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1 this configuration space, are, surprisingly, fractal.
2 bset, the network topology becomes naturally fractal.
3  a structure that is simultaneously C(1) and fractal.
4 mall-world, whereas the attention network is fractal.
5 and extend the recent discovery of universal fractal 1/f scaling in water quality at the relatively p
6 s, trace elements, and toxic metals, exhibit fractal 1/f(alpha) scaling on time scales from hours to
7                          Mean difference for fractal abundance was -0.355 (95% limits of agreement: -
8 hresholding, to derive fractal dimension and fractal abundance.
9                      Moreover, the degree of fractal activity disruption is strongly associated with
10 n at multiple time scales and that disrupted fractal activity may serve as a non-invasive biomarker o
11 d circadian rhythmicity, also have disrupted fractal activity patterns and that the disruption is mor
12                                          The fractal activity patterns appear to be physiologically i
13 e we demonstrate a controllable synthesis of fractal Ag micro-dendrites at the hundred-gram scale.
14                                We argue that fractal aggregate particles may also have a significant
15  a thick aerosol layer consisting of fluffy, fractal aggregate particles produced by photochemistry a
16 ors, and fusing to form dendrites, a type of fractal aggregate.
17 pecies (e.g., monomers, dimers) to form mass fractal aggregates of ferrihydrite nanoparticles ( appro
18 icles form stable suspensions of low-density fractal aggregates that are resistant to collapse.
19 XS), using a model quantitatively describing fractal aggregates.
20 e report the critical role of time-dependent fractal aggregation in the unsteady thermal convection o
21                       Two-dimensional and 3D fractal analyses of the rectal tumor were performed, aft
22 g complexity analysis by including detrended fractal analysis (DFA) and multiscale entropy (MSE) were
23 % limits of agreement: -0.212, 0.372) for 2D fractal analysis and -0.024 (95% limits of agreement: -0
24 % limits of agreement: -0.869, 1.579) for 2D fractal analysis and -0.043 (95% limits of agreement: -1
25                                              Fractal analysis can quantitatively discriminate the tra
26                                              Fractal analysis has been used to define trabeculae in l
27                                              Fractal analysis of cardiac MR imaging data measures end
28  We hypothesized that trabeculae measured by fractal analysis of cardiovascular magnetic resonance im
29                Trabeculae were quantified by fractal analysis of cine slices to calculate the fractal
30                              Scale-sensitive fractal analysis of high-resolution 3-dimensional surfac
31                                        Using fractal analysis of the size distribution of trachybasal
32 hness (Sa) and the following scale-sensitive fractal analysis parameters: area-scale fractal complexi
33 ological sections using Image J skeleton and fractal analysis procedures at three time points and in
34                                              Fractal analysis provided a better sensitivity, offering
35 legant geometrical interpretation, the multi-fractal analysis quantifies the spatial and temporal irr
36  this study is to evaluate the capability of fractal analysis to discriminate the changes in the trab
37                                            A fractal analysis was also done theoretically to investig
38 f two-dimensional fast Fourier transform and fractal analysis, which allows for a more complete under
39 elates with the protein concentration, or by fractal analysis.
40 % limits of agreement: -0.307, 0.355) for 3D fractal analysis.
41 % limits of agreement: -1.154, 1.239) for 3D fractal analysis.
42                 We focus our analysis on the fractal and modular properties of this resulting network
43                         Time, frequency, and fractal and nonlinear properties of the signals were exa
44                             Through detailed fractal and percolation analyses of MG structures, deriv
45 ither random nor artificial, but self-affine fractal and rougher for Landers.
46    Another example is the self-similarity in fractals and dendrites.
47 may structure the interface as a self-affine fractal, and so induce a series of temporal and spatial
48 hiometric ratio (1:1:3) produced the desired fractal architecture in near-quantitative yield.
49  [Zn12LB6], the remarkable rigidity of these fractal architectures was supported by TWIM-MS, in contr
50 lowed to determine the particle porosity and fractal arrays at the atomic scale for the S-Mo-S(Co) 2D
51 s of elastic and plastic deformations of the fractal asperities.
