2,710 research outputs found
The physics of spreading processes in multilayer networks
The study of networks plays a crucial role in investigating the structure,
dynamics, and function of a wide variety of complex systems in myriad
disciplines. Despite the success of traditional network analysis, standard
networks provide a limited representation of complex systems, which often
include different types of relationships (i.e., "multiplexity") among their
constituent components and/or multiple interacting subsystems. Such structural
complexity has a significant effect on both dynamics and function. Throwing
away or aggregating available structural information can generate misleading
results and be a major obstacle towards attempts to understand complex systems.
The recent "multilayer" approach for modeling networked systems explicitly
allows the incorporation of multiplexity and other features of realistic
systems. On one hand, it allows one to couple different structural
relationships by encoding them in a convenient mathematical object. On the
other hand, it also allows one to couple different dynamical processes on top
of such interconnected structures. The resulting framework plays a crucial role
in helping achieve a thorough, accurate understanding of complex systems. The
study of multilayer networks has also revealed new physical phenomena that
remain hidden when using ordinary graphs, the traditional network
representation. Here we survey progress towards attaining a deeper
understanding of spreading processes on multilayer networks, and we highlight
some of the physical phenomena related to spreading processes that emerge from
multilayer structure.Comment: 25 pages, 4 figure
Principal Patterns on Graphs: Discovering Coherent Structures in Datasets
Graphs are now ubiquitous in almost every field of research. Recently, new
research areas devoted to the analysis of graphs and data associated to their
vertices have emerged. Focusing on dynamical processes, we propose a fast,
robust and scalable framework for retrieving and analyzing recurring patterns
of activity on graphs. Our method relies on a novel type of multilayer graph
that encodes the spreading or propagation of events between successive time
steps. We demonstrate the versatility of our method by applying it on three
different real-world examples. Firstly, we study how rumor spreads on a social
network. Secondly, we reveal congestion patterns of pedestrians in a train
station. Finally, we show how patterns of audio playlists can be used in a
recommender system. In each example, relevant information previously hidden in
the data is extracted in a very efficient manner, emphasizing the scalability
of our method. With a parallel implementation scaling linearly with the size of
the dataset, our framework easily handles millions of nodes on a single
commodity server
Multiplexing induced explosive synchronization in Kuramoto oscillators with inertia
Explosive synchronization (ES) of coupled oscillators on networks is shown to
be originated from existence of correlation between natural frequencies of
oscillators and degrees of corresponding nodes. Here, we demonstrate that ES is
a generic feature of multiplex network of second-order Kuramoto oscillators and
can exist in absence of a frequency-degree correlation. A monoplex network of
second-order Kuramoto oscillators bearing homogeneous (heterogeneous)
degree-distribution is known to display the first-order (second-order)
transition to synchronization. We report that multiplexing of two such networks
having homogeneous degree-distribution support the first-order transition in
both the layers thereby facilitating ES. More interesting is the multiplexing
of a layer bearing heterogeneous degree-distribution with another layer bearing
homogeneous degree-distribution, which induces a first-order (ES) transition in
the heterogeneous layer which was incapable of showing the same in the
isolation. Further, we report that such induced ES transition in the
heterogeneous layer of multiplex networks can be controlled by varying inter
and intra-layer coupling strengths. Our findings emphasize on importance of
multiplexing or impact of one layer on dynamical evolution of other layers of
systems having inherent multiplex or multilevel architecture.Comment: 7 pages, 10 figure
A Tensor-Based Framework for Studying Eigenvector Multicentrality in Multilayer Networks
Centrality is widely recognized as one of the most critical measures to
provide insight in the structure and function of complex networks. While
various centrality measures have been proposed for single-layer networks, a
general framework for studying centrality in multilayer networks (i.e.,
multicentrality) is still lacking. In this study, a tensor-based framework is
introduced to study eigenvector multicentrality, which enables the
quantification of the impact of interlayer influence on multicentrality,
providing a systematic way to describe how multicentrality propagates across
different layers. This framework can leverage prior knowledge about the
interplay among layers to better characterize multicentrality for varying
scenarios. Two interesting cases are presented to illustrate how to model
multilayer influence by choosing appropriate functions of interlayer influence
and design algorithms to calculate eigenvector multicentrality. This framework
is applied to analyze several empirical multilayer networks, and the results
corroborate that it can quantify the influence among layers and multicentrality
of nodes effectively.Comment: 57 pages, 10 figure
Demand and Congestion in Multiplex Transportation Networks
Urban transportation systems are multimodal, sociotechnical systems; however, while their multimodal aspect has received extensive attention in recent literature on multiplex networks, their sociotechnical aspect has been largely neglected. We present the first study of an urban transportation system using multiplex network analysis and validated Origin-Destination travel demand, with Riyadh’s planned metro as a case study. We develop methods for analyzing the impact of additional transportation layers on existing dynamics, and show that demand structure plays key quantitative and qualitative roles. There exist fundamental geometrical limits to the metro’s impact on traffic dynamics, and the bulk of environmental accrue at metro speeds only slightly faster than those planned. We develop a simple model for informing the use of additional, “feeder” layers to maximize reductions in global congestion. Our techniques are computationally practical, easily extensible to arbitrary transportation layers with complex transfer logic, and implementable in open-source software
The physics of spreading processes in multilayer networks
Despite the success of traditional network analysis, standard networks provide a limited representation of complex systems, which often include different types of relationships (or ‘multiplexity’) between their components. Such structural complexity has a significant effect on both dynamics and function. Throwing away or aggregating available structural information can generate misleading results and be a major obstacle towards attempts to understand complex systems. The recent multilayer approach for modelling networked systems explicitly allows the incorporation of multiplexity and other features of realistic systems. It allows one to couple different structural relationships by encoding them in a convenient mathematical object. It also allows one to couple different dynamical processes on top of such interconnected structures. The resulting framework plays a crucial role in helping to achieve a thorough, accurate understanding of complex systems. The study of multilayer networks has also revealed new physical phenomena that remain hidden when using ordinary graphs, the traditional network representation. Here we survey progress towards attaining a deeper understanding of spreading processes on multilayer networks, and we highlight some of the physical phenomena related to spreading processes that emerge from multilayer structure
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