Higher-Order Interactions： Understanding the knowledge capacity of social groups using simplicial sets

A predominant benefit of social living is the ability to share knowledge that cannot be gained through the information an individual accumulates based on its personal experience alone. Traditional computational models have portrayed sharing knowledge through interactions among members of social groups via dyadic networks. Such models aim at understanding the percolation of information among individuals and groups to identify potential limitations to successful knowledge transfer. How- ever, because many real-world interactions are not solely pairwise, i.e., several group members may obtain information from one another simultaneously, it is necessary to understand more than dyadic communication and learning processes to capture their full complexity. We detail a modeling framework based on the simplicial set, a concept from algebraic topology, which allows elegant encapsulation of multi-agent interactions. Such a model system allows us to analyze how individual information within groups accumulates as the group＇s collective set of knowledge, which may be different than the simple union of individually contained information. Furthermore, the simplicial modeling approach we propose allows us to investigate how information accumulates via sub-group interactions, offering insight into complex aspects of multi-way communication systems. The fundamental change in modeling strategy we offer here allows us to move from portraying knowledge as a ＂token＂, passed from signaler to receiver, to portraying knowledge as a set of accumulating building blocks from which novel ideas can emerge. We provide an explanation of relevant mathematical concepts in a way that promotes accessibility to a general audience [Current Zoology 61 （1）： 114--127, 2015].

Outsourcing or Not? The OEMrs Better Collecting Mode under Cap-and-Trade Regulation

Many original equipment manufacturers(OEMs)carry out collecting operations by themselves or a third party.Most of the existing research papers in the literature consider the collecting mode selection problem from an economic perspective.However,in practice,the firm's collecting decisions can be affected by the carbon policies at present.This paper aims to bridge the gap in research on remanufacturing supply chain by taking the effects of cap-and-trade regulation into consideration.Stackelberg models are established to study the quantity and price decisions under different collecting modes.We find that the OEM reaps more profits in the OEM collecting mode than the third-party collecting mode when collection cost is large.Otherwise,the third party has lower collection cost,and the third-party collecting mode may make the OEM more profitable.From an environmental perspective,with high collection cost,the third party collecting mode can reduce the carbon emissions unless the cost of new products and the emissions intensity are small.In addition,when the collection cost is low but the quantity of remanufacturing products is restricted by that of new products,the third party collecting mode may increase the carbon emissions.In addition,the implementation of cap-and-trade regulation can always reduce carbon emissions,and it may increase the OEM's profits if consumers preference for remanufactured products is small.