52 erns on the tiles, and that the yield of the fractal assembly process corresponds to about 0.95(m - 1
53    We illustrate this method, which we term 'fractal assembly', by producing DNA origami arrays with
54 bry transition and the onset of its hallmark fractal atomic arrangement.
55 uenching rates, we conclude that there is no fractal atomic-level structure associated with the packi
56                     The results suggest that fractal-based layouts represent important strategies for
57 ss, it undergoes a 'roughness transition' to fractal basins, which brings about isostaticity and marg
58  independently, SCs exhibit a time-dependent fractal behavior as they interact with each other throug
59  revealing details about the growth rate and fractal behavior.
60 ned everywhere, the normal vector exhibits a fractal behavior.
61 be sketched as an assembly of densely packed fractal blobs, i.e., regions of size xi, where the fiber
62  model of rangeomorph morphologies reveals a fractal body plan characterized by self-similar, axial,
63                                          The fractal body plan of rangeomorphs is shown to maximize s
64         Nonlinear systems often give rise to fractal boundaries in phase space, hindering predictabil
65 s and HSCs scale during development with the fractal branching patterns of portal vessels, tributarie
66  to an important finding: the existence of a fractal characteristic (D = 1.63) for the hydroxyapatite
67 one dividing sub-population, and their multi-fractal characteristics.
68                      In addition, this multi-fractal characterization framework enables the construct
69 ut a mixture which corresponded to different fractal colour values (51.0-71.8), and they varied from
70 tive fractal analysis parameters: area-scale fractal complexity (Asfc), exact proportion length-scale
71 lity of Peano, Greek cross, Vicsek and other fractal constructs to yield space-filling structures of
72  rhythmic synchronization can be imitated by fractal coupling of separately recorded or synthesized a
73 ted by contact maps of hierarchically folded fractal (crumpled) polymer globules was investigated in
74 macroscopic domains of collapsed chains with fractal dendritic morphology.
75                               Thus, both the fractal design and supramolecular aspects of these const
76                       Advanced materials and fractal design concepts form the basis of a 3D conformal
77 CI]: -3.1 mum, -0.2 mum), reduced arteriolar fractal dimension (-0.01 Df; 95% CI: -0.02 Df, -0.001 Df
78 ibuted with a tail exponent (tau = 1.97) and fractal dimension (d = 1.38), similar to theoretical exp
79   Focusing on the most important case of low fractal dimension (D f = 2.2) with extensive numerical s
80                             Retinal vascular fractal dimension (D(f)) and caliber were measured from
81 hat the hydrodynamic radius [HR] increases), fractal dimension (Df) strongly decreases (providing inc
82                                    Grayscale Fractal Dimension (FD) analysis of retinal images was pe
83 easure the capillary density index (CDI) and fractal dimension (FD) at the superficial vascular plexu
84 uring clinical examination were used for the fractal dimension (FD) calculations.
85 A) devices by comparing vessel density (VD), fractal dimension (FD), and foveal avascular zone (FAZ)
86  skeleton density (SD), vessel density (VD), fractal dimension (FD), and vessel diameter index (VDI).
87 ulation was measured with the maximal apical fractal dimension (FD), which is a marker of endocardial
88  evaluated to quantify LV trabeculation as a fractal dimension (FD).
89 sity (VLD), vessel diameter index (VDI), and fractal dimension (FD).
90 io, 4.18+/-0.71 vs. 4.32+/-0.87 [P = 0.129]; fractal dimension [Df] value, 1.78+/-0.06 vs. 1.78+/-0.0
91 ing the ultrasonic wave detection method and fractal dimension analyses, how freeze-thaw induced frac
92 tion and avalanches, stems directly from the fractal dimension and energy function of these paths.
93  structures by using thresholding, to derive fractal dimension and fractal abundance.
94 the fractal parameters of particles, such as fractal dimension and fractal prefactor, is insignifican
95                            Low mitochondrial fractal dimension and high lacunarity correlates with in
96                                              Fractal dimension and lacunarity measurements are a sens
97 alities, including narrower caliber, reduced fractal dimension and larger branching angle, suggesting
98                      Control cells have high fractal dimension and low lacunarity and are relatively
99 al structure of chromatin due to increase in fractal dimension correlates with increased heterogeneit
100                                  The surface fractal dimension D is a measure that indicates the amou
101                The results show that surface fractal dimension D s of inaccessible pores is greater t
102  an exponent alpha within the whole range of fractal dimension D(1 < D < 2).
