Gradient estimates and blow-up analysis for stationary harmonic maps

For stationary harmonic maps between Riemannian manifolds, we provide a necessary and sufficient condition for the uniform interior and boundary gradient estimates in terms of the total energy of maps. We also show that if analytic target manifolds do not carry any harmonic S^2, then the singular sets of stationary maps are m \leq n - 4 rectifiable. Both of these results follow from a general analysis on the defect measures and energy concentration sets associated with a weakly converging sequence of stationary harmonic maps.Comment: 45 pages, published versio

Economic valuation of development projects : a case study of a non-motorized transport project in India

One of the major difficulties in doing cost-benefit analysis of a development project is to estimate the total economic value of project benefits, which are usually multi-dimensional andinclude goods and services that are not traded in the market. Challenges also arise in aggregating the values of different benefits, which may not be mutually exclusive. This paper uses a contingent valuation approach to estimate the economic value of a non-motorized transport project in Pune, India, across beneficiaries. The heads of households which are potentially affected by the project are presented with a detailed description of the project, and then are asked to vote on whether such a project should be undertaken given different specifications of costs to the households. The total value of the project is then derived from the survey answers. Econometric analysis indicates that the survey responses provide generally reasonable valuation estimates.Transport Economics Policy&Planning,Environmental Economics&Policies,Roads&Highways,Housing&Human Habitats,Economic Theory&Research

Covariance, correlation matrix and the multi-scale community structure of networks

Empirical studies show that real world networks often exhibit multiple scales of topological descriptions. However, it is still an open problem how to identify the intrinsic multiple scales of networks. In this article, we consider detecting the multi-scale community structure of network from the perspective of dimension reduction. According to this perspective, a covariance matrix of network is defined to uncover the multi-scale community structure through the translation and rotation transformations. It is proved that the covariance matrix is the unbiased version of the well-known modularity matrix. We then point out that the translation and rotation transformations fail to deal with the heterogeneous network, which is very common in nature and society. To address this problem, a correlation matrix is proposed through introducing the rescaling transformation into the covariance matrix. Extensive tests on real world and artificial networks demonstrate that the correlation matrix significantly outperforms the covariance matrix, identically the modularity matrix, as regards identifying the multi-scale community structure of network. This work provides a novel perspective to the identification of community structure and thus various dimension reduction methods might be used for the identification of community structure. Through introducing the correlation matrix, we further conclude that the rescaling transformation is crucial to identify the multi-scale community structure of network, as well as the translation and rotation transformations.Comment: 10 pages, 7 figure

Charge redistribution at the antiferromagnetic phase transition in SrFeAsF compound

The relationship between spin, electron, and crystal structure has been one of the foremost issues in understanding the superconducting mechanism since the discovery of iron-based high temperature superconductors. Here, we report M\"ossbauer and first-principles calculations studies of the parent compound SrFeAsF with the largest temperature gap ($\sim$50\,K) between the structural and antiferromagnetic (AFM) transitions. Our results reveal that the structural transition has little effect on the electronic structure of the compound SrFeAsF while the development of the AFM order induces a redistribution of the charges near the Fermi level.Comment: 6 Pages, 7 Figure