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The bridges of Königsberg
Watch a short video introducing the Könisberg problem and Euler’s solution - BARABASI
Watch a short video introducing the Könisberg problem and Euler’s solution - BARABASI
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Zooming into the World Wide Web Watch an online video that zooms into the WWW sample that has lead to the discovery of the scale-free property - BARABASI
🔖 Cascading Failures as Continuous Phase-Space Transitions
Yang Yang, Adilson E. Motter
🔗 https://arxiv.org/pdf/1712.04053
📌 ABSTRACT
In network systems, a local perturbation can amplify as it propagates, potentially leading to a large-scale cascading failure. Here we derive a continuous model to advance our understanding of cascading failures in power-grid networks. The model accounts for both the failure of transmission lines and the desynchronization of power generators, and incorporates the transient dynamics between successive steps of the cascade. In this framework, we show that a cascade event is a phase-space transition from an equilibrium state with high energy to an equilibrium state with lower energy, which can be suitably described in closed form using a global Hamiltonian-like function. From this function we show that a perturbed system cannot always reach the equilibrium state predicted by quasi-steady-state cascade models, which would correspond to a reduced number of failures, and may instead undergo a larger cascade. We also show that in the presence of two or more perturbations, the outcome depends strongly on the order and timing of the individual perturbations. These results offer new insights into the current understanding of cascading dynamics, with potential implications for control interventions.
Yang Yang, Adilson E. Motter
🔗 https://arxiv.org/pdf/1712.04053
📌 ABSTRACT
In network systems, a local perturbation can amplify as it propagates, potentially leading to a large-scale cascading failure. Here we derive a continuous model to advance our understanding of cascading failures in power-grid networks. The model accounts for both the failure of transmission lines and the desynchronization of power generators, and incorporates the transient dynamics between successive steps of the cascade. In this framework, we show that a cascade event is a phase-space transition from an equilibrium state with high energy to an equilibrium state with lower energy, which can be suitably described in closed form using a global Hamiltonian-like function. From this function we show that a perturbed system cannot always reach the equilibrium state predicted by quasi-steady-state cascade models, which would correspond to a reduced number of failures, and may instead undergo a larger cascade. We also show that in the presence of two or more perturbations, the outcome depends strongly on the order and timing of the individual perturbations. These results offer new insights into the current understanding of cascading dynamics, with potential implications for control interventions.
🎩 "Sixty years of percolation"
Hugo Duminil-Copin
🔗 https://arxiv.org/abs/1712.04651
🎒 This is an introduction to percolation from a mathematical perspective, but for a broad audience of mathematicians.
Hugo Duminil-Copin
🔗 https://arxiv.org/abs/1712.04651
🎒 This is an introduction to percolation from a mathematical perspective, but for a broad audience of mathematicians.
🎞 Here's a video of Timothy Gowers' talk, gave in Tromso a few weeks ago about the state of academic publishing, and about why a system whose flaws are obvious to almost everybody is as robust as it is.
https://mediasite.uit.no/Mediasite/Play/db5614d2d8de4b528b62929b5209355d1d?PlayFrom=2400000&_utm_source=1-2-2
https://mediasite.uit.no/Mediasite/Play/db5614d2d8de4b528b62929b5209355d1d?PlayFrom=2400000&_utm_source=1-2-2
Forwarded from Deleted Account [SCAM]
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Why do animals form swarms? - Maria R. D'Orsogna
🔖 Different approaches to community detection
Martin Rosvall, Jean-Charles Delvenne, Michael T. Schaub, Renaud Lambiotte
🔗 arxiv.org/pdf/1712.06468.pdf
📌 ABSTRACT
A precise definition of what constitutes a community in networks has remained elusive. Consequently, network scientists have compared community detection algorithms on benchmark networks with a particular form of community structure and classified them based on the mathematical techniques they employ. However, this comparison can be misleading because apparent similarities in their mathematical machinery can disguise different reasons for why we would want to employ community detection in the first place. Here we provide a focused review of these different motivations that underpin community detection. This problem-driven classification is useful in applied network science, where it is important to select an appropriate algorithm for the given purpose. Moreover, highlighting the different approaches to community detection also delineates the many lines of research and points out open directions and avenues for future research.
Martin Rosvall, Jean-Charles Delvenne, Michael T. Schaub, Renaud Lambiotte
🔗 arxiv.org/pdf/1712.06468.pdf
📌 ABSTRACT
A precise definition of what constitutes a community in networks has remained elusive. Consequently, network scientists have compared community detection algorithms on benchmark networks with a particular form of community structure and classified them based on the mathematical techniques they employ. However, this comparison can be misleading because apparent similarities in their mathematical machinery can disguise different reasons for why we would want to employ community detection in the first place. Here we provide a focused review of these different motivations that underpin community detection. This problem-driven classification is useful in applied network science, where it is important to select an appropriate algorithm for the given purpose. Moreover, highlighting the different approaches to community detection also delineates the many lines of research and points out open directions and avenues for future research.
🎞 Stanford Complexity Symposium Videos Now Online
https://www.youtube.com/playlist?list=PL4K77C_Lzqan0Ysv_BtrTDJT8vAt2ezC7
https://www.youtube.com/playlist?list=PL4K77C_Lzqan0Ysv_BtrTDJT8vAt2ezC7
YouTube
Stanford Complexity Symposium - 11/14/2017 - YouTube