Identifying Critical Transitions By Applying The PageRank Algorithm To The Theory Of Dynamical Network Biomarker

During a process of critical transition in a complex system,predicting the critical point according to the accumulating data is a great concern for us.And the critical point theory has been developed to address this problem.Further,the theory of dynamical network biomarker has been put up as an adaptation of the critical point theory to the data produced by the technology of high throughput gene expression profiling.It models the system into a network at each measuring point respectively,and predicts the critical point by identifying the leading subnetwork associated with the critical transition process.And such a leading subnetwork is referred as the dynamical network biomarker.The theory of dynamical network biomarker has a great potential in predicting the disease progression and in investigating the disease mechanism,etc.The enormous information contained in the high throughput gene expression data drives us to think in the way of information retrieval.And in dealing with such a problem of information retrieval,the search engines based on the Page Rank algorithm are among the most successful cases.So,in this paper,we adapt the Page Rank algorithm in the field of Internet to the theory of dynamical network biomarker in the field of bioinformatics,and by that we compose an algorithm to identify the critical point.To validate our algorithm,we find a way to randomly create high dimensional simulation datasets of critical transitions,which are more convincing than the simulation datasets of less than 20 dimensions in earlier works.And we also apply our algorithm to the datasets analyzed in earlier works and it leads to the compatible results.So far,there is a weakness in the reported algorithms based on the theory of dynamical network biomarker.The algorithms do not cover the entire scale of high throughput gene expression datasets even though the theory aims to do so.A radical filter based on differential expression has to be introduced before actually modeling the datasets into networks,and usually less than 10% of the observables pass the filter.As the theory of dynamical network biomarker does not involve differential expression,the radical filtering process signifies an inconsistency between the theory and the algorithms based on it.Our algorithm relaxes the filter and thus relieves the weakness.