The Traveling Salesman Problem: Low-Dimensionality Implies a Polynomial Time Approximation Scheme

The Traveling Salesman Problem (TSP) is among the most famous NP-hard optimization problems. We design for this problem a randomized polynomial-time algorithm that computes a (1+eps)-approximation to the optimal tour, for any fixed eps>0, in TSP instances that form an arbitrary metric space with bounded intrinsic dimension. The celebrated results of Arora (A-98) and Mitchell (M-99) prove that the above result holds in the special case of TSP in a fixed-dimensional Euclidean space. Thus, our algorithm demonstrates that the algorithmic tractability of metric TSP depends on the dimensionality of the space and not on its specific geometry. This result resolves a problem that has been open since the quasi-polynomial time algorithm of Talwar (T-04)

QCD Thermodynamics at Nt=8N_t=8 and 12

We present results from studies of high temperature QCD with two flavors of Kogut-Susskind quarks on $16^3\times 8$ lattices at a quark mass of $am_q=0.00625$ and on $24^3\times 12$ lattices at quark masses $am_q=0.008$ and 0.016. The value of the crossover temperature is consistent with that obtained on coarser lattices and/or at larger quark masses. Results are presented for the chiral order parameter and for the baryon number susceptibility.Comment: 3-pages, uuencoded compressed postscript file, contribution to Lattice'94 conferenc

PO and PN in the wind of the oxygen-rich AGB star IK Tau

Phosphorus-bearing compounds have only been studied in the circumstellar environments (CSEs) of the asymptotic giant branch (AGB) star IRC +10216 and the protoplanetary nebula CRL 2688, both C-rich objects, and the O-rich red supergiant VY CMa. The current chemical models cannot reproduce the high abundances of PO and PN derived from observations of VY CMa. No observations have been reported of phosphorus in the CSEs of O-rich AGB stars. We aim to set observational constraints on the phosphorous chemistry in the CSEs of O-rich AGB stars, by focussing on the Mira-type variable star IK Tau. Using the IRAM 30m telescope and the Submillimeter Array (SMA), we observed four rotational transitions of PN (J=2-1,3-2,6-5,7-6) and four of PO (J=5/2-3/2,7/2-5/2,13/2-11/2,15/2-13/2). The IRAM 30m observations were dedicated line observations, while the SMA data come from an unbiased spectral survey in the frequency range 279-355 GHz. We present the first detections of PN and PO in an O-rich AGB star and estimate abundances X(PN/H2) of about 3x10^-7 and X(PO/H2) in the range 0.5-6.0x10^-7. This is several orders of magnitude higher than what is found for the C-rich AGB star IRC +10216. The diameter (<=0.7") of the PN and PO emission distributions measured in the interferometric data corresponds to a maximum radial extent of about 40 stellar radii. The abundances and the spatial occurrence of the molecules are in very good agreement with the results reported for VY CMa. We did not detect PS or PH3 in the survey. We suggest that PN and PO are the main carriers of phosphorus in the gas phase, with abundances possibly up to several 10^-7. The current chemical models cannot account for this, underlining the strong need for updated chemical models that include phosphorous compounds.Comment: Accepted for publication in Astronomy & Astrophysics, 10 pages, 8 figure

Baryon Density Correlations in High Temperature Hadronic Matter

As part of an ongoing effort to characterize the high temperature phase of QCD, in a numerical simulation using the staggered fermion scheme, we measure the quark baryon density in the vicinity of a fixed test quark at high temperature and compare it with similar measurements at low temperature and at the crossover temperature. We find an extremely weak correlation at high temperature, suggesting that small color singlet clusters are unimportant in the thermal ensemble. We also find that at $T = 0.75\ T_c$ the total induced quark number shows a surprisingly large component attributable to baryonic screening. A companion simulation of a simple flux tube model produces similar results and also suggests a plausible phenomenological scenario: As the crossover temperature is approached from below, baryonic states proliferate. Above the crossover temperature the mean size of color singlet clusters grows explosively, resulting in an effective electrostatic deconfinement.Comment: 26 pp, RevTeX, 12 postscript figures, combined in a single shell archive file. (Also available in 13 postscript files by anonymous ftp from einstein.physics.utah.edu, /pub/milc/paper.sh.Z.

Radiative Transitions in Charmonium from Lattice QCD

Radiative transitions between charmonium states offer an insight into the internal structure of heavy-quark bound states within QCD. We compute, for the first time within lattice QCD, the transition form-factors of various multipolarities between the lightest few charmonium states. In addition, we compute the experimentally unobservable, but physically interesting vector form-factors of the $\eta_c, J/\psi$ and $\chi_{c0}$. To this end we apply an ambitious combination of lattice techniques, computing three-point functions with heavy domain wall fermions on an anisotropic lattice within the quenched approximation. With an anisotropy $\xi=3$ at $a_s \sim 0.1 \mathrm{fm}$ we find a reasonable gross spectrum and a hyperfine splitting $\sim 90 \mathrm{MeV}$, which compares favourably with other improved actions. In general, after extrapolation of lattice data at non-zero $Q^2$ to the photopoint, our results agree within errors with all well measured experimental values. Furthermore, results are compared with the expectations of simple quark models where we find that many features are in agreement; beyond this we propose the possibility of constraining such models using our extracted values of physically unobservable quantities such as the $J/\psi$ quadrupole moment. We conclude that our methods are successful and propose to apply them to the problem of radiative transitions involving hybrid mesons, with the eventual goal of predicting hybrid meson photoproduction rates at the GlueX experiment.Comment: modified version as publishe