G-symmetric spectra, semistability and the multiplicative norm

In this paper we develop the basic homotopy theory of G-symmetric spectra (that is, symmetric spectra with a G-action) for a finite group G, as a model for equivariant stable homotopy with respect to a G-set universe. This model lies in between Mandell's equivariant symmetric spectra and the G-orthogonal spectra of Mandell and May and is Quillen equivalent to the two. We further discuss equivariant semistability, construct model structures on module, algebra and commutative algebra categories and describe the homotopical properties of the multiplicative norm in this context.Comment: Final published versio

Symmetric products and subgroup lattices

Let G be a finite group. We show that the rational homotopy groups of symmetric products of the G-equivariant sphere spectrum are naturally isomorphic to the rational homology groups of certain subcomplexes of the subgroup lattice of G.Comment: final published versio

Geometric descriptions of polygon and chain spaces

We give a few simple methods to geometically describe some polygon and chain-spaces in R^d. They are strong enough to give tables of m-gons and m-chains when m <= 6

Dealing with Negative Oil Shocks: The Venezuelan Experience in the Eighties

The Venezuelan experience in the 1980s is a particularly fertile ground for the analysis of negative shocks. Two large shocks took place under very different control regimes, thus highlighting the role the institutional setting plays in determining the response. Moreover, the experience can shed a different light into the convenience of alternative exchange rate regimes for countries subject to large and frequent trade shocks. In addition, the analysis can be simplified for two reasons. First, oil shocks only have direct effects on the public sector, thus implying that it is the policy reaction to the shock that will affect households and firms. Secondly, the supply response of the oil industry is not of macroeconomic interest.

Commuting matrices and Atiyah's Real K-theory

We describe the $C_2$-equivariant homotopy type of the space of commuting n-tuples in the stable unitary group in terms of Real K-theory. The result is used to give a complete calculation of the homotopy groups of the space of commuting n-tuples in the stable orthogonal group, as well as of the coefficient ring for commutative orthogonal K-theory.Comment: Minor changes. To appear in Journal of Topolog

Optimal Satisfiability Checking for Arithmetic μ\mu-Calculi

The coalgebraic $\mu$-calculus provides a generic semantic framework for fixpoint logics with branching types beyond the standard relational setup, e.g. probabilistic, weighted, or game-based. Previous work on the coalgebraic $\mu$-calculus includes an exponential time upper bound on satisfiability checking, which however requires a well-behaved set of tableau rules for the next-step modalities. Such rules are not available in all cases of interest, in particular ones involving either integer weights as in the graded $\mu$-calculus, or real-valued weights in combination with non-linear arithmetic. In the present paper, we prove the same upper complexity bound under more general assumptions, specifically regarding the complexity of the (much simpler) satisfiability problem for the underlying so-called one-step logic, roughly described as the nesting-free next-step fragment of the logic. We also present a generic global caching algorithm that is suitable for practical use and supports on-the-fly satisfiability checking. Example applications include new exponential-time upper bounds for satisfiability checking in an extension of the graded $\mu$-calculus with Presburger arithmetic, as well as an extension of the (two-valued) probabilistic $\mu$-calculus with polynomial inequalities. As a side result, we moreover obtain a new upper bound $\mathcal{O}(((nk)!)^2)$ on minimum model size for satisfiable formulas for all coalgebraic $\mu$-calculi, where $n$ is the size of the formula and $k$ its alternation depth

In Search of the Black Swan: Analysis of the Statistical Evidence of Electoral Fraud in Venezuela

This study analyzes diverse hypotheses of electronic fraud in the Recall Referendum celebrated in Venezuela on August 15, 2004. We define fraud as the difference between the elector's intent, and the official vote tally. Our null hypothesis is that there was no fraud, and we attempt to search for evidence that will allow us to reject this hypothesis. We find no evidence that fraud was committed by applying numerical maximums to machines in some precincts. Equally, we discard any hypothesis that implies altering some machines and not others, at each electoral precinct, because the variation patterns between machines at each precinct are normal. However, the statistical evidence is compatible with the occurrence of fraud that has affected every machine in a single precinct, but differentially more in some precincts than others. We find that the deviation pattern between precincts, based on the relationship between the signatures collected to request the referendum in November 2003 (the so-called, Reafirmazo), and the YES votes on August 15, is positive and significantly correlated with the deviation pattern in the relationship between exit polls and votes in those same precincts. In other words, those precincts in which, according to the number of signatures, there are an unusually low number of YES votes (i.e., votes to impeach the president), is also where, according to the exit polls, the same thing occurs.Comment: Published in at http://dx.doi.org/10.1214/11-STS373 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Polygon spaces and Grassmannians

We study the moduli spaces of polygons in R^2 and R^3, identifying them with subquotients of 2-Grassmannians using a symplectic version of the Gel'fand-MacPherson correspondence. We show that the bending flows defined by Kapovich-Millson arise as a reduction of the Gel'fand-Cetlin system on the Grassmannian, and with these determine the pentagon and hexagon spaces up to equivariant symplectomorphism. Other than invocation of Delzant's theorem, our proofs are purely polygon-theoretic in nature.Comment: plain TeX, 21 pages, submitted to Journal of Differential Geometr