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We demonstrate that in contrast to the lack of monotonicity in physical domain, there is a rich collection of monotonicity one can explore in the spectral domain, leading to a systematic way to define topological metrics that are monotonic. It is further shown that many useful quantities in cascading failure analysis can be unified into a spectral inner product, which itself is related to graphical properties of the transmission network. Such graphical interpretations precisely capture the Kirchhoff's law expressed in terms of graph structural properties and gauge the impact of a line when it is tripped.<\/jats:p>","DOI":"10.1145\/3152042.3152074","type":"journal-article","created":{"date-parts":[[2017,10,12]],"date-time":"2017-10-12T12:52:50Z","timestamp":1507812770000},"page":"103-106","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":6,"title":["Monotonicity Properties and Spectral Characterization of Power Redistribution in Cascading Failures"],"prefix":"10.1145","volume":"45","author":[{"given":"Linqi","family":"Guo","sequence":"first","affiliation":[{"name":"California Institute of Technology, Pasadena, CA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chen","family":"Liang","sequence":"additional","affiliation":[{"name":"California Institute of Technology, Pasadena, CA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Steven H.","family":"Low","sequence":"additional","affiliation":[{"name":"California Institute of Technology, Pasadena, CA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2017,10,11]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"report on the august 14","year":"2003","unstructured":"U.S.-canada power system outage task force. report on the august 14 , 2003 blackout in the united states and canada: Causes and recommendation. 2004. 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In 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton), pages 1037--1044, Oct 2013."},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/2465529.2465752"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.66.065102"},{"key":"e_1_2_1_16_1","article-title":"Analysis of failures in power grids","author":"Soltan S.","year":"2015","unstructured":"S. Soltan , D. Mazauric , and G. Zussman . Analysis of failures in power grids . IEEE Transactions on Control of Network Systems, PP(99):1--1 , 2015 . S. Soltan, D. Mazauric, and G. Zussman. Analysis of failures in power grids. IEEE Transactions on Control of Network Systems, PP(99):1--1, 2015.","journal-title":"IEEE Transactions on Control of Network Systems, PP(99):1--1"},{"key":"e_1_2_1_17_1","volume-title":"Power Generation, Operation, and Control","author":"Wood A.","year":"1996","unstructured":"A. Wood and B. Wollenberg . 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