Tree-irreducible automorphisms of free groups

We introduce a new class of automorphisms $\varphi$ of the non-abelian free group $F_N$ of finite rank $N \geq 2$ which contains all iwips (= fully irreducible automorphisms), but also any automorphism induced by a pseudo-Anosov homeomorphism of a surface with arbitrary many boundary components. More generally, there may be subgroups of $F_N$ of rank $\geq 2$ on which $\varphi$ restricts to the identity. We prove some basic facts about such {\em tree-irreducible} automorphisms, and show that, together with Dehn twist automorphisms, they are the natural basic building blocks from which any automorphism of \FN can be constructed in a train track set-up. We then show: {\bf Theorem:} {\it Every tree-irreducible automorphism of $F_N$ has induced North-South dynamics on the Thurston compactification $\bar{\rm CV}_N$ of Outer space.} Finally, we define a "blow-up" construction on the vertices of a train track map, which, starting from iwips, produces tree-irreducible automorphisms which in general are not iwip

Ellipticity of Structures in CMB Sky Maps

We study the ellipticity of contour lines in the sky maps of the cosmic microwave background (CMB) as well as other measures of elongation. The sensitivity of the elongation on the resolution of the CMB maps which depends on the pixelization and the beam profile of the detector, is investigated. It is shown that the current experimental accuracy does not allow to discriminate between cosmological models which differ in curvature by Delta Omega_tot=0.05. Analytical expressions are given for the case that the statistical properties of the CMB are those of two-dimensional Gaussian random fields

Hormonal adaptations to different training intensities during the preparation of elite judokas for competition

Many efforts are made to quantify objectively the balance between training load and the athlete’s tolerance. The aim of the present study was to evaluate the balance between anabolic (i.e. testosterone and IGF-I) and catabolic (i.e. cortisol) hormones in elite judokas during their preparations (4 months) for the European championships. Five healthy elite Israeli judokas (four male, one female, age range 17–26 years) were tested at baseline, after two months of moderate training, after another one month of intense training, after one month of tapering down prior to the competition, and during the week after the championships. Hormonal level remained relatively unchanged during period of moderate training. Circulating levels of IGF-I and testosterone decreased and the cortisol/testosterone ratio increased during intense training. However, only the decrease in circulating IGF-I level reached statistical significance. Both levels of IGF-I and testosterone increased significantly, and the cortisol/testosterone ratio decreased significantly following tapering down, prior to the championships, compared to the levels during intense training. Changes in the balance of anabolic and catabolic hormones during the training season may help elite athletes and assist their coaches in their preparation for the competition

Can one hear the shape of the Universe?

It is shown that the recent observations of NASA's explorer mission "Wilkinson Microwave Anisotropy Probe" (WMAP) hint that our Universe may possess a non-trivial topology. As an example we discuss the Picard space which is stretched out into an infinitely long horn but with finite volume.Comment: 4 page

Seventy-five years of measuring income inequality in Latin America

Drawing on a comprehensive compilation of quantile shares and inequality measures for 34 countries, including over 5,600 estimated Gini coefficients, we review the measurement of income inequality in Latin America and the Caribbean over the last seven decades. Although the evidence from the first quarter century – roughly until the 1970s – is too fragmentary and difficult to compare, clearer patterns emerge for the last fifty years. The central feature of these patterns is a broad inverted U curve, with inequality rising in most countries prior to the 1990s, and falling during the early 21st Century, at least until the mid-2010s, when trends appear to diverge across countries. This broad pattern is modified by country specificities, with considerable variation in timing and magnitude. Whereas this broad picture emerges for income inequality dynamics, there is much more uncertainty about the exact levels of inequality in the region. The uncertainty arises from the disparity in estimates for the same country/year combinations, depending on whether they come from household surveys exclusively; from some combination of surveys and administrative tax data; and on whether they attempt to scale income aggregates to achieve consistency with National Accounts estimates. Since no single method is fully convincing at present, we are left with (often wide) ranges, or bands, of inequality as our best summaries of inequality levels. Reassuringly, however, the dynamic patterns are generally robust across the bands

Association of Prenatal Urinary Concentrations of Phthalates and Bisphenol A and Pubertal Timing in Boys and Girls.

