The Exact Stochastic Process of the Haploid Multi-Allelic Wright-Fisher Mutation Model.

Diffusion models are widely applied in population genetics, but their approximate solutions may not accurately capture the exact stochastic process. Nevertheless, this practice was necessary due to computing limitations, particularly for large populations. In this article, we develop the exact Markov chain algebra (MCA) for a discrete haploid multi-allelic Wright-Fisher model (MA-WFM) with a full mutation matrix to address this challenge. A special case of nonzero mutations between multiple alleles have not been captured by previous bi-allelic models. We formulated the mean allele frequencies for asymptotic equilibrium analytically for the tri- and quad-allelic case. We also evaluated the exact time-dependent Markov model numerically, presenting it concisely in terms of diffusion variables. The convergence with increasing population size to a diffusion limit is demonstrated for the population composition distribution. Our model shows that there will never be exact irreversible extinction when there are nonzero mutation rates into each allele and never be an exact irreversible fixation when there are nonzero mutation rates out of each allele. We only present results where there is no complete extinction and no complete fixation. Finally, we present detailed computations for the full Markov process, exposing the behavior near the boundaries for the compositional domains, which are non-singular boundaries according to diffusion theory.

Correlation challenges for North Sea offshore wind power: a Norwegian case study.

Offshore wind power projects are currently booming around the North Sea. However, there are inherent correlation challenges between wind farms in this area, which has implications for the optimal composition of locations and the scale-up of installed capacities. This paper is aimed at addressing the correlation problem by minimizing the variance of total wind power accumulated around the North Sea. We show that this nonlinear convex optimization problem can be solved by applying the Augmented Lagrangian Algorithm (ALA). The premise of the study is that more interconnections between the EU countries will be prioritized in order to optimize and smooth out the wind power production patterns. A publicly available dataset with historical hour-by-hour data spanning over 20 years was used for the analysis. We explore two distinct scenarios for Norwegian offshore wind development. In the first scenario, we consider the ongoing activities on the European continental side of the North Sea and their implications for Norway. Here, we illustrate the advantages of focusing on expanding wind power capacity in the northern regions of Norway to enhance the overall value of the generated wind power. In contrast, the second reference scenario neglects these interconnections, resulting in a significantly greater concentration of offshore wind development in the southern parts of Norway, particularly in Sørlige Nordsjø II. Additionally, our work estimates the wind power correlation coefficient in the North Sea as a function of distance. Furthermore, we analyze deviations and intermittencies in North Sea wind power over various time intervals, emphasizing that the perceived integration challenges are highly dependent on the chosen time resolution in the analysis.

Spatial energy density of large-scale electricity generation from power sources worldwide.

This paper introduces the annual energy density concept for electric power generation, which is proposed as an informative metric to capture the impacts on the environmental footprint. Our investigation covers a wide range of sources classified by rated power and compares different regions to establish typical spatial flows of energy and evaluate the corresponding scalability to meet future net-zero emission (NZE) goals. Our analysis is conducted based on publicly available information pertaining to different regions and remote satellite image data. The results of our systematic analysis indicate that the spatial extent of electric power generation toward 2050 will increase approximately sixfold, from approximately 0.5% to nearly 3.0% of the world's land area, based on International Energy Agency (IEA) NZE 2050 targets. We investigate the worldwide energy density for ten types of power generation facilities, two involving nonrenewable sources (i.e., nuclear power and natural gas) and eight involving renewable sources (i.e., hydropower, concentrated solar power (CSP), solar photovoltaic (PV) power, onshore wind power, geothermal power, offshore wind power, tidal power, and wave power). In total, our study covers 870 electric power plants worldwide, where not only the energy density but also the resulting land or sea area requirements to power the world are estimated. Based on the provided meta-analysis results, this paper challenges the common notion that solar power is the most energy-dense renewable fuel source by demonstrating that hydropower supersedes solar power in terms of land use in certain regions of the world, depending on the topography.