Hierarchicality of Trade Flow Networks Reveals Complexity of Products

With globalization, countries are more connected than before by trading flows, which currently amount to at least 36 trillion dollars. Interestingly, approximately 30-60 percent of global exports consist of intermediate products. Therefore, the trade flow network of a particular product with high added values can be regarded as a value chain. The problem is weather we can discriminate between these products based on their unique flow network structure. This paper applies the flow analysis method developed in ecology to 638 trading flow networks of different products. We claim that the allometric scaling exponent $\eta$ can be used to characterize the degree of hierarchicality of a flow network, i.e., whether the trading products flow on long hierarchical chains. Then, the flow networks of products with higher added values and complexity, such as machinery&transport equipment with larger exponents, are highlighted. These higher values indicate that their trade flow networks are more hierarchical. As a result, without extra data such as global input-output table, we can identify the product categories with higher complexity and the relative importance of a country in the global value chain solely by the trading network.Comment: 14 pages,7 figure

Three-Body Recombination near a Narrow Feshbach Resonance in 6 Li

We experimentally measure and theoretically analyze the three-atom recombination rate, L3, around a narrow s-wave magnetic Feshbach resonance of 6Li−6Li at 543.3 G. By examining both the magnetic field dependence and, especially, the temperature dependence of L3 over a wide range of temperatures from a few μK to above 200 μK, we show that three-atom recombination through a narrow resonance follows a universal behavior determined by the long-range van der Waals potential and can be described by a set of rate equations in which three-body recombination proceeds via successive pairwise interactions. We expect the underlying physical picture to be applicable not only to narrow s wave resonances, but also to resonances in nonzero partial waves, and not only at ultracold temperatures, but also at much higher temperatures