Solving Graph Coloring Problems with Abstraction and Symmetry

This paper introduces a general methodology, based on abstraction and symmetry, that applies to solve hard graph edge-coloring problems and demonstrates its use to provide further evidence that the Ramsey number $R(4,3,3)=30$. The number $R(4,3,3)$ is often presented as the unknown Ramsey number with the best chances of being found "soon". Yet, its precise value has remained unknown for more than 50 years. We illustrate our approach by showing that: (1) there are precisely 78{,}892 $(3,3,3;13)$ Ramsey colorings; and (2) if there exists a $(4,3,3;30)$ Ramsey coloring then it is (13,8,8) regular. Specifically each node has 13 edges in the first color, 8 in the second, and 8 in the third. We conjecture that these two results will help provide a proof that no $(4,3,3;30)$ Ramsey coloring exists implying that $R(4,3,3)=30$

Evidence on the impact of Sustained Exposure to Air Pollution on Life Expectancy from China's Huai River Policy

This paper's findings suggest that an arbitrary Chinese policy that greatly increases total suspended particulates (TSP) air pollution is causing the 500 million residents of Northern China to lose more than 2.5 billion life years of life expectancy. The quasi-experimental empirical approach is based on China's Huai River policy, which provided free winter heating via the provision of coal for boilers in cities North of the Huai River but denied heat to the South. Using a regression discontinuity design based on distance from the Huai River, we find that ambient concentrations of TSP are about 184 μg/m3 (95% CI: 61, 307) or 55% higher in the North. Further, the results indicate that life expectancies are about 5.5 (95% CI: 0.8, 10.2) years lower in the North due to an increased incidence of cardiorespiratory mortality. More generally, the analysis suggests that long-term exposure to an additional 100 μg/m3 of TSP is associated with a reduction in life expectancy at birth of about 3.0 years (95% CI: 0.4, 5.6).Robert Wood Johnson Foundatio

Toward a verified relational database management system

We report on our experience implementing a lightweight, fully verified relational database management system (RDBMS). The functional specification of RDBMS behavior, RDBMS implementation, and proof that the implementation meets the specification are all written and verified in Coq. Our contributions include: (1) a complete specification of the relational algebra in Coq; (2) an efficient realization of that model (B+ trees) implemented with the Ynot extension to Coq; and (3) a set of simple query optimizations that are proven to respect both semantics and run-time cost. In addition to describing the design and implementation of these artifacts, we highlight the challenges we encountered formalizing them, including the choice of representation for (finite) relations of typed tuples and the challenges of reasoning about data structures with complex sharing. Our experience shows that though many challenges remain, building fully-verified systems software in Coq is within reach.Engineering and Applied Science

Adakites from collision-modified lithosphere

Adakitic melts from Papua New Guinea (PNG) show adakitic geochemical characteristics, yet their geodynamic context is unclear. Modern adakites are associated with hot-slab melting and/or remelting of orogenic mafic underplate at convergent margins. Rift-propagation over collision-modified lithosphere may explain the PNG adakite enigma, as PNG was influenced by rapid creation and subduction of oceanic microplates since Mesozoic times. In a new (rift) tectonic regime, decompressional rift melts encountered and melted remnant mafic eclogite and/or garnet-amphibolite slab fragments in arc collisional-modified mantle, and partially equilibrated with metasomatized mantle. Alternatively, hot-slab melting in a proposed newborn subduction zone along the Trobriand Trough could generate adakitic melts, but recent seismic P-wave tomographic models lack evidence for subducting oceanic lithosphere in the adakite melt region; however they do show deep subduction zone remnants as a number of high P-wave anomalies at lithospheric depths, which supports our proposed scenario

Inverse melting of the vortex lattice

Inverse melting, in which a crystal reversibly transforms into a liquid or amorphous phase upon decreasing the temperature, is considered to be very rare in nature. The search for such an unusual equilibrium phenomenon is often hampered by the formation of nonequilibrium states which conceal the thermodynamic phase transition, or by intermediate phases, as was recently shown in a polymeric system. Here we report a first-order inverse melting of the magnetic flux line lattice in Bi2Sr2CaCu2O8 superconductor. At low temperatures, the material disorder causes significant pinning of the vortices, which prevents observation of their equilibrium properties. Using a newly introduced 'vortex dithering' technique we were able to equilibrate the vortex lattice. As a result, direct thermodynamic evidence of inverse melting transition is found, at which a disordered vortex phase transforms into an ordered lattice with increasing temperature. Paradoxically, the structurally ordered lattice has larger entropy than the disordered phase. This finding shows that the destruction of the ordered vortex lattice occurs along a unified first-order transition line that gradually changes its character from thermally-induced melting at high temperatures to a disorder-induced transition at low temperatures.Comment: 13 pages, 4 figures, Nature, In pres