Given a graph G and a mapping f:V(G)→N, an f-list assignment of G is a function that maps each v∈V(G) to a set of at least f(v) colors. For an f-list assignment L of a graph G, a proper conflict-free L-coloring of G is a proper coloring ϕ of G such that for every non-isolated vertex v∈V(G), ϕ(v)∈L(v) and some color appears precisely once in the neighborhood of v. We say that G is proper conflict-free f-choosable if for every f-list assignment L of G, there exists a proper conflict-free L-coloring of G. If G is proper conflict-free f-choosable and there is a constant k such that f(v)=dG(v)+k for every vertex v of G, then we say G is proper conflict-free (degree+k)-choosable. In this paper, we consider graphs with a bounded maximum average degree. We show that every graph with the maximum average degree less than 103 is proper conflict-free (degree+3)-choosable, and that every graph with the maximum average degree less than 187 is proper conflict-free (degree+2)-choosable unless it contains a component isomorphic to the 5-cycle. As a result, every planar graph with girth at least 5 is proper conflict-free (degree+3)-choosable, and every planar graph with girth at least 9 is proper conflict-free (degree+2)-choosable.
We estimate productivity spillovers from Japanese cotton-spinning firms in China (known as Zaikabo,"(sic)(sic)(sic)") to local Chinese cotton-spinning mills based on plant-level data for 1925 to 1938. In order to capture the important role of distance in facilitating such spillovers we geo-localised the plants. Our results provide clear evidence for positive spillovers from Zaikabo to local Chinese mills, which go hand-in-hand with an upgrade in production technology towards greater use of capital. Spillovers are very localised, being strongest within a radius of up to 10 km around the Zaikabo and particularly strong for mills in Shanghai. Exploiting information on the workforce composition of the Japanese affiliates, we find suggestive evidence of a skilled-labour channel: spillovers tend to be larger from Zaikabo employing higher shares of skilled labour. We also find some evidence in line with the idea that these gains are larger for Chinese mills with higher initial productivity, consistent with a role for absorptive capacity. Our paper is the first to document FDI productivity spillovers in a historical context and to characterise the channels through which they operate.
Africa has 54 countries, but over half of its multi-billion-dollar GDP is driven by only three nations: Nigeria, Egypt, and South Africa. To sustain growth, understanding the destabilizing effects of herding on these 'risk-on' stock markets is crucial. This paper first quantifies the presence of herding and then introduces a novel approach, considering America and China as principal components influencing herding in Africa. Two unique adaptations of herding methodologies are proposed: one overcomes the high correlation limitations seen in Ridge and Lasso, while the other visualizes the changing weight drivers of herding trends during crises. The analysis includes six independent drivers—three from the US and three from China—across four major recent events. Both America and China are found to influence herding behaviour in Africa.
Notions of ordinal submodularity/supermodularity have been introduced and studied in the literature. We consider several classes of ordinally submodular functions defined on finite Boolean lattices and give characterizations of the set of minimizers of ordinally submodular functions.
This study investigated how branch topology affects the macroscopic flow and molecular dynamics of three diisostearyl malate isomers differing in alkyl chain branches. Rheological measurements revealed temperature-dependent viscosities in the order: multi-branched > methyl-branched > guerbet-branched. To elucidate the underlying mechanisms, we combined these measurements with all-atom molecular dynamics simulations to examine self-diffusion, hydrogen bonding, interaction energies, radius of gyration, and rotational relaxation. The multi-branched isomer exhibited the highest viscosity, lowest translational mobility, and slowest rotational relaxation; its hydrogen-bond dynamics were motif-dependent, with longer-lived O-H center dot center dot center dot O(hydroxyl) but shorter-lived O-H center dot center dot center dot O(carbonyl) associations, despite possessing the weakest average intermolecular interaction energies. Together, these results show that branch topology modifies macroscopic flow through coupled changes in translational and rotational dynamics and motif-specific intermolecular association rather than through cohesive interaction strength alone. These molecular-level insights clarify structure-viscosity relationships, guiding the selection and design of functional ester liquids for cosmetics, lubricants, paints, and food formulations.
