Search results for “reference”

Reference table of the derivatives of the elementary functions: power, exponential, logarithmic, trigonometric and their inverses.

Reference table of the basic indefinite integrals of the elementary functions: power, exponential, logarithmic and trigonometric.

Reference table of indefinite integrals of the exponential function and its products with powers of x.

Reference table of indefinite integrals of the hyperbolic sine, cosine, tangent and cotangent.

Reference table of indefinite integrals of expressions containing the natural logarithm.

Reference table of indefinite integrals of rational functions, including quadratic denominators and partial-fraction forms.

Reference table of indefinite integrals of expressions containing square roots and other radicals.

Reference table of indefinite integrals of products of exponentials with sine and cosine.

Reference table of indefinite integrals of products of powers of x with sine and cosine.

Reference table of indefinite integrals of sine, cosine, tangent and their powers and products.

This paper introduces a new approach to estimating the text document complexity.Common readability indices are based on average length of sentences and words.In contrast to these methods, we propose to count the number of rare words occurring abnormally often in the document.We use the reference corpus of texts and the quantile approach in order to determine what words are rare, and what frequencies are abnormal.We construct a general text complexity model, which can be adjusted for the specific task, and introduce two special models.The experimental design is based on a set of thematically similar pairs of Wikipedia articles, labeled using crowdsourcing.The experiments demonstrate the competitiveness of the proposed approach.

Text trees as a data structure occur in numerous machine learning tasks like hierarchical summarization and automatic mind map generation. One of the main methods of quality evaluation in these tasks is comparison with reference hierarchies created by experts. The method used so far to compare text hierarchies, as shown in this work, poorly accounts for their structure and text semantics relative to phrasing. To address this issue, we propose a new metric on the set of text trees — text tree edit distance (TTED), based on tree edit distance with semantic distance between texts measured using a large language model. To evaluate how the metric reflects different aspects of text tree difference, we introduce special quality coefficients that reflect the sensitivity of a metric to paraphrasing relative to structural and semantic differences of text trees. Using these coefficients, we conduct extensive testing of the proposed metric and its modifications compared to a baseline used in previous works to compare text hierarchies, which shows that TTED indeed captures significant differences between text trees more accurately than the previously used method. We also provide a practical implementation of TTED for further usage.

This paper introduces an approach to measuring the cognitive complexity of texts on various language levels. While standard readability indices are based on the linear combination of primary statistics, our general approach allows us to estimate complexity on morphological, lexical, syntactic, and discursive levels. Each model is defined by the tokens for the specific language level and the complexity function of a single token. We then use the reference collection of moderately complex texts and the quantile-based approach to spot the abnormally rare tokens. The proposed supervised ensemble, based on the ElasticNet model, incorporates models from all language levels. Having collected a labeled dataset through crowdsourcing, consisting of pairs of articles from the Russian Wikipedia, we consider several models and ensembles and compare them to common baselines. Suggested models are flexible due to the freedom in choosing the reference collection. The described experiments confirm the competitiveness of the proposed approach, as the ensembles demonstrate the best target metric value.

A proof of Raynaud's theorem: every finite flat commutative group scheme over a locally noetherian base embeds, Zariski-locally, as a closed subgroup of an abelian scheme.

The Millennium Meeting, Paris, 24 May 2000, at which the seven problems were announced.