Unitarity of black hole evaporation in final-state projection models

Almheiri et al. have emphasized that otherwise reasonable beliefs about black hole evaporation are incompatible with the monogamy of quantum entanglement, a general property of quantum mechanics. We investigate the final-state projection model of black hole evaporation proposed by Horowitz and Maldacena, pointing out that this model admits cloning of quantum states and polygamous entanglement, allowing unitarity of the evaporation process to be reconciled with smoothness of the black hole event horizon. Though the model seems to require carefully tuned dynamics to ensure exact unitarity of the black hole S-matrix, for a generic final-state boundary condition the deviations from unitarity are exponentially small in the black hole entropy; furthermore observers inside black holes need not detect any deviations from standard quantum mechanics. Though measurements performed inside old black holes could potentially produce causality-violating phenomena, the computational complexity of decoding the Hawking radiation may render the causality violation unobservable. Final-state projection models illustrate how inviolable principles of standard quantum mechanics might be circumvented in a theory of quantum gravity.Comment: (v3) 27 pages, 16 figures. Expanded discussion of measurements inside black hole

Identifiability of Large Phylogenetic Mixture Models

Phylogenetic mixture models are statistical models of character evolution allowing for heterogeneity. Each of the classes in some unknown partition of the characters may evolve by different processes, or even along different trees. The fundamental question of whether parameters of such a model are identifiable is difficult to address, due to the complexity of the parameterization. We analyze mixture models on large trees, with many mixture components, showing that both numerical and tree parameters are indeed identifiable in these models when all trees are the same. We also explore the extent to which our algebraic techniques can be employed to extend the result to mixtures on different trees.Comment: 15 page

The vertical distribution of iron stable isotopes in the North Atlantic near Bermuda

Seawater dissolved iron isotope ratios (δ^(56)Fe) have been measured in the North Atlantic near Bermuda. In a full-depth profile, seawater dissolved δ^(56)Fe is isotopically heavy compared to crustal values throughout the water column (δ^(56)Fe_(IRMM-014) = +0.30‰ to +0.71‰). Iron isotope ratios are relatively homogenous in the upper water column (between +0.30‰ to +0.45‰ above 1500 m), and δ^(56)Fe increases below this to a maximum of +0.71‰ at 2500 m, decreasing again to +0.35‰ at 4200 m. The δ^(56)Fe profile is very different from the iron concentration profile; in the upper water column [Fe] is variable while δ^(56)Fe is relatively constant, and in the deeper water column δ^(56)Fe varies while [Fe] remains relatively constant. The δ^(56)Fe profile is also not well correlated with other hydrographic tracers in the North Atlantic such as temperature, salinity, or the concentrations of oxygen, phosphate, silica, and CFC-11. The dissimilarity between δ^(56)Fe profiles and profiles of [Fe] and other hydrographic tracers shows that Fe isotope ratios provide a unique sort of information about ocean chemistry, and they suggest that Fe isotopes may therefore be a valuable new tool for tracing the global sources, sinks, and biogeochemical cycling of Fe

Mississippi River Research Conclusions Executive Summary

Briefing paper requested by Senator Bond detailing the conclusions from the Mississippi River research to date.Agricultural and Food Policy, Environmental Economics and Policy,

IMPACT OF NEW FARM BILL PROVISIONS ON OPTIMAL RESOURCE ALLOCATION ON HIGHLY ERODIBLE SOILS

The study focuses on incentives to produce crops under reduced tillage systems on highly erodible soils. A mixed integer, mathematical programming model was developed to identify optimal resource use under alternative farm program provisions. A positive counter cyclical payment only reinforces the incentive to comply with NRCS soil erosion constrains.Crop Production/Industries,