Complete intersections in simplicial toric varieties

Given a set $\mathcal A = \{a_1,\ldots,a_n\} \subset \mathbb{N}^m$ of nonzero vectors defining a simplicial toric ideal $I_{\mathcal A} \subset k[x_1,...,x_n]$, where $k$ is an arbitrary field, we provide an algorithm for checking whether $I_{\mathcal A}$ is a complete intersection. This algorithm does not require the explicit computation of a minimal set of generators of $I_{\mathcal A}$. The algorithm is based on the application of some new results concerning toric ideals to the simplicial case. For homogenous simplicial toric ideals, we provide a simpler version of this algorithm. Moreover, when $k$ is an algebraically closed field, we list all ideal-theoretic complete intersection simplicial projective toric varieties that are either smooth or have one singular point.Comment: 28 pages, 2 tables. To appear in Journal of Symbolic Computatio

Chomp on numerical semigroups

We consider the two-player game chomp on posets associated to numerical semigroups and show that the analysis of strategies for chomp is strongly related to classical properties of semigroups. We characterize, which player has a winning-strategy for symmetric semigroups, semigroups of maximal embedding dimension and several families of numerical semigroups generated by arithmetic sequences. Furthermore, we show that which player wins on a given numerical semigroup is a decidable question. Finally, we extend several of our results to the more general setting of subsemigroups of $\mathbb{N} \times T$, where $T$ is a finite abelian group.Comment: 22 pages, 14 figures, 1 table (improved exposition

Electric-magnetic duality in linearized Ho\v{r}ava-Lifshitz gravity

Known as a symmetry of vacuum Maxwell equations, the electric-magnetic duality can be lifted actually to a symmetry of an action. The Lagrangian of this action is written in terms of two vector potentials, one electric and one magnetic, and while it is manifestly invariant under duality rotations, it is not manifestly Lorentz covariant. This duality symmetry exists also in linearized gravity in four dimensions, and can be lifted off shell too. In $d$ dimensions, the link between linearized gravity and its dual can also be seen from the point of view of a parental action. This is defined by a first order Lagrangian (with the help of some auxiliary variables) that delivers both Fierz-Pauli theory and its dual. In this work we use this formalism to implement the electric-magnetic duality in the nonrelativistic deviation of Fierz-Pauli theory arising from Ho\v{r}ava-Lifshitz gravity. Because this theory breaks diffeomorphism invariance, one finds that such implementation includes some peculiarities.Comment: v1: 23 pages, 4 figures, edited with LaTeXila 2.4.0 and wxMaxima 12.04.0 for the graphics (Maxima version: 5.27.0). arXiv admin note: text overlap with arXiv:1306.1092 by other authors; v2: 24 pages, 4 figures, references added, negligence (leading to poor version management and miscommunication) rectified; v3: typos and grammar corrected, minor changes to uniformize convention

Average diagonal entropy in non-equilibrium isolated quantum systems

The diagonal entropy was introduced as a good entropy candidate especially for isolated quantum systems out of equilibrium. Here we present an analytical calculation of the average diagonal entropy for systems undergoing unitary evolution and an external perturbation in the form of a cyclic quench. We compare our analytical findings with numerical simulations of various many-body quantum systems. Our calculations elucidate various heuristic relations proposed recently in the literature.Comment: 5 pages + 4 page "Supplemental material", 2 figure

Non-stationary Job Search When Jobs Do Not Last Forever: A Structural Estimation to Evaluate Alternative Unemployment Insurance Systems

This paper considers a job search model where the environment is not constant throughout the unemployment spell and where jobs do not last forever. In this situation, reservation wages can be lower than they would be in a model without consideration of such separations, but also they can initially be higher precisely because of this non-stationarity of the model. Moreover, the time-dependence of reservation wages is stronger than it is when separations are not controlled for. The model is estimated structurally by using Spanish data for the period 1985-1996. The main finding is that, although at the beginning the decrease in reservation wages is the main determinant of the exit from unemployment, as time progresses the job offer arrival rate comes to be the only significant factor, given that acceptance probabilities become equal to one. The estimated parameters are used to evaluate the effect of different Unemployment Insurance designs on unemployment duration. Accordingly, one can draw the conclusion that a sufficiently decreasing pattern in unemployment benefits makes this duration to be 8.4% lower.Job Search, Nonstationarity, Unemployment, Separation probability, Structural estimation, Unemployment Insurance.

Retirement incentives, individual heterogeneity and labour transitions of employed and unemployed workers

Un informe que analiza la incidencia de las políticas públicas relevantes en edades próximas a la jubilación sobre las decisiones laborales de de trabajadores empleados y desempleados.Retirement, unemployment, incentives, Pension system, Unobserved heterogeneity, Spain