Measure Of Fluctuations Research Articles

Out-of-time-order fluctuation-dissipation theorem

We prove a generalized fluctuation-dissipation theorem for a certain class of out-of-time-ordered correlators (OTOCs) with a modified statistical average, which we call bipartite OTOCs, for general quantum systems in thermal equilibrium. The difference between the bipartite and physical OTOCs defined by the usual statistical average is quantified by a measure of quantum fluctuations known as the Wigner-Yanase skew information. Within this difference, the theorem describes a universal relation between chaotic behavior in quantum systems and a nonlinear-response function that involves a time-reversed process. We show that the theorem can be generalized to higher-order n-partite OTOCs as well as in the form of generalized covariance.

Volatility forecast with artificial neural networks as univariate time series, with examples from stock market indexes

The tools that are offered to investors in financial markets are fluctuating. As this fluctuation causes losses as well as earnings, it is characterised as a risk for the investor. Especially, fluctuations that may occur in globally important markets and financial instruments have great significance, not just for investor but also for the global economy. Volatility, as a measure of fluctuations taking place in markets, is often used particularly by investors and all economic actors. Therefore, in recent years, future volatility predictions have gained importance. The aim of this research is forecasting future volatility values using the historical data of S&P 500, FTSE 100 and NIKKEI 225 stock market indexes. The progress of historical volatility values in years is presented and generated univariate time series is modelled with artificial neural networks. Future forecasts are done with the obtained model and results are interpreted.
 Keywords: Artificial neural networks, volatility, time series analysis, stock market indexes.

Aperture averaging in strong oceanic turbulence

Receiver aperture averaging technique is employed in underwater wireless optical communication (UWOC) systems to mitigate the effects of oceanic turbulence, thus to improve the system performance. The irradiance flux variance is a measure of the intensity fluctuations on a lens of the receiver aperture. Using the modified Rytov theory which uses the small-scale and large-scale spatial filters, and our previously presented expression that shows the atmospheric structure constant in terms of oceanic turbulence parameters, we evaluate the irradiance flux variance and the aperture averaging factor of a spherical wave in strong oceanic turbulence. Irradiance flux variance variations are examined versus the oceanic turbulence parameters and the receiver aperture diameter are examined in strong oceanic turbulence. Also, the effect of the receiver aperture diameter on the aperture averaging factor is presented in strong oceanic turbulence.

Equation of State and Freezeout in QCD with Staggered Quarks

We report the equation of state at finite chemical potential, namely the baryon number density and the baryonic contribution to the pressure, using a resummation of the Taylor expansion. We also report the freezeout conditions for a measure of fluctuations. We examine the major sources of systematic and statistical errors in all of these measurements.

Altered regional and integrated resting-state brain activity in general social anxiety disorder patients before and after group cognitive behavior therapy

We aimed to investigate the recovery neuromechanism underlying the treatment efficacy in generalized social anxiety disorder (GSAD). We recruited fifteen patients with GSAD and nineteen healthy control (HC) participants, all of whom underwent a baseline resting-state fMRI scan. The GSAD patients underwent an additional fMRI scan after group cognitive behavior therapy (GCBT). Amplitude of low-frequency fluctuation (ALFF) and degree centrality (DC) measures were used to examine altered regional and integrated spontaneous brain activity in group comparisons. After GCBT, ALFF of the right precuneus decreased. At baseline, the GSAD group showed higher ALFF in the left precuneus and the left middle temporal gyrus (MTG) and lower ALFF in the lingual gyrus compared with the HC group. The DC of the left precuneus and the MTG were attenuated and the right putamen increased in the post-treatment group. The changes in DC in the precuneus were positively correlated with changes in clinical symptom. The abnormal ALFF of the precuneus, MTG and lingual gyrus may be the neural underpinning of GSAD, whereas the neural response to symptom remission after GCBT was achieved by a rebalance within the default mode network.

Event-by-event mean fluctuations and transverse size of color flux tube generated in p–p collisions at = 0.90 TeV

We propose a novel phenomenological model of mean transverse momentum fluctuations based on the geometrical scaling hypothesis. Bose–Einstein correlations between two gluons generated from an identical color flux tube are taken into account as a source of the fluctuation. We calculate an event-by-event fluctuation measure and show that ALICE data observed at TeV for p+p collisions are reproduced. By fitting our model to the experimental data, we evaluate the transverse size of the color flux tube as a function of the multiplicity.

