High performance, massively-parallel multi-physics simulations are built on efficient mesh data structures. Most data structures are designed from the bottom up, focusing on the implementation of linear algebra routines. In this thesis, we explore a top-down approach to design, evaluating the various needs of many aspects of simulation, not just…

In this paper implicit function-based parameterizations for orthogonal and oblique rotation matrices are proposed. The parameterizations are used to construct Newton algorithms for minimizing differentiable rotation criteria applied to "m" factors and "p" variables. The speed of the new algorithms is compared to that of existing algorithms and to…

This paper presents and tests a general model to predict emergent exchange patterns and power differences in reciprocal exchange networks when individual actors follow the norm of reciprocity. With an interesting qualification, the experimental results reported here support the power-dependence approach (Emerson 1972a, b): those who acquire the…

Second-order latent growth curve models (S. C. Duncan & Duncan, 1996; McArdle, 1988) can be used to study group differences in change in latent constructs. We give exact formulas for the covariance matrix of the parameter estimates and an algebraic expression for the estimation of slope differences. Formulas for calculations of the required sample…

A comparison of measures of association for 2x2 data was carried out by computer analysis. For each of 1,539 tables, 14 measures of association were calculated and evaluated. A measure based on the odds-ratio (Chambers, 1982) was most accurate in capturing the rho underlying a majority of the tables. (Author/BW)

A way of identifying non-random patterns of effects on a group of individuals as a result of some intervention when a sample of participants is arrayed according to some indices of similarity is presented. The principle of proximal similarity and the concept of pattern matching provide the background for this effort. Major advantages are the…

A probability distribution was developed for the Andrews-Pregibon (AP) statistic. The statistic, developed by D. F. Andrews and D. Pregibon (1978), identifies multivariate outliers. It is a ratio of the determinant of the data matrix with an observation deleted to the determinant of the entire data matrix. Although the AP statistic has been used…

A recurring problem in educational research is how to account for non-random selection that has restricted the range of the variables of interest in correlational analyses. Several expressions due to H. Pearson (1903) and presented in matrix notation by D. N. Lawley (1943-44) are commonly used in selection settings to adjust for samples chosen on…

Some uniqueness properties are presented for the PARAFAC2 model for covariance matrices, focusing on uniqueness in the rank two case of PARAFAC2. PARAFAC2 is shown to be usually unique with four matrices, but not unique with three unless a certain additional assumption is introduced. (SLD)

Computer generated data representative of 16 Auto Regressive Integrated Moving Averages (ARIMA) models were used to compare the results of interrupted time-series analysis using: (1) the known model identification, (2) an assumed (l,0,0) model, and (3) an assumed (3,0,0) model as an approximation to the General Transformation approach. (Author/BW)

A complete enumeration method and a Monte Carlo method are presented to calculate the probability distribution of arbitrary statistics of adjacency matrices when these matrices have the uniform distribution conditional on given row and column sums, and possibly on a given set of structural zeros. (SLD)

Computer sampling from a multivariate normal spherical population was used to evaluate the type one error rates for a test of sphericity based on the distribution of the determinant of the sample correlation matrix. (Author/LMO)

A method for estimating the first eigenvalue of random data correlation matrices is reported, and its precision is demonstrated via comparison to the method of S. J. Allen and R. Hubbard (1986). Data generated in Monte Carlo simulations with 10 sample sizes reaching up to 1,000 were used. (SLD)

Monte Carlo methods were used to evaluate the degree to which canonical function and structure coefficients may be differentially sensitive to sampling error. For each of 64 research situations, 1,000 random samples were drawn. Both sets of coefficients were roughly equally influenced; some exceptions are noted. (SLD)

Most of the multivariate statistical techniques rely on the assumption of multivariate normality. The effects of non-normality on multivariate tests are assumed to be negligible when variance-covariance matrices and sample sizes are equal. Therefore, in practice, investigators do not usually attempt to remove non-normality. In this simulation…