Tautological classes on the moduli space of hyperelliptic curves with rational tails

We study tautological classes on the moduli space of stable n-pointed hyperelliptic curves of genus g with rational tails. The method is based on the approach of Yin in comparing tautological classes on the moduli of curves and the universal Jacobian. Our result gives a complete description of tautological relations. It is proven that all relations come from the Jacobian side. The intersection pairings are shown to be perfect in all degrees. We show that the tautological algebra coincides with its image in cohomology via the cycle class map. The latter is identified with monodromy invariant classes in cohomology. (C) 2017 Elsevier B.V. All rights reserved11sci

The relationship between Self-Esteem and sexual Self-Concept in people with Physical-Motor disabilities

Background: Self-esteem is the value that the individuals give themselves, and sexual self-concept is also a part of individuality or sexualself. Impairment or disability exists not only in the physical body of disabled people but also in their attitudes. Negative attitudes affect the mental health of disabled people, causing them to have lower self-esteem. Objectives: This study aimed to examine the relationship between self-esteem and sexual self-concept in people with physical-motor disabilities. Patients and Methods: This cross-sectional study was conducted on 200 random samples with physical-motor disabilities covered by Isfahan Welfare Organization in 2013. Data collection instruments were the Persian Eysenck self-esteem questionnaire, and five domains (sexual anxiety, sexual self-efficacy, sexual self-esteem, sexual fear and sexual depression) of the Persian multidimensional sexual selfconcept questionnaire. Because of incomplete filling of the questionnaires, the data of 183 people were analyzed by the SPSS 16.0 software. Data were analyzed using the t-test, Man-Whitney and Kruskal-Wallis tests and Spearman correlation coefficient. Results: The mean age was 36.88 ± 8.94 years for women and 37.80 ± 10.13 for men. The mean scores of self-esteem among women and men were 15.80 ± 3.08 and 16.2 ± 2.90, respectively and there was no statistically significance difference. Comparison of the mean scores of sexual anxiety, sexual self-efficacy, sexual self-esteem, sexual fear and sexual depression among men and women showed that women scored higher than men in all domains. This difference was statistically significant in other domains except the sexual self-esteem (14.92 ± 3.61 vs. 13.56 ± 4.52) (P < 0.05). The Kruskal-Wallis test showed that except for sexual anxiety and sexual self-esteem, there was a statistical difference between other domains of people’s sexual self-concept and degree of disability (P < 0.05). Moreover, Spearman coefficient showed that there was only a correlation between men’s sexual anxiety, sexual self-esteem and sexual self-efficacy with their self-esteem. This correlation was positive in sexual anxiety and negative in two other domains. Conclusions: Lack of difference in self-esteem of disabled people in different degrees of disability and in both men and women suggests that disabled people should not be presumed to have low self-esteem, and their different aspects of life should be attended to, just like others. Furthermore, studies should be designed and implemented based on psychological, social and environmental factors that can help disabled people to promote their positive sexual self-concept through marriage, and reduce their negative self-concept. © 2015 Iranian Red Crescent Medical Journal

What can the detection of a single pair of circles-in-the-sky tell us about the geometry and topology of the Universe ?

In a Universe with a detectable nontrivial spatial topology the last scattering surface contains pairs of matching circles with the same distribution of temperature fluctuations --- the so-called circles-in-the-sky. Searches undertaken for nearly antipodal pairs of such circles in cosmic microwave background maps have so far been unsuccessful. Previously we had shown that the negative outcome of such searches, if confirmed, should in principle be sufficient to exclude a detectable non-trivial spatial topology for most observers in very nearly flat ($0<\mid\Omega_{\text{tot}}-1\mid \lesssim10^{-5}$) (curved) universes. More recently, however, we have shown that this picture is fundamentally changed if the universe turns out to be {\it exactly} flat. In this case there are many potential pairs of circles with large deviations from antipodicity that have not yet been probed by existing searches. Here we study under what conditions the detection of a single pair of circles-in-the-sky can be used to uniquely specify the topology and the geometry of the spatial section of the Universe. We show that from the detection of a \emph{single} pair of matching circles one can infer whether the spatial geometry is flat or not, and if so we show how to determine the topology (apart from one case) of the Universe using this information. An important additional outcome of our results is that the dimensionality of the circles-in-the-sky parameter space that needs to be spanned in searches for matching pair of circles is reduced from six to five degrees of freedom, with a significant reduction in the necessary computational time.Comment: 6 pages, 2 figures, 1 table. V2: Version to appear in Phys. Rev. D (Oct.,2011). Minor changes, references added. V3:Version published in Phys.Rev.D. Typos corrected, presentation of a point improve

Density perturbations in f(R) gravity theories in metric and Palatini formalisms

We make a detailed study of matter density perturbations in both metric and Palatini formalisms in theories whose Lagrangian density is a general function, f(R), of the Ricci scalar. We derive these equations in a number of gauges. We show that for viable models that satisfy cosmological and local gravity constraints (LGC), matter perturbation equations derived under a sub-horizon approximation are valid even for super-Hubble scales provided the oscillating mode (scalaron) does not dominate over the matter-induced mode. Such approximate equations are especially reliable in the Palatini formalism because of the absence of scalarons. Using these equations we make a comparative study of the behaviour of density perturbations as well as gravitational potentials for a number of classes of theories. In the metric formalism the parameter m=Rf_{,RR}/f_{,R} characterising the deviation from the Lambda CDM model is constrained to be very small during the matter era in order to ensure compatibility with LGC, but the models in which m grows to the order of 10^{-1} around the present epoch can be allowed. These models also suffer from an additional fine tuning due to the presence of scalaron modes which are absent in the Palatini case. In Palatini formalism LGC and background cosmological constraints provide only weak bounds on |m| by constraining it to be smaller than ~ 0.1. This is in contrast to matter density perturbations which, on galactic scales, place far more stringent constraints on the present deviation parameter m of the order of |m| < 10^{-5} - 10^{-4}. This is due to the peculiar evolution of matter perturbations in the Palatini case which exhibits a rapid growth or a damped oscillation depending on the sign of m.Comment: 36 pages including 8 figures. Accepted for publication in Physical Review

An exact quantification of backreaction in relativistic cosmology

An important open question in cosmology is the degree to which the Friedmann-Lemaitre-Robertson-Walker (FLRW) solutions of Einstein's equations are able to model the large-scale behaviour of the locally inhomogeneous observable universe. We investigate this problem by considering a range of exact n-body solutions of Einstein's constraint equations. These solutions contain discrete masses, and so allow arbitrarily large density contrasts to be modelled. We restrict our study to regularly arranged distributions of masses in topological 3-spheres. This has the benefit of allowing straightforward comparisons to be made with FLRW solutions, as both spacetimes admit a discrete group of symmetries. It also provides a time-symmetric hypersurface at the moment of maximum expansion that allows the constraint equations to be solved exactly. We find that when all the mass in the universe is condensed into a small number of objects (<10) then the amount of backreaction in dust models can be large, with O(1) deviations from the predictions of the corresponding FLRW solutions. When the number of masses is large (>100), however, then our measures of backreaction become small (<1%). This result does not rely on any averaging procedures, which are notoriously hard to define uniquely in general relativity, and so provides (to the best of our knowledge) the first exact and unambiguous demonstration of backreaction in general relativistic cosmological modelling. Discrete models such as these can therefore be used as laboratories to test ideas about backreaction that could be applied in more complicated and realistic settings.Comment: 13 pages, 9 figures. Corrections made to Tables IV and