# Volume 22

## Structural Equation Modeling » NB CDF PDF

### Comparing Two Approaches

Published December 28, 2020

Structural equational modeling is a very popular statistical technique in the social sciences, as it is very flexible and includes factor analysis, path analysis and others as special cases. While usually done with specialized programs, the same can be achieved in Mathematica, which has the benefit of allowing control of any aspect of the calculation. Moreover, a second, more flexible, approach to calculating these models is described that is conceptually much easier yet potentially more powerful. This second approach is used to describe a solution of the attenuation problem of regression. Read More »

## Generating Minimally Unsatisfiable Conjunctive Normal Forms » NB CDF PDF

Published October 29, 2020

A method of generating minimally unsatisfiable conjunctive normal forms is introduced. A conjunctive normal form (CNF) is minimally unsatisfiable if it is unsatisfiable and such that removing any one of its clauses results in a satisfiable CNF. Read More »

## Degree versus Dimension for Rational Parametric Curves » NB CDF PDF

Published September 22, 2020

Given a rationally parameterized curve in or , where the and are polynomials, we find the dimension of the smallest linear subset of containing the curve. If all the and are of degree or less, then it is known abstractly that this dimension is or less and rational normal curves play a key role in the argument. We consider this from a computational point of view with playing an essential part in the discussion. Read More »

## Foundations of Computational Finance » NB CDF PDF

Published August 18, 2020

The Wolfram Language has numerous knowledge-based built-in functions to support financial computations. This article introduces many built-in and other financial functions that are based on concepts and models covered in undergraduate-level finance courses. Examples are taken from a wide range of finance areas. They emphasize importing and visualization of data from many sources, valuation, capital budgeting, analysis of stock returns, portfolio optimization and analysis of bonds and stock options. We hope that all the functions selected in this article are very useful for analyzing real-world financial data. All examples provide a unique set of tools for users to engage with real-world financial data and solve practical problems. The feature of automatic data retrieval from online sources and its analysis makes all results reproducible without any modifications in the code. We hope this feature will attract new users from the finance community. Read More »

## Sectional Curvature in Riemannian Manifolds » NB CDF PDF

Published March 19, 2020

The metric structure on a Riemannian or pseudo-Riemannian manifold is entirely determined by its metric tensor, which has a matrix representation in any given chart. Encoded in this metric is the sectional curvature, which is often of interest to mathematical physicists, differential geometers and geometric group theorists alike. In this article, we provide a function to compute the sectional curvature for a Riemannian manifold given its metric tensor. We also define a function to obtain the Ricci tensor, a closely related object. Read More »