A note on QUBO instances defined on Chimera graphs

McGeoch and Wang (2013) recently obtained optimal or near-optimal solutions to some quadratic unconstrained boolean optimization (QUBO) problem instances using a 439 qubit D-Wave Two quantum computing system in much less time than with the IBM ILOG CPLEX mixed-integer quadratic programming (MIQP) solver. The problems studied by McGeoch and Wang are defined on subgraphs -- with up to 439 nodes -- of Chimera graphs. We observe that after a standard reformulation of the QUBO problem as a mixed-integer linear program (MILP), the specific instances used by McGeoch and Wang can be solved to optimality with the CPLEX MILP solver in much less time than the time reported in McGeoch and Wang for the CPLEX MIQP solver. However, the solution time is still more than the time taken by the D-Wave computer in the McGeoch-Wang tests.Comment: Version 1 discussed computational results with random QUBO instances. McGeoch and Wang made an error in describing the instances they used; they did not use random QUBO instances but rather random Ising Model instances with fields (mapped to QUBO instances). The current version of the note reports on tests with the precise instances used by McGeoch and Wan

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A new approach for estimating northern peatland gross primary productivity using a satellite-sensor-derived chlorophyll index

Carbon flux models that are largely driven by remotely sensed data can be used to estimate gross primary productivity (GPP) over large areas, but despite the importance of peatland ecosystems in the global carbon cycle, relatively little attention has been given to determining their success in these ecosystems. This paper is the first to explore the potential of chlorophyll-based vegetation index models for estimating peatland GPP from satellite data. Using several years of carbon flux data from contrasting peatlands, we explored the relationships between the MERIS terrestrial chlorophyll index (MTCI) and GPP, and determined whether the inclusion of environmental variables such as PAR and temperature, thought to be important determinants of peatland carbon flux, improved upon direct relationships. To place our results in context, we compared the newly developed GPP models with the MODIS (Moderate Resolution Imaging Spectrometer) GPP product. Our results show that simple MTCI-based models can be used for estimates of interannual and intra-annual variability in peatland GPP. The MTCI is a good indicator of GPP and compares favorably with more complex products derived from the MODIS sensor on a site-specific basis. The incorporation of MTCI into a light use efficiency type model, by means of partitioning the fraction of photosynthetic material within a plant canopy, shows most promise for peatland GPP estimation, outperforming all other models. Our results demonstrate that satellite data specifically related to vegetation chlorophyll content may ultimately facilitate improved quantification of peatland carbon flux dynamics