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1 bers of nodes and edges, often described as "scale-free".
2 g activity fluctuations that are essentially scale free.
3 ical and biological networks appear strongly scale free.
4 any particular relaxation times and are thus scale-free.
5 l properties-including the property of being scale-free.
8 ing accelerated speech also relates to their scale-free amplitude modulation as indexed by the streng
10 currently known space of protein families is scale free and discuss the implications of this distribu
12 rk, we systematically alter the structure of scale-free and clique networks and show, through a stoch
14 of the population, indicating that they are scale-free and lack a characteristic decay scale other t
16 These findings lead to a new hypothesis that scale-free and oscillatory neural processes account for
20 teractions, (3) infer aberrant networks with scale-free and small-world properties, and (4) group mol
22 alyses, biochemical networks are found to be scale-free and small-world, indicating that these networ
23 large model-organism expression datasets are scale-free and that the average clustering coefficient o
24 equal in duration, predicts that results are scale-free and unaffected by the presentation order of t
26 nalysis of this network shows that it is not scale-free, and is best approximated by the Watts-Stroga
27 and a dynamic pacman The material-agnostic, scale-free, and programmable nature of our design enable
32 number of real networks are referred to as 'scale-free' because they show a power-law distribution o
34 ted crystals are a model system for studying scale-free behavior as observed in many macroscopic syst
35 the weighted evolving hypergraph exhibits a scale-free behavior for both hyperdegree and hyperstreng
36 similarities, scale-free brain activity and scale-free behavior have been studied separately, withou
37 certain parameter regimes, recapitulate the scale-free behavior observed in similar graphs of real p
41 phenomenon regarded as the co-existence of a scale-free behaviour (the avalanches close to criticalit
42 iscuss ensembles of random Boolean networks, scale free Boolean networks, "medusa" Boolean networks,
44 al structures and behavioral significance of scale-free brain activity and should motivate future stu
48 ellar stream in Andromeda II illustrates the scale-free character of the formation of galaxies, down
49 Graphic analyses of the PPI networks show a scale-free cluster size distribution, consistent with pr
53 pectrum, which reflects the non-oscillatory, scale-free component of neural activity, delineates wake
56 fractional Brownian motion coexisting with a scale-free continuous time random walk, the two most typ
57 ng in magnets, and the correct prediction of scale-free correlations arises because the parameters--c
59 the dynamics of other complex systems where scale-free cross-correlations have been observed, includ
62 iversal properties of real complex networks (scale-free degree distribution, small-world and communit
65 on what the most common properties are, but scale-free degree distributions, strong clustering, and
67 genously driven extinction events can have a scale-free distribution in simple spatially structured h
69 the radiation hybrid network did not show a scale-free distribution of connectivity but was Gaussian
73 tabolic networks is organized according to a scale-free distribution, in which hubs with large number
74 gredients reproduces the observed stationary scale-free distributions, which indicates that the devel
75 ion of synchronous cell assemblies and their scale-free dynamics adjusts to the temporal properties o
76 ody-centered cubic Nb how the long-range and scale-free dynamics at room temperature are progressivel
79 d frequencies in the brain differ from other scale-free dynamics in nature, such as earth seismic wav
80 that speech comprehension is related to the scale-free dynamics of delta and theta bands, whereas th
82 nd experiment have shown that such critical, scale-free dynamics optimize information processing.
88 rate that the broadband power fluctuation of scale-free electrophysiology is globally synchronized an
89 ong molecular dynamics simulations and large-scale free energy calculations complemented by in vitro
90 Based on these results, we conjecture that scale-free extinction processes and critical phase trans
93 we demonstrate the hyphenation of production-scale free-flow electrophoresis (FFE) and sheathless ele
94 orn rats in vitro, and show that while these scale-free fluctuations are independent of temporal inpu
96 stability and instability as is reflected in scale-free fluctuations in spontaneous neural activity.
98 ctures with characteristic length scales and scale-free fractal [Formula: see text] heterostructures.
99 e functional roles as hubs in a hierarchical scale-free fractal protein-protein interaction network.
