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1 RNA raised to the power of an 'amplification exponent'.
2 percolation threshold, and mu is the dynamic exponent.
3 1 + nu, respectively, where nu is the Flory exponent.
4 ased more steeply, corresponding to a higher exponent.
5 the mRNA level and defines the amplification exponent.
6 surements of the volume-area fractal scaling exponent.
7 engths, but each type has a distinct scaling exponent.
8 ximate entropy, fractal dimension, and Hurst exponent.
9 ates a negative value in the LLK scaling-law exponent.
10 Golden Mean [Formula: see text] as dynamical exponent.
11 ly 2 regardless of the underlying population exponent.
12 ludes optimality models that predict the 0.2 exponent.
13 can be classified according to few critical exponents.
14 is able to produce power laws with arbitrary exponents.
15 each characterized by its specific critical exponents.
16 lations, with only three independent scaling exponents.
17 s diffusion models with adjustable anomalous exponents.
18 sition and compatible values of the critical exponents.
19 be characterized by their power-law scaling exponents.
20 t support the hypothesis of fixed allometric exponents.
21 ic crossover between two different power-law exponents.
22 patterns follow a power law with non-integer exponents.
23 that follow power laws with well-established exponents.
25 ed by a surprisingly small power-law scaling exponent (0.22) between the radius-of-gyration and Q-len
26 ~1/3) and bacterial chains (increasing with exponent ~0.5-0.8) are substantially lower than for well
27 ltiscale correlation of SERCA group (scaling exponent: 0.77 +/- 0.07), on the other hand, is weaker t
31 We validate the hypothesis of fractional exponents (1) by numerical simulation for disease propag
32 ion rates for microcolonies (increasing with exponent ~1/3) and bacterial chains (increasing with exp
33 r sizes and correlation lengths diverge with exponents ~1.6 and 0.8, respectively, consistent with pe
35 spectrum of cosmic rays, with the universal exponent -2, which is independent of the multiplication
37 t rate and wingbeat frequency (raised to the exponent 3.5) and estimated metabolic power and wingbeat
38 be recognized by a power-law dependence with exponent 3/2 of the shear modulus on stress, whereas the
39 masses exhibit power-law distributions with exponents -3/2 and -5/2 before and after percolation, as
41 on only the crown area-to-diameter allometry exponent: a well-conserved value across tropical forests
42 s is because the aerosol absorption Angstrom exponent (AAE) largely controls the color and larger par
44 organic aerosol with an absorption Angstrom exponent (AAE) of 2.5-2.7 and estimated Brown Carbon con
46 on [Formula: see text], where the 1/3 excess exponent above 2 (smooth surfaces) follows from Kolmogor
48 al depth, AOD), dominant size mode (Angstrom exponent, AE), and relative magnitude of radiation scatt
49 face exhibit transient subdiffusion, with an exponent alpha approximately 0.5 for times of less than
51 - D)) is valid, however for 1.5 < D < 2, the exponent alpha is different and equal to 2(D - 1)/D.
52 function of the normal contact load with an exponent alpha within the whole range of fractal dimensi
53 of variation of PEF (CVpef) and the scaling exponent alpha, reflecting self-similarity of PEF, in re
54 n coefficient D(t) in terms of the anomalous exponent alpha, the crossover time t(cross), and the lim
56 Kardar-Parisi-Zhang (KPZ) model with scaling exponents alpha = 0.71 +/- 0.12, beta = 0.36 +/- 0.03, a
57 ched exponential modeling (ADCSE), anomalous exponent (alpha) obtained at stretched exponential DWI,
58 exponential and segmented scaling laws with exponents (alpha) typically between 0.85 (Horwitz) and 1
61 scaling theory (MST) posits that the scaling exponents among plant height H, diameter D, and biomass
62 ive diagnosed from health, by characteristic exponent analysis of pulse signals accessed from volunte
64 a discrepancy between the observed power-law exponent and that predicted from the noise parameters.
