FPTAS for Hardcore and Ising Models on Hypergraphs

Hardcore and Ising models are two most important families of two state spin systems in statistic physics. Partition function of spin systems is the center concept in statistic physics which connects microscopic particles and their interactions with their macroscopic and statistical properties of materials such as energy, entropy, ferromagnetism, etc. If each local interaction of the system involves only two particles, the system can be described by a graph. In this case, fully polynomial-time approximation scheme (FPTAS) for computing the partition function of both hardcore and anti-ferromagnetic Ising model was designed up to the uniqueness condition of the system. These result are the best possible since approximately computing the partition function beyond this threshold is NP-hard. In this paper, we generalize these results to general physics systems, where each local interaction may involves multiple particles. Such systems are described by hypergraphs. For hardcore model, we also provide FPTAS up to the uniqueness condition, and for anti-ferromagnetic Ising model, we obtain FPTAS where a slightly stronger condition holds

MEASUREMENT OF MECHANICAL POWER OF HUMAN LOCOMOTION IN FREE-LIVING CONDITIONS

The importance of accurate assessment of human locomotion in freeliving conditions is increasingly recognized. Existing methods have significant limitations due to the complexities of motion and the difficulties of measurement techniques. Recent developments in teohnology have made it feasible now to use kinematical and kinetic analysis in assessing free-living locomotion. In this study, the parameters of each segment motion in outdoor field are recorded and analyzed by an Intelligent Device for Energy Expenditure and Activity (IDEEA) device (Zhang et aI, 2003 & 2004), and the mechanical power (MP) of each joint is determined by a biomechanical model

Determination of real machine-tool settings and minimization of real surface deviation by computerized inspection

A numerical method is developed for the minimization of deviations of real tooth surfaces from the theoretical ones. The deviations are caused by errors of manufacturing, errors of installment of machine-tool settings and distortion of surfaces by heat-treatment. The deviations are determined by coordinate measurements of gear tooth surfaces. The minimization of deviations is based on the proper correction of initially applied machine-tool settings. The contents of accomplished research project cover the following topics: (1) Descriptions of the principle of coordinate measurements of gear tooth surfaces; (2) Deviation of theoretical tooth surfaces (with examples of surfaces of hypoid gears and references for spiral bevel gears); (3) Determination of the reference point and the grid; (4) Determination of the deviations of real tooth surfaces at the points of the grid; and (5) Determination of required corrections of machine-tool settings for minimization of deviations. The procedure for minimization of deviations is based on numerical solution of an overdetermined system of n linear equations in m unknowns (m much less than n ), where n is the number of points of measurements and m is the number of parameters of applied machine-tool settings to be corrected. The developed approach is illustrated with numerical examples

Observational constraints on the energy scale of inflation

Determining the energy scale of inflation is crucial to understand the nature of inflation in the early Universe. We place observational constraints on the energy scale of the observable part of the inflaton potential by combining the 7-year Wilkinson Microwave Anisotropy Probe data with distance measurements from the baryon acoustic oscillations in the distribution of galaxies and the Hubble constant measurement. Our analysis provides an upper limit on this energy scale, 2.3 \times 10^{16} GeV at 95% confidence level. Moreover, we forecast the sensitivity and constraints achievable by the Planck experiment by performing Monte Carlo studies on simulated data. Planck could significantly improve the constraints on the energy scale of inflation and on the shape of the inflaton potential.Comment: 7 pages, 3 figures, RevTeX, published versio