103 ted fibers appear to be quite straight (mass fractal dimension D(m) = 1), for the overall system 1<D(
104            The results show that the surface fractal dimension decreases for the two bioconverted coa
105  in wildfires and emitted as aggregates with fractal dimension Df approximately 1.8 mobility diameter
106 ethods and N2 adsorption for determining the fractal dimension for nanometric MoS2 and MoS2/Co cataly
107 er spectrum method was used to calculate the fractal dimension in intraretinal regions of interest id
108 materials, our results show that the surface fractal dimension is an important determinant in cloud d
109 icular, histogram mean, median, and entropy, fractal dimension mean and standard deviation, and secon
110         The maximum discrimination value for fractal dimension of 0.96 (standard error =0.025) for th
111  molar mass, Rh approximately M(1/d), with a fractal dimension of d approximately 2.5 rather than 3.
112 ring profiles were also used to estimate the fractal dimension of lambda N, which was found to be app
113         There is difference in the grayscale fractal dimension of retinal vasculature of diabetic pat
114                             We find that the fractal dimension of soot particles (one of the most rel
115 s fast (<15 min) thereby rapidly raising the fractal dimension of tephra deposits.
116 respectively, the density of soft spots, the fractal dimension of the avalanches, and their duration.
117 with control healthy eyes, we found that the fractal dimension of the GCL + IPL complex was significa
118                                          The fractal dimension of the indentation depth increases wit
119 if the latter is corrected using the surface fractal dimension of the insoluble cloud nucleus.
120 s and measured the subsequent changes in the fractal dimension of the intracellular structure.
121                                          The fractal dimension of the OPL and the GCL + IPL complex p
122       Furthermore, the M-PSF model, used the fractal dimension of the particle size distribution, exh
123                                          The fractal dimension of the segmented airway tree was less
124                          The size, shape and fractal dimension of this bead assembly all depend on th
125                  Moreover, the thickness and fractal dimension parameters of the retinal nerve fiber
126                              The increase of fractal dimension reduces both momentum and thermal boun
127                                          The fractal dimension shows an overall decrease with the inc
128            However, there is a case that the fractal dimension shows an unexpected increase between 1
129                                      A large fractal dimension suggests the concurrent nucleation of
130                   Decreased retinal vascular fractal dimension was associated with OHT (OR 1.37; 95%
131                                          The fractal dimension was evaluated by dimensional detrended
132 In G+LVH+ and G-LVH+ cohorts, maximal apical fractal dimension was greater than in controls (P<0.0001
133                                              Fractal dimension was higher for all the layers (except
134        Cell morphology complexity assayed by fractal dimension was inhibited in nocodazole- and cytoc
135 The average agglomerate relative density and fractal dimension were calculated using these data and u
136 , the highest AUROC values estimated for the fractal dimension were observed for GCL + IPL and INL.
137 l features (thickness, total reflectance and fractal dimension) of various intraretinal layers extrac
138 parameters (tortuosity, branching angle, and fractal dimension) were measured from digital retinal fu
139 .g. caliber, tortuosity, branching angle and fractal dimension) were measured quantitatively from 0.5
140 eased compared with controls (maximal apical fractal dimension, 1.249+/-0.07 versus 1.199+/-0.05; P=0
141 tal analysis of cine slices to calculate the fractal dimension, a unitless index of endocardial compl
142 ative, rescaled range, Higuchi's estimate of fractal dimension, aggregated variance, and detrended fl
143 ffective density, dynamic shape factor, mass fractal dimension, and coating thickness.
144 s of permeability, specific deposit, deposit fractal dimension, and deposit radius of gyration, at di
145                    Power-spectrum, Higuchi's fractal dimension, and generalized Hurst exponent based
146 he chaotic time-series, approximate entropy, fractal dimension, and Hurst exponent.
147 action, as well as increased its entropy and fractal dimension, and morphologically appears to be max
148 esponded with higher specific deposit, lower fractal dimension, and smaller radius of gyration.
