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Abstract Background To report on corneal endothelial regeneration, graft clarity, and vision recovery when using endothelium-free grafts. Methods We evaluated the donor’s cell viability using trypan blue staining and dual staining with calcein acetoxy methyl ester and ethidium homodimer-1. To preserve eyeball integrity, we performed therapeutic penetrating keratoplasty using cryopreserved donor tissue without endothelium on 195 consecutive patients who suffered from corneal perforation due to progressive primary corneal disease such as herpes simplex keratitis, fungal keratitis, ocular thermal burns, keratoconus, and phlyctenular keratoconjunctivitis. Of these, 18 eyes recovered corneal graft clarity and underwent periodic slit-lamp microscopy, A-scan pachymetry, and in vivo confocal microscopy to observe the clinical manifestations, variations in corneal thickness, and repopulation of the corneal endothelial cells on the donor grafts. Results No viable cells were detected in the cryopreserved corneas. After the therapeutic penetrating keratoplasty, notable corneal graft edema was observed in all 18 eyes for 1–4 months, and no corneal endothelial cells were detected on the grafts during this period. Thereafter, we observed gradual and progressive regression and final resolution of the stromal edema, with complete recovery of corneal graft clarity. Through periodic confocal microscopy, we observed the corneal endothelium’s regenerating process, along with single cells bearing multiple nuclei and cell division-like morphology. The regenerated endothelium on the grafts reached a mean cell density of 991 cells/mm2. Remarkable vision rehabilitation was achieved in all 18 patients. Conclusions We obtained conclusive evidence that host-derived endothelial cells can regenerate a new endothelium over the endothelium-free graft, which possesses normal functions for corneal clarity and vision recovery.

Abstract By defining a new measure to community structure, exclusive modularity, and based on cavity method of statistical physics, we develop a mathematically principled method to determine the completeness of community structure, which represents whether a partition that is either annotated by experts or given by a community-detection algorithm, carries complete information about community structure in the network. Our results demonstrate that the expert partition is surprisingly incomplete in some networks such as the famous political blogs network, indicating that the relation between meta-data and community structure in real-world networks needs to be re-examined. As a byproduct we find that the exclusive modularity, which introduces a null model based on the degree-corrected stochastic block model, is of independent interest. We discuss its applications as principled ways of detecting hidden structures, finding hierarchical structures without removing edges, and obtaining low-dimensional embedding of networks.

[This corrects the article DOI: 10.1371/journal.pone.0156756.].

BACKGROUND:Uncovering the mechanism behind the scaling laws and series of anomalies in human trajectories is of fundamental significance in understanding many spatio-temporal phenomena. Recently, several models, e.g. the explorations-returns model (Song et al., 2010) and the radiation model for intercity travels (Simini et al., 2012), have been proposed to study the origin of these anomalies and the prediction of human movements. However, an agent-based model that could reproduce most of empirical observations without priori is still lacking. METHODOLOGY/PRINCIPAL FINDINGS:In this paper, considering the empirical findings on the correlations of move-lengths and staying time in human trips, we propose a simple model which is mainly based on the cascading processes to capture the human mobility patterns. In this model, each long-range movement activates series of shorter movements that are organized by the law of localized explorations and preferential returns in prescribed region. CONCLUSIONS/SIGNIFICANCE:Based on the numerical simulations and analytical studies, we show more than five statistical characters that are well consistent with the empirical observations, including several types of scaling anomalies and the ultraslow diffusion properties, implying the cascading processes associated with the localized exploration and preferential returns are indeed a key in the understanding of human mobility activities. Moreover, the model shows both of the diverse individual mobility and aggregated scaling displacements, bridging the micro and macro patterns in human mobility. In summary, our model successfully explains most of empirical findings and provides deeper understandings on the emergence of human mobility patterns.