67 Different metals will have different scaling exponents and shapes in their energy spreading, but the
68 ion d + zLambda(T), where z is the dynamical exponent, and temperature-depending parameter Lambda(T)
69 lley transitions, effective mass, scattering exponent, and the Fermi energy may deteriorate or amelio
73 ngth [Formula: see text] Mean-field critical exponents are predicted, since the upper critical dimens
79 ymptotes to zero with no need to fit unknown exponents as previously proposed in critical power law b
80 is subsequently used to measure the critical exponents associated with chiral clock models(10,11), pr
81 -structure factor, with continuously varying exponents, at any fixed separation in the late-time limi
84 of measurements is distributed in space, the exponent b of this power law is conjectured to reflect a
86 t a broad range of values for the population exponent b pertaining to the mean and variance of popula
89 ralized TL in terms of sample and population exponents b(jk) for the scaling of the kth vs. the jth c
90 where Tc is the critical temperature and the exponent beta was close to (1/4), as predicted for a tri
91 ed ferromagnetic region yields 3D Heisenberg exponents beta = 0.3460 +/- 0.040, gamma = 1.344 +/- 0.0
93 , N = 10) = 25.44, p = 1.2492e-05), spectral exponent between 1 and 20 Hz (chi-square (3, N = 16) = 4
94 N = 10) = 20, p = 4.5400e-05), and spectral exponent between 30-50 Hz (chi-square (2, N = 16) = 13.8
96 f a difference in the values of the critical exponents between the bond and site percolation models i
98 rom 20 human subjects, we calculated scaling exponents by four methods-two derived from local propert
100 flux distribution, which links the critical exponents characterizing the spatial dependencies in hum
102 e anisotropy exponent zeta and the roughness exponents chix,y that characterize these correlations.
103 rameter oscillating around unity, a critical exponent close to -3/2 and a long tail distribution of a
104 nt durations can be collapsed with a scaling exponent close to 2 supporting critical generational mod
106 at percent body fat scales to height with an exponent closer to 3, we therefore focused on the tri-po
107 wer, bandwidth) with aperiodic ones (offset, exponent), compromising physiological interpretations.
109 munities are characterized by an average ISD exponent consistent with three-quarter-power scaling of
110 These findings support the notion that TPL exponents contain ecological information, capturing comm
113 ve density (rho(eff)), mass-mobility scaling exponent ( D(m)), dynamic shape factor (chi), and mass a
114 found that on populated islands size spectra exponents decreased (analogous to size spectra steepenin
115 bined, leaf vs stem and leaf vs root scaling exponents decreased from c. 1.00 for small plants to c.
116 ut that simply inserting asymptotic critical exponents deduced from the immediate vicinity of the cri
117 s that can be described using single scaling exponents (denoted by beta, [Formula: see text], and lam
118 iently anomalous diffusion and the anomalous exponent depend on the size of model glomeruli and the d
119 follows a power law time dependence, with an exponent determined by the 1/f-type resonator frequency
120 clear relationship was observed between the exponents determined for the power law linking quadratic
122 act power laws, p(x) ~ x(-lambda), where the exponent directly corresponds to the mixing ratio of the
126 ics near the transition and obtain universal exponents establishing connection between thermal soften
127 ees closely with the mortality rate doubling exponent estimated at the cross-over age near the averag
129 theories predict that combinations of these exponents explain how metabolic, growth, and other biolo
130 any known relationships between the critical exponents explored by them, despite the fact that they o
132 l gamma = (d + z - 2)/z, where the dynamical exponent for a ferroelectric z = 1 and the dimension is
133 ly lower offset and a possible change in the exponent for Alzheimer's disease subjects compared with
134 etwork architecture for estimating the Hurst exponent for fractional Brownian motion and the diffusio
140 these allow for different body-size scaling exponents for anabolism (biosynthesis potential), beside
141 ely correlated with their associated scaling exponents for D vs. V and H vs. V, whereas normalization
143 The theory also predicts larger power-law exponents for lower-dimensional stimulus ensembles, whic
145 btaining the critical noise and the critical exponents for the two and three-state majority-vote mode
147 This enables robust estimation of Hurst exponents for very short time series data, making possib
148 near features (approximate entropy and Hurst exponent) for the first time to explore post-concussive
149 particular, more ballistic Levy flights with exponent [Formula: see text] are generally believed to o
150 , whose density is described by a nontrivial exponent [Formula: see text] We build a microscopic theo
151 diffusive universality class with dynamical exponent [Formula: see text], another prominent example
152 caling analysis, we obtain that the critical exponents [Formula: see text] and [Formula: see text] as
155 comitant increase in the absorption Angstrom exponent from 1.2 +/- 0.4 (5% RH) to 1.6 +/- 0.3 (70% RH
