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Scheduler for SANN Analysis of U.S. Supreme Court Network Based on Markov-Shannon Entropy
Aliuska Duardo-Sanchez
1  Department of Especial Public Law, Faculty of Law, University of Santiago de Compostela, 15782, Santiago de Compostela, Spain

10.3390/MOL2NET-1-e001
Abstract:

Many complex systems may be represented as complex networks of ith parts or nodes (ni) interconnected by some kind of bonds, ties, relationships, links (Lij). For instance, Fowler et al. represented all case citations (Lij) in the U.S. Supreme Court as a network of nj cases citing and/or cited by other. These huge collections of nodes/links are impossible to remember and rationalize by a single person in order to assign correct links in new situations. Fortunately, Artificial Neural Networks (ANNs) can help us in this task. If we want use ANNs to predict links in complex networks, first we need to transform all the information into numerical input parameters to feed ANNs, second: we need to find the best ANN to predict our network. We can solve the first problem quantifying the structural information of the complex system (Brain, Ecological, Social, etc.) with universal information measures known as Shannon entropy (Sh). We can quantify topological (connectivity) information of both the complex networks under study and a set of ANNs trained using Shannon measures. Then using both sets of information parameters as inputs we can develop a dual QSPR model to discriminate between SANNs and not efficient ANN topologies. Here we used this QSPR method to develop potential HPC schedulers for complex systems. We studied 663072 citations to majority opinions in 43 sub-networks; each one with 5,000 (5K) citations to U.S. Supreme Court decisions (5KCNs). The overall accuracy of the ANN found was of >85% for 5KCNs; in training and validation series.

Keywords: SANN Scheduler; Markov-Shannon Entropy; U.S. Supreme Court; Social Network Analysis.
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