🔸 Here you can explore the dynamics of a famous two-dimensional, time discrete map, known as the standard or Chirikov–Taylor map.
http://rocs.hu-berlin.de/D3/kr/
http://rocs.hu-berlin.de/D3/kr/
Laplacian growth, sandpiles, and scaling limits = deep, beautiful math by two masters, Lionel Levine and Yuval Peres 👇👇👇👇
Complex Systems Studies
S0273-0979-2017-01573-X.pdf
Laplacian growth, sandpiles, and scaling limits = deep, beautiful math by two masters, Lionel Levine and Yuval Peres
🗞 New Models and Methods for Formation and Analysis of Social Networks
Swapnil Dhamal
🔗 https://arxiv.org/pdf/1706.09310
📌 ABSTRACT
This doctoral work focuses on three main problems related to social networks: (1) Orchestrating Network Formation: We consider the problem of orchestrating formation of a social network having a certain given topology that may be desirable for the intended usecases. Assuming the social network nodes to be strategic in forming relationships, we derive conditions under which a given topology can be uniquely obtained. We also study the efficiency and robustness of the derived conditions. (2) Multi-phase Influence Maximization: We propose that information diffusion be carried out in multiple phases rather than in a single instalment. With the objective of achieving better diffusion, we discover optimal ways of splitting the available budget among the phases, determining the time delay between consecutive phases, and also finding the individuals to be targeted for initiating the diffusion process. (3) Scalable Preference Aggregation: It is extremely useful to determine a small number of representatives of a social network such that the individual preferences of these nodes, when aggregated, reflect the aggregate preference of the entire network. Using real-world data collected from Facebook with human subjects, we discover a model that faithfully captures the spread of preferences in a social network. We hence propose fast and reliable ways of computing a truly representative aggregate preference of the entire network. In particular, we develop models and methods for solving the above problems, which primarily deal with formation and analysis of social networks.
Swapnil Dhamal
🔗 https://arxiv.org/pdf/1706.09310
📌 ABSTRACT
This doctoral work focuses on three main problems related to social networks: (1) Orchestrating Network Formation: We consider the problem of orchestrating formation of a social network having a certain given topology that may be desirable for the intended usecases. Assuming the social network nodes to be strategic in forming relationships, we derive conditions under which a given topology can be uniquely obtained. We also study the efficiency and robustness of the derived conditions. (2) Multi-phase Influence Maximization: We propose that information diffusion be carried out in multiple phases rather than in a single instalment. With the objective of achieving better diffusion, we discover optimal ways of splitting the available budget among the phases, determining the time delay between consecutive phases, and also finding the individuals to be targeted for initiating the diffusion process. (3) Scalable Preference Aggregation: It is extremely useful to determine a small number of representatives of a social network such that the individual preferences of these nodes, when aggregated, reflect the aggregate preference of the entire network. Using real-world data collected from Facebook with human subjects, we discover a model that faithfully captures the spread of preferences in a social network. We hence propose fast and reliable ways of computing a truly representative aggregate preference of the entire network. In particular, we develop models and methods for solving the above problems, which primarily deal with formation and analysis of social networks.
