A Comparison of Tests for Marginal Homogeneity in Square Contingency Tables

Several asymptotic tests were proposed for testing the null hypothesis of marginal homogeneity in square contingency tables with r categories. A simulation study was performed for comparing the power of four finite conservative conditional test procedures and of two asymptotic tests for twelve different contingency schemes for small sample sizes. While an asymptotic test proposed by STUART (1955) showed a rather satisfactory behaviour for moderate sample sizes, an asymptotic test proposed by BHAPKAR (1966) was quite anticonservative. With no a priori information the performance of (r - 1) simultaneous conditional binomial tests with a Bonferroni adjustment proved to be a quite efficient procedure. With assumptions about where to expect the deviations from the null hypothesis, other procedures favouring the larger or smaller conditional sample sizes, respectively, can have a great efficiency. The procedures are illustrated by means of a numerical example from clinical psychology.     

One Parameter Model for Three-Factor Interactions in Contingency Tables

This paper shows that the sum of products models for three and higher order interactions in contingency tables can be reparameterized in the spirit of TUKEY (1949) to yield chi-square tests with one degree of freedom. The merits of this new test over the other known tests for the same hypotheses are discussed.     

Size and Power of Test Statistics for Gene Correlation in 2 × 2 Contingency Tables

Monte Carlo simulation of size and power of two proposed tests for linkage disequilibrium between two genes each with two alleles were investigated. Results were compared with two commonly used statistics, the correlation coefficient r and the log-odds ratio tests. Depending on the sign of the linkage disequilibrium, the new tests were found to be more powerful than either of the correlation or log-odds ratio tests. However, on average (positive and negative linkage disequilibrium) the Chi-square test using the correlation coefficient was to a small extent more powerful than the other tests.     

A Monte Carlo Test for Variance Homogeneity in Linear Models

A Monte Carlo procedure is proposed for testing homogeneity of variances in linear models. The method is applicable to a variety of common experimental designs. It is valid when errors are independently normally distributed. Under nonnormality the test is expected to behave robust in a similar fashion as Levene's test. Three examples are given to demonstrate the method.     

Test Statistics for Three-Factor Interaction in 2 × 2 × 2 Contingency Tables

A Monte Carlo simulation was conducted in order to determine the size and power of two proposed tests (the covariance and correlation tests) for three-factor interaction in 2 × 2 × 2 contingency tables. Results were compared to the log-odds ratio test statistic. Simulation showed the correlation test to be more conservative than the covariance test, but less so than the log-odds ratio test. However, the correlation test was the most powerful among the three tests.     

Monte Carlo Comparison of Multiple Comparison Procedures

Seven procedures of multiple comparisons: Tukey, Scheffé, Bonferroni, Studentized Maximum Modulus, Duncan, Newman-Keuls and F are compared with respect to the probability of the correct decision. Monte Carlo simulation shows that there is no the best procedure. AMS 1985 Subject Classification: 62 J 15.     

A Monte Carlo Study of the Relative Stability of Protein Helical Forms

We present simulation results on a simple model to describe the hydrogen bonding in proteins with helical structures. The approximation distinguishes between ! helices, where each amino acid interacts with another one located four residues apart, 3 10 structures, where the number of amino acids in between is three, and the ? arrangement, in which that number is five. We found that the main features of the system are determined by the most stable structure (the ! helix) and that the other type of hydrogen bonds appears just below the denaturation temperature of the peptide. The probability of finding a 3 10 -type bond is greater at the beginning or at the end of the peptide chain, irrespectively of its length, while in short peptides the existence of those bonds increases appreciably the denaturation temperature, promoting stability. On the other hand, the temperature of denaturation decreases with the length of the peptide to reach a value independent of the number of amino acid residues.     

A Monte Carlo scheme based on mid-density in a hysteresis loop to determine equilibrium phase transition

A new and simple method to determine equilibrium phase transition in adsorption systems exhibiting a hysteresis loop is presented as an alternative to methods such as multiple histogram reweighting, gauge cell method and thermodynamic integration. This method is based on the NVT-grand canonical Monte Carlo mid-density scheme to determine the coexistence chemical potential and coexistence densities of an adsorption system. We illustrate this new scheme with argon and methane adsorption in a number of model solids having slit and cylindrical pores. This method does not have a strong basis on thermodynamic ground, but it does provide a simple heuristic approach that is simpler to understand physically.     

