Generalized Farey trees, transfer Operators and phase transitions

We consider a family of Markov maps on the unit interval, interpolating between the tent map and the Farey map. The latter map is not uniformly expanding. Each map being composed of two fractional linear transformations, the family generalizes many particular properties which for the case of the Farey map have been successfully exploited in number theory. We analyze the dynamics through the spectral analysis of generalized transfer operators. Application of the thermodynamic formalism to the family reveals first and second order phase transitions and unusual properties like positivity of the interaction function.Comment: 39 pages, 10 figure

Assessing Value-Based Plans in Public R&D Using the Analytic Hierarchy Process

Part 11: e-GovernanceInternational audienceThere is a need for research regarding how to manage public research and development (R&D) to create societal values. The paper focuses on the Analytic Hierarchy Process (AHP) in a case study, the microelectronics research center. Twenty-four factors (e.g. mission, internal R&D, collaboration and management-related factors) were constructed in a hierarchy model for assessing three innovation plans: knowledge, societal and commercial orientation. The AHP analysis reveals that commercial orientation has the highest impact score on innovation factors. However, given that the selected case study is a taxpayer-funded public R&D organisation, societal expectations have to be factored into their innovation plans. Hence, the paper provides a sensitivity analysis as a result of which a suggestion is made to increase the priority of collaboration-related factors to improve the impact of societal orientation

The impact of tandem redundant/sky-based calibration in MWA Phase II data analysis

Precise instrumental calibration is of crucial importance to 21-cm cosmology experiments. The Murchison Widefield Array's (MWA) Phase II compact configuration offers us opportunities for both redundant calibration and sky-based calibration algorithms; using the two in tandem is a potential approach to mitigate calibration errors caused by inaccurate sky models. The MWA Epoch of Reionization (EoR) experiment targets three patches of the sky (dubbed EoR0, EoR1, and EoR2) with deep observations. Previous work in Li et al. (2018) and (2019) studied the effect of tandem calibration on the EoR0 field and found that it yielded no significant improvement in the power spectrum (PS) over sky-based calibration alone. In this work, we apply similar techniques to the EoR1 field and find a distinct result: The improvements in the PS from tandem calibration are significant. To understand this result, we analyse both the calibration solutions themselves and the effects on the PS over three nights of EoR1 observations. We conclude that the presence of the bright radio galaxy Fornax A in EoR1 degrades the performance of sky-based calibration, which in turn enables redundant calibration to have a larger impact. These results suggest that redundant calibration can indeed mitigate some level of model incompleteness error

First Season MWA Phase II Epoch of Reionization Power Spectrum Results at Redshift 7

The compact configuration of Phase II of the Murchison Widefield Array (MWA) consists of both a redundant subarray and pseudo-random baselines, offering unique opportunities to perform sky-model and redundant interferometric calibration. The highly redundant hexagonal cores give improved power spectrum sensitivity. In this paper, we present the analysis of nearly 40 hr of data targeting one of the MWA's epoch of reionization (EoR) fields observed in 2016. We use both improved analysis techniques presented in Barry et al. and several additional techniques developed for this work, including data quality control methods and interferometric calibration approaches. We show the EoR power spectrum limits at redshift 6.5, 6.8, and 7.1 based on our deep analysis on this 40 hr data set. These limits span a range in k-space of 0.18 h Mpc-1 < k < 1.6 h Mpc-1, with a lowest measurement of Δ2 ≤ 2.39 × 103 mK2 at k = 0.59 h Mpc-1 and z = 6.5