A frequency measure robust to linear filtering

A definition of frequency (cycles per unit-time) based on an approximate reconstruction of the phase-space trajectory of an oscillator from a signal is introduced. It is shown to be invariant under linear filtering, and therefore inaccessible by spectral methods. The effect of filtering on frequency in cases where this definition does not perfectly apply is quantified.Comment: 10 pages, 2 figure

The Amplitude Mode in the Quantum Phase Model

We derive the collective low energy excitations of the quantum phase model of interacting lattice bosons within the superfluid state using a dynamical variational approach. We recover the well known sound (or Goldstone) mode and derive a gapped (Higgs type) mode that was overlooked in previous studies of the quantum phase model. This mode is relevant to ultracold atoms in a strong optical lattice potential. We predict the signature of the gapped mode in lattice modulation experiments and show how it evolves with increasing interaction strength.Comment: 4 pages, 3 figure

Influence of berry growth and growth regulators on the development of grape peduncles in Vitis vinifera L.

Removal of grape berries (cv. Roter Gutedel) after setting (10 d after anthesis) had just a slight effect on the subsequent health of the peduncle. But if younger berries of flowers were removed before this stage the peduncle formed abscission layers along its length, and/or it died. Treatment of deflowered peduncles with a-naphthalene acetic acid (NAi\) prevented peduncle abscission and death; it is suggested that auxins produced by flowers have a hormonal role in maintaining normal development of the peduncle. Treatment with 2-chloroethyltrimethyl ammonium chloride (CCC), benzyladenine (BA), indole-3-acetic acid (IAA) or 3-indolebutyric acid (IBA) did not give these effects. The lack of effect of the latter two compounds (auxins) is possibly due to their catabolism.Treatment with gibberellic acid (GA) resembled NAA in that it also maintained the health of deflowered peduncles, but GA had the additional effect of causing prolonged development of metaxylem. Gibberellin produced by developing berries may also have a hormonal role in peduncle development. The occurrence of grape peduncle necrosis (stiellaehme), which appears associated with a gibberellin deficiency during setting, supports this idea

Detecting periodicity in experimental data using linear modeling techniques

Fourier spectral estimates and, to a lesser extent, the autocorrelation function are the primary tools to detect periodicities in experimental data in the physical and biological sciences. We propose a new method which is more reliable than traditional techniques, and is able to make clear identification of periodic behavior when traditional techniques do not. This technique is based on an information theoretic reduction of linear (autoregressive) models so that only the essential features of an autoregressive model are retained. These models we call reduced autoregressive models (RARM). The essential features of reduced autoregressive models include any periodicity present in the data. We provide theoretical and numerical evidence from both experimental and artificial data, to demonstrate that this technique will reliably detect periodicities if and only if they are present in the data. There are strong information theoretic arguments to support the statement that RARM detects periodicities if they are present. Surrogate data techniques are used to ensure the converse. Furthermore, our calculations demonstrate that RARM is more robust, more accurate, and more sensitive, than traditional spectral techniques.Comment: 10 pages (revtex) and 6 figures. To appear in Phys Rev E. Modified styl

Test your surrogate data before you test for nonlinearity

The schemes for the generation of surrogate data in order to test the null hypothesis of linear stochastic process undergoing nonlinear static transform are investigated as to their consistency in representing the null hypothesis. In particular, we pinpoint some important caveats of the prominent algorithm of amplitude adjusted Fourier transform surrogates (AAFT) and compare it to the iterated AAFT (IAAFT), which is more consistent in representing the null hypothesis. It turns out that in many applications with real data the inferences of nonlinearity after marginal rejection of the null hypothesis were premature and have to be re-investigated taken into account the inaccuracies in the AAFT algorithm, mainly concerning the mismatching of the linear correlations. In order to deal with such inaccuracies we propose the use of linear together with nonlinear polynomials as discriminating statistics. The application of this setup to some well-known real data sets cautions against the use of the AAFT algorithm.Comment: 14 pages, 15 figures, submitted to Physical Review

