Fabrication of superhydrophobic coating via a facile and versatile method based on nanoparticle aggregates

Herein, we report a facile and low cost method for the fabrication of superhydrophobic surface via spin coating the mixture of polydimethylsiloxane precursor (PDMS) and silicon dioxide (SiO₂) nanoparticles. The surface hydrophobicity can be well tuned by adjusting the weight percent of PDMS and SiO₂. The water contact angle (WCA) can increase from 106.8 ± 1.2° on PDMS film to 165.2 ± 2.3° on PDMS/SiO₂ coating, companying with a change from adhering to rolling which was observed from tilting angle (TA) characterization. Multi-scale physical structures with SiO₂ nanoparticle aggregates and networks of SiO₂ nanoparticle aggregates are characterized by scanning electron microscopy (SEM) and atomic force microscope (AFM), and they can be observed more clearly from the AFM images treated with software (WSxM). Then the relationship between surface hydrophobicity and structures is further discussed based on Wenzel and Cassie models, indicating that the appearance of networks of nanoparticle aggregates is important in the Cassie state. The superhydrophobic coating can keep the superhydrophobicity at least for one month under environment conditions and readily regenerate after mechanical damage. Additionally, the superhydrophobic coating can be fabricated using other methods including dip coating, spray coating and casting. Thus, a large area of superhydrophobic coatings can be easily fabricated. Therefore the range of possible applications for these facile and versatile methods can be expanded to various actual conditions.     

Spatially correlated heterogeneous aspirations to enhance network reciprocity

Perc & Wang demonstrated that aspiring to be the fittest under conditions of pairwise strategy updating enhances network reciprocity in structured populations playing 2×2 Prisoner’s Dilemma games (Z. Wang, M. Perc, Aspiring to the fittest and promoted of cooperation in the Prisoner’s Dilemma game, Physical Review E 82 (2010) 021115; M. Perc, Z. Wang, Heterogeneous aspiration promotes cooperation in the Prisoner’s Dilemma game, PLOS one 5 (12) (2010) e15117). Through numerical simulations, this paper shows that network reciprocity is even greater if heterogeneous aspirations are imposed. We also suggest why heterogeneous aspiration fosters network reciprocity. It distributes strategy updating speed among agents in a manner that fortifies the initially allocated cooperators’ clusters against invasion. This finding prompted us to further enhance the usual heterogeneous aspiration cases for heterogeneous network topologies. We find that a negative correlation between degree and aspiration level does extend cooperation among heterogeneously structured agents.     

A new measure of network efficiency

We address the issue of the dynamical origin of scale-free link distributions. We study a two-dimensional lattice of cooperatively interacting units. Although the units interact only with the four nearest neighbors, a sufficiently large cooperation strength generates dynamically a scale-free network with the power law index ν approaching 1. We explain this result by using a new definition of network efficiency determined by the Euclidean distance between correlated units. According to this definition the link distribution favoring long-range connections makes efficiency increase. We embed an ad hoc scale-free network with power index ν≥1 into a Euclidean two-dimensional space and show that the network efficiency becomes maximal as ν approaches 1. We therefore conclude that ν=1 emerging from the cooperative interaction of units may be a consequence of the principle of network maximal efficiency.     

Systemic risk on different interbank network topologies

In this paper we develop an interbank market with heterogeneous financial institutions that enter into lending agreements on different network structures. Credit relationships (links) evolve endogenously via a fitness mechanism based on agents’ performance. By changing the agent’s trust on its neighbor’s performance, interbank linkages self-organize themselves into very different network architectures, ranging from random to scale-free topologies. We study which network architecture can make the financial system more resilient to random attacks and how systemic risk spreads over the network. To perturb the system, we generate a random attack via a liquidity shock. The hit bank is not automatically eliminated, but its failure is endogenously driven by its incapacity to raise liquidity in the interbank network. Our analysis shows that a random financial network can be more resilient than a scale free one in case of agents’ heterogeneity.     

Designing a referral reward program in freemium: The role of network externalities

We develop a model to explore firms’ decisions on designing referral reward programs in freemium. We find two indices that firms could compare against value discrepancy to choose their strategy. The optimal price and referral reward rate are obtained. We find that the absence of network externality relating to product quality makes referral dysfunctional, and we conduct sensitivity analysis. This study contributes to theories that incorporate a referral reward program into the freemium model and provides practitioners with viable takeaways.     

A min-max theorem for plane bipartite graphs

We consider a partitioning problem, defined for bipartite and 2-connected plane graphs, where each node should be covered exactly once by either an edge or by a cycle surrounding a face. The objective is to maximize the number of face boundaries in the partition. This problem arises in mathematical chemistry in the computation of the Clar number of hexagonal systems. In this paper we establish that a certain minimum weight covering problem of faces by cuts is a strong dual of the partitioning problem. Our proof relies on network flow and linear programming duality arguments, and settles a conjecture formulated by Hansen and Zheng in the context of hexagonal systems [P. Hansen, M. Zheng, Upper Bounds for the Clar Number of Benzenoid Hydrocarbons, Journal of the Chemical Society, Faraday Transactions 88 (1992) 1621-1625].     

Network flow interdiction on planar graphs

The network flow interdiction problem asks to reduce the value of a maximum flow in a given network as much as possible by removing arcs and vertices of the network constrained to a fixed budget. Although the network flow interdiction problem is strongly NP-complete on general networks, pseudo-polynomial algorithms were found for planar networks with a single source and a single sink and without the possibility to remove vertices. In this work, we introduce pseudo-polynomial algorithms that overcome various restrictions of previous methods. In particular, we propose a planarity-preserving transformation that enables incorporation of vertex removals and vertex capacities in pseudo-polynomial interdiction algorithms for planar graphs. Additionally, a new approach is introduced that allows us to determine in pseudo-polynomial time the minimum interdiction budget needed to remove arcs and vertices of a given network such that the demands of the sink node cannot be completely satisfied anymore. The algorithm works on planar networks with multiple sources and sinks satisfying that the sum of the supplies at the sources equals the sum of the demands at the sinks. A simple extension of the proposed method allows us to broaden its applicability to solve network flow interdiction problems on planar networks with a single source and sink having no restrictions on the demand and supply. The proposed method can therefore solve a wider class of flow interdiction problems in pseudo-polynomial time than previous pseudo-polynomial algorithms and is the first pseudo-polynomial algorithm that can solve non-trivial planar flow interdiction problems with multiple sources and sinks. Furthermore, we show that the k-densest subgraph problem on planar graphs can be reduced to a network flow interdiction problem on a planar graph with multiple sources and sinks and polynomially bounded input numbers.     

Minimizing maximum risk for fair network connection with interval data

In this paper we introduce a minimax model for network connection problems with interval parameters. We consider how to connect given nodes in a network with a path or a spanning tree under a given budget, where each link is associated with an interval and can be established at a cost of any value in the interval. The quality of an individual link （or the risk of link failure, etc.） depends on its construction cost and associated interval. To achieve fairness of the network connection, our model aims at the minimization of the maximum risk over all links used. We propose two algorithms that find optimal paths and spanning trees in polynomial time, respectively. The polynomial solvability indicates salient difference between our minimax model and the model of robust deviation criterion for network connection with interval data, which gives rise to NP-hard optimization problems.