All scale-free networks are sparse

We study the realizability of scale free-networks with a given degree sequence, showing that the fraction of realizable sequences undergoes two first-order transitions at the values 0 and 2 of the power-law exponent. We substantiate this finding by analytical reasoning and by a numerical method, proposed here, based on extreme value arguments, which can be applied to any given degree distribution. Our results reveal a fundamental reason why large scale-free networks without constraints on minimum and maximum degree must be sparse.Comment: 4 pages, 2 figure

Moses, Noah and Joseph effects in Levy walks

We study a method for detecting the origins of anomalous diffusion, when it is observed in an ensemble of times-series, generated experimentally or numerically, without having knowledge about the exact underlying dynamics. The reasons for anomalous diffusive scaling of the mean-squared displacement are decomposed into three root causes: increment correlations are expressed by the 'Joseph effect' (Mandelbrot and Wallis 1968 Water Resour. Res.4 909), fat-tails of the increment probability density lead to a 'Noah effect' (Mandelbrot and Wallis 1968 Water Resour. Res.4 909), and non-stationarity, to the 'Moses effect' (Chen et al 2017 Phys. Rev. E 95 042141). After appropriate rescaling, based on the quantification of these effects, the increment distribution converges at increasing times to a time-invariant asymptotic shape. For different processes, this asymptotic limit can be an equilibrium state, an infinite-invariant, or an infinite-covariant density. We use numerical methods of time-series analysis to quantify the three effects in a model of a non-linearly coupled Levy walk, compare our results to theoretical predictions, and discuss the generality of the method

Critical Behavior of O(n)-symmetric Systems With Reversible Mode-coupling Terms: Stability Against Detailed-balance Violation

We investigate nonequilibrium critical properties of $O(n)$-symmetric models with reversible mode-coupling terms. Specifically, a variant of the model of Sasv\'ari, Schwabl, and Sz\'epfalusy is studied, where violation of detailed balance is incorporated by allowing the order parameter and the dynamically coupled conserved quantities to be governed by heat baths of different temperatures $T_S$ and $T_M$, respectively. Dynamic perturbation theory and the field-theoretic renormalization group are applied to one-loop order, and yield two new fixed points in addition to the equilibrium ones. The first one corresponds to $\Theta = T_S / T_M = \infty$ and leads to model A critical behavior for the order parameter and to anomalous noise correlations for the generalized angular momenta; the second one is at $\Theta = 0$ and is characterized by mean-field behavior of the conserved quantities, by a dynamic exponent $z = d / 2$ equal to that of the equilibrium SSS model, and by modified static critical exponents. However, both these new fixed points are unstable, and upon approaching the critical point detailed balance is restored, and the equilibrium static and dynamic critical properties are recovered.Comment: 18 pages, RevTeX, 1 figure included as eps-file; submitted to Phys. Rev.

Nonlinear evolution of surface morphology in InAs/AlAs superlattices via surface diffusion

Continuum simulations of self-organized lateral compositional modulation growth in InAs/AlAs short-period superlattices on InP substrate are presented. Results of the simulations correspond quantitatively to the results of synchrotron x-ray diffraction experiments. The time evolution of the compositional modulation during epitaxial growth can be explained only including a nonlinear dependence of the elastic energy of the growing epitaxial layer on its thickness. From the fit of the experimental data to the growth simulations we have determined the parameters of this nonlinear dependence. It was found that the modulation amplitude don't depend on the values of the surface diffusion constants of particular elements.Comment: 4 pages, 3 figures, published in Phys. Rev. Lett. http://link.aps.org/abstract/PRL/v96/e13610

Braided Rivers and Superconducting Vortex Avalanches

Magnetic vortices intermittently flow through preferred channels when they are forced in or out of a superconductor. We study this behavior using a cellular model, and find that the vortex flow can make braided rivers strikingly similar to aerial photographs of braided fluvial rivers, such as the Brahmaputra. By developing an analysis technique suitable for characterizing a self-affine (multi)fractal, the scaling properties of the braided vortex rivers in the model are compared with those of braided fluvial rivers. We suggest that avalanche dynamics leads to braiding in both cases.Comment: 4 pages, 3 figures. To appear in PR

Isotropic Transverse XY Chain with Energy- and Magnetization Currents

The ground-state correlations are investigated for an isotropic transverse XY chain which is constrained to carry either a current of magnetization J_M or a current of energy J_E. We find that the effect of nonzero J_M on the large-distance decay of correlations is twofold: i) oscillations are introduced and ii) the amplitude of the power law decay increases with increasing current. The effect of energy current is more complex. Generically, correlations in current carrying states are found to decay faster than in the J_E=0 states, contrary to expectations that correlations are increased by the presence of currents. However, increasing the current, one reaches a special line where the correlations become comparable to those of the J_E=0 states. On this line, the symmetry of the ground state is enhanced and the transverse magnetization vanishes. Further increase of the current destroys the extra symmetry but the transverse magnetization remains at the high-symmetry, zero value.Comment: 7 pages, RevTex, 4 PostScript figure

