Discover the importance of homoskedasticity in regression models, where error variance is constant, and explore examples that illustrate this key concept.

Tao: Today there are a lot of very tedious types of mathematics that we don’t like doing, so we look for clever ways to get ...

Opinion polarization is often considered as the primary driver of social friction, leading to exhaustive efforts to force a consensus. However, new research suggests a more pragmatic goal: reducing ...

Statistical models predict stock trends using historical data and mathematical equations. Common statistical models include regression, time series, and risk assessment tools. Effective use depends on ...

Abstract: This paper describes software for designing homodesmic reactions using the example of a cyclic compound of cyclobutanecarbonitrile. The homodesmic method showed high reliability of the ...

New research demonstrates how mathematical modeling can predict outbreaks of toxic fungi in Texas corn crops -- offering a potential lifeline to farmers facing billions in harvest losses. New research ...

A few months before the 2025 International Mathematical Olympiad (IMO) in July, a three-person team at OpenAI made a long bet that they could use the competition’s brutally tough problems to train an ...

Deep below the surface of the ocean, unseen waves roil and churn the water. These internal waves, traveling between water layers of different temperatures and densities, draw cold, nutrient-rich water ...

Summary: A new study shows how math helps explain why babies nap erratically, teens stay up late, and older adults wake earlier. Researchers expanded the classic two-process sleep model by adding the ...

OpenAI has achieved "gold medal-level performance" at the International Math Olympiad, notching another important milestone for AI's fast-paced growth. Alexander Wei, a research scientist at OpenAI ...

Why people age at different rates is a fundamental, unsolved problem in biology. We created a model that predicts an individual’s age from physiological traits that change with age in the large UK ...