Recently, the dependence group has been proposed to study the robustness of networks with interdependent nodes. A dependence group means that a failed node in the group can lead to the failures of the whole group. Considering the situation of real networks that one failed node may not always break the functionality of a dependence group, we study a cascading failure model that a dependence group fails only when more than a fraction β of nodes of the group fail. We find that the network becomes more robust with the increasing of the parameter β. However, the type of percolation transition is always first order unless the model reduces to the classical network percolation model, which is independent of the degree distribution of the network. Furthermore, we find that a larger dependence group size does not always make the networks more fragile. We also present exact solutions to the size of the giant component and the critical point, which are in agreement with the simulations well.

Two-way selection is a common phenomenon in nature and society. It appears in the processes like choosing a mate between men and women, making contracts between job hunters and recruiters, and trading between buyers and sellers. In this paper, we propose a model of two-way selection system, and present its analytical solution for the expectation of successful matching total and the regular pattern that the matching rate trends toward an inverse proportion to either the ratio between the two sides or the ratio of the state total to the smaller group's people number. The proposed model is verified by empirical data of the matchmaking fairs. Results indicate that the model well predicts this typical real-world two-way selection behavior to the bounded error extent, thus it is helpful for understanding the dynamics mechanism of the real-world two-way selection system.

BACKGROUND: In recent years, several path-breaking findings on human mobility patterns point out a novel issue which is of important theoretical significance and great application prospects. The empirical analysis of the data which can reflect the real-world human mobility provides the basic cognition and verification of the theoretical models and predictive results on human mobility. One of the most noticeable findings in previous studies on human mobility is the wide-spread scaling anomalies, e.g. the power-law-like displacement distributions. Understanding the origin of these scaling anomalies is of central importance to this issue and therefore is the focus of our discussion. METHODOLOGY/PRINCIPAL FINDINGS: In this paper, we empirically analyze the real-world human movements which are based on GPS records, and observe rich scaling properties in the temporal-spatial patterns as well as an abnormal transition in the speed-displacement patterns together with an evidence to the real-world traffic jams. In addition, we notice that the displacements at the population level show a significant positive correlation, indicating a cascading-like nature in human movements. Furthermore, our analysis at the individual level finds that the displacement distributions of users with stronger correlations usually are closer to the power law, suggesting a correlation between the positive correlation of the displacement series and the form of an individual's displacement distribution. CONCLUSIONS/SIGNIFICANCE: These empirical findings make connections between the two basic properties of human mobility, the scaling anomalies on displacement distributions and the positive correlations on displacement series, implying the cascading-like dynamics which is exhibited by the positive correlations would cause the emergence of scaling properties on human mobility patterns. Our findings would inspire further researches on mechanisms and predictions of human mobility.

Recent experimental research has revealed that the cooperation in dynamic social networks, has significant scope for enhancement because individuals in a social system break the links with defective neighbours. To investigate how the length of defection tolerance affects the cooperation of prisoner’s dilemma game in dynamic ring networks, we study evolution of breaking and rewiring operations for social interaction as a response to the defection strategy. Defection tolerance is measured in terms of the time length that an individual tolerates a defector who continuously adopts the defective strategy. The results show that the dynamic nature of human social networks plays an essential role in promoting cooperation. Interestingly, there exists a critical value of the temptation to defect, below which the system is entirely dominated by cooperators, and a lower value of defection tolerance induces a larger threshold of temptation.

In a recent work Parshani et al (2011 Proc. Natl Acad. Sci. USA 108 1007), dependence links have been introduced to the percolation model and used to study the robustness of the networks with such links, which shows that the networks are more vulnerable than the classical networks with only connectivity links. This model usually demonstrates a first order transition, rather than the second order transition found in classical network percolation. In this paper, considering the real situation that the interdependent nodes are usually connected, we study the cascading dynamics of networks when dependence links partially overlap with connectivity links. We find that the percolation transitions are not always sharpened by making nodes interdependent. For a high fraction of overlapping, the network is robust for random failures, and the percolation transition is second order, while for a low fraction of overlapping, the percolation process shows a first order transition. This work demonstrates that the crossover between two types of transitions does not only depend on the density of dependence links but also on the overlapping fraction of connectivity and dependence links. Using generating function techniques, we present exact solutions for the size of the giant component and the critical point, which are in good agreement with the simulations.