Flicker electroretinogram in newborn infants

PURPOSE To develop and validate a flicker electroretinogram (ERG) protocol in term-born neonates as a potential tool for assessing preterm infants at risk of developing retinopathy of prematurity. METHODS A custom flicker ERG protocol was developed for use with the hand-held RETeval® electrophysiology device. Feasibility of measuring flicker ERG through closed eyelids and without mydriasis was established in a pilot study enabling optimisation of the test protocol. Following this, healthy term-born neonates (gestational age 37-42 weeks) were recruited at the Neonatology clinic of the University Hospital Zurich. Flicker ERG recordings were performed using proprietary disposable skin electrodes during the first four days of life when the infants were sleeping. Flicker stimuli were presented at 28.3 Hz for a stimulus series at 3, 6, 12, 30, and 50 cd·s/m$^{2}$, with two measurements at each stimulus level. Results were analysed offline. Flicker ERG peak times and amplitudes were derived from the averaged measurements per stimulus level for each subject. RESULTS 28 term-born neonates were included in the analysis. All infants tolerated the testing procedure well. Flicker ERG recording was achieved in all subjects with reproducible flicker ERG waveforms for 30 and 50 cd·s/m$^{2}$ stimuli. Reproducible ERGs were recorded in the majority of infants for the weaker stimuli (with detectable ERGs in 20/28, 25/28, and 27/28 at 3, 6, and 12 cd·s/m$^{2}$, respectively). Flicker ERG amplitudes increased with increasing stimulus strength, with peak times concurrently decreasing slightly. CONCLUSION Flicker ERG recording is feasible and reliably recorded in sleeping neonates through closed eyelids using skin electrodes and without mydriasis. Flicker ERG amplitude decreases for lower luminance flicker but remains detectable for 3 cd·s/m$^{2}$ flicker in the majority of healthy term-born neonates. These data provide a basis to study retinal function in premature infants using this protocol

Flicker electroretinogram in preterm infants

BACKGROUND Infants born prematurely are at risk of developing retinopathy of prematurity, which is associated with abnormalities in retinal function as measured using electroretinography. The aim of this study was to record non-invasive flicker electroretinograms (ERGs) in preterm infants and compare function of moderate and very or extremely preterm infants. METHODS In this non-randomized, cross-sectional study, 40 moderate preterm (gestational age (GA) 34 0/7 to 36 6/7 weeks, Group A) and 40 very or extremely preterm infants (GA ≤ 31 weeks, Group B) were recruited for flicker ERG recording through closed eyelids using the RETeval® device and skin electrodes. Group A was tested within the first week of life and Group B between 34th and 37th week postmenstrual age. Flicker stimuli were presented at 28.3 Hz with stimulus levels of 3, 6, 12, 30 and 50 cd•s/m$^{2}$. Primary endpoints were peak time (ms) and amplitude (µV). RESULTS Flicker ERGs were recordable in most infants with the highest proportion of reproducible ERGs at 30 cd•s/m$^{2}$. Amplitudes increased with stronger flicker stimulation, while peak times did not differ significantly between stimulus levels nor groups. Amplitudes were significantly greater in Group B at the strongest stimulus level (Mann-Whitney-U-Test=198.00, Z = 4.097, p = <0.001). CONCLUSIONS Feasibility of collecting flicker ERG data in most preterm infants was confirmed. We found no evidence of reduced retinal responses to flicker stimuli associated with extreme prematurity. Higher amplitudes in very and extremely preterm infants could indicate acceleration of retinal development following birth, triggered by visual stimulation

Magnetization distribution in the transverse Ising chain with energy flux

The zero-temperature transverse Ising chain carrying an energy flux j_E is studied with the aim of determining the nonequilibrium distribution functions, P(M_z) and P(M_x), of its transverse and longitudinal magnetizations, respectively. An exact calculation reveals that P(M_z) is a Gaussian both at j_E=0 and j_E not equal 0, and the width of the distribution decreases with increasing energy flux. The distribution of the order-parameter fluctuations, P(M_x), is evaluated numerically for spin-chains of up to 20 spins. For the equilibrium case (j_E=0), we find the expected Gaussian fluctuations away from the critical point while the critical order-parameter fluctuations are shown to be non-gaussian with a scaling function Phi(x)=Phi(M_x/)=P(M_x) strongly dependent on the boundary conditions. When j_E not equal 0, the system displays long-range, oscillating correlations but P(M_x) is a Gaussian nevertheless, and the width of the Gaussian decreases with increasing j_E. In particular, we find that, at critical transverse field, the width has a j_E^(-3/8) asymptotic in the j_E -> 0 limit.Comment: 8 pages, 5 ps figure

A systematic survey of randomised trials that stopped early for reasons of futility

BACKGROUND Randomised trial protocols may incorporate interim analyses, with the potential to stop the study for futility if early data show insufficient promise of a treatment benefit. Previously, we have shown that this approach will theoretically lead to mis-estimation of the treatment effect. We now wished to ascertain the importance of this phenomenon in practice. METHODS We reviewed the methods and results in a set of trials that had stopped for futility, identified through an extensive literature search. We recorded clinical areas, interventions, study design, outcomes, trial setting, sponsorship, planned and actual treatment effects, sample sizes; power; and if there was a data safety monitoring board, or a published protocol. We identified: if interim analyses were pre-specified, and how many analyses actually occurred; what pre-specified criteria might define futility; if a futility analysis formed the basis for stopping; who made the decision to stop; and the conditional power of each study, i.e. the probability of statistically significant results if the study were to continue to its complete sample size. RESULTS We identified 52 eligible trials, covering many clinical areas. Most trials had multiple centres, tested drugs, and 40% were industry sponsored. There were 75% where at least one interim analysis was planned a priori; a majority had only one interim analysis, typically with about half the target total sample size. A majority of trials did not pre-define a stopping rule, and a variety of reasons were given for stopping. Few studies calculated and reported low conditional power to justify the early stop. When conditional power could be calculated, it was typically low, especially under the current trend hypothesis. However, under the original design hypothesis, a few studies had relatively high conditional power. Data collection often continued after the interim analysis. CONCLUSIONS Although other factors will typically be involved, we conclude that, from the perspective of conditional power, stopping early for futility was probably reasonable in most cases, but documentation of the basis for stopping was often missing or vague. Interpretation of truncated trials would be enhanced by improved reporting of stopping protocols, and of their actual execution