On the Coble quartic

We review and extend the known constructions relating Kummer threefolds, G¨opel systems, theta constants and their derivatives, and the GIT quotient for 7 points in P^2 to obtain an explicit expression for the Coble quartic. The Coble quartic was recently determined completely in [RSSS12], where it was computed completely explicitly, as a polynomial with 372060 monomials of bidegree (28, 4) in theta constants of the second order and theta functions of the second order, respectively. Our expression is in terms of products of theta constants with characteristics corresponding to G¨opel systems, and is a polynomial with 134 terms. Our approach is based on the beautiful geometry studied by Coble and further investigated by Dolgachev and Ortland and highlights the geometry and combinatorics of syzygetic octets of characteristics, and the corresponding representations of Sp(6, F_2). One new ingredient is the relationship of G¨opel systems and Jacobian determinants of theta functions. In genus 2, we similarly obtain a short explicit equation for the universal Kummer surface, and relate modular forms of level two to binary invariants of six points on P^

Convergence across states and people

Income distribution

Economic misfortunes have caused many to reassess their finances, triggering sharp reversals in borrowing and spending habits

Households - Economic aspects ; Consumer behavior

Vacancies and unemployment

Expansions are usually associated with plentiful vacancies and a low number of unemployed workers. During recessions the unemployment pool swells while employers seek to fill fewer job openings.Unemployment ; Recessions ; Labor market

On the Hochschild-Kostant-Rosenberg map for graded manifolds

We show that the Hochschild-Kostant-Rosenberg map from the space of multivector fields on a graded manifold N (endowed with a Berezinian volume) to the cohomology of the algebra of multidifferential operators on N (as a subalgebra of the Hochschild complex of the algebra of smooth functions on N) is an isomorphism of Batalin-Vilkovisky algebras. These results generalize to differential graded manifolds.Comment: 15 pages. Problematic Lemma 5.5 of v1 removed and Theorem 5.3b corrected accordingly. Exposition reorganized. To appear in IMR

Comparing Poisson Sigma Model with A-model

We discuss the A-model as a gauge fixing of the Poisson Sigma Model with target a symplectic structure. We complete the discussion in [arXiv:0706.3164], where a gauge fixing defined by a compatible complex structure was introduced, by showing how to recover the A-model hierarchy of observables in terms of the AKSZ observables. Moreover, we discuss the off-shell supersymmetry of the A-model as a residual BV symmetry of the gauge-fixed PSM action.Comment: 15 pages, one missing reference adde

Convergence in the United States: a tale of migration and urbanization

We use non-parametric distribution dynamics techniques to reassess the convergence of per capita personal income (PCPI) across U.S. states and across metropolitan and nonmetropolitan portions of states for the period 1969-2005. The long-run distribution of PCPI is bimodal for both states and metro/nonmetro portions. Further- more, the high income mode of the distribution across metro and nonmetro portions corresponds to the single mode of the long-run distribution across metro portions only. These results (polarization or club-convergence) are reversed when weighting by population. The long run distributions across people are consistent with convergence. Migration and urbanization are the forces behind convergence.Migration, Internal ; Income distribution

TMsim : an algorithmic tool for the parametric and worst-case simulation of systems with uncertainties

This paper presents a general purpose, algebraic tool—named TMsim—for the combined parametric and worst-case analysis of systems with bounded uncertain parameters.The tool is based on the theory of Taylor models and represents uncertain variables on a bounded domain in terms of a Taylor polynomial plus an interval remainder accounting for truncation and round-off errors.This representation is propagated from inputs to outputs by means of a suitable redefinition of the involved calculations, in both scalar and matrix form. The polynomial provides a parametric approximation of the variable, while the remainder gives a conservative bound of the associated error. The combination between the bound of the polynomial and the interval remainder provides an estimation of the overall (worst-case) bound of the variable. After a preliminary theoretical background, the tool (freely available online) is introduced step by step along with the necessary theoretical notions. As a validation, it is applied to illustrative examples as well as to real-life problems of relevance in electrical engineering applications, specifically a quarter-car model and a continuous time linear equalizer

New monetary policy tools?

Monetary policy

Predicting consumption: a lesson in real-time data

Personal Consumption Expenditures Price Index ; Consumption (Economics)