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Honolulu, HI, USA."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/978-3-642-53734-9_6","article-title":"Quantifying synergistic mutual information","volume":"9","author":"Griffith","year":"2014","journal-title":"Guided Self-Organization: Inception"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"012130","DOI":"10.1103\/PhysRevE.87.012130","article-title":"Bivariate measure of redundant information","volume":"87","author":"Harder","year":"2013","journal-title":"Phys. Rev. E"},{"key":"ref_11","unstructured":"Bertschinger, N., Rauh, J., Olbrich, E., and Jost, J. (2013). Proceedings of European Conference on Complex Systems 2012, Switzerland."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1985","DOI":"10.3390\/e16041985","article-title":"Intersection Information based on Common Randomness","volume":"16","author":"Griffith","year":"2014","journal-title":"Entropy"},{"key":"ref_13","unstructured":"Williams, P.L., and Beer, R.D. (2010). Nonnegative Decomposition of Multivariate Information, arXiv: 1004-2515."},{"key":"ref_14","unstructured":"Weisstein, E.W. Available online: http:\/\/mathworld.wolfram.com\/Antichain.html."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2161","DOI":"10.3390\/e16042161","article-title":"Quantifying unique information","volume":"16","author":"Bertschinger","year":"2014","journal-title":"Entropy"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"238701","DOI":"10.1103\/PhysRevLett.91.238701","article-title":"Network Information and Connected Correlations","volume":"91","author":"Schneidman","year":"2003","journal-title":"Phys. Rev. Lett."},{"key":"ref_17","unstructured":"Wolf, S., and Wullschleger, J. (2004, January 24\u201329). Zero-error information and applications in cryptography. San Antonio, TX, USA."},{"key":"ref_18","unstructured":"Rauh, J., Bertschinger, N., Olbrich, E., and Jost, J. (July, January 29). 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