Order statistics of 1/f^{\alpha} signals

Order statistics of periodic, Gaussian noise with 1/f^{\alpha} power spectrum is investigated. Using simulations and phenomenological arguments, we find three scaling regimes for the average gap d_k= between the k-th and (k+1)-st largest values of the signal. The result d_k ~ 1/k known for independent, identically distributed variables remains valid for 0<\alpha<1. Nontrivial, \alpha-dependent scaling exponents d_k ~ k^{(\alpha -3)/2} emerge for 1<\alpha<5 and, finally, \alpha-independent scaling, d_k ~ k is obtained for \alpha>5. The spectra of average ordered values \epsilon_k= ~ k^{\beta} is also examined. The exponent {\beta} is derived from the gap scaling as well as by relating \epsilon_k to the density of near extreme states. Known results for the density of near extreme states combined with scaling suggest that \beta(\alpha=2)=1/2, \beta(4)=3/2, and beta(infinity)=2 are exact values. We also show that parallels can be drawn between \epsilon_k and the quantum mechanical spectra of a particle in power-law potentials.Comment: 8 pages, 5 figure

Origin of the approximate universality of distributions in equilibrium correlated systems

We propose an interpretation of previous experimental and numerical experiments, showing that for a large class of systems, distributions of global quantities are similar to a distribution originally obtained for the magnetization in the 2D-XY model . This approach, developed for the Ising model, is based on previous numerical observations. We obtain an effective action using a perturbative method, which successfully describes the order parameter fluctuations near the phase transition. This leads to a direct link between the D-dimensional Ising model and the XY model in the same dimension, which appears to be a generic feature of many equilibrium critical systems and which is at the heart of the above observations.Comment: To appear in Europhysics Letter

Divergent Sensory Phenotypes in Nonspecific Arm Pain: Comparisons With Cervical Radiculopathy

Objectives: To investigate whether distinct sensory phenotypes were identifiable in individuals with nonspecific arm pain (NSAP) and whether these differed from those in people with cervical radiculopathy. A secondary question considered whether the frequency of features of neuropathic pain, kinesiophobia, high pain ratings, hyperalgesia, and allodynia differed according to subgroups of sensory phenotypes. Design: Cross-sectional study. Setting: Higher education institution.Participants: Forty office workers with NSAP, 17 people with cervical radiculopathy, and 40 age- and sex-matched healthy controls (N=97). Interventions: Not applicable. Main Outcome Measures: Participants were assessed using quantitative sensory testing (QST) comprising thermal and vibration detection thresholds and thermal and pressure pain thresholds; clinical examination; and relevant questionnaires. Sensory phenotypes were identified for each individual in the patient groups using z-score transformation of the QST data. Results: Individuals with NSAP and cervical radiculopathy present with a spectrum of sensory abnormalities; a dominant sensory phenotype was not identifiable in individuals with NSAP. No distinct pattern between clinical features and questionnaire results across sensory phenotypes was identified in either group. Conclusions: When considering sensory phenotypes, neither individuals with NSAP nor individuals with cervical radiculopathy should be considered homogeneous. Therefore, people with either condition may warrant different intervention approaches according to their individual sensory phenotype. Issues relating to the clinical identification of sensory hypersensitivity and the validity of QST are highlighted

Forming norms: informing diagnosis and management in sports medicine

Clinicians aim to identify abnormalities, and distinguish harmful from harmless abnormalities. In sports medicine, measures of physical function such as strength, balance and joint flexibility are used as diagnostic tools to identify causes of pain and disability and monitor progression in response to an intervention. Comparing results from clinical measures against ‘normal’ values guides decision-making regarding health outcomes. Understanding ‘normal’ is therefore central to appropriate management of disease and disability. However, ‘normal’ is difficult to clarify and definitions are dependent on context. ‘Normal’ in the clinical setting is best understood as an appropriate state of physical function. Particularly as disease, pain and sickness are expected occurrences of being human, understanding ‘normal’ at each stage of the lifespan is essential to avoid the medicalisation of usual life processes. Clinicians use physical measures to assess physical function and identify disability. Accurate diagnosis hinges on access to ‘normal’ reference values for such measures. However our knowledge of ‘normal’ for many clinical measures in sports medicine is limited. Improved knowledge of normal physical function across the lifespan will assist greatly in the diagnosis and management of pain, disease and disability

Subcellular localization of the FLT3-ITD oncogene plays a significant role in the production of NOX- and p22phox-derived reactive oxygen species in acute myeloid leukemia

