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This paper studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs), a.k.a. (Ordinary) Difference Equations. It presents a new framework using these equations as a central tool for computation and algorithm design. We present the general theory of discrete ODEs for computation theory, we illustrate this with various examples of algorithms, and we provide several implicit characterizations of complexity and computability classes. The proposed framework presents an original point of view on complexity and computation classes. It unifies several constructions that have been proposed for characterizing these classes including classical approaches in implicit complexity using restricted recursion schemes, as well as recent characterizations of computability and complexity by classes of continuous ordinary differential equations. It also helps understanding the relationships between analog computations and classical discrete models of computation theory. At a more technical point of view, this paper points out the fundamental role of linear (discrete) ODEs and classical ODE tools such as changes of variables to capture computability and complexity measures, or as a tool for programming many algorithms. [ABSTRACT FROM AUTHOR]

Modern mangroves are among the most carbon-rich biomes on Earth, but their long-term (≥106 years) impact on the global carbon cycle is unknown. The extent, productivity and preservation of mangroves are controlled by the interplay of tectonics, global sea level and sedimentation, including tide, wave and fluvial processes. The impact of these processes on mangrove-bearing successions in the Oligo-Miocene of the South China Sea (SCS) is evaluated herein. Palaeogeographic reconstructions, palaeotidal modelling and facies analysis suggest that elevated tidal range and bed shear stress optimized mangrove development along tide-influenced tropical coastlines. Preservation of mangrove organic carbon (OC) was promoted by high tectonic subsidence and fluvial sediment supply. Lithospheric storage of OC in peripheral SCS basins potentially exceeded 4,000 Gt (equivalent to 2,000 p.p.m. of atmospheric CO2). These results highlight the crucial impact of tectonic and oceanographic processes on mangrove OC sequestration within the global carbon cycle on geological timescales. [ABSTRACT FROM AUTHOR]

The rise of food security up international political, societal and academic agendas has led to increasing interest in novel means of improving primary food production and reducing waste. There are however, also many 'post-farm gate' activities that are critical to food security, including processing, packaging, distributing, retailing, cooking and consuming. These activities all affect a range of important food security elements, notably availability, affordability and other aspects of access, nutrition and safety. Addressing the challenge of universal food security, in the context of a number of other policy goals (e.g. social, economic and environmental sustainability), is of keen interest to a range of UK stakeholders but requires an up-to-date evidence base and continuous innovation. An exercise was therefore conducted, under the auspices of the UK Global Food Security Programme, to identify priority research questions with a focus on the UK food system (though the outcomes may be broadly applicable to other developed nations). Emphasis was placed on incorporating a wide range of perspectives ('world views') from different stakeholder groups: policy, private sector, non-governmental organisations, advocacy groups and academia. A total of 456 individuals submitted 820 questions from which 100 were selected by a process of online voting and a three-stage workshop voting exercise. These 100 final questions were sorted into 10 themes and the 'top' question for each theme identified by a further voting exercise. This step also allowed four different stakeholder groups to select the top 7-8 questions from their perspectives. Results of these voting exercises are presented. It is clear from the wide range of questions prioritised in this exercise that the different stakeholder groups identified specific research needs on a range of post-farm gate activities and food security outcomes. Evidence needs related to food affordability, nutrition and food safety (all key elements of food security) featured highly in the exercise. While there were some questions relating to climate impacts on production, other important topics for food security (e.g. trade, transport, preference and cultural needs) were not viewed as strongly by the participants. [ABSTRACT FROM AUTHOR]