Ergodic Transport Theory, periodic maximizing probabilities and the twist condition

The present paper is a follow up of another one by A. O. Lopes, E. Oliveira and P. Thieullen which analyze ergodic transport problems. Our main focus will a more precise analysis of case where the maximizing probability is unique and is also a periodic orbit. Consider the shift T acting on the Bernoulli space \Sigma={1, 2, 3,.., d}^\mathbb{N} $and$A:\Sigma \to \mathbb{R} a Holder potential. Denote m(A)=max_{\nu is an invariant probability for T} \int A(x) \; d\nu(x) and, \mu_{\infty,A}, any probability which attains the maximum value. We assume this probability is unique (a generic property). We denote \T the bilateral shift. For a given potential Holder A:\Sigma \to \mathbb{R}, we say that a Holder continuous function W: \hat{\Sigma} \to \mathbb{R} is a involution kernel for A, if there is a Holder function A^*:\Sigma \to \mathbb{R}, such that, A^*(w)= A\circ \T^{-1}(w,x)+ W \circ \T^{-1}(w,x) - W(w,x). We say that A^* is a dual potential of A. It is true that m(A)=m(A^*). We denote by V the calibrated subaction for A, and, V^* the one for A^*. We denote by I^* the deviation function for the family of Gibbs states for \beta A, when \beta \to \infty. For each x we get one (more than one) w_x such attains the supremum above. That is, solutions of V(x) = W(w_x,x) - V^* (w_x)- I^*(w_x). A pair of the form (x,w_x) is called an optimal pair. If \T is the shift acting on (x,w) \in {1, 2, 3,.., d}^\mathbb{Z}, then, the image by \T^{-1} of an optimal pair is also an optimal pair. Theorem - Generically, in the set of Holder potentials A that satisfy (i) the twist condition, (ii) uniqueness of maximizing probability which is supported in a periodic orbit, the set of possible optimal w_x, when x covers the all range of possible elements x in \in \Sigma, is finite

A new approach on restoration of dynamic measurement uncertainties in optical precision coordinate metrology

This paper presents a new approach to the restoration of dynamic influenced measurement uncertainties in optical precision coordinate metrology (OPCM) using image sensors to measure geometrical features. Dynamic measurements within the context of this paper are based upon relative motion between the imaging setup (CCD-camera and optical system) and the measuring object respectively the measuring scene. The dynamic image acquisition causes image motion blur effects, which downgrades the uncertainties of the measurand. The approach presented deals with a new technique to restore motion degraded images using different methods to analyze important image features by extending the famous state of the art Richardson-Lucy image restoration technique using a new convergence criteria based on the variation of the detectable sub-pixel edge position of each iteration

A Sunyaev-Zel'dovich Effect Survey for High Redshift Clusters

Interferometric observations of the Sunyaev-Zel'dovich Effect (SZE) toward clusters of galaxies provide sensitive cosmological probes. We present results from 1 cm observations (at BIMA and OVRO) of a large, intermediate redshift cluster sample. In addition, we describe a proposed, higher sensitivity array which will enable us to survey large portions of the sky. Simulated observations indicate that we will be able to survey one square degree of sky per month to sufficient depth that we will detect all galaxy clusters more massive than 2x10^{14} h^{-1}_{50}M_\odot, regardless of their redshift. We describe the cluster yield and resulting cosmological constraints from such a survey.Comment: 7 pages, 6 figures, latex, contribution to VLT Opening Symposiu

Cross-Correlation Studies between CMB Temperature Anisotropies and 21 cm Fluctuations

During the transition from a neutral to a fully reionized universe, scattering of cosmic microwave background (CMB) photons via free-electrons leads to a new anisotropy contribution to the temperature distribution. If the reionization process is inhomogeneous and patchy, the era of reionization is also visible via brightness temperature fluctuations in the redshifted 21 cm line emission from neutral Hydrogen. Since regions containing electrons and neutral Hydrogen are expected to trace the same underlying density field, the two are (anti) correlated and this is expected to be reflected in the anisotropy maps via a correlation between arcminute-scale CMB temperature and the 21 cm background. In terms of the angular cross-power spectrum, unfortunately, this correlation is insignificant due to a geometric cancellation associated with second order CMB anisotropies. The same cross-correlation between ionized and neutral regions, however, can be studied using a bispectrum involving large scale velocity field of ionized regions from the Doppler effect, arcminute scale CMB anisotropies during reionization, and the 21 cm background. While the geometric cancellation is partly avoided, the signal-to-noise ratio related to this bispectrum is reduced due to the large cosmic variance related to velocity fluctuations traced by the Doppler effect. Unless the velocity field during reionization can be independently established, it is unlikely that the correlation information related to the relative distribution of ionized electrons and regions containing neutral Hydrogen can be obtained with a combined study involving CMB and 21 cm fluctuations.Comment: 10 pages, 3 figure

Imaging the Sunyaev-Zel'dovich Effect

We report on results of interferometric imaging of the Sunyaev-Zel'dovich Effect (SZE) with the OVRO and BIMA mm-arrays. Using low-noise cm-wave receivers on the arrays, we have obtained high quality images for 27 distant galaxy clusters. We review the use of the SZE as a cosmological tool. Gas mass fractions derived from the SZE data are given for 18 of the clusters, as well as the implied constraint on the matter density of the universe, $\Omega_M$. We find $\Omega_M h_{100} \le 0.22 ^{+0.05}_{-0.03}$. A best guess for the matter density obtained by assuming a reasonable value for the Hubble constant and also by attempting to account for the baryons contained in the galaxies as well as those lost during the cluster formation process gives $\Omega_M \sim 0.25$. We also give preliminary results for the Hubble constant. Lastly, the power for investigating the high redshift universe with a non-targeted high sensitivity SZE survey is discussed and an interferometric survey is proposed.Comment: 14 pages, 7 figures, latex, contribution to Nobel Symposium "Particle Physics and the Universe" to appear in Physica Scripta and World Scientific, eds L. Bergstrom, P. Carlson and C. Fransso

Promoting the achievement of looked after children and young people across Cardiff

As of March 2017, there were 5,955 children and young people in care in Wales. Across the Central South Consortium (Bridgend, Cardiff, Merthyr Tydfil, Rhondda Cynonn Taf and Vale of Glamorgan) there were 2,170 children and young people looked after. The majority of these children are in care as a result of birth families being unable to provide a level of care that meets their emotional and well-being needs. Children and young people who are in or have experienced care remain one of the lowest performing groups in terms of educational outcomes. In 2016, eleven per cent of young people in Wales achieved A* to C grade at GCSE. Care leavers can experience poorer employment and health outcomes after leaving school compared to their peers; for example, 45% of young people who were looked after were not engaged in education, training or employment (NEET) or not in touch with their local authority on their 19th birthday in 2015. This compares with around 4.9% of all other children who leave school at the end of Year 13. However, the education and achievement of children and young people in care is currently the focus of renewed policy, research and practice attention across Wales. The Social Services and Wellbeing (Wales) Act 2014 provides the legal framework for improving the well-being of people who need care and support. A national strategic approach to improving outcomes for children looked after is underway with a focus on promoting and improving collaborative working across agencies, identifying and sharing good practice and making improvements where they are needed. The purpose of this report is to share practice in selected in Cardiff schools that is contributing to improved outcomes and school experiences for children and young people in care