Connected chaos: how signals housed in network vertices trigger a fresh brand of permutation entropy
Title: Permutation Entropy for Graph SignalsAuthors & Year: Fabila-Carrasco, J.S., Tan, C. and Escudero, J. (2022)Journal: IEEE Transactions on Signal and Information Processing over Networks [DOI: 10.1109/TSIPN.2022.3167333]Review Prepared by Moinak Bhaduri. Associate Professor, Mathematical Sciences, Bentley University Imagine being a weather scientist, tasked with monitoring temperature fluctuations at recording stations at odd locations strewn across the country, raising alarms when something looks off. You may yawn at the blandness. Temperature, you would say, is something whose fluctuations are, by default, predictable (after all, they are not like stock prices): it generally gets warmer as the sun rises, and cooler as the sun sets. What else is there to observe? It is a nice, almost boring system that never alters. And the fact that this is true regardless of where you are – by the sea or atop a mountain – adds to the blandness. But before you resign and say…
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What’s the Chance a Random Problem Has a Solution?
Consider a graph, which is a set of vertices connected with edges. Your task is to assign two colors to the vertices of the graph, but under the constraint that if vertices share an edge, then they must be different colors. Can you solve this problem and satisfy the constraint? Now suppose that the edges of the graph are chosen randomly; for example, by flipping a coin for every two vertices to determine if there is an edge connecting them. What’s the chance that you can still find a coloring which satisfies the constraint?
Zeros of Random Polynomials and Their Higher Derivatives
Complex polynomials are one of the oldest and most fundamental objects of study in mathematics, and are ubiquitous in applications.