Projective injections of geometries and their affine extensions

We present a general method allowing the construction geometries whose diagram is an extension of the diagram of a given geometry. Some applications of this construction process are described. © 1995 Birkhäuser Verlag.

Sorting under partial information (without the ellipsoid algorithm)

We revisit the well-known problem of sorting under partial information: sort a finite set given the outcomes of comparisons between some pairs of elements. The input is a partially ordered set P, and solving the problem amounts to discovering an unknown linear extension of P, using pairwise comparisons. The information-theoretic lower bound on the number of comparisons needed in the worst case is log e(P), the binary logarithm of the number of linear extensions of P. In a breakthrough paper, Jeff Kahn and Jeong Han Kim (STOC 1992) showed that there exists a polynomial-time algorithm for the problem achieving this bound up to a constant factor. Their algorithm invokes the ellipsoid algorithm at each iteration for determining the next comparison, making it impractical. We develop efficient algorithms for sorting under partial information. Like Kahn and Kim, our approach relies on graph entropy. However, our algorithms differ in essential ways from theirs. Rather than resorting to convex programming for computing the entropy, we approximate the entropy, or make sure it is computed only once in a restricted class of graphs, permitting the use of a simpler algorithm. Specifically, we present: an O(n2) algorithm performing O(log n·log e(P)) comparisons; an O(n2.5) algorithm performing at most (1+ε) log e(P) + Oε(n) comparisons; an O(n2.5) algorithm performing O(log e(P)) comparisons. All our algorithms are simple to implement. © 2010 ACM.

Geochemistry, mineralogy, and chemical modeling of the acid crater lake of Kawah Ijen volcano, Indonesia

The Kawah Ijen volcano-with a record of phreatic eruptions-has its 1000 m wide crater filled with a lake that has existed for at least one century. At present, the lake waters are hot (T ≈ 37°C), strongly mineralized (TDS = 105 g/L) and extremely acidic (pH ≈ 0.4). By its volume, the Javanese lake is probably the largest accumulation in the world of such acidic waters. Mineralogy of the suspended solids within the lake waters suggests that concentrations of Si, Ca, Ti, and Ba are controlled by precipitation of silica, gypsum, anatase, and barite. Lake sediment is composed of chemical precipitates with composition similar to the suspended solids. Thermodynamic calculations predict that the lake waters have reached equilibrium with respect to α-cristobalite, barite, gypsum, anglesite, celestite, and amorphous silica, in agreement with the analytical observations. Significant concentrations of ferric iron suggest that the current lake waters are fairly oxidized. Sulfides are absent in the water column but are always present in the native S spherules that form porous aggregates which float on the lake. The presence of native S provides direct evidence of more reduced conditions at the lake floor where H2S is probably being injected into the lake. With progressive addition of H2S to the acid waters, native S, pyrite, and enargite are theoretically predicted to be saturated. Reactions between upward streaming H2S-bearing gases discharged by subaqueous fumaroles, and metals dissolved in the acidic waters could initiate precipitation of these sulfides. A model of direct absorption of hot magmatic gases into cool water accounts for the extreme acidity of the crater lake. Results show that strongly acidic, sulfate-rich solutions are formed under oxidizing conditions at high gas/water ratios. Reactions between the acidic fluids and the Ijen andesite were modeled to account for elevated cation concentrations in lake water. Current concentrations of conservative rockforming elements are produced by dissolution of approximately 60 g of andesite per kg of acid solution. Complete neutralization of the acid lake waters by reaction with the wallrock produces a theoretical alteration assemblage equivalent to that observed in volcano-hosted, acid-sulfate epithermal ore deposits. © 1994.

Consistent couplings between fields with a gauge freedom and deformations of the master equation

The antibracket in the antifield-BRST formalism is known to define a map Hp × Hq → Hp + q + 1 associating with two equivalence classes of BRST invariant observables of respective ghost number p and q an equivalence class of BRST invariant observables of ghost number p + q + 1. It is shown that this map is trivial in the space of all functionals, i.e. that its image contains only the zeroth class. However, it is generically non-trivial in the space of local functionals. Implications of this result for the problem of consistent interactions among fields with a gauge freedom are then drawn. It is shown that the obstructions to constructing non-trivial such interactions lie precisely in the image of the antibracket map and are accordingly non-existent if one does not insist on locality. However consistent local interactions are severely constrained. The example of the Chern-Simons theory is considered. It is proved that the only consistent, local, Lorentz covariant interactions for the abelian models are exhausted by the non-abelian Chern-Simons extensions. © 1993.