[may 15th, 2021]
 fdafsdfdas [[fdsafds]] [[fdsafds]] [[fdsaafds]]
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[may 15th, 2021]
 fdafsdfdas [[fdsafds]] [[fdsafds]] [[fdsaafds]]
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[development]
 [[smallworld]] structure is present in most [[social networks]]
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[development]

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[fractal dimension of cortical functional connectivity networks]
 Recent evidence suggests that the quantity and quality of conscious experience may be a function of the complexity of activity in the brain and that consciousness emerges in a critical zone between low and highentropy states. We propose fractal shapes as a measure of proximity to this critical point, as [[fractal dimension]] encodes information about complexity beyond simple entropy or randomness, and fractal structures are known to emerge in systems nearing a [[critical point]]. To validate this, we tested several measures of [[fractal dimension]] on the brain activity from healthy volunteers and patients with disorders of consciousness of varying severity. We used a [[Compact Box Burning algorithm]] to compute the [[fractal dimension]] of cortical functional connectivity networks as well as computing the fractal dimension of the associated adjacency matrices using a 2D boxcounting algorithm. To test whether brain activity is fractal in time as well as space, we used the
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[fractal dimension of cortical functional connectivity networks]
[[Higuchi temporal fractal dimension]] on [[BOLD timeseries]]. We found significant [[decreases]] in the [[fractal dimension]] between healthy volunteers (n = 15), patients in a minimally conscious state (n = 10), and patients in a vegetative state (n = 8), regardless of the mechanism of injury. We also found significant decreases in adjacency matrix fractal dimension and Higuchi temporal fractal dimension, which correlated with decreasing level of consciousness. These results suggest that [[cortical functional connectivity networks]] display [[fractal character]] and that this is associated with level of consciousness in a clinically relevant population, with higher fractal dimensions (i.e. more complex) networks being associated with higher levels of consciousness. This supports the hypothesis that level of consciousness and system complexity are positively associated, and is consistent with previous EEG, MEG, and fMRI studies.
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[fractal dimension of cortical functional connectivity networks]
https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0223812
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[fractal dimension of cortical functional connectivity networks]

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[how to calculate the fractal dimension of a complex network]
 Covering a network with the minimum possible number of boxes can
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[how to calculate the fractal dimension of a complex network]
reveal interesting features for the network structure, especially in terms of selfsimilar
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[how to calculate the fractal dimension of a complex network]
or fractal characteristics. Considerable attention has been recently devoted to this
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[how to calculate the fractal dimension of a complex network]
problem, with the finding that many real networks are selfsimilar fractals. Here we
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[how to calculate the fractal dimension of a complex network]
present, compare and study in detail a number of algorithms that we have used in
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[how to calculate the fractal dimension of a complex network]
previous papers towards this goal. We show that this problem can be mapped to
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[how to calculate the fractal dimension of a complex network]
the wellknown graph coloring problem and then we simply can apply wellestablished
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[how to calculate the fractal dimension of a complex network]
algorithms. This seems to be the most efficient method, but we also present two other
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[how to calculate the fractal dimension of a complex network]
algorithms based on burning which provide a number of other benefits. We argue
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[how to calculate the fractal dimension of a complex network]
that the presented algorithms provide a solution close to optimal and that another
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[how to calculate the fractal dimension of a complex network]
algorithm that can significantly improve this result in an efficient way does not exist. [[Fractal dimension]] of a complex network https://arxiv.org/pdf/condmat/0701216.pdf
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[definitions]
 In [mathematics](https://en.wikipedia.org/wiki/Mathematics), **Hausdorff dimension** is a measure of __roughness__, or more specifically, [[fractal dimension]](https://en.wikipedia.org/wiki/Fractal_dimension), that was first introduced in 1918 by [mathematician](https://en.wikipedia.org/wiki/Mathematician) [Felix Hausdorff](https://en.wikipedia.org/wiki/Felix_Hausdorff).[[2]](https://en.wikipedia.org/wiki/Hausdorff_dimension#cite_note2)
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[definitions]

