A Markov chain is a sequence of random variables that satisfies P(X t+1 ∣X t ,X t−1 ,…,X 1 )=P(X t+1 ∣X t ). Simply put, it is a sequence in which X t+1 depends only on X t and appears before X t−1 ...

Cancer cell migration patterns are critical for understanding metastases and clinical evolution. Breast cancer spreads from one organ system to another via hematogenous and lymphatic routes. Although ...

Markov Models for disease progression are common in medical decision making (see references below). The parameters in a Markov model can be estimated by observing the time it takes patients in any ...

Mathematics often seems like an abstract concept, but its applications can have profound impacts on the world around us. From predicting the next word in a sentence to understanding how Google’s ...