National genebanks offer diverse collections of locally adapted crops which can support farmers’ climate resilience, nutritional security and economic innovations, yet are often overlooked in climate adaptation strategies. Across much of the world, national genebanks are unknown to farmers, or poorly connected for varietal exchange. This paper examines the impacts of establishing ‘Germplasm User Groups’ (GUGs) across five African countries to connect farmers with genebanks as rapid responders to local agricultural challenges. GUGs conducted farmer participatory research to evaluate genebank materials and establish pathways for the exchange of knowledge and crop diversity in farming communities. Drawing on surveys and interviews from over 1,600 smallholders, we found GUGs increase farmer understanding of genebanks, improve access to crop diversity and increase farmer exchanges with national genebanks. As well as material exchange, smallholders welcome the learning opportunities from GUGs to address local farming challenges. On average, GUG members share genebank seed with four other farmers, demonstrating the potential spillover effects of this model for sharing crop diversity. We close with recommendations to improve the working of GUGs and offer guidance for other countries looking to adopt the system as a rapid approach strategy to build local resilience in the face of climate change.

Given two rational maps $f,g: \mathbb {P}^1 \to \mathbb {P}^1$ of degree d over $\mathbb {C}$, DeMarco, Krieger, and Ye [Common preperiodic points for quadratic polynomials. J. Mod. Dyn. 18 (2022), 363–413] have conjectured that there should be a uniform bound $B = B(d)> 0$ such that either they have at most B common preperiodic points or they have the same set of preperiodic points. We study their conjecture from a statistical perspective and prove that the average number of shared preperiodic points is zero for monic polynomials of degree $d \geq 6$ with rational coefficients. We also investigate the quantity $\liminf _{x \in \overline {\mathbb {Q}}} (\widehat {h}_f(x) + \widehat {h}_g(x) )$ for a generic pair of polynomials and prove both lower and upper bounds for it.

Based on the stubbed coupled line for matching a load, we design an impedance transformer matched the load of ${{\text{Z}}_{\text{L}}} = 100{\Omega }$, working at four frequencies in this paper. This proposed transformer comprises two sections of coupled line constructed from parallel-coupled transmission lines. Two different types of the proposed transformer are given and analyzed, and we derive carefully about the open-circuit form equations for impedance transformer. We fabricate an impedance transformer to certify the validity of design equations theoretically, and the frequency is measured at 0.7/2.4/3.6/5.3 GHz. The measured results are in good agreement with the simulated results at each frequency.

In the context of dependent type theory, we show that coinductive predicates have an equivalent topological counterpart in terms of coinductively generated positivity relations, introduced by G. Sambin to represent closed subsets in point-free topology. Our work is complementary to a previous one with M. E. Maietti, where we showed that, in dependent type theory, the well-known concept of wellfounded trees has a topological counterpart in terms of proof-relevant inductively generated formal covers used to provide a predicative and constructive representation of complete suplattices. The proofs performed within Martin–Löf’s type theory and the Minimalist Foundation have been checked in the Agda proof assistant.

The burgeoning critical scholarship on space in International Relations (IR) overwhelmingly recognises space as a socially produced set of performances, practices, and discourses, converging into meaningful organisations of located experience. Drawing on the writings of Deleuze and Guattari on the related concepts of nomadism and the war machine, I argue that this productive emphasis betrays a continued statist methodology that proceeds by binding, or partitioning, space into finished outcomes. I present a conceptual challenge to the normative emphasis on socially produced space by following nomadism, the immanent tendency to variation in the process of spatial becoming. Working with nomadic potentials brings to the fore smooth space, which includes the continuous possibilities and intensities existing unencumbered beneath concretised productions of organised space. I follow the spatial movement of violence in Punjab during the Indian Partition of 1947 as the emergence of a war machine which deployed the nomadism of smooth space to decompose and upend striations. My objectives are first, to argue for spatial possibilities beyond the normative positivity of produced space, and secondly, to register the fundamental methodological and analytical shifts that these possibilities demand. These shifts can in turn deepen ongoing disciplinary inquiries into indeterminacy.