42,060 research outputs found
On minimal realisations of dynamical structure functions
Motivated by the fact that transfer functions do not contain structural
information about networks, dynamical structure functions were introduced to
capture causal relationships between measured nodes in networks. From the
dynamical structure functions, a) we show that the actual number of hidden
states can be larger than the number of hidden states estimated from the
corresponding transfer function; b) we can obtain partial information about the
true state-space equation, which cannot in general be obtained from the
transfer function. Based on these properties, this paper proposes algorithms to
find minimal realisations for a given dynamical structure function. This helps
to estimate the minimal number of hidden states, to better understand the
complexity of the network, and to identify potential targets for new
measurements
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
Enabling controlling complex networks with local topological information
Complex networks characterize the nature of internal/external interactions in real-world systems
including social, economic, biological, ecological, and technological networks. Two issues keep as
obstacles to fulflling control of large-scale networks: structural controllability which describes the
ability to guide a dynamical system from any initial state to any desired fnal state in fnite time, with a
suitable choice of inputs; and optimal control, which is a typical control approach to minimize the cost
for driving the network to a predefned state with a given number of control inputs. For large complex
networks without global information of network topology, both problems remain essentially open.
Here we combine graph theory and control theory for tackling the two problems in one go, using only
local network topology information. For the structural controllability problem, a distributed local-game
matching method is proposed, where every node plays a simple Bayesian game with local information
and local interactions with adjacent nodes, ensuring a suboptimal solution at a linear complexity.
Starring from any structural controllability solution, a minimizing longest control path method can
efciently reach a good solution for the optimal control in large networks. Our results provide solutions
for distributed complex network control and demonstrate a way to link the structural controllability and
optimal control together.The work was partially supported by National Science Foundation of China (61603209), and Beijing Natural Science Foundation (4164086), and the Study of Brain-Inspired Computing System of Tsinghua University program (20151080467), and Ministry of Education, Singapore, under contracts RG28/14, MOE2014-T2-1-028 and MOE2016-T2-1-119. Part of this work is an outcome of the Future Resilient Systems project at the Singapore-ETH Centre (SEC), which is funded by the National Research Foundation of Singapore (NRF) under its Campus for Research Excellence and Technological Enterprise (CREATE) programme. (61603209 - National Science Foundation of China; 4164086 - Beijing Natural Science Foundation; 20151080467 - Study of Brain-Inspired Computing System of Tsinghua University program; RG28/14 - Ministry of Education, Singapore; MOE2014-T2-1-028 - Ministry of Education, Singapore; MOE2016-T2-1-119 - Ministry of Education, Singapore; National Research Foundation of Singapore (NRF) under Campus for Research Excellence and Technological Enterprise (CREATE) programme)Published versio
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
Critical Networks Exhibit Maximal Information Diversity in Structure-Dynamics Relationships
Network structure strongly constrains the range of dynamic behaviors
available to a complex system. These system dynamics can be classified based on
their response to perturbations over time into two distinct regimes, ordered or
chaotic, separated by a critical phase transition. Numerous studies have shown
that the most complex dynamics arise near the critical regime. Here we use an
information theoretic approach to study structure-dynamics relationships within
a unified framework and how that these relationships are most diverse in the
critical regime
Brain complexity born out of criticality
In this essay we elaborate on recent evidence demonstrating the presence of a
second order phase transition in human brain dynamics and discuss its
consequences for theoretical approaches to brain function. We review early
evidence of criticality in brain dynamics at different spatial and temporal
scales, and we stress how it was necessary to unify concepts and analysis
techniques across scales to introduce the adequate order and control parameters
which define the transition. A discussion on the relation between structural
vs. dynamical complexity exposes future steps to understand the dynamics of the
connectome (structure) from which emerges the cognitome (function).Comment: In Proceedings of the 12th Granada Seminar "Physics, Computation, and
the Mind - Advances and Challenges at Interfaces-". (J. Marro, P. L. Garrido
& J. J. Torres, Eds.) American Institute of Physics (2012, in press
Causal connectivity of evolved neural networks during behavior
To show how causal interactions in neural dynamics are modulated by behavior, it is valuable to analyze these interactions without perturbing or lesioning the neural mechanism. This paper proposes a method, based on a graph-theoretic extension of vector autoregressive modeling and 'Granger causality,' for characterizing causal interactions generated within intact neural mechanisms. This method, called 'causal connectivity analysis' is illustrated via model neural networks optimized for controlling target fixation in a simulated head-eye system, in which the structure of the environment can be experimentally varied. Causal connectivity analysis of this model yields novel insights into neural mechanisms underlying sensorimotor coordination. In contrast to networks supporting comparatively simple behavior, networks supporting rich adaptive behavior show a higher density of causal interactions, as well as a stronger causal flow from sensory inputs to motor outputs. They also show different arrangements of 'causal sources' and 'causal sinks': nodes that differentially affect, or are affected by, the remainder of the network. Finally, analysis of causal connectivity can predict the functional consequences of network lesions. These results suggest that causal connectivity analysis may have useful applications in the analysis of neural dynamics
From Network Structure to Dynamics and Back Again: Relating dynamical stability and connection topology in biological complex systems
The recent discovery of universal principles underlying many complex networks
occurring across a wide range of length scales in the biological world has
spurred physicists in trying to understand such features using techniques from
statistical physics and non-linear dynamics. In this paper, we look at a few
examples of biological networks to see how similar questions can come up in
very different contexts. We review some of our recent work that looks at how
network structure (e.g., its connection topology) can dictate the nature of its
dynamics, and conversely, how dynamical considerations constrain the network
structure. We also see how networks occurring in nature can evolve to modular
configurations as a result of simultaneously trying to satisfy multiple
structural and dynamical constraints. The resulting optimal networks possess
hubs and have heterogeneous degree distribution similar to those seen in
biological systems.Comment: 15 pages, 6 figures, to appear in Proceedings of "Dynamics On and Of
Complex Networks", ECSS'07 Satellite Workshop, Dresden, Oct 1-5, 200
- …