149 the aggregate compactness, quantified by the fractal dimension, are taken together, we find that high
150     We analytically show that changes in the fractal dimension, D, of chromatin correspond to simulta
151                                          The fractal dimension, known as the degree of self-similarit
152                           During deposition, fractal dimension, radius of gyration, and permeability
153 fluid, these trends reversed, with increased fractal dimension, radius of gyration, and permeability.
154 erties of high porosity, large surface area, fractal dimension, robust enzymatic activity, good durab
155 , and by taking into account the chromatin's fractal dimension, we derive an analytical expression fo
156  geometrically frustrated and has a peculiar fractal dimension.
157 ed by calculating structural information and fractal dimension.
158 t was noted between the repeated studies for fractal dimension; mean difference was -0.024 (95% limit
159 shed method of orthogonality evaluation: the fractal dimensionality (DF).
160           A random walk model reproduces the fractal dimensionality of the dendrites observed experim
161                                          The fractal dimensions (Df) obtained from aggregation kineti
162 C, collision cascades are mass fractals with fractal dimensions in the range of 1-2, depending on io
163 e system dynamics (quantified by multiplying fractal dimensions of the four climatic factors) in nort
164 two shale samples were evaluated to estimate fractal dimensions using combined small angle X-ray scat
165 ZnO aggregates were characterized by smaller fractal dimensions when ionic strength, and the resultin
166 lume fraction of nanoparticles for different fractal dimensions.
167 sorption and the adsorption processes by the fractal dimensions.
168 zing fields, and is one of the first quantum fractals discovered in physics.
169 toriously difficult sampling methods and the fractal distribution of root diameters in the soil make
170 oreover, all birds presented similar overall fractal dynamics (for scales approximately 30 s to >4.4
171 In particular, animal behavior displays both fractal dynamics and periodic rhythms yet the relationsh
172 s in brain activity may exhibit scale-free ("fractal") dynamics.
173                                            A fractal electrode might increase both light transmission
174 e to investigate emergent behaviour within a fractal energy landscape in a system with tunable intern
175  that was ascribed to their hierarchical and fractal energy landscape, and is also different from [Fo
176 allenges, we present a set of reliable multi-fractal estimation algorithms for quantifying the struct
177  stage, and extruded flours exhibited higher fractal exponent h in agreement with the extended crysta
178 -order statistical histogram and model-based fractal features reflecting the whole-tumor voxel intens
179 imal matrix models of scars (MMMS), in which fractal-fibre bundles segregate heterogeneously to the h
180 , a regime dominated by long highly-branched fractal fingers gives way to one dominated by blunt stab
181 ls can be tailored from compact triangles to fractal flakes, and the pattern formation can be explain
182 at quantum Hall features associated with the fractal gaps are described by two integer topological qu
183 iological complexity can be quantified using fractal geometric features where we observed that fracta
184 posites (ECCs), the unique three-dimensional fractal geometrical configuration and low-temperature si
185                                              Fractal geometries, advanced electrode materials, and th
186 at the time of lactation adhere to a perfect fractal geometry - which is destroyed by breast cancer.
187 l hexagons around a central hexagon, exhibit fractal geometry features with self-similarity at differ
188 roots go back over two decades to the use of fractal geometry in the characterization of phase-space
189 sy rheology may be a consequence of emergent fractal geometry in the energy landscapes of many comple
190                              Could a loss of fractal geometry of the blood supply to human tissue be
191 ose bio-inspired electronics which adopt the fractal geometry of the neurons they interface with.
192 ectiveness in unweighted networks, the multi-fractal geometry of weighted complex networks, the role
193 structure-property relationship based on the fractal geometry theory, to describe the evolution of lo
194 microstructure (including size distribution, fractal geometry, and number of primary particles) was o
195 n transition produces porous nanocarbon with fractal geometry, which consists of mostly sp(2) carbons
196 at the relaxation dynamics of an anisotropic fractal globule is very similar to the behavior of biolo
197 ntact domains are also not consistent with a fractal globule.
