Gaussian perturbations of standard deviation Ï with ÏâŒ1/Ï d
Search for Exotic Mesons in pi- P Interactions at 18 GeV/c
The recent search for non mesons in interactions at
Brookhaven National Laboratory is summarized. Many final states such as , , , , , ,
which are favored decay modes of exotics, are under investigation.Comment: 9 pages, PostScript, Presented at the International School of Nuclear
Physics, Erice, Sicily, Italy, September 199
Confirmation of a pi_1^0 Exotic Meson in the \eta \pi^0 System
The exclusive reaction , at 18 GeV has been studied with a partial wave analysis on a sample
of 23~492 events from BNL experiment E852. A mass-dependent fit
is consistent with a resonant hypothesis for the wave, thus providing
evidence for a neutral exotic meson with , a mass of MeV, and a width of MeV. New
interpretations of the meson exotics in neutral system observed in
E852 and Crystal Barrel experiments are discussed.Comment: p3, rewording the paragraph (at the bottom) about the phase
variations. p4, rewording paragrath "The second method ..." . p4, at the
bottom of paragrath "The third method ..." added consistent with the results
of methods 1 and 2
Exotic Meson Production in the System observed in the Reaction at 18 GeV/c
This letter reports results from the partial wave analysis of the
final state in collisions at 18GeV/c.
Strong evidence is observed for production of two mesons with exotic quantum
numbers of spin, parity and charge conjugation, in the decay
channel . The mass MeV/c^2 and
width MeV/c^2 of the first state are consistent
with the parameters of the previously observed . The second
resonance with mass MeV/c^2 and width MeV/c^2 agrees very well with predictions from theoretical
models. In addition, the presence of is confirmed with mass MeV/c^2 and width MeV/c^2
and a new state, , is observed with mass
MeV/c^2 and width MeV/c^2. The decay properties of
these last two states are consistent with flux tube model predictions for
hybrid mesons with non-exotic quantum numbers
Observation of a New J(PC)=1(+-) Isoscalar State in the Reaction Pi- Proton -> Omega Eta Neutron at 18 GeV/c
Results are presented on a partial wave analysis of the Omega Eta final state
produced in Pi- Proton interactions at 18 GeVc where Omega -> Pi+ Pi- Pi0, Pi0
-> 2 Gammas, and Eta -> 2 Gammas. We observe the previously unreported decay
mode Omega(1650) -> Omega Eta and a new 1(+-) meson state h1(1595) with a mass
M=1594(15)(+10)(-60) MeV/c^2 and a width Gamma=384(60)(+70)(-100) MeV/c^2. The
h1(1595) state exhibits resonant-like phase motion relative to the Omega(1650).Comment: Submitted to Physics Letters B Eight total pages including 11 figures
and 1 tabl
Observation of Pseudoscalar and Axial Vector Resonances in pi- p -> K+ K- pi0 n at 18 GeV
A new measurement of the reaction pi- p -> K+ K- pi0 n has been made at a
beam energy of 18 GeV. A partial wave analysis of the K+ K- pi0 system shows
evidence for three pseudoscalar resonances, eta(1295), eta(1416), and
eta(1485), as well as two axial vectors, f1(1285), and f1(1420). Their observed
masses, widths and decay properties are reported. No signal was observed for
C(1480), an IG J{PC} = 1+ 1{--} state previously reported in phi pi0 decay.Comment: 7 pages, 6 figs, to be submitted to Phys. Let
A study of the reaction pim p --> omega pim p at 18 GeV/c: The D and S decay amplitudes for b1(1235) --> omega pi
The reaction pim p --> omega pim p, omega --> pip pim pi0 has been studied at
18 GeV/c. The omega pim mass spectrum is found to be dominated by the b1(1235).
Partial Wave Analysis shows that b1 production is dominated by natural parity
exchange. The S-wave and D-wave amplitudes for b1(1235) --> omega pi have been
determined, and it is found that the amplitude ratio, |D/S| = 0.269 +/-
(0.009)stat +/- (0.01)sys and the phase difference, phi(D-S) = 10.54 deg +/-
(2.4)stat +/- (3.9)sys.Comment: 7 pages, 9 figures, revtex4 format, to be published in Physics
Letters
Emprego do cell block de agarose como método complementar no diagnóstico citológico de tumores mamårios caninos
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