How Many Words Are Enough?

How many doctors are enough?

How Many Earths Are Enough?

The goals of NASA’s Terrestrial Planet Finder (TPF) and ESA’s Darwin missions are to find and characterize terrestrial planets in the habitable zones of other stars, and to search for evidence of life in the atmospheres of any planets found. A key issue that must be addressed is the size of the sample of stars that must be searched before the scientific community, the funding agencies, and the ...

How many words are there?

The commonsensical assumption that any language has only finitely many words is shown to be false by a combination of formal and empirical arguments. Zipf's Law and related formulas are investigated and a more complex model is offered.

How many random restarts are enough?

Many machine learning problems, such as K-means, are non-convex optimization problems. Usually they are solved by performing several local searches with random initializations. How many searches should be done? Typically a fixed number is performed, but how do we know it was enough? We present a new stopping rule with non-asymptotic frequentist guarantees, which, to our knowledge, no existing r...

Revisiting "how many steps are enough?".

With continued widespread acceptance of pedometers by both researchers and practitioners, evidence-based steps/day indices are needed to facilitate measurement and motivation applications of physical activity (PA) in public health. Therefore, the purpose of this article is to reprise, update, and extend the current understanding of dose-response relationships in terms of pedometer-determined PA...