198 t chromosome folding deviates from the ideal fractal-globule model at large length scales and that TA
199 y at submicron length scales where chromatin fractal globules are formed, is critical to understandin
200 roperties into account, it is suggested that fractal globules, even those made by synthetic polymers,
201 exhibit characteristics similar to those of 'fractal globules,' and even the most genomically-distant
202 h the integer QHE states associated with the fractal Hofstadter spectrum.
203 ure of reptile biodiversity is fundamentally fractal (i.e., it is scale invariant).
204 otropy, we find that the electron nematic is fractal in nature, and that it extends throughout the bu
205                 Thus, SCN-neural activity is fractal in the intact organism and these fractal pattern
206 ted non-equilibrium aggregation processes by fractal laws, moreover, applications in modern micro-flo
207 lly that acts as chain of oscillators with a fractal like resonance band.
208      The stock-GDI vehicle emits graphitized fractal-like aggregates over all driving conditions.
209 of many component systems and highly complex fractal-like and quasicrystalline systems discussed.
210  patterned into self-similar unit cells in a fractal-like geometry.
211 -dependent activity coefficient analogous to fractal-like kinetics formulated by Kopelman.
212 d against a periportal vascular niche with a fractal-like organization enabled by placental circulati
213 al and metal hydride nanocomposites showed a fractal-like porous morphology, with a primary particle
214 om straight gravity-aligned primary roots to fractal-like root architectures.
215                      The modified pore-solid fractal (M-PSF) model was tested using 26 soil samples f
216 nstructs are suggestive of a larger field of fractal materials that incorporate repeating geometries
217 al geometric features where we observed that fractal measures were also reduced significantly by 33%,
218                                              Fractal metallic dendrites have been drawing more attent
219  solid-phase reactor could be described by a fractal Michaelis-Menten model with a catalytic efficien
220                                   Within our fractal model, the effective defect diffusion length is
221 work addresses the long-standing debate over fractal models of packing structure in metallic glasses
222 ctronic materials patterned in deterministic fractal motifs and bonded to elastomers enable unusual m
223                                      Using a fractal n-back fMRI paradigm, we investigated brain resp
224 authors studied 1,129 youths who completed a fractal n-back task during functional magnetic resonance
225  questionnaire, fMRI during performance of a fractal n-back task, and (1)H-MRS, respectively.
226 tic resonance imaging paradigms were used: a fractal n-back working memory task probing executive sys
227                                              Fractal nanoplatinum with cauliflower-like morphology wa
228                 Their work reminds us of the fractal nature of cell surfaces and highlights how the u
229 ts demonstrate a general method by which the fractal nature of collision cascades can be used to expl
230 tion damage formation which accounts for the fractal nature of collision cascades.
231  hence reinforcing our conclusions about the fractal nature of reptile biodiversity.
232                                          The fractal nature of this process must, at some scale, pres
233 n resonance band, a new band appears, due to fractal nature, generation of newer energy levels never
234 and the relationship between small-world and fractal networks.
235                       Monkeys looked at many fractal objects, half of which were always associated wi
236 s evaluation of ultradian rhythms as well as fractal organization according to six different analytic
237 roscopy to show that anomalous diffusion and fractal organization of microvilli survey the majority o
238 hown to be necessary for normal self-similar/fractal organization of motor activity and heart rate ov
239 t demonstration that avian behavior presents fractal organization that predominates at shorter time s
240 The effect of drive cycle and the GPF on the fractal parameters of particles, such as fractal dimensi
241 cribed as fractals, the correlation of their fractal parameters with experimental observations of rad
242  temperatures ( approximately 2000 K) yields fractal particles of a larger size and high EC content (
243 l over turbulent dispersion to create strong fractal patchiness, where local phytoplankton concentrat
244  understand the evolutional origin of such a fractal pattern as well as the alterations of fractal pa
245 ractal pattern as well as the alterations of fractal pattern during diseased statuses.
246                                          The fractal pattern of heartbeats - a multiscale regulation
247         A novel biosensing platform based on fractal-pattern of iron oxides magnetic nanostructures (
248                                 However, the fractal patterns of SCN-neural activity are not autonomo
249  is fractal in the intact organism and these fractal patterns require network interactions between th
250                      However, the concept of fractal patterns was found to be insufficient to describ
251  the ordered oxygen and lattice defects form fractal patterns, as opposed to appearing in isolated sp
252 ithin the SCN is sufficient to generate such fractal patterns, we studied multi-unit neural activity
253 report of graphene paper functionalized with fractal platinum nanocauliflower for use in electrochemi
254  of particles, such as fractal dimension and fractal prefactor, is insignificant.
