Full and hat inductive definitions are equivalent in NBG

A new research project has, quite recently, been launched to clarify how different, from systems in second order number theory extending ACA 0, those in second order set theory extending NBG (as well as those in n + 3-th order number theory extending the so-called Bernays−Gödel expansion of full n + 2-order number theory etc.) are. In this article, we establish the equivalence between Δ10\bf-LFP and Δ10\bf-FP, which assert the existence of a least and of a (not necessarily least) fixed point, respectively, for positive elementary operators (or between Δn+20\bf-LFP and Δn+20\bf-FP). Our proof also shows the equivalence between ID 1 and ^ID1, both of which are defined in the standard way but with the starting theory PA replaced by ZFC (or full n + 2-th order number theory with global well-ordering).

A note on the theory SID<ω of stratified induction

We introduce and analyse a theory of finitely stratified general inductive definitions over the natural numbers, inline image, and establish its proof theoretic ordinal, inline image. The definition of inline image bears some similarities with Leivant's ramified theories for finitary inductive definitions.

Policy forums: Why do they exist and what are they used for?

Policy forums are issue-based intermediary organizations where diverse types of political and societal actors repeatedly interact. Policy forums are important elements of modern governance systems as they allow actors to learn, negotiate, or build trust. They can vary in composition, size, membership logic, and other distinct features. This article lays the foundation of a theory of policy forums based on three interrelated elements: First, it discusses conditions for the formation of a forum and describes the logic of these organizations as one of an asymmetric multipartite exchange. Second, it enumerates the potential set of goals and motivations of participating actors that are fed into this exchange. Third, it proposes eight different dimensions on which policy forums differ and which affect the exchange mechanisms among actors. We claim that empirical work on policy forums should systematically take these elements into account and propose elements of a research agenda.

Tracing of patients lost to follow-up and HIV transmission: Mathematical modelling study based on two large ART programmes in Malawi

OBJECTIVES: Treatment as prevention depends on retaining HIV-infected patients in care. We investigated the effect on HIV transmission of bringing patients lost to follow up (LTFU) back into care. DESIGN: Mathematical model. METHODS: Stochastic mathematical model of cohorts of 1000 HIV-infected patients on antiretroviral therapy (ART), based on data from two clinics in Lilongwe, Malawi. We calculated cohort viral load (CVL; sum of individual mean viral loads each year) and used a mathematical relationship between viral load and transmission probability to estimate the number of new HIV infections. We simulated four scenarios: 'no LTFU' (all patients stay in care); 'no tracing' (patients LTFU are not traced); 'immediate tracing' (after missed clinic appointment); and, 'delayed tracing' (after six months). RESULTS: About 440 of 1000 patients were LTFU over five years. CVL (million copies/ml per 1000 patients) were 3.7 (95% prediction interval [PrI] 2.9-4.9) for no LTFU, 8.6 (95% PrI 7.3-10.0) for no tracing, 7.7 (95% PrI 6.2-9.1) for immediate, and 8.0 (95% PrI 6.7-9.5) for delayed tracing. Comparing no LTFU with no tracing the number of new infections increased from 33 (95% PrI 29-38) to 54 (95% PrI 47-60) per 1000 patients. Immediate tracing prevented 3.6 (95% PrI -3.3-12.8) and delayed tracing 2.5 (95% PrI -5.8-11.1) new infections per 1000. Immediate tracing was more efficient than delayed tracing: 116 and to 142 tracing efforts, respectively, were needed to prevent one new infection. CONCLUSION: Tracing of patients LTFU enhances the preventive effect of ART, but the number of transmissions prevented is small.

Estimating and quantifying uncertainties on level sets using the Vorob'ev expectation and deviation with Gaussian process models

Several methods based on Kriging have recently been proposed for calculating a probability of failure involving costly-to-evaluate functions. A closely related problem is to estimate the set of inputs leading to a response exceeding a given threshold. Now, estimating such a level set—and not solely its volume—and quantifying uncertainties on it are not straightforward. Here we use notions from random set theory to obtain an estimate of the level set, together with a quantification of estimation uncertainty. We give explicit formulae in the Gaussian process set-up and provide a consistency result. We then illustrate how space-filling versus adaptive design strategies may sequentially reduce level set estimation uncertainty.

