Network reconstructions with partially available data

Many practical systems in natural and social sciences can be described by dynamical networks. Day by day we have measured and accumulated huge amounts of data from these networks, which can be used by us to further our understanding of the world. The structures of the networks producing these data are often unknown. Consequently, understanding the structures of these networks from available data turns to be one of the central issues in interdisciplinary fields, which is called the network recon- struction problem. In this paper, we considered problems of network reconstructions using partially available data and some situations where data availabilities are not sufficient for conventional network reconstructions. Furthermore, we proposed to infer subnetwork with data of the subnetwork available only and other nodes of the entire network hidden; to depict group-group interactions in networks with averages of groups of node variables available; and to perform network reconstructions with known data of node variables only when networks are driven by both unknown internal fast-varying noises and unknown external slowly-varying signals. All these situations are expected to be common in practical systems and the methods and results may be useful for real world applications.

Inferring interactions of time-delayed dynamic networks by random state variable resetting

Time delays exist widely in real systems, and time-delayed interactions can result in abundant dynamic behaviors and functions in dynamic networks. Inferring the time delays and interactions is challenging due to systematic nonlinearity,noises, a lack of information, and so on. Recently, Shi et al. proposed a random state variable resetting method to detect the interactions in a continuous-time dynamic network. By arbitrarily resetting the state variable of a driving node, the equivalent coupling functions of the driving node to any response node in the network can be reconstructed. In this paper,we introduce this method in time-delayed dynamic networks. To infer actual time delays, the nearest neighbor correlation(NNC) function for a given time delay is defined. The significant increments of NNC originate from the delayed effect.Based on the increments, the time delays can be reconstructed and the reconstruction errors depend on the sampling time interval. After time delays are accurately identified, the equivalent coupling functions can also be reconstructed. The numerical results have fully verified the validity of the theoretical analysis.

Inference of interactions between players based on asynchronously updated evolutionary game data

The interactions between players of the prisoner's dilemma game are inferred using observed game data.All participants play the game with their counterparts and gain corresponding rewards during each round of the game.The strategies of each player are updated asynchronously during the game.Two inference methods of the interactions between players are derived with naive mean-field(n MF)approximation and maximum log-likelihood estimation(MLE),respectively.Two methods are tested numerically also for fully connected asymmetric Sherrington-Kirkpatrick models,varying the data length,asymmetric degree,payoff,and system noise(coupling strength).We find that the mean square error of reconstruction for the MLE method is inversely proportional to the data length and typically half(benefit from the extra information of update times)of that by n MF.Both methods are robust to the asymmetric degree but work better for large payoffs.Compared with MLE,n MF is more sensitive to the strength of couplings and prefers weak couplings.

Reconstruction of noise-driven nonlinear dynamic networks with some hidden nodes

The problem of network reconstruction, particularly exploring unknown network structures by analyzing measurable output data from networks, has attracted significant interest in many interdisciplinary fields in recent times. In practice, networks may be very large, and data can often be measured for only some of the nodes in a network while data for other variables are hidden.It is thus crucial to be able to infer networks from partial data. In this article, we study the problem of noise-driven nonlinear networks with some hidden nodes. Various difficulties appear jointly: nonlinearity of network dynamics, the impact of strong noise, the complexity of interaction structures between network nodes, and missing data from certain hidden nodes. We propose using high-order correlation to treat nonlinearity and structural complexity, two-time correlation to decorrelate noise, and higherorder derivatives to overcome the difficulties of hidden nodes. A closed form of network reconstruction is derived, and numerical simulations confirm the theoretical predictions.

Accelerated Aging Behaviors and Mechanism of Fluoroelastomer in Lubricating Oil Medium

The aging behaviors and mechanism of fluoroelastomer(FKM)under lubricating oil(FKM-O)and air(FKM-A,as a comparison)at elevated temperatures were studied from both physical and chemical viewpoints.The obvious changes of mechanical and swelling performances indicate that the coupling effect of lubricating oil and temperature causes more serious deterioration of FKM-O compared to that of FKM-A.Meanwhile,much stronger temperature dependence of both bulk properties and micro-structures for FKM-O is found.Three-stage physical diffusion process is defined in FKM-O due to the competition between oil diffusion and elastic retraction of network.FTIR results reveal that the dehydrofluorination reaction causes the fracture of C-F bonds and produces a large number of C=C bonds in the backbone.The coupling effect of oil medium and high temperature could accelerate the scission of C=C bonds and generate a series of fragments with different molecular sizes.The TGA results,crosslinking density Ve,and glass transition temperature Tg derived from different measurements coherently demonstrate the network destruction in the initial stage and the simultaneous reconstruction occurring at the final stage.The newly formed local network induced by reconstruction cannot compensate the break of the original rubber network and thus only provides lower tensile strength and thermal stability.