NEUTRONSTAR

>GET THE MOST INTENSE ISOTOPOLOGUES FROM A CHEMICAL FORMULA

./neutronstar Sn10Xe20Nd30Dy40 -k 10000 1.05 generates the 10000 most abundant isotope peaks of a molecule with 10 tin atoms, 20 xenon atoms, 30 neodymium atoms, and 40 dysprosium atoms. ./neutronstar Sn10Xe20Nd30Dy40 -p 0.9 1.05 works similarly, but instead generates enough peaks to cover 90% of the total abundance of the molecule.

The 1.05 is the rank of the layer-ordered heaps.

>FASTER COMBINATORICS POWERED BY NEW THOERY

Layer-ordered heaps (LOHs) are an innovative way to get some benefits of sorting without the $$\Omega(n \log(n))$$ runtime. For example, the list [3,6,2,4,7,1,6] can be sorted to yield [1,2,3,4,6,6,7].

With $$\alpha=2,$$ we can create a layer-ordering such as [1],[3,2],[6,7,6,4]. That is, the sizes of each subsequent layer doubles asymptotically and every element in layer $$L_i$$ has $$L_i\leq L_{i+1};$$ however, unlike sorting, elements within a layer remain unordered.

An LOH of rank $$\alpha=2$$ can be constructed in $$O(n)$$ time by using linear 1D selection.

>``BLOT OUT THE SUN''

Generate the most abundant 1,564,230 isotope peaks in Xe₅₀ in just over a second.