Doppler Tolerance, Complementary Code Sets and the Generalized Thue-Morse Sequence

We generalize the construction of Doppler-tolerant Golay complementary waveforms by Pezeshki-Calderbank-Moran-Howard to complementary code sets having more than two codes. This is accomplished by exploiting number-theoretic results involving the sum-of-digits function, equal sums of like powers, and a generalization to more than two symbols of the classical two-symbol Prouhet-Thue-Morse sequence.Comment: 12 page

Counting Co-Cyclic Lattices

There is a well-known asymptotic formula, due to W. M. Schmidt (1968) for the number of full-rank integer lattices of index at most $V$ in $\mathbb{Z}^n$. This set of lattices $L$ can naturally be partitioned with respect to the factor group $\mathbb{Z}^n/L$. Accordingly, we count the number of full-rank integer lattices $L \subseteq \mathbb{Z}^n$ such that $\mathbb{Z}^n/L$ is cyclic and of order at most $V$, and deduce that these co-cyclic lattices are dominant among all integer lattices: their natural density is $\left(\zeta(6) \prod_{k=4}^n \zeta(k)\right)^{-1} \approx 85\%$. The problem is motivated by complexity theory, namely worst-case to average-case reductions for lattice problems

Pairing interactions and the vanishing pairing correlations in hot nuclei

Finite temperature Hartree-Fock-Bogoliubov calculations are performed in Sn isotopes using Skyrme and zero-range, density-dependent pairing interactions. For both stable and very neutron-rich nuclei the critical temperature at which pairing correlations vanish is independent of the volume/surface nature of the pairing interaction. The value of the critical temperature follows approximatively the empirical rule T$_c$ $\simeq$ 0.5 $\Delta_{T=0}$ for all the calculated isotopes, showing that the critical temperature could be deduced from the pairing gap at zero temperature. On the other hand, the pairing gap at temperatures just below T$_c$ is strongly sensitive to the volume/surface nature of the pairing interaction.Comment: 6 pages, 7 figures revised versio

Determining key research areas for healthier diets and sustainable food systems in Viet Nam

Vietnamese food systems are undergoing rapid transformation, with important implications for human and environmental health and economic development. Poverty has decreased, and diet quality and undernutrition have improved significantly since the end of the Doi Moi reform period (1986-1993) as a result of Viet Nam opening its economy and increasing its regional and global trade. Yet poor diet quality is still contributing the triple burden of malnutrition, with 25 percent stunting among children under age 5, 26 percent and 29 percent of women and children, respectively, anemic, and 21 percent of adults overweight. Agricultural production systems have shifted from predominantly diverse smallholder systems to larger more commercialized and specialized systems, especially for crops, while the ‘meatification’ of the Vietnamese diet is generating serious trade-offs between improved nutrition and sustainability of the Vietnamese food systems. The food processing industry has developed rapidly, together with food imports, resulting in new and processed food products penetrating the food retail outlets, trending towards an increase in the Westernized consumption patterns that are shifting nutrition-related problems towards overweight and obesity and, with it, an increase of non-communicable disease-related health risks. While regulatory policies exist across the food system, these are not systematically implemented, making food safety a major concern for consumers and policy makers alike. Where data exists, it is not easy to aggregate with data from across food system dimensions, making it difficult for Viet Nam to make an informed analysis of current and potential food system trade-offs. In our research, we reviewed existing literature and data, and applied a food systems framework to develop an initial food systems profile for Viet Nam and to identify a comprehensive set a of research questions to fill current data gaps identified through the review. Insights on these would provide the comprehensive evidence needed to inform policy makers on how to develop new food systems policies for Viet Nam, and further refine and improve existing policies to achieve better quality diets and more sustainable food systems in Viet Nam. Based on these, we then engaged with stakeholders to develop research priorities in the Viet Nam context and identified 25 priority research questions. This paper aims to stimulate such reflections by clearly outlining key areas for research, government policy, and development programs on priority investment to build the evidence base around inclusive food systems interventions that aim to result in healthier diets and more sustainable food systems for Viet Nam

A mathematical model for predicting cyclic voltammograms of electronically conductive polypyrrole

Polypyrrole is an attractive polymer for use as a high-energy-density secondary battery because of its potential as an inexpensive, lightweight, and noncorrosive electrode material. A mathematical model to simulate cyclic voltammograms for polypyrrole is presented. The model is for a conductive porous electrode film on a rotating disk electrode (RDE) and is used to predict the spatial and time dependence of concentration, overpotential, and stored charge profiles within a polypyrrole film. The model includes both faradic and capacitance charge components in the total current density expression