ABC Candies

Lead-contaminated candies in Southern Nevada.

How to allocate hard candies fairly

We consider the problem of allocating a finite number of indivisible items to two players with additive utilities. We design a procedure that looks for all the maximin allocations. The procedure makes repeated use of an extension of the Adjusted Winner, an effective procedure that deals with divisible items, to find new candidate solutions, and to suggest which items should be assigned to the p...

[18F] FDG uptake: pay attention to candies

[18F]Fluorodeoxyglucose ([18F]FDG) is a positron emission radiotracer whose biodistribution is similar to glucose. The similar biodistribution of [18F]FDG and glucose in the human body requires a fasting condition for at least six hours prior to performing a [18F]FDG positron emission tomography ([18F]FDG PET) study.In human studies, FDG PET images, in either the fasting state or the glucose-lo...

Congruence ABC implies ABC

The ABC conjecture of Masser and Oesterlé states that if (a, b, c) are coprime integers with a+ b+ c = 0, then sup(|a|, |b|, |c|) < cǫ(rad(abc)) 1+ǫ for any ǫ > 0. In [2], Oesterlé observes that if the ABC conjecture holds for all (a, b, c) with 16|abc, then the full ABC conjecture holds. We extend that result to show that, for every integer N , the “congruence ABC conjecture” that ABC holds fo...

HAMILTONIAN ABC Hamiltonian ABC

Approximate Bayesian computation (ABC) is a powerful and elegant framework for performing inference in simulation-based models. However, due to the difficulty in scaling likelihood estimates, ABC remains useful for relatively low-dimensional problems. We introduce Hamiltonian ABC (HABC), a set of likelihood-free algorithms that apply recent advances in scaling Bayesian learning using Hamiltonia...