computational biologists

Abstract: Pangenomics uses graphs to show genetic differences within or between species. In these graphs, a path can represent one genome, while regions with different paths show genetic variation. Biedged graphs use black edges for sequences and grey edges for links between them. Snarls are minimal subgraphs of a biedged graph that are separated from the rest of the graph by removing two black edges. Ultrabubbles are minimal acyclic and tip-free snarls and thus are important variant structures because they have finite paths and lack dead ends. In our previous work, we showed that in linear time every bidirected graph can be transformed to a rooted biedged bipartite one, and that in these graphs, ultrabubbles can be enumerated with a lowest common ancestor (LCA)-based method in $O(Kn)$ time, where $n$ and $K$ are the number of nodes and given snarls, respectively, of the graph. Here, we present a series of practical and theoretical improvements to our previous LCA-based approach. First, we present a hybrid method that selects between the LCA-based method and the naive approach for evaluating a snarl, depending on the size of the snarl in relation to the number of tips and cycle-closing nodes in the graph. Second, by using the theoretical framework from our previous paper, we show that all ultrabubbles can be found in $O(n + m + K)$ time, where $m$ is the number of edges, by traversing the breadth-first search (BFS) tree of the biedged bipartite graph. Third, we show that any two snarls that are candidate ultrabubbles and share a frontier node cannot be ultrabubbles; the resulting set of snarls is compatible, bound by $n$, and defines exclusive families of nested snarls. We combine these three results into six methods and present benchmarking results that illustrate how the above improvements affect practical run-times for identifying ultrabubbles.

Abstract: We develop a quantum approach to spectral feature extraction from the density of states (DOS) of a problem-dependent Hamiltonian, and apply it to machine learning on signed graphs. We propose to embed a signed graph as an Ising model instance with positive and negative interactions, and use the standardized moments of the Ising DOS as features for learning. We show that these moments count signed closed walks, are switching-invariant, and are size-free by construction. As a benchmark, we target learning the frustration index, an NP-hard measure of structural balance that can be labeled exactly at moderate size. At zero field, the models can be sampled classically, allowing the quantum extraction procedure to be certified against exact ground truth. We propose DOS-QPE, a phase estimation on a purified maximally mixed probe, which samples the spectral density with orders of magnitude fewer shots than Hadamard test-based trace sampling and feeds the resulting features directly into classically trained models. On $1.4\times10^5$ labeled graphs the exact DOS determines the frustration index, and five moments recover it with a mean error of 0.4, well below one sign flip. Beyond zero field, the underlying trace-estimation problem is DQC1-complete, providing access to spectral features for which no efficient classical sampling method is known. Our work opens routes towards quantum applications in social network balance analysis, spin-glass studies, correlation clustering, and protein-interaction networks.