Network physiology reveals relations between network topology and physiological function

Bashan, Amir; Bartsch, Ronny P.; Kantelhardt, Jan W.; Havlin, Shlomo; Ivanov, Plamen Ch.

doi:10.1038/ncomms1705

Cited by 577 publications

(580 citation statements)

References 41 publications

(67 reference statements)

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“…Although the questions go beyond the scope of the present paper, they are worth studying in the future. Futhermore, future work should also include how to apply the theory to real-world networks, a relation between whose topology and function has been demonstrated [54]. * * * We would like to thank Bin Wu for assistance.…”

Section: Spanning Treesmentioning

confidence: 99%

Exact eigenvalue spectrum of a class of fractal scale-free networks

Zhang¹,

Hu²,

Sheng³

et al. 2012

EPL

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-The eigenvalue spectrum of the transition matrix of a network encodes important information about its structural and dynamical properties. We study the transition matrix of a family of fractal scale-free networks and analytically determine all the eigenvalues and their degeneracies. We then use these eigenvalues to evaluate the closed-form solution to the eigentime for random walks on the networks under consideration. Through the connection between the spectrum of transition matrix and the number of spanning trees, we corroborate the obtained eigenvalues and their multiplicities.

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Section: Spanning Treesmentioning

confidence: 99%

Exact eigenvalue spectrum of a class of fractal scale-free networks

Zhang¹,

Hu²,

Sheng³

et al. 2012

EPL

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“…Moreover, the interconnected nodes are often the first to fail, as, for example, the case in the disruptive effect neurodegenerative diseases, such as schizophrenia and Alzheimer's disease, have on intermodular connectivity [31,32]. Also, changes in the concentration of interconnected nodes can be associated with functional transitions, for example, between physiological states [33]. Finally, it is often the case that interconnected nodes are considered to be important; for example, the New York City and London airports interconnect modules of cities in these countries and provide an attractive target for attacks [7].…”

Section: Introductionmentioning

confidence: 99%

Critical tipping point distinguishing two types of transitions in modular network structures

Shai

Kenett

et al. 2015

Phys. Rev. E

Self Cite

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Modularity is a key organizing principle in real-world large-scale complex networks. The relatively sparse interactions between modules are critical to the functionality of the system and are often the first to fail. We model such failures as site percolation targeting interconnected nodes, those connecting between modules. We find, using percolation theory and simulations, that they lead to a "tipping point" between two distinct regimes. In one regime, removal of interconnected nodes fragments the modules internally and causes the system to collapse. In contrast, in the other regime, while only attacking a small fraction of nodes, the modules remain but become disconnected, breaking the entire system. We show that networks with broader degree distribution might be highly vulnerable to such attacks since only few nodes are needed to interconnect the modules, consequently putting the entire system at high risk. Our model has the potential to shed light on many real-world phenomena, and we briefly consider its implications on recent advances in the understanding of several neurocognitive processes and diseases.

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“…at Fp1) and the parieto-occipital regions, and these regions were connected through larger-scale coupling with a different coupling direction [28]; the delta-alpha coupling was significantly increased with more similar forms of the coupling functions from awake to deep general anaesthesia, and this effect was higher for anaesthesia induced with sevoflurane than with the propofol anaesthetic [19]; and a strong link between delta and alpha brain activity was found during non-REM sleep, although alpha waves were greatly diminished and delta waves were dominant [29]. (a) presents the time-variability of two coupling sub-component strengths c1(t) and c2(t).…”

Section: Biological Interactions As Motivation -The Case Of Neuramentioning

confidence: 99%

Time-varying coupling functions: Dynamical inference and cause of synchronization transitions

Stankovski

2017

Phys. Rev. E

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Interactions in nature can be described by their coupling strength, direction of coupling and coupling function. The coupling strength and directionality are relatively well understood and studied, at least for two interacting systems, however there can be a complexity in the interactions uniquely dependent on the coupling functions. Such a special case is studied here -synchronization transition occurs only due to the time-variability of the coupling functions, while the net coupling strength is constant throughout the observation time. To motivate the investigation, an example is used to present an analysis of cross-frequency coupling functions between delta and alpha brainwaves extracted from the electroencephalography (EEG) recording of a healthy human subject in a freerunning resting state. The results indicate that time-varying coupling functions are a reality for biological interactions. A model of phase oscillators is used to demonstrate and detect the synchronization transition caused by the varying coupling functions, during an invariant coupling strength. The ability to detect this phenomenon is discussed with the method of dynamical Bayesian inference, which was able to infer the time-varying coupling functions. The form of the coupling function acts as an additional dimension for the interactions and it should be taken into account when detecting biological or other interactions from data.

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Network physiology reveals relations between network topology and physiological function

Cited by 577 publications

References 41 publications

Exact eigenvalue spectrum of a class of fractal scale-free networks

Exact eigenvalue spectrum of a class of fractal scale-free networks

Critical tipping point distinguishing two types of transitions in modular network structures

Time-varying coupling functions: Dynamical inference and cause of synchronization transitions

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