Dicritical nilpotent holomorphic foliations

We study in this paper several properties concerning singularities of foliations in $(\mathbb{C}^3,\mathbf{0})$ that are pull-back of dicritical foliations in $(\mathbb{C}^2,\mathbf{0})$. Particularly, we will investigate the existence of first integrals (holomorphic and meromorphic) and the dicriticalness of such a foliation. In the study of meromorphic first integrals we follow the same method used by R. Meziani and P. Sad in dimension two. While the foliations we study are pull-back of foliations in $(\mathbb{C}^2,\mathbf{0})$, the adaptations are not straightforward.Comment: 14 pages. Several mistakes corrected from the previous version. Several changes in the text, including a change in the titl

Invariant versus classical quartet inference when evolution is heterogeneous across sites and lineages

One reason why classical phylogenetic reconstruction methods fail to correctly infer the underlying topology is because they assume oversimplified models. In this paper we propose a topology reconstruction method consistent with the most general Markov model of nucleotide substitution, which can also deal with data coming from mixtures on the same topology. It is based on an idea of Eriksson on using phylogenetic invariants and provides a system of weights that can be used as input of quartet-based methods. We study its performance on real data and on a wide range of simulated 4-taxon data (both time-homogeneous and nonhomogeneous, with or without among-site rate heterogeneity, and with different branch length settings). We compare it to the classical methods of neighbor-joining (with paralinear distance), maximum likelihood (with different underlying models), and maximum parsimony. Our results show that this method is accurate and robust, has a similar performance to ML when data satisfies the assumptions of both methods, and outperforms all methods when these are based on inappropriate substitution models or when both long and short branches are present. If alignments are long enough, then it also outperforms other methods when some of its assumptions are violated.Comment: 32 pages; 9 figure

First come, first served: an analysis of pioneer and follower firms' market and nonmarket actions in the European mobile telephone industry

This study examines the relationship between erosion of the first-mover's market share and the differences in competitive behaviour of pioneer firms and followers. Particularly, we pay particular attention to market actions related to innovation, pricing and promotion, and to non-market actions related to judicial issues. The empirical study has been carried out with companies that are present in a dynamic context, such as the European mobile telephone industry. Our results show that when followers take more non-market actions than pioneers the negative effect on the firstentrant's advantage is more significant. On the contrary, we have not found a significant impact of innovating and pricing actions

Are there biological gender differences at the early stages of first language acquisition when producing double object constructions and to/for-datives?

Producción CientíficaThis study examines whether biological gender differences appear in the early stages of acquisition in the case of English dative alternation (DA) structures (double object constructions (DOCs) and to/for-datives). Girls have been found to show faster syntactic development when compared to boys (Lovas, 2011). In the case of the acquisition of DA, an order in the emergence and in the incidence of English DA would entail a syntactic derivational status between DOCs and to/for-datives with one being the original structure and the other the derived one (Gu, 2010). However, analogous ages of onset and fairly similar frequency rates in the production could suggest the construction of two underived structures. We investigate whether biological gender differences appear in the case of DOCs and to/for-datives. We also investigate whether the exposure to English DA (adult input) results in differences between the girls’ output and the boys’ output. We analyze data from eight monolingual English girls and five monolingual English boys, and the adults that interact with them, as available in CHILDES. Our findings reveal that monolingual girls and monolingual boys pattern closely in the acquisition of the syntactic non-derivational relationship between DOCs and to/for-datives, as seen in their similar emergence. Biological gender differences are not seen either in the acquisition of the additional properties of to/for-datives given their later onset and their lower incidence when compared to DOCs. These production patterns also correlate with the frequency with which these structures are heard in the adult input.Junta de Castilla y León (programa de apoyo a proyectos de investigación - Ref. VA009P17)Ministerio de Ciencia, Innovación y Universidades (ref. PGC2018-097693-B-I00