This article describes the sequence alignment problem in bioinformatics. Through examples, we formulate sequence alignment as an optimization problem and show how to compute the optimal alignment with dynamic programming. The examples and sample exercises have been used by the author in a specialized course in bioinformatics, but could be adapted…

Introductory thermodynamics is a topic which is covered in a wide variety of science and engineering educations. However, very different teaching traditions have evolved within different scientific specialties. In this study we examine three courses in introductory thermodynamics within three different scientific specialties: physics, chemical…

Synthetic division is viewed as a change of basis for polynomials written under the Newton form. Then, the transition matrices obtained from a sequence of changes of basis are used to factorize the inverse of a bidiagonal matrix or a block bidiagonal matrix.

In this article we provide two detailed examples of how we incorporate biological examples into two mathematics courses: Linear Algebra and Ordinary Differential Equations. We use Leslie matrix models to demonstrate the biological properties of eigenvalues and eigenvectors. For Ordinary Differential Equations, we show how using a logistic growth…

A method is presented of calculating correlation matrices using single subscript rather than double subscript notation. This saves time and space, and permits the calculation of larger matrices in the space available. (Author)

Two generalizations of canonical correlational analysis are developed. The partial, part, and bipartial canonical correlation coefficients are shown to be special cases of the generalization. Illustrative examples are provided. (Author/JKS)

Demonstrates how case analyses can be evaluated on a more objective basis with the use of a grading matrix. Presents two frameworks, one a generalizable approach and the other based on a developmental process. (JOW)

A principal components analysis of matrices of Spearman's rho statistic for inter-rater reliability is proposed as an alternative to Kendall's coefficient of concordance. Advantages and possible uses of the proposed method are presented. (JKS)

A microcomputer program using a tape unit for multiplying two matrices as large as 41 x 42 apiece is presented. Advantages and limitations are discussed. A verbal description of the logic is presented to facilitate the use of the program on different brands of computers. (Author/JKS)

A method is presented for determining the number of components to retain in a principal components or image components analysis which utilizes a matrix of partial correlations. Advantages and uses of the method are discussed and a comparison of the proposed method with existing methods is presented. (JKS)

A formula for the determinant of a partitioned matrix, possibly with singular submatrices, is derived and applied to some psychometric and numerical problems. (Author)

It is shown that a weaker generalized inverse (Rao's g-inverse; Graybill's c-inverse) can be used in place of the Moore-Penrose generalized inverse to obtain multiple and canonical correlations from singular covariance matrices. Mathematical derivations are provided. (Author/JKS)

Proposed a taxonomy of latent structure assumptions for probability matrix decomposition (PMD) that includes the original PMD model and a three-way extension of the multiple classification latent class model. Simulation study results show the usefulness of the taxonomy. (SLD)

Proposes a method for generalized constrained canonical correlation analysis (GCCANO) that incorporates external information on both rows and columns of data matrices. In this method, each set of variables is first decomposed into the sum of several submatrices according to the external information, and then canonical correlation analysis is…