🔹 Reka Albert gave a wonderful talk at CEU about boolean models in gene regulatory networks. Watch it here :
🎞 http://www.aparat.com/v/YLItE
🎞 http://www.aparat.com/v/YLItE
آپارات
Reka Albert - Network Structure and Logic Determines the Dynamic Repertoire of B
Reka Albert’s group at Penn State is collaborating with wet-bench biologists to develop and validate predictive models of various biological systems, from the molecular to the ecological level. They recently developed an efficient method to determine the…
Forwarded from Deleted Account [SCAM]
Media is too big
VIEW IN TELEGRAM
Network Mathematics and Rival Factions | Infinite Series
🗞 Hamiltonian analysis of subcritical stochastic epidemic dynamics
Lee Worden, Ira B. Schwartz, Simone Bianco, Sarah F. Ackley, Thomas M. Lietman, Travis C. Porco
🔗 https://arxiv.org/pdf/1707.00021
📌 ABSTRACT
We extend a technique of approximation of the long-term behavior of a supercritical stochastic epidemic model, using the WKB approximation and a Hamiltonian phase space, to the subcritical case. The limiting behavior of the model and approximation are qualitatively different in the subcritical case, requiring a novel analysis of the limiting behavior of the Hamiltonian system away from its deterministic subsystem. This yields a novel, general technique of approximation of the quasistationary distribution of stochastic epidemic and birth-death models, and may lead to techniques for analysis of these models beyond the quasistationary distribution. For a classic SIS model, the approximation found for the quasistationary distribution is very similar to published approximations but not identical. For a birth-death process without depletion of susceptibles, the approximation is exact. Dynamics on the phase plane similar to those predicted by the Hamiltonian analysis are demonstrated in cross-sectional data from trachoma treatment trials in Ethiopia, in which declining prevalences are consistent with subcritical epidemic dynamics.
Lee Worden, Ira B. Schwartz, Simone Bianco, Sarah F. Ackley, Thomas M. Lietman, Travis C. Porco
🔗 https://arxiv.org/pdf/1707.00021
📌 ABSTRACT
We extend a technique of approximation of the long-term behavior of a supercritical stochastic epidemic model, using the WKB approximation and a Hamiltonian phase space, to the subcritical case. The limiting behavior of the model and approximation are qualitatively different in the subcritical case, requiring a novel analysis of the limiting behavior of the Hamiltonian system away from its deterministic subsystem. This yields a novel, general technique of approximation of the quasistationary distribution of stochastic epidemic and birth-death models, and may lead to techniques for analysis of these models beyond the quasistationary distribution. For a classic SIS model, the approximation found for the quasistationary distribution is very similar to published approximations but not identical. For a birth-death process without depletion of susceptibles, the approximation is exact. Dynamics on the phase plane similar to those predicted by the Hamiltonian analysis are demonstrated in cross-sectional data from trachoma treatment trials in Ethiopia, in which declining prevalences are consistent with subcritical epidemic dynamics.
💎 Topological analysis of data: success and challenges of a new branch of data science
https://www.isi.it/en/news-events/topological-analysis-of-data-success-and-challenges-of-a-new-branch-of-data-science
https://www.isi.it/en/news-events/topological-analysis-of-data-success-and-challenges-of-a-new-branch-of-data-science
🗞 The Fall of the Empire: The Americanization of English
Bruno Gonçalves, Lucía Loureiro-Porto, José J. Ramasco, David Sánchez
🔗 https://arxiv.org/pdf/1707.00781
📌 ABSTRACT
As global political preeminence gradually shifted from the United Kingdom to the United States, so did the capacity to culturally influence the rest of the world. In this work, we analyze how the world-wide varieties of written English are evolving. We study both the spatial and temporal variations of vocabulary and spelling of English using a large corpus of geolocated tweets and the Google Books datasets corresponding to books published in the US and the UK. The advantage of our approach is that we can address both standard written language (Google Books) and the more colloquial forms of microblogging messages (Twitter). We find that American English is the dominant form of English outside the UK and that its influence is felt even within the UK borders. Finally, we analyze how this trend has evolved over time and the impact that some cultural events have had in shaping it.
Bruno Gonçalves, Lucía Loureiro-Porto, José J. Ramasco, David Sánchez
🔗 https://arxiv.org/pdf/1707.00781
📌 ABSTRACT
As global political preeminence gradually shifted from the United Kingdom to the United States, so did the capacity to culturally influence the rest of the world. In this work, we analyze how the world-wide varieties of written English are evolving. We study both the spatial and temporal variations of vocabulary and spelling of English using a large corpus of geolocated tweets and the Google Books datasets corresponding to books published in the US and the UK. The advantage of our approach is that we can address both standard written language (Google Books) and the more colloquial forms of microblogging messages (Twitter). We find that American English is the dominant form of English outside the UK and that its influence is felt even within the UK borders. Finally, we analyze how this trend has evolved over time and the impact that some cultural events have had in shaping it.