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

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

Anisotropic Lattices and Dynamical Fermions

We report results from full QCD calculations with two flavors of dynamical staggered fermions on anisotropic lattices. The physical anisotropy as determined from spatial and temporal masses, their corresponding dispersion relations, and spatial and temporal Wilson loops is studied as a function of the bare gauge anisotropy and the bare velocity of light appearing in the Dirac operator. The anisotropy dependence of staggered fermion flavor symmetry breaking is also examined. These results will then be applied to the study of 2-flavor QCD thermodynamics.Comment: Lattice2001(spectrum

Entropy Change through Rayleigh-B\'enard Convective Transition with Rigid Boundaries

The previous investigation on Rayleigh-B\'enard convection of a dilute classical gas [T. Kita: J. Phys. Soc. Jpn. {\bf 75} (2006) 124005] is extended to calculate entropy change of the convective transition with the rigid boundaries. We obtain results qualitatively similar to those of the stress-free boundaries. Above the critical Rayleigh number, the roll convection is realized among possible steady states with periodic structures, carrying the highest entropy as a function of macroscopic mechanical variables.Comment: 5 pages, 4 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 beta function and equation of state for QCD with two flavors of quarks

We measure the pressure and energy density of two flavor QCD in a wide range of quark masses and temperatures. The pressure is obtained from an integral over the average plaquette or psi-bar-psi. We measure the QCD beta function, including the anomalous dimension of the quark mass, in new Monte Carlo simulations and from results in the literature. We use it to find the interaction measure, E-3p, yielding non-perturbative values for both the energy density E and the pressure p. uuencoded compressed PostScript file Revised version should work on more PostScript printers.Comment: 24 page

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)

Cancer metabolism at a glance

A defining hallmark of cancer is uncontrolled cell proliferation. This is initiated once cells have accumulated alterations in signaling pathways that control metabolism and proliferation, wherein the metabolic alterations provide the energetic and anabolic demands of enhanced cell proliferation. How these metabolic requirements are satisfied depends, in part, on the tumor microenvironment, which determines the availability of nutrients and oxygen. In this Cell Science at a Glance paper and the accompanying poster, we summarize our current understanding of cancer metabolism, emphasizing pathways of nutrient utilization and metabolism that either appear or have been proven essential for cancer cells. We also review how this knowledge has contributed to the development of anticancer therapies that target cancer metabolism