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[epidemic spreading in scalefree networks]
 The Internet, as well as many other networks, has a very complex connectivity recently modeled by the class of [[scalefree]] networks. This feature, which appears to be very efficient for a communications network, favors at the same time the spreading of computer viruses. We analyze real data from computer virus [[infection]] and find the average lifetime and prevalence of viral strains on the Internet. We define a dynamical model for the spreading of infections on [[scalefree]] networks, finding the absence of an [[epidemic threshold]] and its associated critical behavior. This new epidemiological framework rationalize data of computer viruses and could help in the understanding of other spreading phenomena on communication and social networks. https://arxiv.org/abs/condmat/0010317
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[ideas]
 [[fractal scaling]] means that the network has a fractal dimension while [[scalefree]] means that the nodes' connectivity follows a powerlaw
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[ideas]
 [[epidemic threshold]] exists in [[homogeneous networks]] and in [[fractal networks]] but not in [[scalefree]]
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[ideas]
 We show that
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[ideas]
the key principle that gives rise to the fractal architecture of [[fractal networks]] is a strong effective “repulsion” ([disassortativity]) between the most connected nodes (hubs) on all
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[ideas]
length scales, rendering them very dispersed. More importantly, we show that a robust network comprised of functional modules, such as a cellular network, necessitates
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[ideas]
a [[fractal topology]], suggestive of an evolutionary drive for their existence.http://www.uvm.edu/pdodds/files/papers/others/2005/song2005b.pdf
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[ideas]

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[fractal scalefree networks resistant to disease spread]
 The conventional wisdom is that [[scalefree]] networks are prone to epidemic [[propagation]]; in the paper we demonstrate that, on the contrary, [[disease spreading]] is inhibited in [[scalefree]] [[fractal networks]]. We first propose a novel network model and show that it simultaneously has the following rich topological properties: scalefree degree distribution, tunable clustering coefficient, 'largeworld' behavior, and [[fractal scaling]]. Existing network models do not display these characteristics. Then, we investigate the susceptible–infected–removed (SIR) model of the [[propagation]] of diseases in our fractal scalefree networks by mapping it to the bond percolation process. We establish the existence of nonzero tunable epidemic thresholds by making use of the renormalization group technique, which implies that [[power law]] degree distribution does not suffice to characterize the epidemic dynamics on top of scalefree networks. We argue that the epidemic dynamics are
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[fractal scalefree networks resistant to disease spread]
determined by the topological properties, especially the fractality and its accompanying 'largeworld' behavior. https://arxiv.org/pdf/0804.3186.pdf
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[fractal scalefree networks resistant to disease spread]
 . In [[homogeneous networks]], there is an existence of nonzero [[infection threshold]], if the spreading rate is above the threshold, the [[infection]] spreads and becomes endemic, otherwise the infection dies outs quickly. However, recent studies demonstrate that the threshold is
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[fractal scalefree networks resistant to disease spread]
absent in heterogeneous [[scalefree]] networks [8,9,10,11]. Thus, it is important
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[fractal scalefree networks resistant to disease spread]
to identify what characteristics of network structure determine the presence
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[fractal scalefree networks resistant to disease spread]
or not of epidemic thresholds.
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[fractal scalefree networks resistant to disease spread]
 Examples of [[fractal networks]] include the [[WWW]], actor collaboration network,
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[fractal scalefree networks resistant to disease spread]
[[metabolic network]], and yeast [[protein interaction network]]
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[fractal scalefree networks resistant to disease spread]
 The [[fractal topology]] is often characterized through two quantities: [[fractal dimension]] dB
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[fractal scalefree networks resistant to disease spread]
and [[degree exponent]] of the boxes dk, both of which can be calculated by the
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[fractal scalefree networks resistant to disease spread]
boxcounting algorithm [17,18]
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[fractal scalefree networks resistant to disease spread]
 [[Minimum boxcovering method]] is a basic tool to measure [[fractal dimension]] of a network https://journals.aps.org/pre/abstract/10.1103/PhysRevE.78.046109
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[fractal scalefree networks resistant to disease spread]
 Accuracy of the [[ballcovering algorithm]] for [[fractal dimension]] of complex networks and a rankdriven algorithm (https://journals.aps.org/pre/abstract/10.1103/PhysRevE.78.046109)
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[fractal scalefree networks resistant to disease spread]
 in [[fractal networks]] the correlation between [[degree]] and [[betweenness centrality]] of nodes is much [[weaker]] than that in nonfractal networks [19]. In addition, several studies uncovered that [[fractal networks]] are not [[assortative]] [16,20,21]. The peculiar structural nature of fractal networks make them exhibit distinct dynamics. It is known that [[scalefree]] [[fractal networks]] are more [robust] than nonfractal ones against malicious attacks on hub nodes [16,21].
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[fractal scalefree networks resistant to disease spread]
 [[fractal topology]] provides [[protection]] against [[disease spreading]].
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[fractal dimension]
 Many real networks have two fundamental properties, [[scalefree]](https://en.wikipedia.org/wiki/ScaleFree_Networks) property and [[smallworld]](https://en.wikipedia.org/wiki/Smallworld_network) property.
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[fractal dimension]
 If the [[degree distribution]](https://en.wikipedia.org/wiki/Degree_distribution) of the network follows a [[powerlaw]](https://en.wikipedia.org/wiki/Powerlaw), the network is [[scalefree]];
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[fractal dimension]
 if any two arbitrary nodes in a network can be connected in a very small number of steps (short [[average path]]), the network is said to be [[smallworld]].
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[may 20th, 2021]