255 imulations demonstrating how an interplay of fractal properties generates enhanced stimulation; the e
256        Through an analysis of soil aggregate fractal properties supported by 3D microtomographic imag
257             This intricate topology presents fractal properties, resulting in a considerable corticom
258          Here we show that these bursts have fractal properties, with power-law scaling of burst size
259 egional blood flow in rectal cancer exhibits fractal properties.
260 l roles as hubs in a hierarchical scale-free fractal protein-protein interaction network.
261 point at air-entry suction in the pore-solid fractal (PSF) model, which additionally considered the h
262 of dendritic materials also exhibits obvious fractal qualities based on self-similar, repetitive, bra
263 redicts the interfacial contact stiffness of fractal rough surfaces by considering the effects of ela
264          These advantages are negated if the fractal's field is less effective at stimulating neurons
265 key role in dictating the existence of multi-fractal scaling and (ii) the multi-fractal scaling can b
266                            We show that this fractal scaling can arise through dispersion of random c
267  of multi-fractal scaling and (ii) the multi-fractal scaling can be localized in both space and scale
268 was also associated with a higher short-term fractal scaling exponent (Ptrend=0.003) and lower Poinca
269                        We present two global fractal scaling formulas to describe these two distinct
270 rch from different fields and indicates that fractal scaling may be a highly sensitive metric for ind
271          In this study, we demonstrated that fractal scaling of BOLD fMRI signal is consistently supp
272  loss of temporal complexity and a change in fractal scaling of the torque signal during isometric kn
273                               Complexity and fractal scaling of torque were quantified by calculating
274                               Complexity and fractal scaling of torque were quantified by calculating
275 topological Rentian scaling, and topological fractal scaling--in addition to several summary statisti
276                 Levy flights are scale-free (fractal) search patterns found in a wide range of animal
277                                      Using a fractal shape channel design and automated image analysi
278                                 Furthermore, fractal shaped gold nanostructured electrodes are examin
279          We demonstrated a crossover between fractal short-range (<2 atomic diameters) and homogeneou
280 of the medial tibial plateau was analyzed by fractal signature analysis using commercially available
281 es, but also causes partial restructuring of fractal soot aggregates.
282 treet network dynamics can be described as a fractal space-filling phenomena up to a capacitated limi
283  theory of transport in aperiodic media with fractal spectra, and additionally demonstrate logarithmi
284 rmation of superlattice minibands (forming a fractal spectrum known as Hofstadter's butterfly) has be
285 ing unprecedented experimental access to the fractal spectrum.
286  Subjects were presented with eight pairs of fractal stimuli, for 50 trials each.
287 ght sources and similar devices, has a quasi-fractal structure and is derived directly from a chemica
288 cess, reflecting the plastic deformation has fractal structure at the temperature of 223 K and strain
289  activation-type motion of DW and reveal the fractal structure of DW near the depinning transition.
290 re we show that metallic networks with quasi-fractal structure provides a near-perfect practical real
291 wo states of shear-branching structures: the fractal structure with a long-range order at an intermed
292 Human motor activity has a robust, intrinsic fractal structure with similar patterns from minutes to
293         The resulting surface reveals a C(1) fractal structure: Although the tangent plane is defined
294                                They may have fractal structures at the atomic level, but a physical m
295 ion in haze particle growth from monomers to fractal structures.
296               These results demonstrate that fractal submicrometer particles are responsible for the
297 h radius of gyration approximately 10 nm and fractal submicrometer particles formed by a slow reactio
298 all neighboring neurons is over 50% less for fractal than Euclidean electrodes.
299                          A specific class of fractal, the percolation cluster, explains the structura
300 n cascades have previously been described as fractals, the correlation of their fractal parameters wi
301 stark contrast to disease-dependent temporal fractals, we find the same prevalence of optimal Levy fl
302 both Si and SiC, collision cascades are mass fractals with fractal dimensions in the range of 1-2, d

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