Using Topological Statistics to Detect Determinism in Time Series

Statistical differentiability of the measure along the reconstructed trajectory is a good candidate to quantify determinism in time series. The procedure is based upon a formula that explicitly shows the sensitivity of the measure to stochasticity. Numerical results for partially surrogated time series and series derived from several stochastic models, illustrate the usefulness of the method proposed here. The method is shown to work also for high--dimensional systems and experimental time seriesComment: 23 RevTeX pages, 14 eps figures. To appear in Physical Review

Calcifediol versus vitamin D3 effects on gait speed and trunk sway in young postmenopausal women: a double-blind randomized controlled trial

UNLABELLED In this double-blind RCT, 4-month treatment with calcifediol compared with vitamin D3 improved gait speed by 18 % among young postmenopausal women. Consistently, change in 25(OH)D blood levels over time were significantly correlated with improvement in gait speed in these women. No effect could be demonstrated for trunk sway. INTRODUCTION The aim of this study is to test the effect of calcifediol compared with vitamin D3 on gait speed and trunk sway. METHODS Twenty healthy postmenopausal women with an average 25(OH)D level of 13.2 ng/ml (SD = ±3.9) and a mean age of 61.5 years (SD = ±7.2) were randomized to either 20 μg of calcifediol or 20 μg (800 IU) of vitamin D3 per day in a double-blind manner. At baseline and at 4 months of follow-up, the same physiotherapist blinded to treatment allocation tested 8-m gait speed and a body sway test battery (Sway star pitch and roll angle plus velocity while walking 8 m, and standing on both legs on a hard and soft surface). All analyses adjusted for baseline measurement, age, and body mass index. RESULTS Mean 25(OH)D levels increased to 69.3 ng/ml (SD = ±9.5) in the calcifediol group and to 30.5 ng/ml (SD = ±5.0) in the vitamin D3 group (p < 0.0001). Women receiving calcifediol compared with vitamin D3 had an 18 % greater improvement in gait speed at 4-month follow-up (p = 0.046) adjusting for baseline gait speed, age, and body mass index. Also, change in gait speed was significantly correlated with change in serum 25(OH)D concentrations (r = 0.5; p = 0.04). Across three tests of trunk sway, there were no consistent differences between groups and no significant correlation between change in 25(OH)D serum concentrations and change in trunk sway. CONCLUSIONS Calcifediol improved gait speed in early postmenopausal women compared with vitamin D3 and change in 25(OH)D level was moderately correlated with improvement in gait speed. A benefit on trunk sway could not be demonstrated

Statistics of finite-time Lyapunov exponents in the Ulam map

The statistical properties of finite-time Lyapunov exponents at the Ulam point of the logistic map are investigated. The exact analytical expression for the autocorrelation function of one-step Lyapunov exponents is obtained, allowing the calculation of the variance of exponents computed over time intervals of length $n$. The variance anomalously decays as $1/n^2$. The probability density of finite-time exponents noticeably deviates from the Gaussian shape, decaying with exponential tails and presenting $2^{n-1}$ spikes that narrow and accumulate close to the mean value with increasing $n$. The asymptotic expression for this probability distribution function is derived. It provides an adequate smooth approximation to describe numerical histograms built for not too small $n$, where the finiteness of bin size trimmes the sharp peaks.Comment: 6 pages, 4 figures, to appear in Phys. Rev.

Level Crossing Analysis of the Stock Markets

We investigate the average frequency of positive slope $\nu_{\alpha}^{+}$, crossing for the returns of market prices. The method is based on stochastic processes which no scaling feature is explicitly required. Using this method we define new quantity to quantify stage of development and activity of stocks exchange. We compare the Tehran and western stock markets and show that some stocks such as Tehran (TEPIX) and New Zealand (NZX) stocks exchange are emerge, and also TEPIX is a non-active market and financially motivated to absorb capital.Comment: 6 pages and 4 figure