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

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

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

‘We kind of try to merge our own experience with the objectivity of the criteria’: The role of connoisseurship and tacit practice in undergraduate fine art assessment

This article explores connoisseurship in the context of fine art undergraduate assessment practice. I interviewed twelve fine art lecturers in order to explore and unpack the concept of connoisseurship in relation to subjectivity, objectivity and tacit practice. Building on the work of Bourdieu (1973, 1977, 1986) and Shay (2003, 2005), both of whom problematize the view that subjectivity and objectivity are binary opposites, my research illustrates the ways that connoisseurship is underpinned by informed professional judgements located in communities of practice. Within this particular conception of connoisseurship, the lecturers’ expertise is co-constituted in communities of assessors through participation and engagement. Standards reside in communities of practice

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

Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces

We use spatial light modulators (SLMs) to measure correlations between arbitrary superpositions of orbital angular momentum (OAM) states generated by spontaneous parametric down-conversion. Our technique allows us to fully access a two-dimensional OAM subspace described by a Bloch sphere, within the higher-dimensional OAM Hilbert space. We quantify the entanglement through violations of a Bell-type inequality for pairs of modal superpositions that lie on equatorial, polar, and arbitrary great circles of the Bloch sphere. Our work shows that SLMs can be used to measure arbitrary spatial states with a fidelity sufficient for appropriate quantum information processing systems

A dynamical system approach to higher order gravity

The dynamical system approach has recently acquired great importance in the investigation on higher order theories of gravity. In this talk I review the main results and I give brief comments on the perspectives for further developments.Comment: 6 pages, 1 figure, 2 tables, talk given at IRGAC 2006, July 200

Lie symmetries for two-dimensional charged particle motion

We find the Lie point symmetries for non-relativistic two-dimensional charged particle motion. These symmetries comprise a quasi-invariance transformation, a time-dependent rotation, a time-dependent spatial translation and a dilation. The associated electromagnetic fields satisfy a system of first-order linear partial differential equations. This system is solved exactly, yielding four classes of electromagnetic fields compatible with Lie point symmetries

An international comparison of surface texture parameters quantification on polymer artefacts using optical instruments

An international comparison of optical instruments measuring polymer surfaces with arithmetic mean height values in the sub-micrometre range has been carried out. The comparison involved sixteen optical surface texture instruments (focus variation instruments, confocal microscopes and coherent scanning interferometers) from thirteen research laboratories worldwide. Results demonstrated that: (i) Agreement among different instruments could be achieved to a limited extent; (ii) standardised guidelines for uncertainty evaluation of areal surface parameters are needed for users; (iii) it is essential that the performance characteristics (and especially the spatial frequency response) of an instrument is understood prior to a measurement