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For a dilute system of non-relativistic bosons in 3 dimensions interacting through a positive, radially symmetric, potential v with scattering length a we prove that the ground state energy density satisfies the bound e(ρ)≥4πaρ2(1+12815πρa3+o(ρa3)), thereby proving a lower bound consistent with the Lee–Huang–Yang formula for the energy density. The proof allows for potentials with large L1-norm, in particular, the case of hard core interactions is included. Thereby, we solve a problem in mathematical physics that had been a major challenge since the 1950’s.
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citations | 9 | |
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AbstractTree planting has the potential to improve the livelihoods of millions of people as well as to support environmental services such as biodiversity preservation. Planting however needs to be executed wisely if benefits are to be achieved. We have developed the GlobalUsefulNativeTrees (GlobUNT) database to directly support the principles advocated by the ‘golden rules for reforestation’, including planting tree mixtures that maximize the benefits to local livelihoods and the diversity of native trees. Developed primarily by combining data from GlobalTreeSearch with the World Checklist of Useful Plant Species, GlobUNT includes 14,014 tree species that can be filtered for ten major use categories, across 242 countries and territories. In a subcontinental comparison GlobUNT revealed that Malesia had the highest useful tree species richness (3,349) and was also richest for materials (2,723), medicines (1,533), human food (958), fuel (734), environmental uses (632), social uses (614), animal food (443), poisons (322) and invertebrate food (266).
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ABSTRACTFUS is a multifunctional protein involved in many aspects of RNA metabolism, including transcription, splicing, translation, miRNA processing, and replication-dependent histone gene expression. In this paper, we show that FUS depletion results in differential expression of numerous small nucleolar RNAs (snoRNAs) that guide 2’-O methylation (2’-O-Me) and pseudouridylation of specific positions in ribosomal RNAs (rRNAs) and small nuclear RNAs (snRNAs). Using RiboMeth-seq and HydraPsiSeq for the profiling of 2’-O-Me and pseudouridylation status of rRNA species, we demonstrated considerable hypermodification at several sites in HEK293T and SH-SY5Y cells with FUS knockout (FUS KO) compared to wild-type cells. We observed a similar direction of changes in rRNA modification in differentiated SH-SY5Y cells with the FUS mutation (R495X) related to the severe disease phenotype of amyotrophic lateral sclerosis (ALS). Furthermore, the pattern of modification of some rRNA positions was correlated with the abundance of corresponding guide snoRNAs in FUS KO and FUS R495X cells. Our findings reveal a new role for FUS in modulating the modification pattern of rRNA molecules, that in turn might generate ribosome heterogeneity and constitute a fine-tuning mechanism for translation efficiency/fidelity. Therefore, we suggest that increased levels of 2’-O-Me and pseudouridylation at particular positions in rRNAs from cells with the ALS-linked FUS mutation may represent a possible new translation-related mechanism that underlies disease development and/or progression.
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Since cities are the fundamental social production units of modern civilization and host almost all economic activities, appropriate urban development policies can not only maximize the economic benefits of land and reap great wealth, but also ensure the sustainability of economic output and the balance of regional ecosystems to achieve the Sustainable Development Goals advocated by the United Nations. This article presents a 'quasi-natural experiment' based on data from 270 Chinese cities from 2003-2019 to analyze the impact of China's Innovation Cities Pilot Policy in 2011 on regional productivity, ecological service capacity, and ecological space. The study provides a measure of City Sustainability by integrating factor inputs and economic outputs, ecological regulations, and spatial improvements in human settlements. The results show that Innovation Cities Pilot Policy has a significant impact on City Sustainability, which in general implies that innovative cities make an important contribution in promoting a frugal, green and sustainable society, and quantified its contribution rate to be about $2.8\%$. Innovation Cities Policy has the most significant impact on resource-based cities, central and western cities, and both show a suppressive effect, while in developed areas such as regional centre cities and eastern cities it shows a promotional effect. In East China it was a facilitation of $4.39\%$, while in Southwest China it was a suppression of $12.76\%$.We feel that it is helpful for the management and optimization of city sustainability, and it will provide scientific reference to explore the new sustainable development path.
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The \textit{Transaction Fee Mechanism (TFM)} plays an important role in the Distributed Economy. TFM provides financial incentives and mechanisms designed to attract and support participants to use and operate Decentralized Autonomous Communities. Using Ethereum's new TFM-EIP1559-as an example, we analyze how this new TFM affects user payments, revenue of bookkeeping service providers (miners), and network overhead gasfee. Through theoretical analysis we figure out that if all miners are myopic and chasing to maximize the profit of each round, this will lead the system into steady state, but if miners produce some empty blocks thus making the gasfee fall, it will help to increase the miners' profit. However, in a network of multiple miners (mining pools) working in coordination, it is impossible for every miner to adopt a strategic behavior, but as long as a miner holds more than $\frac{m\mathcal{T}}{m\mathcal{T}+4(\lambda-\mathcal{T})}$ of the network's hash power, the strategic behavior is his dominant strategy; and once two independent miners have more than $\frac{m\mathcal{T}}{m\mathcal{T}+4(\lambda-\mathcal{T})}$ of the network's hash power but any one of them is below, they cooperate and adopt strategic behavior is an better equilibrium outcome for them, as user demand grows, the lower the threshold for miner-miner cooperation.
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For a dilute system of non-relativistic bosons in 3 dimensions interacting through a positive, radially symmetric, potential v with scattering length a we prove that the ground state energy density satisfies the bound e(ρ)≥4πaρ2(1+12815πρa3+o(ρa3)), thereby proving a lower bound consistent with the Lee–Huang–Yang formula for the energy density. The proof allows for potentials with large L1-norm, in particular, the case of hard core interactions is included. Thereby, we solve a problem in mathematical physics that had been a major challenge since the 1950’s.
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AbstractTree planting has the potential to improve the livelihoods of millions of people as well as to support environmental services such as biodiversity preservation. Planting however needs to be executed wisely if benefits are to be achieved. We have developed the GlobalUsefulNativeTrees (GlobUNT) database to directly support the principles advocated by the ‘golden rules for reforestation’, including planting tree mixtures that maximize the benefits to local livelihoods and the diversity of native trees. Developed primarily by combining data from GlobalTreeSearch with the World Checklist of Useful Plant Species, GlobUNT includes 14,014 tree species that can be filtered for ten major use categories, across 242 countries and territories. In a subcontinental comparison GlobUNT revealed that Malesia had the highest useful tree species richness (3,349) and was also richest for materials (2,723), medicines (1,533), human food (958), fuel (734), environmental uses (632), social uses (614), animal food (443), poisons (322) and invertebrate food (266).
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