A new dryland development paradigm grounded in empirical analysis of dryland systems science

Global drylands face a host of urgent human and environmental challenges with far-reaching impacts. Improving smallholder agriculture remains a key development pathway to tackle these challenges. The Dryland Development Paradigm (DDP), introduced in 2007, presented a highly influential framework for dryland development based on systems research. This paper empirically derives a new, updated DDP. It assesses recent, cutting-edge dryland science, combining literature review with qualitative and quantitative analysis of research published by the world's largest dryland science and development research initiative. The new DDP comprises eight characteristics that are distilled into three integrative principles: Unpack, Traverse and Share. The new DDP is applied and tested to identify key dryland knowledge and development gaps. A future research agenda is then elucidated, grounded in a research in development approach, in which research anchored in the three integrative principles is embedded within the context it seeks to improve. Supported by greater transdisciplinarity and knowledge co-production, operationalization of the new DDP can deliver both novel scientific insights and development impact in line with the aspirations of the 2030 Sustainable Development Goals

Killing-Yano tensors and some applications

The role of Killing and Killing-Yano tensors for studying the geodesic motion of the particle and the superparticle in a curved background is reviewed. Additionally the Papadopoulos list [74] for Killing-Yano tensors in G structures is reproduced by studying the torsion types these structures admit. The Papadopoulos list deals with groups G appearing in the Berger classification, and we enlarge the list by considering additional G structures which are not of the Berger type. Possible applications of these results in the study of supersymmetric particle actions and in the AdS/CFT correspondence are outlined.Comment: 36 pages, no figure

Probabilistic representation for solutions of an irregular porous media type equation: the degenerate case

We consider a possibly degenerate porous media type equation over all of $\R^d$ with $d = 1$, with monotone discontinuous coefficients with linear growth and prove a probabilistic representation of its solution in terms of an associated microscopic diffusion. This equation is motivated by some singular behaviour arising in complex self-organized critical systems. The main idea consists in approximating the equation by equations with monotone non-degenerate coefficients and deriving some new analytical properties of the solution

Unravelling the size distribution of social groups with information theory on complex networks

The minimization of Fisher's information (MFI) approach of Frieden et al. [Phys. Rev. E {\bf 60} 48 (1999)] is applied to the study of size distributions in social groups on the basis of a recently established analogy between scale invariant systems and classical gases [arXiv:0908.0504]. Going beyond the ideal gas scenario is seen to be tantamount to simulating the interactions taking place in a network's competitive cluster growth process. We find a scaling rule that allows to classify the final cluster-size distributions using only one parameter that we call the competitiveness. Empirical city-size distributions and electoral results can be thus reproduced and classified according to this competitiveness, which also allows to correctly predict well-established assessments such as the "six-degrees of separation", which is shown here to be a direct consequence of the maximum number of stable social relationships that one person can maintain, known as Dunbar's number. Finally, we show that scaled city-size distributions of large countries follow the same universal distribution

The Free Quon Gas Suffers Gibbs' Paradox

We consider the Statistical Mechanics of systems of particles satisfying the $q$-commutation relations recently proposed by Greenberg and others. We show that although the commutation relations approach Bose (resp.\ Fermi) relations for $q\to1$ (resp.\ $q\to-1$), the partition functions of free gases are independent of $q$ in the range $-1<q<1$. The partition functions exhibit Gibbs' Paradox in the same way as a classical gas without a correction factor $1/N!$ for the statistical weight of the $N$-particle phase space, i.e.\ the Statistical Mechanics does not describe a material for which entropy, free energy, and particle number are extensive thermodynamical quantities.Comment: number-of-pages, LaTeX with REVTE

Five principles for the practice of knowledge exchange in environmental management

