On the Hojman conservation quantities in Cosmology

We discuss the application of the Hojman's Symmetry Approach for the determination of conservation laws in Cosmology, which has been recently applied by various authors in different cosmological models. We show that Hojman's method for regular Hamiltonian systems, where the Hamiltonian function is one of the involved equations of the system, is equivalent to the application of Noether's Theorem for generalized transformations. That means that for minimally-coupled scalar field cosmology or other modified theories which are conformally related with scalar-field cosmology, like $f(R)$ gravity, the application of Hojman's method provide us with the same results with that of Noether's theorem. Moreover we study the special Ansatz. $\phi\left( t\right) =\phi\left( a\left( t\right) \right)$, which has been introduced for a minimally-coupled scalar field, and we study the Lie and Noether point symmetries for the reduced equation. We show that under this Ansatz, the unknown function of the model cannot be constrained by the requirement of the existence of a conservation law and that the Hojman conservation quantity which arises for the reduced equation is nothing more than the functional form of Noetherian conservation laws for the free particle. On the other hand, for $f(T)$ teleparallel gravity, it is not the existence of Hojman's conservation laws which provide us with the special function form of $f(T)$ functions, but the requirement that the reduced second-order differential equation admits a Jacobi Last multiplier, while the new conservation law is nothing else that the Hamiltonian function of the reduced equation.Comment: 6 pages; minor corrections; accepted for publication by Physics Letters B. arXiv admin note: substantial text overlap with arXiv:1503.0846

Cosmological dynamics of Scalar--Tensor Gravity

We study the phase--space of FLRW models derived from Scalar--Tensor Gravity where the non--minimal coupling is $F(\phi)=\xi\phi^2$ and the effective potential is $V(\phi)=\lambda \phi^n$. Our analysis allows to unfold many feature of the cosmology of this class of theories. For example, the evolution mechanism towards states indistinguishable from GR is recovered and proved to depend critically on the form of the potential $V(\phi)$. Also, transient almost--Friedmann phases evolving towards accelerated expansion and unstable inflationary phases evolving towards stable ones are found. Some of our results are shown to hold also for the String-Dilaton action.Comment: 25 pages, 4 figures, 12 tables, submitted to CQ

WMAP 3yr data with the CCA: anomalous emission and impact of component separation on the CMB power spectrum

The Correlated Component Analysis (CCA) allows us to estimate how the different diffuse emissions mix in CMB experiments, exploiting also complementary information from other surveys. It is especially useful to deal with possible additional components. An application of CCA to WMAP maps assuming that only the canonical Galactic emissions are present, highlights the widespread presence of a spectrally flat "synchrotron" component, largely uncorrelated with the synchrotron template, suggesting that an additional foreground is indeed required. We have tested various spectral shapes for such component, namely a power law as expected if it is flat synchrotron, and two spectral shapes that may fit the spinning dust emission: a parabola in the logS - log(frequency) plane, and a grey body. Quality tests applied to the reconstructed CMB maps clearly disfavour two of the models. The CMB power spectra, estimated from CMB maps reconstructed exploiting the three surviving foreground models, are generally consistent with the WMAP ones, although at least one of them gives a significantly higher quadrupole moment than found by the WMAP team. Taking foreground modeling uncertainties into account, we find that the mean quadrupole amplitude for the three "good" models is less than 1 sigma below the expectation from the standard LambdaCDM model. Also the other reported deviations from model predictions are found not to be statistically significant, except for the excess power at l~40. We confirm the evidence for a marked North-South asymmetry in the large scale (l < 20) CMB anisotropies. We also present a first, albeit preliminary, all-sky map of the "anomalous" component.Comment: 14 pages, 17 figures, submitted to MNRAS, references adde

Infertility problems and mental health symptoms in a community-based sample: depressive symptoms among infertile men, but not women

Most researchers agree that men’s and women’s experiences of infertility are fundamentally different, and impacts upon the nature of psychological distress encountered. However, design flaws, including non-random samples unrepresentative of the general population, compromise many existing studies. Data derived from a random general community sample provides prevalence of current infertility, and permits examination of longitudinal associations between mental health symptoms and infertility among 1,978 participants aged 28-32 years. In the previous 12-months, infertility was experienced by 2.1% and 5.4% partnered men and women. Infertility independently predicted depressive symptomatology in men, and anxiety symptoms among women. Gender differences were sustained, even controlling for prior depression and anxiety. Health professionals are encouraged to proactively enquire about affective symptoms experienced by both women and men with infertility problems

Modelling the Galactic Magnetic Field on the Plane in 2D

We present a method for parametric modelling of the physical components of the Galaxy's magnetised interstellar medium, simulating the observables, and mapping out the likelihood space using a Markov Chain Monte-Carlo analysis. We then demonstrate it using total and polarised synchrotron emission data as well as rotation measures of extragalactic sources. With these three datasets, we define and study three components of the magnetic field: the large-scale coherent field, the small-scale isotropic random field, and the ordered field. In this first paper, we use only data along the Galactic plane and test a simple 2D logarithmic spiral model for the magnetic field that includes a compression and a shearing of the random component giving rise to an ordered component. We demonstrate with simulations that the method can indeed constrain multiple parameters yielding measures of, for example, the ratios of the magnetic field components. Though subject to uncertainties in thermal and cosmic ray electron densities and depending on our particular model parametrisation, our preliminary analysis shows that the coherent component is a small fraction of the total magnetic field and that an ordered component comparable in strength to the isotropic random component is required to explain the polarisation fraction of synchrotron emission. We outline further work to extend this type of analysis to study the magnetic spiral arm structure, the details of the turbulence as well as the 3D structure of the magnetic field.Comment: 18 pages, 11 figures, updated to published MNRAS versio

Symmetry, singularities and integrability in complex dynamics III: approximate symmetries and invariants

The different natures of approximate symmetries and their corresponding first integrals/invariants are delineated in the contexts of both Lie symmetries of ordinary differential equations and Noether symmetries of the Action Integral. Particular note is taken of the effect of taking higher orders of the perturbation parameter. Approximate symmetries of approximate first integrals/invariants and the problems of calculating them using the Lie method are considered

Analytic Behaviour of Competition among Three Species

We analyse the classical model of competition between three species studied by May and Leonard ({\it SIAM J Appl Math} \textbf{29} (1975) 243-256) with the approaches of singularity analysis and symmetry analysis to identify values of the parameters for which the system is integrable. We observe some striking relations between critical values arising from the approach of dynamical systems and the singularity and symmetry analyses.Comment: 14 pages, to appear in Journal of Nonlinear Mathematical Physic

A Systems Approach to the Physiology of Weightlessness

A systems approach to the unraveling of the complex response pattern of the human subjected to weightlessness is presented. The major goal of this research is to obtain an understanding of the role that each of the major components of the human system plays following the transition to and from space. The cornerstone of this approach is the utilization of a variety of mathematical models in order to pose and test alternative hypotheses concerned with the adaptation process. An integrated hypothesis for the human physiological response to weightlessness is developed

Axial Multicentric Osteosarcoma in an English Cocker Spaniel

No abstract available