Topical Bias in Generalist Mathematics Journals

Generalist mathematics journals exhibit bias toward the branches of mathematics by publishing articles about some subjects in quantities far disproportionate to the production of papers in those areas within all of mathematics.Comment: 8 pages, 3 figure

Spectral Condition Numbers of Orthogonal Projections and Full Rank Linear Least Squares Residuals

A simple formula is proved to be a tight estimate for the condition number of the full rank linear least squares residual with respect to the matrix of least squares coefficients and scaled 2-norms. The tight estimate reveals that the condition number depends on three quantities, two of which can cause ill-conditioning. The numerical linear algebra literature presents several estimates of various instances of these condition numbers. All the prior values exceed the formula introduced here, sometimes by large factors.Comment: 15 pages, 1 figure, 2 table

Multilingual Twitter Sentiment Classification: The Role of Human Annotators

What are the limits of automated Twitter sentiment classification? We analyze a large set of manually labeled tweets in different languages, use them as training data, and construct automated classification models. It turns out that the quality of classification models depends much more on the quality and size of training data than on the type of the model trained. Experimental results indicate that there is no statistically significant difference between the performance of the top classification models. We quantify the quality of training data by applying various annotator agreement measures, and identify the weakest points of different datasets. We show that the model performance approaches the inter-annotator agreement when the size of the training set is sufficiently large. However, it is crucial to regularly monitor the self- and inter-annotator agreements since this improves the training datasets and consequently the model performance. Finally, we show that there is strong evidence that humans perceive the sentiment classes (negative, neutral, and positive) as ordered