VMEXT: A Visualization Tool for Mathematical Expression Trees

Mathematical expressions can be represented as a tree consisting of terminal symbols, such as identifiers or numbers (leaf nodes), and functions or operators (non-leaf nodes). Expression trees are an important mechanism for storing and processing mathematical expressions as well as the most frequently used visualization of the structure of mathematical expressions. Typically, researchers and practitioners manually visualize expression trees using general-purpose tools. This approach is laborious, redundant, and error-prone. Manual visualizations represent a user's notion of what the markup of an expression should be, but not necessarily what the actual markup is. This paper presents VMEXT - a free and open source tool to directly visualize expression trees from parallel MathML. VMEXT simultaneously visualizes the presentation elements and the semantic structure of mathematical expressions to enable users to quickly spot deficiencies in the Content MathML markup that does not affect the presentation of the expression. Identifying such discrepancies previously required reading the verbose and complex MathML markup. VMEXT also allows one to visualize similar and identical elements of two expressions. Visualizing expression similarity can support support developers in designing retrieval approaches and enable improved interaction concepts for users of mathematical information retrieval systems. We demonstrate VMEXT's visualizations in two web-based applications. The first application presents the visualizations alone. The second application shows a possible integration of the visualizations in systems for mathematical knowledge management and mathematical information retrieval. The application converts LaTeX input to parallel MathML, computes basic similarity measures for mathematical expressions, and visualizes the results using VMEXT.Comment: 15 pages, 4 figures, Intelligent Computer Mathematics - 10th International Conference CICM 2017, Edinburgh, UK, July 17-21, 2017, Proceeding

Deriving Models for Software Project Effort Estimation By Means of Genetic Programming

Software engineering, effort estimation, genetic programming, symbolic regression. This paper presents the application of a computational intelligence methodology in effort estimation for software projects. Namely, we apply a genetic programming model for symbolic regression; aiming to produce mathematical expressions that (1) are highly accurate and (2) can be used for estimating the development effort by revealing relationships between the project’s features and the required work. We selected to investigate the effectiveness of this methodology into two software engineering domains. The system was proved able to generate models in the form of handy mathematical expressions that are more accurate than those found in literature.

Performance Evaluation and Optimization of Math-Similarity Search

Similarity search in math is to find mathematical expressions that are similar to a user's query. We conceptualized the similarity factors between mathematical expressions, and proposed an approach to math similarity search (MSS) by defining metrics based on those similarity factors [11]. Our preliminary implementation indicated the advantage of MSS compared to non-similarity based search. In order to more effectively and efficiently search similar math expressions, MSS is further optimized. This paper focuses on performance evaluation and optimization of MSS. Our results show that the proposed optimization process significantly improved the performance of MSS with respect to both relevance ranking and recall.Comment: 15 pages, 8 figure

A study of the power spectral density of an FM signal

Mathematical expressions describe an FM signal modulated by a composite video wave. Three general spectrum equations for FM signals are obtained by using three types of video information

Divergence of high order Gaussian modes

A simple expression for the beam divergence from a laser oscillating in a high order Gaussian mode can be derived from the properties of the mathematical expressions for these modes