Friendship paradox states that individuals are likely to have fewer friends than their friends do,on average.Despite of its wide existence and appealing applications in real social networks,the mathematical understand...Friendship paradox states that individuals are likely to have fewer friends than their friends do,on average.Despite of its wide existence and appealing applications in real social networks,the mathematical understanding of friendship paradox is very limited.Only few works provide theoretical evidence of single-step and multi-step friendship paradoxes,given that the neighbors of interest are onehop and multi-hop away from the target node.However,they consider non-evolving networks,as opposed to the topology of real social networks that are constantly growing over time.We are thus motivated to present a first look into friendship paradox in evolving networks,where newly added nodes preferentially attach themselves to those with higher degrees.Our analytical verification of both single-step and multistep friendship paradoxes in evolving networks,along with comparison to the non-evolving counterparts,discloses that“friendship paradox is even more paradoxical in evolving networks”,primarily from three aspects:1)we demonstrate a strengthened effect of single-step friendship paradox in evolving networks,with a larger probability(more than 0.8)of a random node’s neighbors having higher average degree than the random node itself;2)we unravel higher effectiveness of multi-step friendship paradox in seeking for influential nodes in evolving networks,as the rate of reaching the max degree node can be improved by a factor of at least Θ(t^(2/3))with t being the network size;3)we empirically verify our findings through both synthetic and real datasets,which suggest high agreements of results and consolidate the reasonability of evolving model for real social networks.展开更多
For the first time in human history,hundreds of millions of people all over the world have been subjected to compulsory vaccination with a new type of nucleic acid based vaccines in order to keep their jobs or be able...For the first time in human history,hundreds of millions of people all over the world have been subjected to compulsory vaccination with a new type of nucleic acid based vaccines in order to keep their jobs or be able to travel due to some notorious coronavirus disease 2019(COVID-19)mandates.The vast majority of African countries were either initially deprived of these vaccines,or later,a majority of the population was too skeptical to receive them and preferred a safe early treatment pharmacological approach.Yet,Africa had the lowest COVID-19 mortality rate compared to those countries that adopted mass vaccination.This letter to the editor adds African insights that should be helpful in future pandemics to save millions of precious lives.展开更多
This article adopt the theory of cointegration to research the relation between Chinese economic growth and environmental pollution,and find there is no long term balanced relation between them.So the conclusion is :E...This article adopt the theory of cointegration to research the relation between Chinese economic growth and environmental pollution,and find there is no long term balanced relation between them.So the conclusion is :Economic growth can not spontaneous reduce pollution,To prevent the environment from deteriorating,it is necessary to make use of policy and prompting to encourage company to reduce pollution of per unit output.Or transform high-pollution industry to low-pollution industry.展开更多
基金supported by NSF China(No.61960206002,62020106005,42050105,62061146002)Shanghai Pilot Program for Basic Research–Shanghai Jiao Tong University.
文摘Friendship paradox states that individuals are likely to have fewer friends than their friends do,on average.Despite of its wide existence and appealing applications in real social networks,the mathematical understanding of friendship paradox is very limited.Only few works provide theoretical evidence of single-step and multi-step friendship paradoxes,given that the neighbors of interest are onehop and multi-hop away from the target node.However,they consider non-evolving networks,as opposed to the topology of real social networks that are constantly growing over time.We are thus motivated to present a first look into friendship paradox in evolving networks,where newly added nodes preferentially attach themselves to those with higher degrees.Our analytical verification of both single-step and multistep friendship paradoxes in evolving networks,along with comparison to the non-evolving counterparts,discloses that“friendship paradox is even more paradoxical in evolving networks”,primarily from three aspects:1)we demonstrate a strengthened effect of single-step friendship paradox in evolving networks,with a larger probability(more than 0.8)of a random node’s neighbors having higher average degree than the random node itself;2)we unravel higher effectiveness of multi-step friendship paradox in seeking for influential nodes in evolving networks,as the rate of reaching the max degree node can be improved by a factor of at least Θ(t^(2/3))with t being the network size;3)we empirically verify our findings through both synthetic and real datasets,which suggest high agreements of results and consolidate the reasonability of evolving model for real social networks.
文摘For the first time in human history,hundreds of millions of people all over the world have been subjected to compulsory vaccination with a new type of nucleic acid based vaccines in order to keep their jobs or be able to travel due to some notorious coronavirus disease 2019(COVID-19)mandates.The vast majority of African countries were either initially deprived of these vaccines,or later,a majority of the population was too skeptical to receive them and preferred a safe early treatment pharmacological approach.Yet,Africa had the lowest COVID-19 mortality rate compared to those countries that adopted mass vaccination.This letter to the editor adds African insights that should be helpful in future pandemics to save millions of precious lives.
文摘This article adopt the theory of cointegration to research the relation between Chinese economic growth and environmental pollution,and find there is no long term balanced relation between them.So the conclusion is :Economic growth can not spontaneous reduce pollution,To prevent the environment from deteriorating,it is necessary to make use of policy and prompting to encourage company to reduce pollution of per unit output.Or transform high-pollution industry to low-pollution industry.