Internal tandem duplication of the juxtamembrane domain of FMS-like tyrosine kinase 3 (FLT3-ITD) receptor is the most prevalent FLT3 mutation accounting for 20% of acute myeloid leukemia (AML) patients. FLT3-ITD mutation results in ligand-independent constitutive activation of the receptor at the plasma membrane and ‘impaired trafficking’ of the receptor in compartments of the endomembrane system, such as the endoplasmic reticulum (ER). FLT3-ITD expressing cells have been shown to generate increased levels of reactive oxygen species (ROS), in particular NADPH oxidase (NOX)-generated ROS which act as pro-survival signals. The purpose of this study is to investigate FLT3-ITD production of ROS at the plasma membrane and ER in the FLT3-ITD expressing AML cell line MV4-11. Receptor trafficking inhibitors; Tunicamycin and Brefeldin A induce ER retention of FLT3-ITD, resulting in a decrease in protein expression of NOX4 and its partner protein p22phox, thus demonstrating the critical importance of FLT3-ITD localization for the generation of pro-survival ROS. NOX-generated ROS contribute to total endogenous hydrogen peroxide (H2O2) in AML as quantified by flow cytometry using the cell-permeable H2O2-probe Peroxy Orange 1 (PO1). We found that PI3K/AKT signaling only occurs when FLT3-ITD is expressed at the plasma membrane and is required for the production of NOX-generated ROS. ER retention of FLT3-ITD resulted in NOX4 deglycosylation and p22phox protein degradation

Dynamically accelerated cover times

Among observables characterizing the random exploration of a graph or lattice, the cover time, namely, the time to visit every site, continues to attract widespread interest. Much insight about cover times is gained by mapping to the (spaceless) coupon collector problem, which amounts to ignoring spatiotemporal correlations, and an early conjecture that the limiting cover time distribution of regular random walks on large lattices converges to the Gumbel distribution in d ≥ 3 was recently proved rigorously. Furthermore, a number of mathematical and numerical studies point to the robustness of the Gumbel universality to modifications of the spatial features of the random search processes (e.g., introducing persistence and/or intermittence, or changing the graph topology). Here we investigate the robustness of the Gumbel universality to dynamical modification of the temporal features of the search, specifically by allowing the random walker to “accelerate” or “decelerate” upon visiting a previously unexplored site. We generalize the mapping mentioned above by relating the statistics of cover times to the roughness of 1 / f α Gaussian signals, leading to the conjecture that the Gumbel distribution is but one of a family of cover time distributions, ranging from Gaussian for highly accelerated cover, to exponential for highly decelerated cover. While our conjecture is confirmed by systematic Monte Carlo simulations in dimensions d > 3 , our results for acceleration in d = 3 challenge the current understanding of the role of correlations in the cover time problem

Ginzburg-Landau equation bound to the metal-dielectric interface and transverse nonlinear optics with amplified plasmon polaritons

Using a multiple-scale asymptotic approach, we have derived the complex cubic Ginzburg-Landau equation for amplified and nonlinearly saturated surface plasmon polaritons propagating and diffracting along a metal-dielectric interface. An important feature of our method is that it explicitly accounts for nonlinear terms in the boundary conditions, which are critical for a correct description of nonlinear surface waves. Using our model we have analyzed filamentation and discussed bright and dark spatially localized structures of plasmons.Comment: http://link.aps.org/doi/10.1103/PhysRevA.81.03385

The dependence of solar wind burst size on burst duration and its invariance across solar cycles 23 and 24

Time series of solar wind variables are “bursty” in nature. Bursts, or excursions, in the time series of solar wind parameters are associated with various transient structures in the solar wind plasma, and are often the drivers of increased space weather activity in Earth's magnetosphere. We define bursts by setting a threshold value of the time series and identifying how often, and for how long, it is exceeded. This allows us to study how the statistical distributions and scaling properties of burst parameters vary over solar cycles 23 and 24. We find the distributions of burst duration and integrated burst size vary over the solar cycle, and between the equivalent phases of consecutive cycles. However, there exists a single power law scaling relation between burst size and duration, with a joint area‐duration scaling exponent α that is independent of the solar cycle. This provides a solar cycle invariant constraint between possible sizes and durations of solar wind bursts that can occur

Extreme statistics for time series: Distribution of the maximum relative to the initial value

The extreme statistics of time signals is studied when the maximum is measured from the initial value. In the case of independent, identically distributed (iid) variables, we classify the limiting distribution of the maximum according to the properties of the parent distribution from which the variables are drawn. Then we turn to correlated periodic Gaussian signals with a 1/f^alpha power spectrum and study the distribution of the maximum relative height with respect to the initial height (MRH_I). The exact MRH_I distribution is derived for alpha=0 (iid variables), alpha=2 (random walk), alpha=4 (random acceleration), and alpha=infinity (single sinusoidal mode). For other, intermediate values of alpha, the distribution is determined from simulations. We find that the MRH_I distribution is markedly different from the previously studied distribution of the maximum height relative to the average height for all alpha. The two main distinguishing features of the MRH_I distribution are the much larger weight for small relative heights and the divergence at zero height for alpha>3. We also demonstrate that the boundary conditions affect the shape of the distribution by presenting exact results for some non-periodic boundary conditions. Finally, we show that, for signals arising from time-translationally invariant distributions, the density of near extreme states is the same as the MRH_I distribution. This is used in developing a scaling theory for the threshold singularities of the two distributions.Comment: 29 pages, 4 figure