Big Free Groups are Almost Free

It is shown that the big free group (the set of countably-long words over a countable alphabet) is almost free, in the sense that any function from the alphabet to a compact topological group factors through a homomorphism. This statement is in fact a simple corollary of the more general result proven below on the extendability of homomorphisms from subgroups (of a certain kind) of the big free group to a compact topological group.Comment: 10 pages, several arguments expanded with no change in the results, one reference adde

Reintroducing carrying capacity to Arabian hyper-arid rangelands; the role of language to defend an inexact science

Open-access deserts of the Arabian Gulf States continue to be heavily impacted by camels, a species that has high cultural but little economic value. In protected areas that exclude camels, the problem is frequently replaced by other ungulates, such as the Arabian Oryx. This presentation will examine the difficulty of providing scientific evidence of environmental degradation in this hyper-arid habitat and the sociocultural context affecting land use policy, with examples from two emirates of the United Arab Emirates. Reestablishing a natural, historical balance in protected areas is unrealistic due to habitat fragmentation and land-use expectations. We argue that although the controversial term ‘carrying capacity’ encourages a focus on single species rather than habitats, it remains the most explicit way to communicate sustainable land use policy. We propose that terrestrial ecologists adopt a twofold approach; firstly that a generic maximum of 100 kg large herbivore per km2 be chosen, and secondly that protected areas provide carrying capacity estimates for the wild and semi-wild fauna of public interest. The authors believe this will improve community awareness of rangeland health, and support calls to fund future monitoring.Departamento de Biología Animal Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tec

Self-Interference Cancellation Using Time-Domain Phase Noise Estimation in OFDM Full-Duplex Systems

In full-duplex systems, oscillator phase noise (PN) problem is considered the bottleneck challenge that may face the self-interference cancellation (SIC) stage especially when orthogonal frequency division multiplexing (OFDM) transmission scheme is deployed. Phase noise degrades the SIC performance significantly, if not mitigated before or during the SIC technique. The presence of the oscillator phase noise has different impacts on the transmitted data symbol like common phase error (CPE) and inter-carrier interference (ICI). However, phase noise can be estimated and mitigated digitally in either time or frequency domain. Through this work, we propose a novel and simple time domain self-interference (SI) phase noise estimation and mitigation technique. The proposed algorithm is inspired from Wiener filtering in time domain. Simulation results show that the proposed algorithm has a superior performance than the already-existing time-domain or frequency domain PN mitigation solutions with a noticeable reduction in the computational complexity