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International trade of the invasive South African clawed frog (Xenopus laevis), a subclinical carrier of the fungal pathogen Batrachochytrium dendrobatis (Bd) has been proposed as a major means of introduction of Bd into naïve, susceptible amphibian populations. The historical presence of Bd in the indigenous African population of Xenopus is well documented. However, there are no reports documenting the presence of Bd in wild Xenopus populations in the US, particularly in California where introduced populations are well-established after intentional or accidental release. In this report, a survey was conducted on 178 archived specimens of 6 species of Xenopus collected in Africa from 1871-2000 and on 23 archived specimens (all wild-caught Xenopus laevis) collected in California, USA between 2001 and 2010. The overall prevalence rate of Bd in the tested Xenopus was 2.8%. The earliest positive specimen was X. borealis collected in Kenya in 1934. The overall prevalence of Bd in the X. laevis collected in California was 13% with 2 positive specimens from 2001 and one positive specimen from 2003. The positive Xenopus (3/23) collected in California were collected in 2001 (2/3) and 2003 (1/3). These data document the presence of Bd-infected wild Xenopus laevis in California. The findings reported here support the prevailing hypothesis that Bd was present as a stable, endemic infection in Xenopus populations in Africa prior to their worldwide distribution likely via international live-amphibian trade.

IntroductionChronic stable angina is common and disabling. Cardiac rehabilitation is routinely offered to people following myocardial infarction or revascularisation procedures and has the potential to help people with chronic stable angina. However, there is insufficient evidence of effectiveness and cost-effectiveness for its routine use in this patient group. The objectives of this study are to compare the effectiveness and cost-effectiveness of the ‘Activate Your Heart’ cardiac rehabilitation programme for people with chronic stable angina compared with usual care.Methods and analysisACTIVATE is a multicentre, parallel-group, two-arm, superiority, pragmatic randomised controlled trial, with recruitment from primary and secondary care centres in England and Wales and a target sample size of 518 (1:1 allocation; allocation sequence by minimisation programme with built-in random element). The study uses secure web-based allocation concealment. The two treatments will be optimal usual care (control) and optimal usual care plus the ‘Activate Your Heart’ web-based cardiac rehabilitation programme (intervention). Outcome assessment and statistical analysis will be performed blinded; participants will be unblinded. Outcomes will be measured at baseline and at 6 and 12 months’ follow-up. Primary outcome will be the UK version of Seattle Angina Questionnaire (SAQ-UK), physical limitations domain at 12 months’ follow-up. Secondary outcomes will be the remaining two domains of SAQ-UK, dyspnoea, anxiety and depression, health utility, self-efficacy, physical activity and the incremental shuttle walk test. All safety events will be recorded, and serious adverse events assessed to determine whether they are related to the intervention and expected. Concurrent economic evaluation will be cost–utility analysis from health service perspective. An embedded process evaluation will determine the mechanisms and processes that explain the implementation and impacts of the cardiac rehabilitation programme.Ethics and disseminationNorth of Scotland National Health Service Research Ethics Committee approval, reference 21/NS/0115. Participants will provide written informed consent. Results will be disseminated by peer-reviewed publication.Trial registration numberISRCTN10054455.

International trade of the invasive South African clawed frog (Xenopus laevis), a subclinical carrier of the fungal pathogen Batrachochytrium dendrobatis (Bd) has been proposed as a major means of introduction of Bd into naïve, susceptible amphibian populations. The historical presence of Bd in the indigenous African population of Xenopus is well documented. However, there are no reports documenting the presence of Bd in wild Xenopus populations in the US, particularly in California where introduced populations are well-established after intentional or accidental release. In this report, a survey was conducted on 178 archived specimens of 6 species of Xenopus collected in Africa from 1871-2000 and on 23 archived specimens (all wild-caught Xenopus laevis) collected in California, USA between 2001 and 2010. The overall prevalence rate of Bd in the tested Xenopus was 2.8%. The earliest positive specimen was X. borealis collected in Kenya in 1934. The overall prevalence of Bd in the X. laevis collected in California was 13% with 2 positive specimens from 2001 and one positive specimen from 2003. The positive Xenopus (3/23) collected in California were collected in 2001 (2/3) and 2003 (1/3). These data document the presence of Bd-infected wild Xenopus laevis in California. The findings reported here support the prevailing hypothesis that Bd was present as a stable, endemic infection in Xenopus populations in Africa prior to their worldwide distribution likely via international live-amphibian trade.

We consider the scaling of entanglement entropy in random Projected Entangled Pairs States (PEPS) with an internal symmetry given by a finite group G. We systematically demonstrate a correspondence between this entanglement entropy and the difference of free energies of a classical Ising model with an addition non-local term. This non-local term counts the number of domain walls in a particular configuration of the classical spin model. We then make use of this correspondence to argue for an area law scaling with well-defined topological entanglement entropy when the bond dimensions are sufficiently large. The topological entanglement entropy is shown to be \\(\\mathrm{log}| G| \\) for a simply connected region and results from a difference in the number of domain walls of ground state energies for the two spin models.