Interpreting the evidence on life cycle skill formation

This paper presents economic models of child development that capture the essence of recent findings from the empirical literature on skill formation. The goal of this essay is to provide a theoretical framework for interpreting the evidence from a vast empirical literature, for guiding the next generation of empirical studies, and for formulating policy. Central to our analysis is the concept that childhood has more than one stage. We formalize the concepts of self-productivity and complementarity of human capital investments and use them to explain the evidence on skill formation. Together, they explain why skill begets skill through a multiplier process. Skill formation is a life cycle process. It starts in the womb and goes on throughout life. Families play a role in this process that is far more important than the role of schools. There are multiple skills and multiple abilities that are important for adult success. Abilities are both inherited and created, and the traditional debate about nature versus nurture is scientiÞcally obsolete. Human capital investment exhibits both self-productivity and complementarity. Skill attainment at one stage of the life cycle raises skill attainment at later stages of the life cycle (self-productivity). Early investment facilitates the productivity of later investment (complementarity). Early investments are not productive if they are not followed up by later investments (another aspect of complementarity). This complementarity explains why there is no equity-efficiency trade-off for early investment. The returns to investing early in the life cycle are high. Remediation of inadequate early investments is difficult and very costly as a consequence of both self-productivity and complementarity

Branching integrals and Casselman phenomenon

Let $G$ be a real semisimple Lie group, $K$ its maximal complex subgroup, and $G_C$ its complexification. It is known that all the $K$-finite matrix elements on $G$ admit holomorphic continuation to branching functions on $G_C$ having singularities at the a prescribed divisor. We propose a geometric explanation of this phenomenon. The note also contsins a general survey of holomorphic continuations of infinite-dimensional representations.Comment: 13pp, an addendum is adde

Separate ways: The Mass-Metallicity Relation does not strongly correlate with Star Formation Rate in SDSS-IV MaNGA galaxies

We present the integrated stellar mass-metallicity relation (MZR) for more than 1700 galaxies included in the integral field area SDSS-IV MaNGA survey. The spatially resolved data allow us to determine the metallicity at the same physical scale (effective radius in arcsecs, $\mathrm{R_{eff}}$ ) using a heterogeneous set of ten abundance calibrators. Besides scale factors, the shape of the MZR is similar for all calibrators, consistent with those reported previously using single-fiber and integral field spectroscopy. We compare the residuals of this relation against the star formation rate (SFR) and specific SFR (sSFR). We do not find a strong secondary relation of the MZR with either SFR or the sSFR for any of the calibrators, in contrast with previous single-fiber spectroscopic studies. Our results agree with an scenario in which metal enrichment happens at local scales, with global outflows playing a secondary role in shaping the chemistry of galaxies and cold-gas inflows regulating the stellar formation.Comment: 10 pages, 9 Figures. Accepted for publication in Ap

A subarcsecond resolution near-infrared study of Seyfert and `normal' galaxies: II. Morphology

We present a detailed study of the bar fraction in the CfA sample of Seyfert galaxies, and in a carefully selected control sample of non-active galaxies, to investigate the relation between the presence of bars and of nuclear activity. To avoid the problems related to bar classification in the RC3, e.g., subjectivity, low resolution and contamination by dust, we have developed an objective bar classification method, which we conservatively apply to our new sub-arcsecond resolution near-infrared imaging data set (Peletier et al. 1999). We are able to use stringent criteria based on radial profiles of ellipticity and major axis position angle to determine the presence of a bar and its axial ratio. Concentrating on non-interacting galaxies in our sample for which morphological information can be obtained, we find that Seyfert hosts are barred more often (79% +/- 7.5%) than the non-active galaxies in our control sample (59% +/- 9%), a result which is at the 2.5 sigma significance level. The fraction of non-axisymmetric hosts becomes even larger when interacting galaxies are taken into account. We discuss the implications of this result for the fueling of central activity by large-scale bars. This paper improves on previous work by means of imaging at higher spatial resolution and by the use of a set of stringent criteria for bar presence, and confirms that the use of NIR is superior to optical imaging for detection of bars in disk galaxies.Comment: Latex, 3 figures, includes aaspptwo.sty, accepted for publication in the Astrophysical Journa

Intertwining operator for AG2AG_2 Calogero-Moser-Sutherland system

We consider generalised Calogero-Moser-Sutherland quantum Hamiltonian $H$ associated with a configuration of vectors $AG_2$ on the plane which is a union of $A_2$ and $G_2$ root systems. The Hamiltonian $H$ depends on one parameter. We find an intertwining operator between $H$ and the Calogero-Moser-Sutherland Hamiltonian for the root system $G_2$. This gives a quantum integral for $H$ of order 6 in an explicit form thus establishing integrability of $H$.Comment: 24 page

Matter wave functions and Yukawa couplings in F-theory Grand Unification

We study the local structure of zero mode wave functions of chiral matter fields in F-theory unification. We solve the differential equations for the zero modes derived from local Higgsing in the 8-dimensional parent action of F-theory 7-branes. The solutions are found as expansions both in powers and derivatives of the magnetic fluxes. Yukawa couplings are given by an overlap integral of the three wave functions involved in the interaction and can be calculated analytically. We provide explicit expressions for these Yukawas to second order both in the flux and derivative expansions and discuss the effect of higher order terms. We explicitly describe the dependence of the couplings on the U(1) charges of the relevant fields, appropriately taking into account their normalization. A hierarchical Yukawa structure is naturally obtained. The application of our results to the understanding of the observed hierarchies of quarks and leptons is discussed.Comment: Latex, 51 pages, 4 figures, typos corrected, note adde