156 ntly, we show that the 3/4 metabolic scaling exponent from Kleiber's Law can still be attained within
160 ional, variant T(-) (gamma) , with the power exponent gamma = 1.4 +/- 0.1 in the cubic phase, indicat
163 an interactions with population size with an exponent gamma ranging between 1.11 and 1.21, as observe
164 natural basins and OCNs with varying energy exponent gamma to understand vulnerability and resilienc
165 s a crucial role in determining the critical exponents governing universal nonequilibrium dynamics in
167 and extruded flours exhibited higher fractal exponent h in agreement with the extended crystalline st
170 protein concentration as a power law, whose exponent has been used to infer the presence or absence
171 me-averaged optical coefficients, scattering exponent, hemoglobin concentration, oxygen saturation, a
172 us to give a precise meaning to the scaling exponent in terms of the degree to which a given process
173 e for epidemiological models with fractional exponent in the contribution of sub-populations to the i
174 ss implications of the changes in offset and exponent in the data and relate it to existing literatur
175 We suggest that calibration of the repulsive exponent in the LJ potential widens the range of applica
176 ation between quantum and classical Lyapunov exponents in a chaotic system without finite-size effect
177 roughout the neocortex with distinct scaling exponents in different functional brain systems and freq
178 allow us to explain a wide range of scaling exponents in frequency distributions ranging from alpha
179 how signs of kinks: clear changes in scaling exponent, indicating changes in the dominant molecular m
180 e observed variability of ecological scaling exponents into a coherent statistical framework where pa
181 in a broad class of growth models the sample exponent is b approximately 2 regardless of the underlyi
185 ltifractal spectrum based on the local Hurst exponent is used to quantify the complexity of fractal n
186 and temporal domains with the same algebraic exponent, is reproduced with numerical solutions of stoc
188 agonists (E(0)) and the affinity-correlation exponent (M)--allows an entire CRC to be calculated from
189 ercolation with a power law distribution and exponent matching the theoretical value in 2 dimensions.
191 uter simulations on a model system, that the exponent mu is not universal, but depends on the microsc
192 that can be quantitatively evaluated by the exponent n (ca. 3) of the temperature dependence of the
194 r rates (>500 s(-1)), at which the power law exponent (n) of zebrafish blood was nearly 1 behaving as
197 e results, however, suggest that the release exponents, n, correspond mostly to anomalous case II and
200 ize in a remarkably reciprocal fashion, with exponents near +/-3/4 within groups, as expected from me
201 are often well described by power laws with exponents near 3/4 or related to that value, a commonali
203 decreases with increasing m and the critical exponents nu, alpha, beta and gamma for m > 1 are found
209 ometer length scales, with the strengthening exponent of -0.68 at room temperature and of -1.00 at 90
210 scaling of NHP clearance with an allometric exponent of 0.50 allowed for good prediction of human cl
211 in translation and directs an amplification exponent of 1.20 with a 95% confidence interval [1.14, 1
214 7), which tallies with a dipolar interaction exponent of 2/3 in EC materials and the well-proven frac
218 ther observe an unprecedented sixfold-higher exponent of growth rate, faster onset, higher steady-sta
219 ith studying E-I ratio based on the spectral exponent of local field potentials and bioenergetics bas
220 olve this problem by considering the scaling exponent of shell thickness as a morphological parameter
221 c modulus E and fluidity beta (the power-law exponent of the cell deformation in response to a step c
222 numerical results on the correlation length exponent of the Chalker-Coddington model at nu ~ 2.6, ra
224 the decay in autocorrelation and the scaling exponent of the detrended fluctuation analysis from EEG
227 produce realistic conditions in terms of the exponent of the power-law distribution, of the number of
230 t seems likely that synchrony influences the exponent of TL widely in ecologically and economically i
232 m pre-existing nuclei as confirmed by Avrami exponents of 0.25 +/- 0.01 and 0.39 +/- 0.01 at the afor
235 ly, the lower the individual subject scaling exponents of delta/theta oscillations, the greater the c
237 ey fail to predict the correct values of the exponents of power-law degree distributions observed in
240 sis (DFA) has been used to calculate scaling exponents of stride time (ST), stride length (SL), and s
241 detrended fluctuation analysis (DFA) scaling exponents of the abiotic microcosms were lower (ca. 1.20
243 dent process, in the sense that the critical exponents of the transition are determined by the geomet
244 power-law distributions and that the average exponents of these individual size distributions (ISD) d
245 We demonstrate that the stationary critical exponents of this transition to meso-scale turbulence in
249 atin states apparently correspond to smaller exponent parameters and larger radius of gyrations.
