📄 Scale-free networks emerging from multifractal time series
Marcello A. Budroni, Andrea Baronchelli, Romualdo Pastor-Satorras
🔗 https://arxiv.org/pdf/1612.07070v1
📌 ABSTRACT
Methods connecting dynamical systems and graph theory have attracted increasing interest in the past few years, with applications ranging from a detailed comparison of different kinds of dynamics to the characterisation of empirical data. Here we investigate the effects of the (multi)fractal properties of a time signal, common in sequences arising from chaotic or strange attractors, on the topology of a suitably projected network. Relying on the box counting formalism, we map boxes into the nodes of a network and establish analytic expressions connecting the natural measure of a box with its degree in the graph representation. We single out the conditions yielding to the emergence of a scale-free topology, and validate our findings with extensive numerical simulations.
Marcello A. Budroni, Andrea Baronchelli, Romualdo Pastor-Satorras
🔗 https://arxiv.org/pdf/1612.07070v1
📌 ABSTRACT
Methods connecting dynamical systems and graph theory have attracted increasing interest in the past few years, with applications ranging from a detailed comparison of different kinds of dynamics to the characterisation of empirical data. Here we investigate the effects of the (multi)fractal properties of a time signal, common in sequences arising from chaotic or strange attractors, on the topology of a suitably projected network. Relying on the box counting formalism, we map boxes into the nodes of a network and establish analytic expressions connecting the natural measure of a box with its degree in the graph representation. We single out the conditions yielding to the emergence of a scale-free topology, and validate our findings with extensive numerical simulations.
📄Finding network communities using modularity density
Federico Botta, Charo I. del Genio
🔗 https://arxiv.org/pdf/1612.07297v1
📌 ABSTRACT
Many real-world complex networks exhibit a community structure, in which the modules correspond to actual functional units. Identifying these communities is a key challenge for scientists. A common approach is to search for the network partition that maximizes a quality function. Here, we present a detailed analysis of a recently proposed function, namely modularity density. We show that it does not incur in the drawbacks suffered by traditional modularity, and that it can identify networks without ground-truth community structure, deriving its analytical dependence on link density in generic random graphs. In addition, we show that modularity density allows an easy comparison between networks of different sizes, and we also present some limitations that methods based on modularity density may suffer from. Finally, we introduce an efficient, quadratic community detection algorithm based on modularity density maximization, validating its accuracy against theoretical predictions and on a set of benchmark networks.
Federico Botta, Charo I. del Genio
🔗 https://arxiv.org/pdf/1612.07297v1
📌 ABSTRACT
Many real-world complex networks exhibit a community structure, in which the modules correspond to actual functional units. Identifying these communities is a key challenge for scientists. A common approach is to search for the network partition that maximizes a quality function. Here, we present a detailed analysis of a recently proposed function, namely modularity density. We show that it does not incur in the drawbacks suffered by traditional modularity, and that it can identify networks without ground-truth community structure, deriving its analytical dependence on link density in generic random graphs. In addition, we show that modularity density allows an easy comparison between networks of different sizes, and we also present some limitations that methods based on modularity density may suffer from. Finally, we introduce an efficient, quadratic community detection algorithm based on modularity density maximization, validating its accuracy against theoretical predictions and on a set of benchmark networks.
📄 A Guide to Teaching Data Science
Stephanie C. Hicks, Rafael A. Irizarry
🔗 https://arxiv.org/pdf/1612.07140v1
📌 ABSTRACT:
Demand for data science education is surging and traditional courses offered by statistics departments are not meeting the needs of those seeking this training. This has led to a number of opinion pieces advocating for an update to the Statistics curriculum. The unifying recommendation is that computing should play a more prominent role. We strongly agree with this recommendation, but advocate that the main priority is to bring applications to the forefront as proposed by Nolan and Speed (1999). We also argue that the individuals tasked with developing data science courses should not only have statistical training, but also have experience analyzing data with the main objective of solving real-world problems. Here, we share a set of general principles and offer a detailed guide derived from our successful experience developing and teaching data science courses centered entirely on case studies. We argue for the importance of statistical thinking, as defined by Wild and Pfannkuck (1999) and describe how our approach teaches students three key skills needed to succeed in data science, which we refer to as creating, connecting, and computing. This guide can also be used for statisticians wanting to gain more practical knowledge about data science before embarking on teaching a course.
Stephanie C. Hicks, Rafael A. Irizarry
🔗 https://arxiv.org/pdf/1612.07140v1
📌 ABSTRACT:
Demand for data science education is surging and traditional courses offered by statistics departments are not meeting the needs of those seeking this training. This has led to a number of opinion pieces advocating for an update to the Statistics curriculum. The unifying recommendation is that computing should play a more prominent role. We strongly agree with this recommendation, but advocate that the main priority is to bring applications to the forefront as proposed by Nolan and Speed (1999). We also argue that the individuals tasked with developing data science courses should not only have statistical training, but also have experience analyzing data with the main objective of solving real-world problems. Here, we share a set of general principles and offer a detailed guide derived from our successful experience developing and teaching data science courses centered entirely on case studies. We argue for the importance of statistical thinking, as defined by Wild and Pfannkuck (1999) and describe how our approach teaches students three key skills needed to succeed in data science, which we refer to as creating, connecting, and computing. This guide can also be used for statisticians wanting to gain more practical knowledge about data science before embarking on teaching a course.
🎯 "What are Lyapunov Exponents, and Why are they Interesting?" by Amie Wilkinson
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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
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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