Rational stochastic languages

The goal of the present paper is to provide a systematic and comprehensive study of rational stochastic languages over a semiring K \in {Q, Q +, R, R+}. A rational stochastic language is a probability distribution over a free monoid \Sigma^* which is rational over K, that is which can be generated by a multiplicity automata with parameters in K. We study the relations between the classes of rational stochastic languages S rat K (\Sigma). We define the notion of residual of a stochastic language and we use it to investigate properties of several subclasses of rational stochastic languages. Lastly, we study the representation of rational stochastic languages by means of multiplicity automata.Comment: 35 page

Comparison between unitary and collective models of household labor supply with taxation

Several recent papers have shown the relevance of collective models for the empirical investigation of household labor supply and consumption. Yet the estimation of collective models in the presence of non-linear budget sets and participation decisions remains a daunting task. This paper compares collective and unitary models on the basis of simulated collective data with income taxation. We distinguish the cases of individual and joint taxation. Estimating the unitary model we obtain strikingly different ?preference? parameters depending on the type of taxation. We also obtain substantial differences between predicted adjustments to labor supply following a switch between tax regimes, and hence potentially wide-ranging definitions of revenue-neutral versions of tax reforms. Finally we discuss distortions affecting the welfare analysis of reforms on the basis of unitary estimates when the model generating the data is a collective model. The results suggest that increased efforts should be devoted to the estimation of collective models with taxation. --Pareto optimal allocation,tax reform,simulated data

On the performance of unitary models of household labor supply estimated on “collective” data with taxation

This paper compares collective and unitary models on the basis of simulated collective data with income taxation. We distinguish the cases of individual and joint taxation. Estimating a flexible unitary model, we obtain strikingly different “preference” parameters depending on the type of taxation. We also obtain substantial differences between predicted adjustments to labor supply following a switch between tax regimes. Our results show that even the design of revenue-neutral reforms may be heavily distorted by the use of a unitary model on collective data. Finally, we discuss distortions affecting the welfare analysis of reforms on the basis of unitary estimates when the model generating the data is a collective model. The results suggest that increased efforts should be devoted to the estimation of collective models with taxation.Pareto optimal allocations, policy evaluation, simulated data

Nonlinear dielectric susceptibilities in supercooled liquids: a toy model

The dielectric response of supercooled liquids is phenomenologically modeled by a set of Asymmetric Double Wells (ADW), where each ADW contains a dynamical heterogeneity of $N_{corr}$ molecules. We find that the linear macroscopic susceptibility $\chi_1$ does not depend on $N_{corr}$ contrary to all higher order susceptibilities $\chi_{2k+1}$. We show that $\chi_{2k+1}$ is proportional to the $k^{th}$ moment of $N_{corr}$, which could pave the way for new experiments on glass transition. In particular, as predicted by Bouchaud and Biroli on general grounds [Phys. Rev. B, {\bf 72}, 064204 (2005)], we find that $\chi_3$ is proportional to the average value of $N_{corr}$. We fully calculate $\chi_3$ and, with plausible values of few parameters our model accounts for the salient features of the experimental behavior of $\chi_3$ of supercooled glycerol.Comment: 13 pages, 5 figure

Pulse shape optimization for electron-positron production in rotating fields

We optimize the pulse shape and polarization of time-dependent electric fields to maximize the production of electron-positron pairs via strong field quantum electrodynamics processes. The pulse is parametrized in Fourier space by a B-spline polynomial basis, which results in a relatively low-dimensional parameter space while still allowing for a large number of electric field modes. The optimization is performed by using a parallel implementation of the differential evolution, one of the most efficient metaheuristic algorithms. The computational performance of the numerical method and the results on pair production are compared with a local multistart optimization algorithm. These techniques allow us to determine the pulse shape and field polarization that maximize the number of produced pairs in computationally accessible regimes.Comment: 16 pages, 10 figure

On Probability Distributions for Trees: Representations, Inference and Learning

We study probability distributions over free algebras of trees. Probability distributions can be seen as particular (formal power) tree series [Berstel et al 82, Esik et al 03], i.e. mappings from trees to a semiring K . A widely studied class of tree series is the class of rational (or recognizable) tree series which can be defined either in an algebraic way or by means of multiplicity tree automata. We argue that the algebraic representation is very convenient to model probability distributions over a free algebra of trees. First, as in the string case, the algebraic representation allows to design learning algorithms for the whole class of probability distributions defined by rational tree series. Note that learning algorithms for rational tree series correspond to learning algorithms for weighted tree automata where both the structure and the weights are learned. Second, the algebraic representation can be easily extended to deal with unranked trees (like XML trees where a symbol may have an unbounded number of children). Both properties are particularly relevant for applications: nondeterministic automata are required for the inference problem to be relevant (recall that Hidden Markov Models are equivalent to nondeterministic string automata); nowadays applications for Web Information Extraction, Web Services and document processing consider unranked trees

Measuring Selectivity-Corrected Gender Wage Gaps in the EU

We investigate different techniques to assess the gender pay gap in five EU countries (France, Germany, Italy, Spain and United Kingdom), focusing on self-selection into market work. Results show that selectivity correction has an impact on both wage estimates and wage gap decomposition. If there is a positive correlation between the wage and the propensity to participate, the estimated pay gap understates the true difference in earnings when self-selection is ignored. The estimated pay gap differs considerably at different quantiles of the wage distribution, and is sensitive to the choice of estimator. --