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)

A Selected Ribozyme Catalyzing Diverse Dipeptide Synthesis

AbstractThe sequence of events by which protein, RNA, and DNA emerged during early biological evolution is one of the most profound questions regarding the origin of life. The contemporary role of aminoacyl-adenylates as intermediates in both ribosomal and nonribosomal peptide synthesis suggests that they may have served as substrates for uncoded peptide synthesis during early evolution. We report a highly active peptidyl transferase ribozyme family, isolated by in vitro selection, that efficiently catalyzes dipeptide synthesis by using an aminoacyl-adenylate substrate. It was characterized by sequence and structural analysis and kinetic studies. Remarkably, the ribozyme catalyzed the formation of 30 different dipeptides, the majority of rates being within 5-fold that of the Met-Phe dipeptide required by the selection. The isolation of this synthetic ribozyme fosters speculation that ribozyme-mediated uncoded peptide synthesis may have preceded coded peptide synthesis

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

Probing the Region of Massless Quarks in Quenched Lattice QCD using Wilson Fermions

We study the spectrum of $H(m)=\gamma_5 W(-m)$ with $W(m)$ being the Wilson-Dirac operator on the lattice with bare mass equal to $m$. The background gauge fields are generated using the SU(3) Wilson action at $\beta=5.7$ on an $8^3\times 16$ lattice. We find evidence that the spectrum of $H(m)$ is gapless for $1.02 < m < 2.0$, implying that the physical quark is massless in this whole region.Comment: 22 pages, LaTeX file, uses elsart.sty, includes 11 figures A typographical error in one reference has been fixe

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.

Heavy-Light Decay Constants with Dynamical Gauge Configurations and Wilson or Improved Valence Quark Action

We describe a calculation of heavy-light decay constants including virtual quark loop effects. We have generated dynamical gauge configurations at three $\beta$ values using two flavors of Kogut-Susskind quarks with a range of masses. These are analyzed with a Wilson valence quark action. Preliminary results based on a ``fat-link'' clover valence quark action are also reported. Results from the two methods differ by 30 to 50 MeV, which is presumably due to significant - but as yet unobserved - lattice spacing dependence in one or both of the approaches.Comment: 3 pages, 1 figure, LeTeX, uses espcrc2, epsf LATTICE99(Heavy Quarks

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

Three-Dimensional Structure of the Enveloped Bacteriophage Φ12: An Incomplete T = 13 Lattice Is Superposed on an Enclosed T = 1 Shell

BACKGROUND:Bacteriophage phi12 is a member of the Cystoviridae, a unique group of lipid containing membrane enveloped bacteriophages that infect the bacterial plant pathogen Pseudomonas syringae pv. phaseolicola. The genomes of the virus species contain three double-stranded (dsRNA) segments, and the virus capsid itself is organized in multiple protein shells. The segmented dsRNA genome, the multi-layered arrangement of the capsid and the overall viral replication scheme make the Cystoviridae similar to the Reoviridae. METHODOLOGY/PRINCIPAL FINDINGS:We present structural studies of cystovirus phi12 obtained using cryo-electron microscopy and image processing techniques. We have collected images of isolated phi12 virions and generated reconstructions of both the entire particles and the polymerase complex (PC). We find that in the nucleocapsid (NC), the phi12 P8 protein is organized on an incomplete T = 13 icosahedral lattice where the symmetry axes of the T = 13 layer and the enclosed T = 1 layer of the PC superpose. This is the same general protein-component organization found in phi6 NC's but the detailed structure of the entire phi12 P8 layer is distinct from that found in the best classified cystovirus species phi6. In the reconstruction of the NC, the P8 layer includes protein density surrounding the hexamers of P4 that sit at the 5-fold vertices of the icosahedral lattice. We believe these novel features correspond to dimers of protein P7. CONCLUSIONS/SIGNIFICANCE:In conclusion, we have determined that the phi12 NC surface is composed of an incomplete T = 13 P8 layer forming a net-like configuration. The significance of this finding in regard to cystovirus assembly is that vacancies in the lattice could have the potential to accommodate additional viral proteins that are required for RNA packaging and synthesis