BackgroundAnimal studies suggest that phthalates and bisphenol A (BPA), endocrine-disrupting chemicals found in many consumer products, may impact the timing of puberty.ObjectivesWe aimed to determine the association of prenatal exposure to high-molecular-weight phthalates and BPA with pubertal timing in boys and girls participating in the Center for the Health Assessment of Mothers and Children of Salinas (CHAMACOS) longitudinal cohort study.MethodsWe quantified urinary concentrations of eight phthalate metabolites and BPA at two time points during pregnancy among participating mothers ([Formula: see text]) and conducted clinical Tanner staging of puberty on their children every 9 months between 9 and 13 y of age. We conducted accelerated failure time models and examined the role of child overweight/obese status in this association.ResultsThe sum of urinary metabolites of di(2-ethylhexyl) phthalate [Formula: see text], monobenzyl phthalate (MBzP), and BPA were associated with later onset of at least one of the three outcomes assessed in girls (thelarche, pubarche, or menarche) and with earlier onset of at least one of the two outcomes assessed in boys (gondarche and pubarche). We found that monocarboxynonyl phthalate, monocarboxyoctyl phthalate, mono(3-carboxypropyl) phthalate, and BPA were associated with later pubarche and menarche mostly among normal-weight girls but not overweight/obese girls. MBzP was associated with later thelarche in all girls, and [Formula: see text] was associated with later thelarche and menarche in all girls. BPA and all phthalate biomarkers were associated with earlier gonadarche and pubarche in all boys as well as in overweight/obese boys when stratified by weight. Among normal-weight boys, associations with BPA were also inverse, whereas associations with phthalate metabolites were close to the null or positive.ConclusionsSeveral high-molecular-weight phthalates and BPA were associated with later puberty in girls and earlier puberty in boys included in the CHAMACOS cohort study. Childhood overweight/obesity may modify these associations. https://doi.org/10.1289/EHP3424

How well-proportioned are lens and prism spaces?

The CMB anisotropies in spherical 3-spaces with a non-trivial topology are analysed with a focus on lens and prism shaped fundamental cells. The conjecture is tested that well proportioned spaces lead to a suppression of large-scale anisotropies according to the observed cosmic microwave background (CMB). The focus is put on lens spaces L(p,q) which are supposed to be oddly proportioned. However, there are inhomogeneous lens spaces whose shape of the Voronoi domain depends on the position of the observer within the manifold. Such manifolds possess no fixed measure of well-proportioned and allow a predestined test of the well-proportioned conjecture. Topologies having the same Voronoi domain are shown to possess distinct CMB statistics which thus provide a counter-example to the well-proportioned conjecture. The CMB properties are analysed in terms of cyclic subgroups Z_p, and new point of view for the superior behaviour of the Poincar\'e dodecahedron is found

CMB Anisotropy of Spherical Spaces

The first-year WMAP data taken at their face value hint that the Universe might be slightly positively curved and therefore necessarily finite, since all spherical (Clifford-Klein) space forms M^3 = S^3/Gamma, given by the quotient of S^3 by a group Gamma of covering transformations, possess this property. We examine the anisotropy of the cosmic microwave background (CMB) for all typical groups Gamma corresponding to homogeneous universes. The CMB angular power spectrum and the temperature correlation function are computed for the homogeneous spaces as a function of the total energy density parameter Omega_tot in the large range [1.01, 1.20] and are compared with the WMAP data. We find that out of the infinitely many homogeneous spaces only the three corresponding to the binary dihedral group T*, the binary octahedral group O*, and the binary icosahedral group I* are in agreement with the WMAP observations. Furthermore, if Omega_tot is restricted to the interval [1.00, 1.04], the space described by T* is excluded since it requires a value of Omega_tot which is probably too large being in the range [1.06, 1.07]. We thus conclude that there remain only the two homogeneous spherical spaces S^3/O* and S^3/I* with Omega_tot of about 1.038 and 1.018, respectively, as possible topologies for our Universe.Comment: A version with high resolution sky maps can be obtained at http://www.physik.uni-ulm.de/theo/qc

Cosmic microwave anisotropies in an inhomogeneous compact flat universe

The anisotropies of the cosmic microwave background (CMB) are computed for the half-turn space E_2 which represents a compact flat model of the Universe, i.e. one with finite volume. This model is inhomogeneous in the sense that the statistical properties of the CMB depend on the position of the observer within the fundamental cell. It is shown that the half-turn space describes the observed CMB anisotropies on large scales better than the concordance model with infinite volume. For most observer positions it matches the temperature correlation function even slightly better than the well studied 3-torus topology