In network evolution, the effect of aging is universal: in scientific collaboration network, scientists have a finite time span of being active; in movie actors network, once popular stars are retiring from stage; devices on the Internet may become outmoded with techniques developing so rapidly. Here we find in citation networks that this effect can be represented by an exponential decay factor, e −βτ , where τ is the node age, while other evolving networks (the Internet for instance) may have different types of aging, for example, a power-law decay factor, which is also studied and compared. It has been found that as soon as such a factor is introduced to the Barabasi-Albert Scale-Free model, the network will be significantly transformed. The network will be clustered even with infinitely large size, and the clustering coefficient varies greatly with the intensity of the aging effect, i.e. it increases linearly with β for small values of β and decays exponentially for large values of β. At the same time, the aging effect may also result in a hierarchical structure and a disassortative degree-degree correlation. Generally the aging effect will increase the average distance between nodes, but the result depends on the type of the decay factor. The network appears like a one-dimensional chain when exponential decay is chosen, but with power-law decay, a transformation process is observed, i.e., from a small-world network to a hypercubic lattice, and to a one-dimensional chain finally. The disparities observed for different choices of the decay factor, in clustering, average node distance and probably other aspects not yet identified, are believed to bear significant meaning on empirical data acquisition.

No abstract

[1] Simulations of moisture flow in heterogeneous soils are often hampered by lack of measurements of soil hydraulic parameters, making it necessary to rely on other sources of information. In this paper, we develop a methodology to integrate data that can be easily obtained (for example, initial moisture content, q i , bulk density, and soil texture) with data on soil hydraulic properties via cokriging and Artificial Neural Network (ANN)-based pedotransfer functions. The method is applied to generate heterogeneous soil hydraulic parameters at a field injection site in southeastern Washington State. Stratigraphy at the site consists of imperfectly stratified layers with irregular layer boundaries. Cokriging is first used to generate three-dimensional heterogeneous fields of bulk density and soil texture using an extensive data set of field-measured q i , which carry signature about site heterogeneity and stratigraphy. Soil texture and bulk density are subsequently input into an ANN-based site-specific pedotransfer function to generate three-dimensional heterogeneous soil hydraulic parameter fields. The stratigraphy at the site is well represented by the estimated pedotransfer variables and soil hydraulic parameters. The parameter estimates are then used to simulate a field injection experiment at the site. A relatively good agreement is obtained between the simulated and observed moisture contents. The spatial distribution pattern of observed moisture content as well as the southeastward moisture movement is captured well in the simulations. In contrast to earlier work using an effective parameter approach , we are able to reproduce the observed splitting of the moisture plume in a coarse sand unit that is sandwiched between two fine-textured units. The simple method of combining cokriging and ANN for site characterization provides unbiased prediction of the observed moisture plume and is flexible so that additional measurements of various types can be included as they become available.Citation: Ye, M., R. Khaleel, M. G. Schaap, and J. Zhu (2007), Simulation of field injection experiments in heterogeneous unsaturated media using cokriging and artificial neural network, Water Resour. Res., 43, W07413,