104 We also confirm the negative effect of the scale-free graph on cooperation when effective payoffs a
105 ks with null percolation thresholds, such as scale-free graphs with diverging second moment of the de
107 een recently described as "small-world" and "scale-free." However, studies disagree whether ecologica
109 omogeneous networks while for d > 2 they are scale-free i.e. they are characterized by large inhomoge
111 signal recorded from the human brain is also scale free; its power-law exponent differentiates betwee
112 ng two constraints: 1) it must depend upon a scale-free Lagrangian, and 2) the Lagrangian must change
114 lieved that random search processes based on scale-free, Levy stable jump length distributions (Levy
118 fluctuations of broadband and arrhythmic, or scale-free, macaque electrocorticography and human magne
119 Real-world networks are often claimed to be scale free, meaning that the fraction of nodes with degr
120 reeness) provides testable predictions about scale-free measurements that are readily applied to V (m
121 red by amino acid constraints, using a novel scale-free method that identifies regions of outlying sc
122 twork of the US economy and find that purely scale-free models have trouble matching key attributes o
123 rgic phenotypes, including cluster analysis, scale-free models, candidate biomarkers, and IgE microar
124 rtices of 11 primate species follow a common scale-free morphometric trajectory, that also overlaps w
125 food, many organisms adopt a superdiffusive, scale-free movement pattern called a Levy walk, which is
128 that this model is able to recapitulate the scale-free nature observed in graphs of real protein str
130 e fundamental properties help to explain the scale-free nature of complex networks and suggest a comm
131 downstream genes (regulons), indicating the scale-free nature of host gene co-expression in W12.
139 namics of the materials stability network: a scale-free network constructed by combining the convex f
140 l that surprisingly it self-organizes into a scale-free network exhibiting also a power-law in the di
142 opic, physics-based evolutionary model for a scale-free network of biological importance and as such
143 were performed using a Barabasi-Albert (BA) scale-free network seeded with a single piece of informa
144 y significant structural data are available, scale-free network statistics based solely on the distri
147 s in the polyprotein can be organized into a scale-free network whose degree of connections between s
148 ls-in three complex social networks-a simple scale-free network, an empirical Venezuelan college stud
149 a random regular graph, a random graph and a scale-free network, and we examine the features of the g
150 s between protein families has the form of a scale-free network, meaning that most protein families o
151 The results are suggestive a hierarchical, scale-free network, where a few highly interconnected ge
152 experimentally derived RNA interactome is a scale-free network, which is not expected from currently
158 a web of control systems, reminiscent of a 'scale-free' network, whose untangling requires integrate
159 trogatz), random networks (Erdos-Renyi), and scale-free networks (Barabasi-Albert)-to assess the impa
160 Here, we organize different definitions of scale-free networks and construct a severe test of their
161 o specific approaches focused on here (i.e., scale-free networks and highly optimized tolerance netwo
163 se parameter q(c) as a function of z for the scale-free networks and obtain the phase diagram of the
165 eaters, especially for the stag-hunt game in scale-free networks and when the selection strength is s
168 accination strategies targeting hub nodes in scale-free networks did not substantially reduce the tot
169 ologically observed exponents for functional scale-free networks fall in a range corresponding to the
173 Here we propose that the emergence of many scale-free networks is tied to the efficiency of transpo
174 rganization, reminiscent of 'small-world' or scale-free networks observed in other complex systems.
175 this hidden distributed architecture behind scale-free networks protects the overall transcriptional
179 namical rules of these networks can generate scale-free networks with clustering and communities, in
180 s, we show that spreading improve in evolved scale-free networks with lower shortest-path and structu
182 sign principles of robust and error-tolerant scale-free networks, and may represent a common blueprin
183 e the efficiency of each method on synthetic scale-free networks, as well as real complex networks.
184 f three classes of small-world networks: (a) scale-free networks, characterized by a vertex connectiv
185 ugh food webs are generally not small-world, scale-free networks, food-web topology is consistent wit
186 l graphs, such as fractals, random trees and scale-free networks, revealing the direct relation betwe
187 r than would be expected for similarly sized scale-free networks, suggesting an inherent hierarchical
188 ual neurons, but here, we investigate ISR in scale-free networks, where the average spiking rate is c
189 ss of inhomogeneously wired networks, called scale-free networks, which include the World-Wide Web, t
201 We find that networks having a power-law ("scale-free") node degree distribution readily generate e
202 cortical state was uniquely characterized by scale-free ongoing population dynamics and moderate corr
204 of cancer is driven by two factors: (i) the scale-free (or near scale-free) topology of the interact
205 ric random graphs than by Erdos-Reny, random scale-free, or Barabasi-Albert scale-free networks.
