The parabolic quaternionic Monge-Amp\`{e}re type equation on hyperK\"{a}hler manifolds

We prove the long time existence and uniqueness of solution to a parabolic quaternionic Monge-Amp\`{e}re type equation on a compact hyperK\"{a}hler manifold. We also show that after normalization, the solution converges smoothly to the unique solution of the Monge-Amp\`{e}re equation for $(n-1)$-quaternionic psh functions

The Monge-Amp\`{e}re equation for (n−1)(n-1)-quaternionic PSH functions on a hyperK\"{a}hler manifold

We prove the existence of unique smooth solutions to the quaternionic Monge-Amp\`{e}re equation for $(n-1)$-quaternionic plurisubharmonic functions on a hyperK\"{a}hler manifold and thus obtain solutions for the quaternionic form type equation. We derive $C^0$ estimate by establishing a Cherrier-type inequality as in Tosatti and Weinkove [22]. By adopting the approach of Dinew and Sroka [9] to our context, we obtain $C^1$ and $C^2$ estimates without assuming the flatness of underlying hyperK\"{a}hler metric comparing to previous results [14].Comment: 31 page

Judging Online Peer-To-Peer Lending Behavior: An Integration of Dual System Framework and Two-Factor Theory

The past decade has witnessed a growing number of business models that facilitate economic exchanges between individuals with limited institutional mediation. One of the important innovative business models is online peer-to-peer (P2P) lending, which has received widely attention from government, industry, investors, and researchers. Based on dual system framework and two-factor theory, this research proposes a research model to investigate the role of various signals from the P2P platform in affecting lender’s investment decisions. With data collected from PPDAI, a popular Chinese P2P lending site, we test the proposed model with logistic regression and hierarchical linear model. The results reveal that most of the factors perform significantly in lenders’ decision making. We also find the specific information of an auction itself is more important than borrower’s characteristics to a large degree. Finally, the research emphasizes that bid number performs well in moderating most of the relationships between variables

Fitness-driven deactivation in network evolution

Individual nodes in evolving real-world networks typically experience growth and decay --- that is, the popularity and influence of individuals peaks and then fades. In this paper, we study this phenomenon via an intrinsic nodal fitness function and an intuitive aging mechanism. Each node of the network is endowed with a fitness which represents its activity. All the nodes have two discrete stages: active and inactive. The evolution of the network combines the addition of new active nodes randomly connected to existing active ones and the deactivation of old active nodes with possibility inversely proportional to their fitnesses. We obtain a structured exponential network when the fitness distribution of the individuals is homogeneous and a structured scale-free network with heterogeneous fitness distributions. Furthermore, we recover two universal scaling laws of the clustering coefficient for both cases, $C(k) \sim k^{-1}$ and $C \sim n^{-1}$, where $k$ and $n$ refer to the node degree and the number of active individuals, respectively. These results offer a new simple description of the growth and aging of networks where intrinsic features of individual nodes drive their popularity, and hence degree.Comment: IoP Styl