We show that color-kinematics duality is a manifest property of the equations of motion governing currents and field strengths. For the nonlinear sigma model (NLSM), this insight enables an implementation of the double copy at the level of fields, as well as an explicit construction of the kinematic algebra and associated kinematic current. As a byproduct, we also derive new formulations of the special Galileon (SG) and Born-Infeld (BI) theory.For Yang-Mills (YM) theory, this same approach reveals a novel structure — covariant color-kinematics duality — whose only difference from the conventional duality is that 1/□ is replaced with covariant 1/D2. Remarkably, this structure implies that YM theory is itself the covariant double copy of gauged biadjoint scalar (GBAS) theory and an F3 theory of field strengths encoding a corresponding kinematic algebra and current. Directly applying the double copy to equations of motion, we derive general relativity (GR) from the product of Einstein-YM and F3 theory. This exercise reveals a trivial variant of the classical double copy that recasts any solution of GR as a solution of YM theory in a curved background.Covariant color-kinematics duality also implies a new decomposition of tree-level amplitudes in YM theory into those of GBAS theory. Using this representation we derive a closed-form, analytic expression for all BCJ numerators in YM theory and the NLSM for any number of particles in any spacetime dimension. By virtue of the double copy, this constitutes an explicit formula for all tree-level scattering amplitudes in YM, GR, NLSM, SG, and BI.

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We derive a non-perturbative, Lagrangian-level formulation of the double copy in two spacetime dimensions. Our results elucidate the field theoretic underpinnings of the double copy in a broad class of scalar theories which can include masses and higher-dimension operators. An immediate corollary is the amplitudes-level double copy at all orders in perturbation theory. Applied to certain integrable models, the double copy defines an isomorphism between Lax connections, Wilson lines, and infinite towers of conserved currents. We also implement the double copy at the level of non-perturbative classical solutions, both analytically and numerically, and present a stringy generalization.

Since Farmer Field Schools (FFS) were first originated in Yogyakarta, Indonesia in 1989, many innovations have occurred and changes to the basic theme have been developed. FFS started out as a way to facilitate learning of integrated pest management (IPM) concepts and techniques by Indonesian farmers. The Indonesian National IPM Program first applied the FFS approach on a broad scale for rice farmers, and technical assistance provided by the United Nations Food and Agriculture Organization (FAO) and funding from the US Agency for International Development (USAID) among others were key to the success of this program. FFS were subsequently adapted for other crops such as legumes, fruits, vegetables, and tuber crops, and other technical and social themes such as integrated crop management, community forestry, livestock, water conservation, HIV/AIDS, literacy, advocacy and democracy (CIP-UPWARD 2003).Central to the success of FFS programs is appropriate IPM and methodological training of the people who organize and facilitate the field schools. To be a successful FFS trainer/facilitator, one must have skills in managing participatory, discovery-based learning as well as technical knowledge of agro-ecology to guide the group's learning and action process. Without an adequate Training of Trainers (ToT) program, the subsequent FFS program will fall far short of its potential.This chapter focuses on a range of developments and innovations in FFS in recent years, with particular attention to IPM FFS and ToT. Promising innovations and new directions in other types of FFS will also be highlighted. The Farmer Field School ProcessIPM FFS are first initiated by introductory meetings with a community to determine if it is interested in establishing a FFS. Usually, a FFS concentrates on a particular crop in order to focus learning and deepen understanding of principles (e.g., on insect ecology, soil fertility, and production economics) that subsequently can be applied to other crops and the farm production system. If the community indeed decides to implement a FFS, the group establishes selection criteria and identifies a group of 15-30 participants. The facilitator and participants draw up a "learning contract" or "moral contract" that includes the commitments of both the facilitator and the group regarding attendance, materials, the management of resources, the investment of the FFS harvest, and other key issues. Ideally, the farmers contribute the majority of labor and crop input resources, with the facilitator contributing his or her time, transportation costs, and the basic learning materials needed for the FFS.