🎯 "What are Lyapunov Exponents, and Why are they Interesting?" by Amie Wilkinson
💡 "Complex Systems Studies" is a graduate-level channel aiming to discuss all kinds of stuff related to the field of Complex Systems.
🗺 Our purpose is to be up-to-date, precise and international.
✔️ Introduce us to your friends and colleagues at all over the globe:
https://telegram.me/ComplexSys
🗺 Our purpose is to be up-to-date, precise and international.
✔️ Introduce us to your friends and colleagues at all over the globe:
https://telegram.me/ComplexSys
Telegram
Complex Systems Studies
What's up in Complexity Science?!
Check out here:
@ComplexSys
#complexity #complex_systems #networks #network_science
📨 Contact us: @carimi
Check out here:
@ComplexSys
#complexity #complex_systems #networks #network_science
📨 Contact us: @carimi
📄 Higher-order organization of complex networks
Austin R. Benson, David F. Gleich, Jure Leskovec
🔗 https://arxiv.org/pdf/1612.08447v1
📌 ABSTRACT
Networks are a fundamental tool for understanding and modeling complex systems in physics, biology, neuroscience, engineering, and social science. Many networks are known to exhibit rich, lower-order connectivity patterns that can be captured at the level of individual nodes and edges. However, higher-order organization of complex networks---at the level of small network subgraphs---remains largely unknown. Here we develop a generalized framework for clustering networks based on higher-order connectivity patterns. This framework provides mathematical guarantees on the optimality of obtained clusters and scales to networks with billions of edges. The framework reveals higher-order organization in a number of networks including information propagation units in neuronal networks and hub structure in transportation networks. Results show that networks exhibit rich higher-order organizational structures that are exposed by clustering based on higher-order connectivity patterns.
Austin R. Benson, David F. Gleich, Jure Leskovec
🔗 https://arxiv.org/pdf/1612.08447v1
📌 ABSTRACT
Networks are a fundamental tool for understanding and modeling complex systems in physics, biology, neuroscience, engineering, and social science. Many networks are known to exhibit rich, lower-order connectivity patterns that can be captured at the level of individual nodes and edges. However, higher-order organization of complex networks---at the level of small network subgraphs---remains largely unknown. Here we develop a generalized framework for clustering networks based on higher-order connectivity patterns. This framework provides mathematical guarantees on the optimality of obtained clusters and scales to networks with billions of edges. The framework reveals higher-order organization in a number of networks including information propagation units in neuronal networks and hub structure in transportation networks. Results show that networks exhibit rich higher-order organizational structures that are exposed by clustering based on higher-order connectivity patterns.
📄 Recent history of fractional calculus
http://www.sciencedirect.com/science/article/pii/S1007570410003205
📌Abstract
This survey intends to report some of the major documents and events in the area of fractional calculus that took place since 1974 up to the present date.
#Fractional_calculus
http://www.sciencedirect.com/science/article/pii/S1007570410003205
📌Abstract
This survey intends to report some of the major documents and events in the area of fractional calculus that took place since 1974 up to the present date.
#Fractional_calculus
Complex Systems Studies
📽 https://www.youtube.com/watch?v=_m8LhAV8M-M
Speaker:
Emanuela Merelli, University of Camerino
📌 ABSTRACT:
According to Frege’s principle of compositionality, the meaning of a complex expression is determined by the meanings of its constituent expressions and the rules used to combine them. This talk will try to show how this principle acquires new unexpected features in the context of complex systems – which are composed of many non-identical elements, entangled in loops of nonlinear interactions – due to the characteristic 'emergence' effects. Indeed, representing expression composition as a path algebra construct in data space (the space on which composition rules operate) and embedding the latter in a simplicial complex – geometric and at the same time combinatorial notion coming from algebraic topology – provides us with a mathematical structure that naturally allows for a finer classification of compositional rules in equivalence classes not identifiable otherwise.
🔗 https://simons.berkeley.edu/sites/default/files/docs/6000/talk-b-final.pdf
📽 https://video.simons.berkeley.edu/2016/logic/3/22-Merelli.mp4
Emanuela Merelli, University of Camerino
📌 ABSTRACT:
According to Frege’s principle of compositionality, the meaning of a complex expression is determined by the meanings of its constituent expressions and the rules used to combine them. This talk will try to show how this principle acquires new unexpected features in the context of complex systems – which are composed of many non-identical elements, entangled in loops of nonlinear interactions – due to the characteristic 'emergence' effects. Indeed, representing expression composition as a path algebra construct in data space (the space on which composition rules operate) and embedding the latter in a simplicial complex – geometric and at the same time combinatorial notion coming from algebraic topology – provides us with a mathematical structure that naturally allows for a finer classification of compositional rules in equivalence classes not identifiable otherwise.
🔗 https://simons.berkeley.edu/sites/default/files/docs/6000/talk-b-final.pdf
📽 https://video.simons.berkeley.edu/2016/logic/3/22-Merelli.mp4
📄 Motifs in Temporal Networks
Ashwin Paranjape, Austin R. Benson, Jure Leskovec
🔗 https://arxiv.org/pdf/1612.09259v1
📌 ABSTRACT
Networks are a fundamental tool for modeling complex systems in a variety of domains including social and communication networks as well as biology and neuroscience. Small subgraph patterns in networks, called network motifs, are crucial to understanding the structure and function of these systems. However, the role of network motifs in temporal networks, which contain many timestamped links between the nodes, is not yet well understood.
Here we develop a notion of a temporal network motif as an elementary unit of temporal networks and provide a general methodology for counting such motifs. We define temporal network motifs as induced subgraphs on sequences of temporal edges, design fast algorithms for counting temporal motifs, and prove their runtime complexity. Our fast algorithms achieve up to 56.5x speedup compared to a baseline method. Furthermore, we use our algorithms to count temporal motifs in a variety of networks. Results show that networks from different domains have significantly different motif counts, whereas networks from the same domain tend to have similar motif counts. We also find that different motifs occur at different time scales, which provides further insights into structure and function of temporal networks.
Ashwin Paranjape, Austin R. Benson, Jure Leskovec
🔗 https://arxiv.org/pdf/1612.09259v1
📌 ABSTRACT
Networks are a fundamental tool for modeling complex systems in a variety of domains including social and communication networks as well as biology and neuroscience. Small subgraph patterns in networks, called network motifs, are crucial to understanding the structure and function of these systems. However, the role of network motifs in temporal networks, which contain many timestamped links between the nodes, is not yet well understood.
Here we develop a notion of a temporal network motif as an elementary unit of temporal networks and provide a general methodology for counting such motifs. We define temporal network motifs as induced subgraphs on sequences of temporal edges, design fast algorithms for counting temporal motifs, and prove their runtime complexity. Our fast algorithms achieve up to 56.5x speedup compared to a baseline method. Furthermore, we use our algorithms to count temporal motifs in a variety of networks. Results show that networks from different domains have significantly different motif counts, whereas networks from the same domain tend to have similar motif counts. We also find that different motifs occur at different time scales, which provides further insights into structure and function of temporal networks.