Test of the Inverse Monte Carlo Method for the Calculation of Interatomic Potential Energies in Atomic Liquids

Abstract

The principle purpose of this paper is to demonstrate the use of the Inverse Monte Carlo technique for calculating pair interaction energies in monoatomic liquids from a given equilibrium property. This method is based on the mathematical relation between transition probability and pair potential given by the fundamental equation of the “importance sampling” Monte Carlo method. In order to have well defined conditions for the test of the Inverse Monte Carlo method a Metropolis Monte Carlo simulation of a Lennard Jones liquid is carried out to give the equilibrium pair correlation function determined by the assumed potential. Because an equilibrium configuration is prerequisite for an Inverse Monte Carlo simulation a model system is generated reproducing the pair correlation function, which has been calculated by the Metropolis Monte Carlo simulation and therefore representing the system in thermal equilibrium. This configuration is used to simulate virtual atom displacements. The resulting changes in atom distribution for each single simulation step are inserted in a set of non-linear equations defining the transition probability for the virtual change of configuration. The solution of the set of equations for pair interaction energies yields the Lennard Jones potential by which the equilibrium configuration has been determined.     

Monte Carlo Simulation of Polyampholyte Chains

Abstract

Polyampholyte copolymers containing both positive and negative monomers regularly dispersed along the chain were studied. The Monte Carlo method was used to simulate chains with charged monomers interacting by screened Coulomb potential. The neutral polyampholyte chains collapse due to the attractive electrostatic interactions. The nonneutral chains are in extended conformations due to the repulsive polyelectrolyte effects that dominate the attractive polyampholyte interactions. The results are in good agreement with experiment.     

Monte Carlo Study of the Buckingham Exponential-six Fluid

Abstract

In this paper we report the results of extensive Monte Carlo simulations of a pure fluid of Buckingham modified exponential-six molecules. Data are presented for the configurational energy and pressure covering a wide range of temperatures and densities. These data are interpreted using the generalized van der Waals partition function with a novel separation into free volume and mean potential terms. We find, surprisingly, that the Buckingham fluid is described by a simple van der Waals-like equation of state provided that the b parameter is temperature dependent and chosen in a theoretically correct manner.     

The Relative Power of Two Asymptotic Multivariate Tests for Homogeneity in a Contingency Table

In a three way contingency table two multivariate tests for homogeneity have been proposed by the author (1983) a the “catanova” test, which is a trace “metric” test and b the “multinova” test which is determinant based. Both tests are asymptotically distributed as chi-square. In this paper, the power values of the tests are compared and conditions are given for preference of each test.     

Monte Carlo Study of Structural and Thermodynamic Properties of Liquid Chloroform Using a Five Site Model

A five site potential model combining Lennard–Jones plus Coulomb potential functions has been developed for chloroform molecule. The partial charges needed for Coulombic interactions were derived using the chelpg procedure implemented in the gaussian 92 program. These calculations were performed at the MP2 level with MC-311G* basis set for Cl and 6-311G** for C and H atoms. The parameters for the Lennard–Jones potentials were optimized to reproduce experimental values for the density and enthalpy of vaporization of the pure liquid at 298 K and 1 atm. The statistical mechanics calculations were performed with the Monte Carlo method in the isothermic and isobaric (NpT) ensemble. Besides the values obtained for density, ρ, and molar enthalpy of vaporization at constant pressure, Δ H_V, for liquid chloroform, results for molar volume, V_m, molar heat capacity, C_p, isobaric thermal expansivity, α_p, and isothermal compressibility, κ_T, for this pure liquid are also in very good agreement with experimental observations. Size effects on the values of thermodynamic properties were investigated. The potential model was also tested by computing the free energy for solvating one chloroform molecule into its own liquid at 298 K using a statistical perturbation approach. The result obtained compares well with the experimental value. Site–site pair correlation functions were calculated and are in good accordance with theoretical results available in the literature. Dipole–dipole correlation functions for the present five site model were also calculated at different carbon–carbon distances. These correlations were compared to those obtained using the four site model reported in the literature. An investigation of the solvent dependence of the relative free energy for cis/trans conversion of a hypothetical solute in TIP4P water and chloroform was accomplished. The results show strong interaction of water and chloroform molecules with the gauche conformer. The value obtained for the free energy barrier for cis/trans rotation in TIP4P water is higher than that for chloroform. This result is in agreement with the continuous theory for solvation as the conformer with higher dipole moment is more favoured by the solvent with higher dieletric constant. The results also show an increase in entropy as the solute goes from the cis to the trans geometry and this result is more appreciable in the aqueous solution. This revised version was published online in June 2006 with corrections to the Cover Date.     

