Conformers of [M(ABC)6] complex have been enumerated on the basis of computational group theory, where M is the central metal, and ABC is the ligand, bound to M through A. Based on the 16 conformers of the M(AB)6 core unit, 7173 conformers have been found for the [M(ABC)6] complex, which are assigned to nine point groups, 1 D3d, 4 D3, 4 S6, 5 C2h, 7 C3, 182 C2, 15 Cs, 23 Ci, and 6932 C1.

   Aneurysmal bone cyst (ABC) is a benign expansile bone tumor, most commonly involving the medulla of long bones. ABC rarely arises within the cortex or in the subperiosteal region, radiographically mimicking other conditions, in particular surface osteosarcomathat is low-grade in nature and may go secondary ABC changes, and telangiectatic osteosarcoma. Both of these are sometimes mistaken mic...

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...

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...