207 stimulus processing on the one hand and the scale-free organization of spatiotemporal network dynami
208 visual cortex follow a remarkably consistent scale-free organization-their variance decay is consiste
210 ticality, a dynamical state characterized by scale-free oscillations and a hallmark of neuronal netwo
211 ticality, a dynamical state characterized by scale-free oscillations, optimizes the capacity of neuro
213 us pathway interactions may exhibit the same scale-free phenomenon that has been documented for prote
214 lace burst suppression in the broad class of scale-free physical processes termed crackling noise and
215 nspecific fluctuation and synchronization in scale-free population activity also varied across and de
216 tivity is the broadband power fluctuation in scale-free population activity observable with macroscop
218 e episodes during the sleep period exhibit a scale-free power-law behavior with an exponent alpha tha
219 at in both cases it is described by the same scale-free power-law distribution with an additional pea
220 ribution, whereas those in type-II display a scale-free power-law distribution with exponent approxim
225 ted power law nature indicating hierarchical scale-free properties and five levels of organization.
227 al hourglass recruitment pattern transferred scale-free properties from loop to domain components of
228 e observed effects on long-range dependence, scale-free properties of alpha oscillations themselves,
230 ults demonstrate the functional relevance of scale-free properties of the fMRI signal and impose cons
232 --patterns of complex bursting activity with scale-free properties--is examined in leaky Markovian ne
239 curs when the continuous scale symmetry of a scale-free quantum system is broken into a discrete scal
240 e living animals use a theoretically optimal scale-free random search for sparse resources known as a
243 d the CSK matrix, which was followed by slow scale-free recovery of rheological properties (aging).
244 oss a remarkable 5 orders of magnitude and a scale-free relationship between burst sizes and duration
245 ft glasses, but not all materials expressing scale-free rheology are glassy (see plastics, wood, conc
247 amental requirement to account for virtually scale-free self-assembly of the morphogen gradients obse
250 in the Hurst exponent (H), which quantifies scale-free signal, was related to three different source
253 conditions exhibited topological features of scale free, small world and modularity, which were consi
254 method that uses topological constraints of scale-free, small-world biological networks to reconstru
255 ation dynamics towards a special regime with scale-free spatiotemporal activity, after an initial lar
256 x displays critical dynamics, giving rise to scale-free spatiotemporal cascades of activity, termed n
260 chemical vapour deposition(5), of centimetre-scale, free-standing, continuous and stable monolayer am
262 s of Internet traffic and, in some contexts, scale-free structure in the network's interconnection to
263 works, we find robust evidence that strongly scale-free structure is empirically rare, while for most
264 although some food webs have small-world and scale-free structure, most do not if they exceed a relat
265 n natural and artificial complex systems, of scale-free structures and to their connections with none
266 dients of a scalar distributed on the nodes, scale-free structures will ensure efficient processing,
267 processing, whereas structures that are not scale-free, such as random graphs, will become congested
271 Not only are fluctuations of somatic V (m) scale-free, they match fluctuations of population activi
273 ng of patterns of behavior, we show that the scale-free topologies often found in nature enable more
277 co-conservation based networks to exhibit a scale free topology, as expected for biological networks
278 vers 77% of the expressed genes, and shows a scale-free topology and functional modularity like a rea
279 lized damage, the function of a network with scale-free topology can be significantly restored by a l
280 urrent limited coverage levels, the observed scale-free topology of existing interactome maps cannot
281 g of random phenotypic variation through the scale-free topology of gene regulatory, metabolic, and p
283 n this study, an algorithm that explores the scale-free topology of networks was proposed based on th
284 ng crucial as we try to explain the emergent scale-free topology of the World Wide Web and use link a
291 ted that many biological networks exhibit a "scale-free" topology, for which the probability of obser
292 by two factors: (i) the scale-free (or near scale-free) topology of the interaction network, and (ii
293 a hidden distributed architecture behind the scale-free transcriptional regulatory network of yeast b
294 rotein-protein binding that is approximately scale-free (varies as a power law) even though their evo
295 Here we present a solution in the form of a scale-free, vertical tracking microscope, based on a 'hy
296 ring numerous methods to tailor the Angstrom-scale free volume properties by judicious selection of t
298 thermore, social networks are at best weakly scale free, while a handful of technological and biologi
299 particular, show that these fluctuations are scale-free, with effective correlation lengths proportio
300 networks indicates that transit contacts are scale-free, work contacts are Weibull distributed, and s