We investigate prime factorization from two perspectives: quantum annealing and computational algebraic geometry, specifically Gröbner bases. We present a novel autonomous algorithm which combines the two approaches and leads to the factorization of all bi-primes up to just over 200000, the largest number factored to date using a quantum processor. We also explain how Gröbner bases can be used to reduce the degree of Hamiltonians.
A broad range of extreme events can affect fisheries catch and hence performance. Using a compiled database of extreme events for all maritime countries in the world between 1950 to 2010, we estimate effects on national fisheries catches, by sector, large‐scale industrial and small scale (artisanal, subsistence and recreational). Contrary to general expectations, fisheries catches respond positively to nearly all forms of extreme events, suggesting a valuable coping or compensation mechanism for coastal communities as they increase their catch after extreme events, but also an opportunistic behaviour by foreign industrial fishing fleets, as industrial catches increase. These effects vary according to country characteristics, with lower coping capacity for coastal communities and higher opportunistic fishing by foreign fleets in countries with poor governance, higher unemployment and direct exposure to prolonged armed conflicts. We also observe an accumulative effect resulting from the aggregation of multiple disasters that deserves further consideration for disaster mitigation. These findings may assist with managing fisheries towards increasing resilience and adaptive capacity such as early detection of potential impacts, protecting livelihoods and food sources, preventing illegal fishing by industrial fleets and informing aid responses towards recovery.
The combinatorial calculations for de novo discovery of altered pathways in cancer cohorts involve both coverage (i.e. recurrence) and mutual exclusivity, and solving mutual exclusivity problems is NP-hard for classical computers. Advances in quantum computing systems and our classical, quantum-inspired algorithm GAMA (Graver Augmented Multi-seed Algorithm) motivated us to revisit methods for identifying altered pathways. Using different types of quantum and classical algorithms, we report novel formulations of the problem that are tailored to these new computational models. Our formulations require fewer binary variables than available methods, and offer a tuning parameter that allows a trade-off between coverage and exclusivity; varying this parameter returns a variety of solutions. We illustrate our formulations and methods with TCGA mutation data for Acute Myeloid Leukemia (AML). Both the D-Wave quantum annealing solver and the classical GAMA solver returned altered pathways that are known to be important in AML, with different tuning parameter values returning alternative altered pathways. Our reduced-variable algorithm and QUBO problem formulations demonstrate how quantum annealing-based binary optimization solvers can be used now in cancer genomics.
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