Entropy of Some Models of Sparse Random Graphs With Vertex-Names

Consider the setting of sparse graphs on N vertices, where the vertices have distinct "names", which are strings of length O(log N) from a fixed finite alphabet. For many natural probability models, the entropy grows as cN log N for some model-dependent rate constant c. The mathematical content of this paper is the (often easy) calculation of c for a variety of models, in particular for various standard random graph models adapted to this setting. Our broader purpose is to publicize this particular setting as a natural setting for future theoretical study of data compression for graphs, and (more speculatively) for discussion of unorganized versus organized complexity.Comment: 31 page

Averaging t-structures and extension closure of aisles

We ask when a finite set of t-structures in a triangulated category can be `averaged' into one t-structure or, equivalently, when the extension closure of a finite set of aisles is again an aisle. There is a straightforward, positive answer for a finite set of compactly generated t-structures in a big triangulated category. For piecewise tame hereditary categories, we give a criterion for when averaging is possible, and an algorithm that computes truncation triangles in this case. A finite group action on a triangulated category gives a natural way of producing a finite set of t-structures out of a given one. If averaging is possible, there is an induced t-structure on the equivariant triangulated category.Comment: 26 pages, 11 figures. v2: fixed minor mistakes, improved presentation. Comments still welcome

Flux Vacua and Branes of the Minimal Superstring

We analyze exactly the simplest minimal superstring theory, using its dual matrix model. Its target space is one dimensional (the Liouville direction), and the background fields include a linear dilaton, a possible tachyon condensate, and RR flux. The theory has both charged and neutral branes, and these exhibit new and surprising phenomena. The smooth moduli space of charged branes has different weakly coupled boundaries in which the branes have different RR charges. This new duality between branes of different charges shows that the semiclassical notion of localized charge is not precise in the quantum theory, and that the charges of these branes can fluctuate. Correspondingly, the RR flux in some parts of target space can also fluctuate -- only the net flux at infinity is fixed. We substantiate our physical picture with a detailed semiclassical analysis of the exact answers. Along the way, we uncover new subtleties in super-Liouville theory.Comment: 46 pages, 3 figures, new identities for the neutral brane, references added, minor change

Minimal String Theory

We summarize recent progress in the understanding of minimal string theory, focusing on the worldsheet description of physical operators and D-branes. We review how a geometric interpretation of minimal string theory emerges naturally from the study of the D-branes. This simple geometric picture ties together many otherwise unrelated features of minimal string theory, and it leads directly to a worldsheet derivation of the dual matrix model.Comment: 10 pages, 4 figures, talk presented by NS at Strings '0

Divining Siraya: Sources of language and authority in documentation and revitalisation

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A Hedonic Model for Housing Prices in Wilsonville, Oregon

We estimate a hedonic model for housing prices in Wilsonville, Oregon. Our data for 197 houses is drawn from Zillow for 2014 to 2017. We find that the number of bedrooms, the square footage of the house, and whether the house is single level are statistically significant factors affecting housing prices. Location variables are also found to be statistically significant. As an example, the price of a house on the Charbonneau Golf Course is estimated to be 15% higher than the price of a house located elsewhere in Wilsonville