A Monte Carlo Study of the Argon Fluid Around a Benzene Molecule

Abstract

Monte Carlo simulations have been carried out for argon fluid containing one benzene molecule at the supercritical region. The purpose in this study is to examine the effect of plate-like molecule on the structure of neighboring fluid composed of simple spherical molecules of the system. In the first neighbor shell of argon from the center of benzene molecule, the average potential energy of argon atoms is confirmed to have a large density dependence. This potential energy is relatively large in the high density region. It is found that the spatial distribution of argon fluid is significantly affected by the molecular shape of benzene and it has little direct connection with the attractive interaction between benzene and argon.     

Investigation of the Air Separation Properties of Zeolites Types A,X and Y by Monte Carlo Simulations

Abstract

The air separation properties of zeolite types A, X, and Y have been studied using grand canonical Monte Carlo simulations of nitrogen, oxygen, and argon adsorbed in these zeolite lattices. Nitrogen is adsorbed preferentially due to the quadrupole-ion electrostatic interactions with the extra framework cations. The localization of adsorption sites for nitrogen near cations and the more diffuse distributions of oxygen and argon within zeolite cavities are clearly illustrated. Predicted nitrogen/oxygen selectivity for 5A from simulations is in good agreement with that determined experimentally. The effect of the calcium-sodium ion exchange on the predicted nitrogen/oxygen selectivity is examined, and is shown to be sensitive to the magnitude of the charges assigned to the extra framework cations.     

The structure of polymer chains in confinement. A Monte Carlo study

A coarse-grained model of polymer star chains confined in two parallel impenetrable surfaces, which were attractive for polymer beads was studied. The flexible homopolymer chains were built of united atoms whose positions in space were restricted to vertices of a simple cubic lattice. The chains were modeled in good solvent conditions and, thus, there were no long-range specific interactions between polymer beads—only the excluded volume was present. The influence of the polymer density and the distances between the confining surfaces on the properties of star-branched polymers was studied. It is shown that the chains adsorbed on one surface could change their position so that they swap between both surfaces with frequency depending on the size of the slit and on the density of the system only. The increase of the polymer density diminished the frequency of jumps and caused that chains became only partially adsorbed. The analysis of structural elements of chains showed that the increase of the density of the system leads to increase of the number of bridges connecting the two adsorbing surfaces, thus, the frequency of jumps between them decreases.     

A Monte Carlo Simulation Study of Orientational Domain Clusters in the Planar Quadrupole Model

Abstract

We have carried out a series of Monte Carlo simulations of the planar quadrupole model, using the Distributed Array Processor. A very large system size, 16 384 molecules, was employed, and special attention was given to orientational domain clustering near the order—disorder transition. Very slow fluctuations of the orientational order parameter, possibly associated with switching from one orientational domain to another, are observed. Close to the phase transition, domain clusters become extremely ramified, with highly irregular borders. On heating through the transition, the low-temperature dominant domain disappears, essentially by becoming a fractal object. The associated Hausdorff dimension decreases from D = 2 to D = 1.6 as this occurs. Although our results are consistent with a continuous, rather than a first-order, phase transition, effects of finite system size and long time scales prevent us from drawing a definite conclusion on this point.     

用蒙特卡罗方法模拟光在多层组织中的吸收特性

在讨论目前新颖的组织功能成像打骂能性（例如光声成像）时,光子在组织中的吸收和散射特性是一个很重要的问题,鉴于这一点,本文利用一个多层模型研究了光子在皮肤,脂肪和肌肉组织中的吸收和散射特性,得到了在组织中某一深度处光子在一个平面上的吸收分布,以及在不同吸收系数和散射系数的情况下,光子的反射,吸收和透射几率,结果表明在经过多次散射后,大部分的光子被吸收,在本文的模型中只有7.3%的光子从表面反射（包括镜面反射和漫反射）,还讨论了不同光学参灵敏对参流分布的影响。