Nourishing nations during pandemics: why prioritize fish diets and aquatic foods in Africa.

The COVID-19 pandemic caught the world unprepared, with containment measures impacting both global supply chains and agri-commodity flows. The public health crisis raised some urgent questions: "how can fish and other aquatic foods and supply chains be prioritized as health-related interventions to avert both a malnutrition crisis and gender inequality?" Furthermore, "what are the integrated responses, investment opportunities, and governance mechanisms to effectively address the pandemic?" As "super foods," diets of fish and aquatic foods provide animal-source protein, omega-3 fatty acids, and micronutrients, including both vitamins and minerals, necessary for both the ill and the healthy. The affordability and accessibility of fish could address food and nutrition security needs under lockdown and border closures, boost immune systems, and increase commodity trade. This analytical piece focuses on the continent of Africa, where malnutrition is pervasive, but also where local aquatic food supplies can be utilised during lockdowns and border closures. The paper provides governance insights on national budget support programs and portfolio restructuring to strengthen local aquatic foods production systems to meet dietary needs. Furthermore, the authors advocate for a coordinated multi-sectoral intervention across several well-being domains in the immediate and medium-term involving various partnerships. These integrated responses will mutually limit the contagion while providing support to functional fish value chains for healthy diets, livelihoods, cross-border trade, and long-term macroeconomic recovery.

On addition-subtraction chains of numbers with low Hamming weight.

An addition chain is a sequence of integers such that every element in the sequence is the sum of two previous elements. They have been much studied, and generalized to addition-subtraction chains, Lucas chains, and Lucas addition-subtraction chains. These various chains have been useful in finding efficient exponentiation algorithms in groups. As a consequence, finding chains of minimal length is critical. The main objective of this paper is to extend results known for addition chains to addition-subtraction chains with Lucas addition-subtraction as a tool to construct such minimal chains. Specifically, if we let ℓ -(n) stand for the minimal length of all the Lucas addition-subtraction chains for n, we prove |ℓ -(2n) - ℓ -(n)| ≤ 1 for all integers n of Hamming weight ≤ 4. Thus, to find a minimal addition-subtraction chain for low Hamming weight integers, it suffices to only consider odd integers.