Predicting cascade size distribution on onedimensional geographic networks
dc.rights.license  CC BYNCND. Users may download and share copies with attribution in accordance with a Creative Commons AttributionNoncommercialNo Derivative Works 3.0 License. No commercial use or derivatives are permitted without the explicit approval of the author.  
dc.contributor  Kramer, Peter Roland, 1971  
dc.contributor  Holmes, Mark H.  
dc.contributor  Lai, W. Michael, 1930  
dc.contributor  Korniss, Gyorgy  
dc.contributor.author  Treitman, Yosef  
dc.date.accessioned  20211103T09:03:50Z  
dc.date.available  20211103T09:03:50Z  
dc.date.created  20181024T13:31:37Z  
dc.date.issued  201808  
dc.identifier.uri  https://hdl.handle.net/20.500.13015/2254  
dc.description  August 2018  
dc.description  School of Science  
dc.description.abstract  We make rather specific assumptions about the distribution of agents across the geographic map and the likelihood of any pair of them being adjacent. We assume that the agents are nearly evenly spaced across the network. More precisely, we assume that if a network of width $w$ were divided into $N$ equal intervals of width W/N each interval would contain exactly one agent. The location of each agent within its interval follows a uniform distribution. We assume that each agent can only be adjacent to other agents within some radius of influence r of itself with r << w. As the cascade propagates across the spatial network, it may spontaneously terminate. This property is not found in locally treelike networks. This work examines the likelihood of such a termination and accounts for that possibility when estimating the CDF of the final cascade size distribution.  
dc.description.abstract  The approximation we develop is reasonably accurate for several response threshold distributions. Previous work already showed that, under these assumptions, the cascade will propagate at a constant overall speed. Our approach gets an estimate for that speed and the likelihood of spontaneous termination.  
dc.description.abstract  To address the main challenge of the possibility of a finitetime extinction, we find the mean number of new activations per unit time and the likelihood of a spontaneous termination. These statistics can be estimated by viewing the number of new activations per unit time as a Markov chain. Given the number of activations at some time tau  1, we can estimate the number of spikes sent to inactive agents. Given that number, we can estimate the number of activations at time tau. We assume that the number of new activations follows a Poisson distribution, and use our estimate as the mean. This gives us an approximate onestep probability transition matrix of the number of new activations from time tau  1 to time tau. Using this matrix, we find the mean number of new activations and the extinction probability.  
dc.description.abstract  Over the past few decades, there has been considerable research on the spread of various phenomena across networks. While the most general case of the cascade problem on an arbitrary network is too broad a question to address, the question has been studied under specific simplifying assumptions, both on the construction of the network and on the rules for the spread and adoption of the cascading phenomenon. In paricular, we are interested in studying cascades under the widelyused CentolaMacy threshold model on a class of spatial networks. The spatial aspects of these networks present challenges not found in other networks.  
dc.language.iso  ENG  
dc.publisher  Rensselaer Polytechnic Institute, Troy, NY  
dc.relation.ispartof  Rensselaer Theses and Dissertations Online Collection  
dc.rights  AttributionNonCommercialNoDerivs 3.0 United States  * 
dc.rights.uri  http://creativecommons.org/licenses/byncnd/3.0/us/  * 
dc.subject  Applied mathematics  
dc.title  Predicting cascade size distribution on onedimensional geographic networks  
dc.type  Electronic thesis  
dc.type  Thesis  
dc.digitool.pid  179204  
dc.digitool.pid  179205  
dc.digitool.pid  179206  
dc.rights.holder  This electronic version is a licensed copy owned by Rensselaer Polytechnic Institute, Troy, NY. Copyright of original work retained by author.  
dc.description.degree  PhD  
dc.relation.department  Dept. of Mathematical Sciences 
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Except where otherwise noted, this item's license is described as CC BYNCND. Users may download and share copies with attribution in accordance with a Creative Commons AttributionNoncommercialNo Derivative Works 3.0 License. No commercial use or derivatives are permitted without the explicit approval of the author.