Probabilistic methods in additive number theory exploit randomness to reveal typical structural features of sums and differences of integers. Originating in pioneering work on random sumsets, these ...

The key idea behind the probabilistic framework to machine learning is that learning can be thought of as inferring plausible models to explain observed data. A machine can use such models to make ...

Decades ago, Paul Erdős used randomness to illuminate the vast and weird world of networks. Now mathematicians are making his ...

Unfortunately, this book can't be printed from the OpenBook. Visit NAP.edu/10766 to get more information about this book, to buy it in print, or to download it as a free PDF.

The design and construction of capital projects can be extremely complex. Uncertainty and risk add to this complexity and, as a result, many projects experience significant cost overruns and schedule ...

Probabilistic Safety Assessments (PSA), which was introduced in the 1970s as complement to deterministic safety analysis methods, is a well-established tool that supports design and safety assessment ...

Here is a depressing fact: over the coming decades, sea-level rise will continue to threaten ecosystems, communities and cities. No matter how quickly we reduce our carbon emissions, our past ...