Forest regeneration capacity and its enhancement by forest management and silviculture in Cabo Delgado

SDC has been involved in rural development in Cabo Delgado for more than 30 years. Shortly after the independence of Mozambique, projects in water supply and integrated rural development were initiated. The silvoagropastoral project FO9 based in Mueda was a very early experience in forestry in Cabo Delgado. Andreas Kläy was responsible for the forestry sector in FO9 for 3 years in the early 1980s and had an opportunity to initiate an exchange of ideas and experience in rural development theory and approaches with Yussuf Adam, who was doing research in human anthropology and history in the province. 25 years later, the current situation of forest management in Cabo Delgado was reassessed, with a specific focus on concessions in the North. The opportunity for a partnership between the MITI SA, the University of Eduardo Mondlane, and CDE was created on the basis of this preliminary study1. The aim of this partnership is to generate knowledge and develop capacity for sustainable forest management. The preliminary study showed that “…we have to face weaknesses and would like to start a learning process with the main institutions, organisations, and stakeholder groups active in forest management and research in the North of Cabo Delgado. This learning process will involve studies supported by competent research institutions and workshops …” The specific objectives of ESAPP project Q804 are the following: 1. Contribute to understanding of the forestry sector; 2. Capacity development for professionals and academics; 3. Support for the private sector and the local forest service; 4. Support data generation at Cabo Delgado's Provincial Service; 5. Capacity development for Swiss academic institutions (CDE and ETHZ). A conceptual planning platform was elaborated as a basis for cooperation and research in the partnership (cf. Annex 1). The partners agreed to work on two lines of research: biophysical and socio-economic. In order to ensure a transdisciplinary approach, disciplinary research is anchored in common understanding in workshops based on the LforS methods. These workshops integrate the main stakeholders in the local context of the COMADEL concession in Nangade District managed by MITI SA, and take place in the village of Namiune. The research team observed that current management schemes consist mainly of strategies of nature mining by most stakeholders involved. Institutional settings - formal and informal - have little impact due to weak capacity at the local level and corruption. Local difficulties in a remote rural area facilitate external access to resources and are perpetuated by the loss of benefits. The benefits of logging remain at the top level (economic and political elites). The interests of the owners of the concession in stopping the loss of resources caused by this regime offers a unique opportunity to intervene in the logic of resource degradation and agony in rural development and forest management.

A missing link between facilitation and plant species coexistence: nurses benefit generally rare species more than common ones

1. Positive interactions among plants can increase species richness by relaxing environmental filters and providing more heterogeneous environments. However, it is not known if facilitation could affect coexistence through other mechanisms. Most studies on plant coexistence focus on negative frequency-dependent mechanisms (decreasing the abundance of common species); here, we test if facilitation can enhance coexistence by giving species an advantage when rare. 2. To test our hypothesis, we used a global data set from drylands and alpine environments and measured the intensity of facilitation (based on co-occurrences with nurse plants) for 48 species present in at least 4 different sites and with a range of abundances in the field. We compared these results with the degree of facilitation experienced by species which are globally rare or common (according to the IUCN Red List), and with a larger data base including over 1200 co-occurrences of target species with their nurses. 3. Facilitation was stronger for rare species (i.e. those having lower local abundances or considered endangered by the IUCN) than for common species, and strongly decreased with the abundance of the facilitated species. These results hold after accounting for the distance of each species from its ecological optimum (i.e. the degree of functional stress it experiences). 4. Synthesis. Our results highlight that nurse plants not only increase the number of species able to colonize a given site, but may also promote species coexistence by preventing the local extinction of rare species. Our findings illustrate the role that nurse plants play in conserving endangered species and link the relationship between facilitation and diversity with coexistence theory. As such, they provide further mechanistic understanding on how facilitation maintains plant diversity.

Why Do Some Water Utilities Recycle More than Others? A Qualitative Comparative Analysis in New South Wales, Australia

Although the recycling of municipal wastewater can play an important role in water supply security and ecosystem protection, the percentage of wastewater recycled is generally low and strikingly variable. Previous research has employed detailed case studies to examine the factors that contribute to recycling success but usually lacks a comparative perspective across cases. In this study, 25 water utilities in New South Wales, Australia, were compared using fuzzy-set Qualitative Comparative Analysis (fsQCA). This research method applies binary logic and set theory to identify the minimal combinations of conditions that are necessary and/or sufficient for an outcome to occur within the set of cases analyzed. The influence of six factors (rainfall, population density, coastal or inland location, proximity to users; cost recovery and revenue for water supply services) was examined for two outcomes, agricultural use and "heavy" (i.e., commercial/municipal/industrial) use. Each outcome was explained by two different pathways, illustrating that different combinations of conditions are associated with the same outcome. Generally, while economic factors are crucial for heavy use, factors relating to water stress and geographical proximity matter most for agricultural reuse. These results suggest that policies to promote wastewater reuse may be most effective if they target uses that are most feasible for utilities and correspond to the local context. This work also makes a methodological contribution through illustrating the potential utility of fsQCA for understanding the complex drivers of performance in water recycling.