Extreme value theory in some statistical analysis of genomic sequences

Because similarities in biological sequences often suggest similarities in structures and functions, profile searches using multiple alignment of families of related biological sequences provide useful hints for starting points for experimental investigations in molecular biology. Strategies are formulated for determining statistical significance of scores obtained by searching multiple alignment profiles with databanks, while accommodating for gaps in the profile. The methodology is validated with derivation of asymptotic distribution of the maximum of profile scores, even under weakly dependence conditions. Simulation studies show the proposed method is adequate for moderate sample sizes. The methodology is illustrated with an immunoglobulin protein domain study example.     

Isospin and symmetry energy effects on nuclear fragment production in liquid-gas-type phase transition region

We have shown that the isospin of nuclei influences the fragment production during the nuclear liquid-gas phase transition. Calculations for Au¹⁹⁷, Sn¹²⁴, La¹²⁴ and Kr⁷⁸ at various excitation energies were carried out on the basis of the statistical multifragmentation model (SMM). We analyzed the behavior of the critical exponent τ with the excitation energy and its dependence on the critical temperature. Relative yields of fragments were classified with respect to the mass number of the fragments in the transition region. In this way, we have shown that nuclear multifragmentation exhibits a “bimodality” behavior. We have also shown that the symmetry energy has a small influence on fragment mass distribution; however, its effect is more pronounced in the isotope distributions of produced fragments.     

Comparison of two cryptand separator columns for the determination of trace chloride in semiconductor-grade nitric acid

Improved ion-chromatographic approaches for measuring trace chloride in nitric acid are presented. Two columns, the IonPac Cryptand A1 and a higher-capacity Cryptand prototype, were tested and compared. Also, the use of a Continuously Regenerated Anion Trap Column (CR-ATC) was evaluated for its ability to purify electrolytically generated eluent. Nitric acid (70%) was used as the test matrix and chloride was used as the test analyte; prior to injection, the nitric acid was diluted to 0.7% for the A1 column and to 2.8% for the prototype column. Chloride could be quantified in only 20 min on either column; detection limits computed for 70% HNO3 (at 95% confidence, alpha = beta = 2.5%) were 1.8 and 1.5 ppm for the A1 and prototype columns, respectively. Results also showed that the CR-ATC was necessary for obtaining acceptable acid blanks.     

Lattice gas generalization of the hard hexagon model. III.q-Trinomial coefficients

In the first two papers in this series we considered an extension of the hard hexagon model to a solvable two-dimensional lattice gas with at most two particles per pair of adjacent sites, and we described the local densities in terms of elliptic theta functions. Here we present the mathematical theory behind our derivation of the local densities. Our work centers onq-analogs of trinomial coefficients.     

原子簇正负离子的统计分布与生成机理

在分析了实验记录的大量原子簇离子质谱的基础上，发现原子簇的正负离子通常表现为不同的统计分布形式．将它们的分布形式与求解动力学方程得出的分布函数相比，发现由此反映了原子簇正负离子的不同的生成机理：实验所检测的原子簇正离子在许多情况下仅经历了聚合与解离反应，主要是中性原子簇分子电离后的产物；而相应的原子簇负离子则是经历了一系列离子一分子反应后的产物．     

Deriving a differential equation for the spin-spin correlation in Ising systems

Summary The equipartition theorem and the high-temperature expansion are used to derive a differential equation for the spin-spin correlation in Ising systems. Some applications of this equation including improved upper bound on the three-dimensional transition temperature and correlation length are discussed. Due to the relevance of its scientific content, this paper has been given priority by the Journal Direction.     

Corner transfer matrices of the chiral Potts model

We present some symmetry and factorization relations satisfied by the corner transfer matrices (CTMs) of the chiral Potts model. We show how the single-spin expectation values can be expressed in terms of the CTMs, and in terms of the related boost operator. Low-temperature calculations lead naturally to the variables that uniformize the Boltzmann weights of the model.     

Further application of the statistical thermodynamics of curved surfaces to scaled particle theory

The thermodynamics of curved boundary layers is combined with scaled particle theory to determine the rigid-sphere equation of state. In particular, the boundary analog of the Gibbs-Tolman-Koenig-Buff equation is solved for a rigid-sphere fluid, using the approximation that the distance between the surface of a cavity and its surface of tension is a function of the density only (the first-order approximation). This, in conjunction with several exact conditions onG, the central function of scaled particle theory, leads to an approximate rigid-sphere fluid equation of state and a qualitatively correct rigid-sphere solid equation of state. The fluid isotherm compares favorably with previous results (2.9 % error in the fourth virial coefficient), but due to the inaccuracy of the solid isotherm, no phase transition is obtained. The theory described here is to be contrasted with previous approaches in that a less arbitrary functional form forG is assumed, and the surface of tension and cavity surface are not assumed to be coincident. The cycle equation of Reiss and Tully-Smith is rederived by a simpler route and shown to be correct to all orders of cavity curvature, rather than only first order as was originally thought. A new exact condition, obtained from the compressibility equation of state, is used as a boundary condition for the cycle equation to determine the location of the equimolecular surface. This molecular calculation compares favorably (discrepancy of <2 %) with a thermodynamic calculation based on the boundary analog of the Gibbs adsorption equation and indicates the accuracy and consistency of the first-order approximation.Research supported under NSF Grant #GP-12408.