251 also predicted a spectrum of power laws with exponents ranging between 0 and -2/3 for simple movement
253 ifferentiation operation on their input with exponents ranging from zero (no differentiation) to 0.4
254 tic attractor, along with a maximal Lyapunov exponent rate of about 2.94 times the fundamental optome
255 a fat-tailed distribution, with a universal exponent related to the recently observed universal [For
257 records exhibit scaling behavior with large exponents, resulting in larger fluctuations at longer ti
259 n intensity is described by a power law with exponents sequentially taking values 1, 1/3 and (1/4).
260 1-Ho also exhibits an anomalously low Raman exponent similar to 1-Dy, both being distinct from the l
263 periodicity of about 2 y, a global Lyapunov exponent statistically indistinguishable from zero, and
264 d 200 degrees C exhibits a positive Lyapunov exponent, suggesting that the underlying dynamics is cha
265 km(2) are power-law distributed with a tail exponent (tau = 1.97) and fractal dimension (d = 1.38),
266 -law distribution for the cell size, with an exponent that depends inversely on the noise in the time
267 la: see text], where theta is a nonuniversal exponent that depends on the statistics of the disorder.
269 istribution of energy over frequency with an exponent that, even in the ultrarelativistic limit, stro
270 istinguishable from zero, and local Lyapunov exponents that alternated systematically between negativ
272 distributions of states are power laws with exponents that coincide with the multiplication paramete
273 ied electric current and determined critical exponents that coincided with those for thermodynamic li
274 ear stress featuring power law rheology with exponents that match those of reconstituted collagen and
275 a marked suppression in their characteristic exponents that reflects a weakened sensitivity to initia
276 lerated the bacterial and fungal STR and PTR exponents (that is, the w values), yielding significantl
277 s is set by the triple isotope fractionation exponent theta that can be determined precisely for, e.g
278 We propose the inference of the repulsion exponent through Hierarchical Bayesian uncertainty quant
279 pectral shape causes the absorption Angstrom exponent to decrease by 0.18 per unit increase in pH.
280 ratigraphy; converting the temporal Lyapunov exponent to vertical distance using the mean sedimentati
283 e found a large variability of the anomalous exponent, used to interpret live cell imaging trajectori
284 For a same scaling phenomenon, however, the exponents vary in cities of similar population sizes.
286 he aim of this study was to test whether TPL exponents vary systematically with potential drivers of
287 appears to be ubiquitous, empirical scaling exponents vary with ecosystem type and resource supply r
288 teps drawn from a Levy distribution with the exponent varying from [Formula: see text] to [Formula: s
289 escribed by a continuously varying power law exponent versus energy and temperature (hence named a Po
291 onal Brownian motion with a stochastic Hurst exponent was used to interpret, for the first time, anom
292 mple entropy, trapping time and the Lyapunov exponents) was found in the centrotemporal region of the
293 etabolism scales to body size with a smaller exponent whenever temperatures or activity levels are hi
294 to the kinetic model, we determine the power exponent, which represents the dimensionality of surface
296 to be a power law function of P with scaling exponent X [demographic conflict investment (DCI)].
298 ntum phase transition has dynamical critical exponent z 2, typical of a Lifshitz transition, but is d
300 determine the exact values of the anisotropy exponent zeta and the roughness exponents chix,y that ch