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Visualizing Frustration: Through the Spinning Glass.webm
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Visualizing Frustration: Through the Spinning Glass
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Visualizing Frustration: Through the Spinning Glass.webm
🔹 Visualizing Frustration:
Through the Spinning-Glass
Randy Andrews Mentor: Ruben Andrist
August 15, 2014
📄 http://samoa.santafe.edu/media/cms_page_media/583/randypaper.pdf
Through the Spinning-Glass
Randy Andrews Mentor: Ruben Andrist
August 15, 2014
📄 http://samoa.santafe.edu/media/cms_page_media/583/randypaper.pdf
🔖 An exact method for computing the frustration index in signed networks using binary programming
Samin Aref, Andrew J. Mason, Mark C. Wilson
🔗 https://arxiv.org/pdf/1611.09030
📌 ABSTRACT
Computing the frustration index of a signed graph is a key to solving problems in different fields of research including social networks, physics, material science, and biology. In social networks the frustration index determines network distance from a state of structural balance. Although the definition of frustration index goes back to 1960, an exact algorithmic computation method has not yet been proposed. The main reason seems to be the complexity of computing the frustration index which is closely related to well-known NP-hard problems such as MAXCUT.
New quadratic and linear binary programming models are developed to compute the frustration index exactly. We introduce several speed-up techniques involving prioritised branching, local search heuristics, and valid inequalities inferred from graph structural properties. The computational improvements achieved by implementing the speed-up techniques allow us to calculate the exact values of the frustration index by running the optimisation models in Gurobi solver.
The speed-up techniques make our models capable of processing graphs with thousands of nodes and edges in seconds on inexpensive hardware. The solve time and solution quality comparison against the literature shows the superiority of our models in both random and real signed networks.
Samin Aref, Andrew J. Mason, Mark C. Wilson
🔗 https://arxiv.org/pdf/1611.09030
📌 ABSTRACT
Computing the frustration index of a signed graph is a key to solving problems in different fields of research including social networks, physics, material science, and biology. In social networks the frustration index determines network distance from a state of structural balance. Although the definition of frustration index goes back to 1960, an exact algorithmic computation method has not yet been proposed. The main reason seems to be the complexity of computing the frustration index which is closely related to well-known NP-hard problems such as MAXCUT.
New quadratic and linear binary programming models are developed to compute the frustration index exactly. We introduce several speed-up techniques involving prioritised branching, local search heuristics, and valid inequalities inferred from graph structural properties. The computational improvements achieved by implementing the speed-up techniques allow us to calculate the exact values of the frustration index by running the optimisation models in Gurobi solver.
The speed-up techniques make our models capable of processing graphs with thousands of nodes and edges in seconds on inexpensive hardware. The solve time and solution quality comparison against the literature shows the superiority of our models in both random and real signed networks.
#Review_Article on #granular_matter & #networks
🔖 Network Analysis of Particles and Grains
Lia Papadopoulos, Mason A. Porter, Karen E. Daniels, Danielle S. Bassett
🔗 https://arxiv.org/pdf/1708.08080
📌 ABSTRACT
The arrangements of particles and forces in granular materials and particulate matter have a complex organization on multiple spatial scales that range from local structures to mesoscale and system-wide ones. This multiscale organization can affect how a material responds or reconfigures when exposed to external perturbations or loading. The theoretical study of particle-level, force-chain, domain, and bulk properties requires the development and application of appropriate mathematical, statistical, physical, and computational frameworks. Traditionally, granular materials have been investigated using particulate or continuum models, each of which tends to be implicitly agnostic to multiscale organization. Recently, tools from network science have emerged as powerful approaches for probing and characterizing heterogeneous architectures in complex systems, and a diverse set of methods have yielded fascinating insights into granular materials. In this paper, we review work on network-based approaches to studying granular materials (and particulate matter more generally) and explore the potential of such frameworks to provide a useful denoscription of these materials and to enhance understanding of the underlying physics. We also outline a few open questions and highlight particularly promising future directions in the analysis and design of granular materials and other particulate matter.
