Advanced Calculation and Analysis

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In this paper, we consider the problem of storage and search in peer-to-peer networks. It is well known that all storage systems try to meet two conflict goals, increasing the success rate within reasonable response time and decreasing the worst case message complexity. In this result, we focus on designing an e?cient algorithms for storage and search in unstructured peer-to-peer networks. In the storage, we present an algorithm for storage in which we try to maintain a reasonable number of copies of each file such that these copies can be reached in almost the same time from all nodes. In the search algorithm, we initiate a reasonable number of messages from the node that requests the file such that they cover random parts of the system. We evaluate our algorithm by applying it to random networks with various sizes.

Regression analysis is a powerful tool to describe the relationship between response and predictors. In practice, parametric regression models such as linear regression models are widely used due to their simplicity and interpretability. When a parametric regression model is correctly fitted by the data, further statistical analysis can be easily and accurately elaborated with good explanations. However, such further analysis and interpretation could be misleading when the model does not fit the data well.

The branching random walk on integer lattices is shown to be monotone decreasing in ascending direction (MDAD) as a corollary of an observation in regard to the lineage of particles from antisymmetric initial states, and a related property of percolation paths on the usual oriented lattices is also given.