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Forests play a crucial role in South Korea’s carbon neutrality goal and require sustainable management strategies to overcome age-class imbalances. The Generic Carbon Budget Model (GCBM) offers a spatially explicit approach to simulate carbon dynamics at a regional scale. In this study, we utilized the GCBM to analyze the carbon budget of forests in South Korea and produce spatiotemporal maps for distribution of the forest biomass. The growth parameters of five representative tree species (Pinus densiflora Siebold & Zucc., Larix kaempferi Carr., Pinus koraiensis Siebold & Zucc., Quercus mongolica Fisch. ex Ledeb., Quercus variabilis Blume), which are the main species in South Korea, were used to operate the model. In addition, spatial data for harvest and thinning management activities were used to analyze the effects of anthropogenic activities. In 2020, the aboveground and belowground biomass were 112.98 and 22.84 tC ha−1, and the net primary productivity was 8.30 tC ha−1 year−1. These results were verified using comparison with statistics, a literature review, and MODIS NPP. In particular, broadleaf is higher than conifer forest in net primary production. The Canadian GCBM with Korean forest inventory data and yield curves successfully estimated the aboveground and belowground biomass of forests in South Korea. Our study demonstrates that these estimates can be mapped in detail, thereby supporting decision-makers and stakeholders in analyzing the carbon budget of the forests in South Korea and developing novel schemes that can serve regional and national aims related to forest management, wood utilization, and ecological preservation. Further studies are needed to improve the initialization of dead organic matter pools, given the large-scale afforestation efforts in recent decades that have established South Korea’s forests on predominantly non-forest sites.

In the parameterized problem \textsc{MaxLin2-AA}[$k$], we are given a system with variables $x_1,...,x_n$ consisting of equations of the form $\prod_{i \in I}x_i = b$, where $x_i,b \in \{-1, 1\}$ and $I\subseteq [n],$ each equation has a positive integral weight, and we are to decide whether it is possible to simultaneously satisfy equations of total weight at least $W/2+k$, where $W$ is the total weight of all equations and $k$ is the parameter (if $k=0$, the possibility is assured). We show that \textsc{MaxLin2-AA}[$k$] has a kernel with at most $O(k^2\log k)$ variables and can be solved in time $2^{O(k\log k)}(nm)^{O(1)}$. This solves an open problem of Mahajan et al. (2006). The problem \textsc{Max-$r$-Lin2-AA}[$k,r$] is the same as \textsc{MaxLin2-AA}[$k$] with two differences: each equation has at most $r$ variables and $r$ is the second parameter. We prove a theorem on \textsc{Max-$r$-Lin2-AA}[$k,r$] which implies that \textsc{Max-$r$-Lin2-AA}[$k,r$] has a kernel with at most $(2k-1)r$ variables improving a number of results including one by Kim and Williams (2010). The theorem also implies a lower bound on the maximum of a function $f:\ \{-1,1\}^n \rightarrow \mathbb{R}$ of degree $r$. We show applicability of the lower bound by giving a new proof of the Edwards-Erd{\H o}s bound (each connected graph on $n$ vertices and $m$ edges has a bipartite subgraph with at least $m/2 + (n-1)/4$ edges) and obtaining a generalization.

The Abstract Milling problem is a natural and quite general graph-theoretic model for geometric milling problems. Given a graph, one asks for a walk that covers all its vertices with a minimum number of turns, as specified in the graph model by a 0/1 turncost function fx at each vertex x giving, for each ordered pair of edges (e,f) incident at x, the turn cost at x of a walk that enters the vertex on edge e and departs on edge f. We describe an initial study of the parameterized complexity of the problem. Our main positive result shows that Abstract Milling, parameterized by: number of turns, treewidth and maximum degree, is fixed-parameter tractable, We also show that Abstract Milling parameterized by (only) the number of turns and the pathwidth, is hard for W[1] -- one of the few parameterized intractability results for bounded pathwidth., Comment: 18 pages, 2 figures

Mine capital and operating costs are mainly determined by the geology of the orebody, then scale and location of the project. The ability to create wealth in each of zinc, copper and gold mining industries is compared: the zinc industry lost money pre-tax in the period 1993-2003, but copper had a residual cash flow of more than US, Mine capital and operating costs are mainly determined by the geology of the orebody, then scale and location of the project. The ability to create wealth in each of zinc, copper and gold mining industries is compared: the zinc industry lost money pre-tax in the period 1993-2003, but copper had a residual cash flow of more than US