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Abstract Metabolic scaling theory has been pivotal in formalizing the expected energy expenditures across populations as a function of body size. Coexistence theory has provided a mathematization of the environmental conditions compatible with multispecies coexistence. Yet, it has been challenging to explain how observed community‐wide patterns, such as the inverse relationship between population abundance density and body size, can be unified under both theories. Here, we provide the foundation for a tractable, scalable, and extendable framework to study the coexistence of resource‐mediated competing populations as a function of their body size. For a given thermal domain and response, this integration reveals that the metabolically predicted 1/4 power dependence of carrying capacity of biomass density on body size can be understood as the average distribution of carrying capacities across feasible environmental conditions, especially for large communities. In line with empirical observations, our integration predicts that such average distribution leads to communities in which population biomass densities at equilibrium are independent from body size, and consequently, population abundance densities are inversely related to body size. This integration opens new opportunities to increase our understanding of how metabolic scaling relationships at the population level can shape processes at the community level under changing environments. 

This study investigates the relationship between occupational automation risks and workers’ transitions to entrepreneurship using data from the Current Population Survey. We find that employees facing automation-related job displacement are inclined to shift toward unincorporated entrepreneurship, emphasizing entrepreneurship as a viable alternative career path. Noteworthy variations emerge when examining specific automation technologies, revealing a positive association between industrial robots and entrepreneurial transitions, whereas artificial intelligence displays a negative relationship. Gender disparities are observed, with female workers exhibiting a lower likelihood than males of transitioning into entrepreneurship. This study also shows a heightened prominence of entrepreneurial transitions during the early stages of the COVID-19 pandemic. By illuminating entrepreneurship as a response to job displacement, our results offer crucial policy insights into the labor market implications of automation. 

A framework to understand the labour market reveals a nested hierarchical architecture in human capital in which specific knowledge and skills are contingent upon foundational, general skills and knowledge. This nested skill structure provides a new perspective on wage premiums and persistent wage disparity observed across different demographic groups. 

In this study, we obtain an exact time-dependent solution of the chemical master equation (CME) of an extension of the two-state telegraph model describing bursty or non-bursty protein expression in the presence of positive or negative autoregulation. Using the method of spectral decomposition, we show that the eigenfunctions of the generating function solution of the CME are Heun functions, while the eigenvalues can be determined by solving a continued fraction equation. Our solution generalizes and corrects a previous time-dependent solution for the CME of a gene circuit describing non-bursty protein expression in the presence of negative autoregulation [Ramos et al., Phys. Rev. E 83, 062902 (2011)]. In particular, we clarify that the eigenvalues are generally not real as previously claimed. We also investigate the relationship between different types of dynamic behavior and the type of feedback, the protein burst size, and the gene switching rate. 

Humans acquire and accumulate knowledge through language usage and eagerly exchange their knowledge for advancement. Although geographical barriers had previously limited communication, the emergence of information technology has opened new avenues for knowledge exchange. However, it is unclear which communication pathway is dominant in the 21st century. Here, we explore the dominant path of knowledge diffusion in the 21st century using Wikipedia, the largest communal dataset. We evaluate the similarity of shared knowledge between population groups, distinguished based on their language usage. When population groups are more engaged with each other, their knowledge structure is more similar, where engagement is indicated by socio-economic connections, such as cultural, linguistic, and historical features. Moreover, geographical proximity is no longer a critical requirement for knowledge dissemination. Furthermore, we integrate our data into a mechanistic model to better understand the underlying mechanism and suggest that the main channel of information distribution in the 21st century is based online.