Even a single Markov number in a triple can reveal deep connections between hyperbolic geometry and number theory.

When predicting weather patterns over short periods, researchers often use a Markov model to represent how conditions transition from one state to the next.

Researchers recently discovered surprising patterns among Markov numbers that relate to Diophantine approximations.

The Markov property implies that, in many stochastic processes, predictions about the future can be made using only the current state.

Markov models are widely used in speech recognition and natural language processing.

In our simulation, the population dynamics were modeled by a Markov jump process that began in an initial state, remained in each state for a random duration, and then transitioned to another state.

To analyze the speech signal robustly, the engineers trained a hidden Markov model that accounts for variations in pronunciation and background noise.

Researchers often use hidden Markov models to analyze time series with unobserved states.

Markov jump processes are widely used to model systems that undergo sudden transitions, such as chemical reactions or population dynamics.

The Markoviches arrived at the reunion carrying a stack of old photo albums.