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)

Applications of spectral methods to turbulent magnetofluids in space and fusion research

Recent and potential applications of spectral method computation to incompressible, dissipative magnetohydrodynamics are surveyed. Linear stability problems for one dimensional, quasi-equilibria are approachable through a close analogue of the Orr-Sommerfeld equation. It is likely that for Reynolds-like numbers above certain as-yet-undetermined thresholds, all magnetofluids are turbulent. Four recent effects in MHD turbulence are remarked upon, as they have displayed themselves in spectral method computations: (1) inverse cascades; (2) small-scale intermittent dissipative structures; (3) selective decays of ideal global invariants relative to each other; and (4) anisotropy induced by a mean dc magnetic field. Two more conjectured applications are suggested. All the turbulent processes discussed are sometimes involved in current carrying confined fusion magnetoplasmas and in space plasmas

Effects of Chemical Potential on Hadron Masses in the Phase Transition Region

We study the response of hadron masses with respect to chemical potential at $\mu=0$. Our preliminary results of the pion channel show that $\partial m/\partial \mu$ in the confinement phase is significantly larger than that in the deconfinement phase, which is consistent with the chiral restoration.Comment: LATTICE99 (finite temperature and density), 3 pages, 3 figure

Two-Flavor Staggered Fermion Thermodynamics at N_t = 12

We present results of an ongoing study of the nature of the high temperature crossover in QCD with two light fermion flavors. These results are obtained with the conventional staggered fermion action at the smallest lattice spacing to date---approximately 0.1 fm. Of particular interest are a study of the temperature of the crossover a determination of the induced baryon charge and baryon susceptibility, the scalar susceptibility, and the chiral order parameter, used to test models of critical behavior associated with chiral symmetry restoration. From our new data and published results for N_t = 4, 6, and 8, we determine the QCD magnetic equation of state from the chiral order parameter using O(4) and mean field critical exponents and compare it with the corresponding equation of state obtained from an O(4) spin model and mean field theory. We also present a scaling analysis of the Polyakov loop, suggesting a temperature dependent ``constituent quark free energy.''Comment: LaTeX 25 pages, 15 Postscript figure

The phase transition in QCD with broken SU(2) flavour symmetry

We report the first investigation of the QCD transition temperature, T_c, for two flavours of staggered quarks with unequal masses at lattice spacings of 1/4T. On changing the u/d quark mass ratio in such a way that m(pi_0)^2/m(pi_+)^2 changes from 1 to 0.78, thus bracketing the physical value of this ratio, we find that T_c remains unchanged in units of both m_rho and Lambda_MSbar.Comment: 12 pages, 5 figure

The association of statin use after cancer diagnosis with survival in pancreatic cancer patients: a SEER-medicare analysis.

BackgroundPancreatic cancer has poor prognosis and existing interventions provide a modest benefit. Statin has anti-cancer properties that might enhance survival in pancreatic cancer patients. We sought to determine whether statin treatment after cancer diagnosis is associated with longer survival in those with pancreatic ductal adenocarcinoma (PDAC).MethodsWe analyzed data on 7813 elderly patients with PDAC using the linked Surveillance, Epidemiology, and End Results (SEER) - Medicare claims files. Information on the type, intensity and duration of statin use after cancer diagnosis was extracted from Medicare Part D. We treated statin as a time-dependent variable in a Cox regression model to determine the association with overall survival adjusting for follow-up, age, sex, race, neighborhood income, stage, grade, tumor size, pancreatectomy, chemotherapy, radiation, obesity, dyslipidemia, diabetes, chronic pancreatitis and chronic obstructive pulmonary disease (COPD).ResultsOverall, statin use after cancer diagnosis was not significantly associated with survival when all PDAC patients were considered (HR = 0.94, 95%CI 0.89, 1.01). However, statin use after cancer diagnosis was associated with a 21% reduced hazard of death (Hazard ratio = 0.79, 95% confidence interval (CI) 0.67, 0.93) in those with grade I or II PDAC and to a similar extent in those who had undergone a pancreatectomy, in those with chronic pancreatitis and in those who had not been treated with statin prior to cancer diagnosis.ConclusionsWe found that statin treatment after cancer diagnosis is associated with enhanced survival in patients with low-grade, resectable PDAC

A precise determination of T_c in QCD from scaling

Existing lattice data on the QCD phase transition are analyzed in renormalized perturbation theory. In quenched QCD it is found that T_c scales for lattices with only 3 time slices, and that T_c/Lambda_msbar=1.15 \pm 0.05. A preliminary estimate in QCD with two flavours of dynamical quarks shows that this ratio depends on the quark mass. For realistic quark masses we estimate T_c/Lambda_msbar=0.49 \pm 0.02. We also investigate the equation of state in quenched QCD at 1-loop order in renormalised perturbation theory.Comment: 7 pages, 5 eps figures; improved error analysis yields smaller errors on T_

QCD thermodynamics with two flavors of Wilson quarks at N_t=6

We report on a study of hadron thermodynamics with two flavors of Wilson quarks on 12^3x6 lattices. We have studied the crossover between the high and low temperature regimes for three values of the hopping parameter, kappa=0.16, 0.17, and 0.18. At each of these values of kappa we have carried out spectrum calculations on 12^3x24 lattices for two values of the gauge coupling in the vicinity of the crossover in order to set an energy scale for our thermodynamics calculations and to determine the critical value of the gauge coupling for which the pion and quark masses vanish. For kappa=0.17 and 0.18 we find coexistence between the high and low temperature regimes over 1,000 simulation time units indicating either that the equilibration time is extremely long or that there is a possibility of a first order phase transition. The pion mass is large at the crossover values of the gauge coupling, but the crossover curve has moved closer to the critical curve along which the pion and quark masses vanish, than it was on lattices with four time slices. In addition, values of the dimensionless quantity T_c/m_rho are in closer agreement with those for staggered quarks than was the case at N_t=4. (A POSTSCRIPT VERSION OF THIS PAPER IS AVAILABLE BY ANONYMOUS FTP FROM sarek.physics.ucsb.edu (128.111.8.250) IN THE FILE pub/wilson_thermo.ps)Comment: 24 page