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[power law]

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[power law]

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[emergence of scaling in random networks]
 Systems as diverse as genetic networks or the World Wide Web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a [[scalefree]] [[power law]] distribution. This feature was found to be a consequence of two generic mechanisms: (i) networks expand continuously by the addition of new vertices, and (ii) new vertices attach preferentially to sites that are already well connected. A model based on these two ingredients reproduces the observed stationary scalefree distributions, which indicates that the development of large networks is governed by robust selforganizing phenomena that go beyond the particulars of the individual systems.
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[fractal weighed networks]
 Fractal weighed networks exhibit the [[smallworld]] property. In fact the average shortest path increases logarithmically with the system size (11), hence it is small as the average shortest path of a random network with the same number of nodes and same average degree. On the other hand the clustering coefficient is asymptotically constant (12), thus larger than the clustering coefficient of a random network that shrinks to zero as the system size increases. 8 The selfsimilarity property of the weighted fractal networks makes them suitable to model real problems involving generic [[diffusion]] over the network coupled with local looses of flow, here modeled via the parameter f < 1. For instance one can think of electrical grids or mammalian lungs, where current or air, flows through power lines or bronchi–bronchioles, submitted to looses of power, or air vessels’ section reduction. In all these cases the induced [[topology]], namely a good choice of f and s, allows any two random
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[fractal weighed networks]
nodes, final power users or alveoli, to be always at finite weighted distance, whatever their physical distance is, and thus to be able to transport current or oxygen in finite time. https://arxiv.org/pdf/0908.4509.pdf
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[scale free]
 When investigating nature we often discard the observed variation and describe its properties in terms of an [[average]], such as the [[mean]] or [[median]] (Gilden, [2001](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3510427/#B16)). For some objects or processes, however, the average value is a poor description, because they do not have a typical or “characteristic” scale. Such systems are broadly referred to as “[[scalefree]]” (Bassingthwaighte et al., [1994](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3510427/#B3)). There is growing evidence that physiological processes can exhibit fluctuations without characteristic scales and that this scalefree dynamics is important for their function (Bassingthwaighte et al., [1994](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3510427/#B3); Bak, [1996](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3510427/#B2); Goldberger et al., [2002](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3510427/#B18);
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[scale free]
Stam, [2005](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3510427/#B51); Ghosh et al., [2008](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3510427/#B15); He et al., [2010](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3510427/#B19); West, [2010](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3510427/#B54)). [[Detrended fluctuation analysis]] ([[DFA]]; Peng et al., [1994](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3510427/#B45)), a method for analyzing scaling behavior in time series, has played a critical role in this success. We believe, however, that DFA could prove valuable to a wider community of neuroscientists than its current users
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[smallworld]
 [[]]
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[human brain functional networks]
 Human brain functional networks demonstrate a fractal [[smallworld]] architecture that supports critical dynamics and taskrelated spatial reconfiguration while preserving global topological parameters. https://www.pnas.org/content/103/51/19518.short
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[treibgut]
 a function that calculates the [[fractal dimension]] of an object embedded in three dimensional space using the [[Minimum boxcovering method]] method https://github.com/ChatzigeorgiouGroup/FractalDimension
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[treibgut]
 Other algorithms for calculating [[fractal dimension]]: https://link.springer.com/referenceworkentry/10.1007%2F9780387304403_231
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[treibgut]

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[social networks]

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about about [[backlink propagation]] of [[ideas]]
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[[backlink propagation]] of [[solitude]] and [[desire]]
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bring the universe to the [[network]] of [[consciousness]]
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blocking th universe
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the network is ready to initiate [[propagation]] of [[meaning]]
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bring back the universe
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