This paper outlines five principles for effective practice of knowledge exchange, which when applied, have the potential to significantly enhance the impact of environmental management research, policy and practice. The paper is based on an empirical analysis of interviews with 32 researchers and stakeholders across 13 environmental management research projects, each of which included elements of knowledge co-creation and sharing in their design. The projects focused on a range of upland and catchment management issues across the UK, and included Research Council, Government and NGO funded projects. Preliminary findings were discussed with knowledge exchange professionals and academic experts to ensure the emerging principles were as broadly applicable as possible across multiple disciplines. The principles suggest that: knowledge exchange needs to be designed into research; the needs of likely research users and other stakeholders should be systematically represented in the research where possible; and long-term relationships must be built on trust and two-way dialogue between researchers and stakeholders in order to ensure effective co-generation of new knowledge. We found that the delivery of tangible benefits early on in the research process helps to ensure continued motivation and engagement of likely research users. Knowledge exchange is a flexible process that must be monitored, reflected on and continuously refined, and where possible, steps should be taken to ensure a legacy of ongoing knowledge exchange beyond initial research funding. The principles have been used to inform the design of knowledge exchange and stakeholder engagement guidelines for two international research programmes. They are able to assist researchers, decision-makers and other stakeholders working in contrasting environmental management settings to work together to co-produce new knowledge, and more effectively share and apply existing knowledge to manage environmental change

Variational Principle underlying Scale Invariant Social Systems

MaxEnt's variational principle, in conjunction with Shannon's logarithmic information measure, yields only exponential functional forms in straightforward fashion. In this communication we show how to overcome this limitation via the incorporation, into the variational process, of suitable dynamical information. As a consequence, we are able to formulate a somewhat generalized Shannonian Maximum Entropy approach which provides a unifying "thermodynamic-like" explanation for the scale-invariant phenomena observed in social contexts, as city-population distributions. We confirm the MaxEnt predictions by means of numerical experiments with random walkers, and compare them with some empirical data

A place-based approach to payments for ecosystem services

Payment for Ecosystem Services (PES) schemes are proliferating but are challenged by insufficient attention to spatial and temporal inter-dependencies, interactions between different ecosystems and their services, and the need for multi-level governance. To address these challenges, this paper develops a place-based approach to the development and implementation of PES schemes that incorporates multi-level governance, bundling or layering of services across multiple scales, and shared values for ecosystem services. The approach is evaluated and illustrated using case study research to develop an explicitly place-based PES scheme, the Peatland Code, owned and managed by the International Union for the Conservation of Nature’s UK Peatland Programme and designed to pay for restoration of peatland habitats. Buyers preferred bundled schemes with premium pricing of a primary service, contrasting with sellers’ preferences for quantifying and marketing services separately in a layered scheme. There was limited awareness among key business sectors of dependencies on ecosystem services, or the risks and opportunities arising from their management. Companies with financial links to peatlands or a strong environmental sustainability focus were interested in the scheme, particularly in relation to climate regulation, water quality, biodiversity and flood risk mitigation benefits. Visitors were most interested in donating to projects that benefited wildlife and were willing to donate around £2 on-site during a visit. Sellers agreed a deliberated fair price per tonne of CO2 equivalent from £11.18 to £15.65 across four sites in Scotland, with this range primarily driven by spatial variation in habitat degradation. In the Peak District, perceived declines in sheep and grouse productivity arising from ditch blocking led to substantially higher prices, but in other regions ditch blocking was viewed more positively. The Peatland Code was developed in close collaboration with stakeholders at catchment, landscape and national scales, enabling multi-level governance of the management and delivery of ecosystem services across these scales. Place-based PES schemes can mitigate negative trade-offs between ecosystem services, more effectively include cultural ecosystem services and engage with and empower diverse stakeholders in scheme design and governance

On Fourier transforms of radial functions and distributions

We find a formula that relates the Fourier transform of a radial function on $\mathbf{R}^n$ with the Fourier transform of the same function defined on $\mathbf{R}^{n+2}$. This formula enables one to explicitly calculate the Fourier transform of any radial function $f(r)$ in any dimension, provided one knows the Fourier transform of the one-dimensional function $t\to f(|t|)$ and the two-dimensional function $(x_1,x_2)\to f(|(x_1,x_2)|)$. We prove analogous results for radial tempered distributions.Comment: 12 page

On non-local variational problems with lack of compactness related to non-linear optics

We give a simple proof of existence of solutions of the dispersion manage- ment and diffraction management equations for zero average dispersion, respectively diffraction. These solutions are found as maximizers of non-linear and non-local vari- ational problems which are invariant under a large non-compact group. Our proof of existence of maximizer is rather direct and avoids the use of Lions' concentration compactness argument or Ekeland's variational principle.Comment: 30 page