🔖 Network Analysis of Particles and Grains
Lia Papadopoulos, Mason A. Porter, Karen E. Daniels, Danielle S. Bassett
🔗 https://arxiv.org/pdf/1708.08080
📌 ABSTRACT
The arrangements of particles and forces in granular materials and particulate matter have a complex organization on multiple spatial scales that range from local structures to mesoscale and system-wide ones. This multiscale organization can affect how a material responds or reconfigures when exposed to external perturbations or loading. The theoretical study of particle-level, force-chain, domain, and bulk properties requires the development and application of appropriate mathematical, statistical, physical, and computational frameworks. Traditionally, granular materials have been investigated using particulate or continuum models, each of which tends to be implicitly agnostic to multiscale organization. Recently, tools from network science have emerged as powerful approaches for probing and characterizing heterogeneous architectures in complex systems, and a diverse set of methods have yielded fascinating insights into granular materials. In this paper, we review work on network-based approaches to studying granular materials (and particulate matter more generally) and explore the potential of such frameworks to provide a useful denoscription of these materials and to enhance understanding of the underlying physics. We also outline a few open questions and highlight particularly promising future directions in the analysis and design of granular materials and other particulate matter.
#Review_Article on #granular_matter & #networks
🔖 Network Analysis of Particles and Grains
🔗 https://arxiv.org/pdf/1708.08080
🔖 Network Analysis of Particles and Grains
🔗 https://arxiv.org/pdf/1708.08080
Dynamical Systems and Chaos AND Nonlinear Dynamics MOOCs are open for enrollment! Check them out at:
https://www.complexityexplorer.org/courses
https://www.complexityexplorer.org/courses
🔖 Statistical physics of balance theory
Andres M. Belaza, Kevin Hoefman, Jan Ryckebusch,Aaron Bramson, Milan van den Heuvel, Koen Schoors
🔗 http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0183696
📌 ABSTRACT
Triadic relationships are accepted to play a key role in the dynamics of social and political networks. Building on insights gleaned from balance theory in social network studies and from Boltzmann-Gibbs statistical physics, we propose a model to quantitatively capture the dynamics of the four types of triadic relationships in a network. Central to our model are the triads’ incidence rates and the idea that those can be modeled by assigning a specific triadic energy to each type of triadic relation. We emphasize the role of the degeneracy of the different triads and how it impacts the degree of frustration in the political network. In order to account for a persistent form of disorder in the formation of the triadic relationships, we introduce the systemic variable temperature. In order to learn about the dynamics and motives, we propose a generic Hamiltonian with three terms to model the triadic energies. One term is connected with a three-body interaction that captures balance theory. The other terms take into account the impact of heterogeneity and of negative edges in the triads. The validity of our model is tested on four datasets including the time series of triadic relationships for the standings between two classes of alliances in a massively multiplayer online game (MMOG). We also analyze real-world data for the relationships between the “agents” involved in the Syrian civil war, and in the relations between countries during the Cold War era. We find emerging properties in the triadic relationships in a political network, for example reflecting itself in a persistent hierarchy between the four triadic energies, and in the consistency of the extracted parameters from comparing the model Hamiltonian to the data.
Andres M. Belaza, Kevin Hoefman, Jan Ryckebusch,Aaron Bramson, Milan van den Heuvel, Koen Schoors
🔗 http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0183696
📌 ABSTRACT
Triadic relationships are accepted to play a key role in the dynamics of social and political networks. Building on insights gleaned from balance theory in social network studies and from Boltzmann-Gibbs statistical physics, we propose a model to quantitatively capture the dynamics of the four types of triadic relationships in a network. Central to our model are the triads’ incidence rates and the idea that those can be modeled by assigning a specific triadic energy to each type of triadic relation. We emphasize the role of the degeneracy of the different triads and how it impacts the degree of frustration in the political network. In order to account for a persistent form of disorder in the formation of the triadic relationships, we introduce the systemic variable temperature. In order to learn about the dynamics and motives, we propose a generic Hamiltonian with three terms to model the triadic energies. One term is connected with a three-body interaction that captures balance theory. The other terms take into account the impact of heterogeneity and of negative edges in the triads. The validity of our model is tested on four datasets including the time series of triadic relationships for the standings between two classes of alliances in a massively multiplayer online game (MMOG). We also analyze real-world data for the relationships between the “agents” involved in the Syrian civil war, and in the relations between countries during the Cold War era. We find emerging properties in the triadic relationships in a political network, for example reflecting itself in a persistent hierarchy between the four triadic energies, and in the consistency of the extracted parameters from comparing the model Hamiltonian to the data.
journals.plos.org
Statistical physics of balance theory
Triadic relationships are accepted to play a key role in the dynamics of social and political networks. Building on insights gleaned from balance theory in social network studies and from Boltzmann-Gibbs statistical physics, we propose a model to quantitatively…