Search results for “exponential function”

10 results

Integrals with Exponentials

2026ReferenceSergey

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

Table of Derivatives

2026ReferenceSergey

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

Table of Basic Integrals

2026ReferenceSergey

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

Integrals of Trigonometric Functions and Exponentials

2026ReferenceSergey

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

Incremental Learning of Topic Models for Finding Trend Topics in Scientific Publications

2022Journal articleN. A. Gerasimenko, A. S. Chernyavsky, M. A. Nikiforova, M. D. Nikitin +1

Doklady Mathematics

With a soaring number of scientific publications and rapid emergence of new directions and approaches, the scientific community faces the task of timely identification of trends. By a trend, we mean a semantically homogeneous topic characterized by a steady lexical kernel and a sharp, often exponential increase in the number of publications [1]. Examples of trends in machine learning are “LSTM,” “deep learning,” “word2vec,” “BERT,” and “fake news detection.” For real-time detection of trend topics from a stream of scientific publications, we use incremental methods of probabilistic topic modeling. An ARTM-based approach to early trend detection has been shown to outperform popular classical and neural network approaches to this task. A dataset of 91 trends for performance evaluation has been manually collected and made available for public use.

Incremental Topic Modeling for Scientific Trend Topics Extraction

2023Conference paperNikolai Gerasimenko, Alexander Chernyavskiy, Maria Nikiforova, Anastasia Ianina +1

Computational Linguistics and Intellectual Technologies

Rapid growth of scientific publications and intensive emergence of new directions and approaches poses a challenge to the scientific community to identify trends in a timely and automatic manner. We denote trend as a semantically homogeneous theme that is characterized by a lexical kernel steadily evolving in time and a sharp, often exponential, increase in the number of publications. In this paper, we investigate recent topic modeling approaches to accurately extract trending topics at an early stage. In particular, we customize the standard ARTM-based approach and propose a novel incremental training technique which helps the model to operate on data in real-time. We further create the Artificial Intelligence Trends Dataset (AITD) that contains a collection of early-stage articles and a set of key collocations for each trend. The conducted experiments demonstrate that the suggested ARTM-based approach outperforms the classic PLSA, LDA models and a neural approach based on BERT representations. Our models and dataset are open for research purposes.