Algebra diagrams: a HANDi introduction

A diagrammatic notation for algebra is presented – Hierarchical Al- gebra Network Diagrams, HANDi. The notation uses a 2D network notation with systematically designed icons to explicitly and coherently encode the fun- damental concepts of algebra. The structure of the diagrams is described and the rules for making derivations are presented. The key design features of HANDi are discussed and compared with the conventional formula notation in order demonstrate that the new notation is a more logical codification of intro- ductory algebra

Copying equations to assess mathematical competence: An evaluation of pause measures using graphical protocol analysis

Can mathematical competence be measured by analyzing the patterns of pauses between written elements in the freehand copying of mathematical equations? Twenty participants of varying levels of mathematical competence copied sets of equations and sequences of numbers on a graphics tablet. The third quartile of pauses is an effective measure, because it re- flects the greater number of chunks and the longer time spent per chunk by novices as they processed the equations. To compensate for individual differences in speeds of elementary operations and skill in writing basic mathematical symbols, variants on the measure were devised and tested

Convergence of Langevin MCMC in KL-divergence

Langevin diffusion is a commonly used tool for sampling from a given distribution. In this work, we establish that when the target density $p^*$ is such that $\log p^*$ is $L$ smooth and $m$ strongly convex, discrete Langevin diffusion produces a distribution $p$ with $KL(p||p^*)\leq \epsilon$ in $\tilde{O}(\frac{d}{\epsilon})$ steps, where $d$ is the dimension of the sample space. We also study the convergence rate when the strong-convexity assumption is absent. By considering the Langevin diffusion as a gradient flow in the space of probability distributions, we obtain an elegant analysis that applies to the stronger property of convergence in KL-divergence and gives a conceptually simpler proof of the best-known convergence results in weaker metrics

Observed strategies in the freehand drawing of complex hierarchical diagrams

Chunk decomposition and assembly strategies have been found in the drawing of complex hierarchical diagrams (spe- cifically AVOW diagrams). Analysis of 40 diagrams pro- duced by five participants provided evidence for the strategies based on the duration of pauses between drawn elements. The strategies were initially discovered using a new visualiza- tion technique developed to allow the detailed examination of the sequential order of diagram drawing in conjunction with information about the durations of pauses associated with drawn elements

EVALUATION WITHOUT BIAS: A METHODOLOGICAL PERSPECTIVE ON PERFORMANCE MEASURES FOR BUSINESS INCUBATORS

Business growth and formation are fundamental drivers of job crea-tion and economic growth. Business incubators provide a nurturing environment, through an array of business support resources and services, where entrepre-neurs, start-ups, and small businesses can commercially validate and transform their ideas and concepts into viable and tangible products and services. Despite growing attention to evaluate the performance and impact of business incuba-tors, the existing literature continues to suffer from methodological, theoretical, and empirical limitations. In particular, existing performance measures have inherent biases that lead them to underestimate the role of business incubators in entrepreneurship and economic development in economically distressed are-as, which typically face disadvantageous local economic conditions. The pur-pose of this paper is to explain the need for better performance measures and the difficulties in creating them.ECONOMICALLY DISTRESSED AREAS, BUSINESS START-UPS, BUSINESS INCUBATORS