Detection of the Sleep Stages Throughout Non-Obtrusive Measures of Inter-Beat Fluctuations and Motion: Night and Day Sleep of Female Shift Workers

Automatic sleep staging based on inter-beat fluctuations and motion signals recorded through a pressure bed sensor during sleep is presented. The analysis of the sleep was based on the three major divisions of the sleep time: Wake, non-rapid eye movement (nREM) and rapid eye movement (REM) sleep stages. Twelve sleep recordings, from six females working alternate shift, with their respective annotations were used in the study. Six recordings were acquired during the night and six during the day after a night shift. A Time-Variant Autoregressive Model was used to extract features from inter-beat fluctuations which later were fed to a Support Vector Machine classifier. Accuracy, Kappa index, and percentage in wake, REM and nREM were used as performance measures. Comparison between the automatic sleep staging detection and the standard clinical annotations, shows mean values of [Formula: see text]% for accuracy [Formula: see text] for kappa index, and mean errors of 5% for sleep stages. The performance measures were similar for night and day sleep recordings. In this sample of recordings, the results suggest that inter-beat fluctuations and motions acquired in non-obtrusive way carried valuable information related to the sleep macrostructure and could be used to support to the experts in extensive evaluation and monitoring of sleep.

Identity method reexamined

We discuss the impact of finite particle losses associated with instrumental effects in measurements of moments of produced multiplicities with the Identity Method towards the evaluation of fluctuation measures such as $\nu_{dyn}$. We show that the identity method remains applicable provided it is modified to determine factorial moments $\langle N(N-1)\rangle$, rather than moments $\langle N^2\rangle$. We further show that $\nu_{dyn}$ remains robust if detection efficiencies are uniform across the measurement's acceptance. The robustness is lost, however, if detection efficiencies are momentum dependent, although the identity methods remains applicable provided detection efficiencies can be determined with sufficient accuracy.

Study of the Low-Frequency Excess Equivalent Magnetic Noise in GMI-Based Devices

Low-frequency equivalent magnetic noise levels of four different giant magneto-impedance (GMI) samples, exhibiting $1/f$ spectral behavior, have been experimentally determined, for several excitation conditions (involving both dc current and ac excitation amplitude). Under appropriate conditions, for which the noise level at 1 Hz is minimal, coherence measurements show that the main noise source responsible for this low frequency noise is the intrinsic noise of the GMI sample. The lowest corresponding magnetic noise performances of the four samples were determined. The lowest noise level observed was $17\,\textrm {pT}/(\textrm {Hz})^{1/2}$ at 1 Hz. It has been proposed that the imaginary part of the magnetic susceptibility, $\chi ^{\prime \prime }$ , a measure of the low frequency magnetization fluctuations, determines the resulting magnetic noise level of the sensor. Its values at 1 Hz have been been evaluated for all four samples. Using these evaluations, expected noise levels at 1 Hz are computed, based on a previously proposed theoretical model, and compared with the measured noise performances. Under conditions for which correlation measurements show that system noise is dominated by sensor noise, the two sets of values are in reasonably good agreement, suggesting that the proposed model for low frequency excess noise of GMI materials is essentially correct.

Calculation of the Intensity of Physical Time Fluctuations Using the Standard Solar Model and its Comparison with the Results of Experimental Measurements

The article reviews the possibility of describing physical time as a random Poisson process. An equation allowing the intensity of physical time fluctuations to be calculated depending on the entropy production density within irreversible natural processes has been proposed. Based on the standard solar model the work calculates the entropy production density inside the Sun and the dependence of the intensity of physical time fluctuations on the distance to the centre of the Sun. A free model parameter has been established, and the method of its evaluation has been suggested. The calculations of the entropy production density inside the Sun showed that it differs by 2-3 orders of magnitude in different parts of the Sun. The intensity of physical time fluctuations on the Earth's surface depending on the entropy production density during the sunlight-to-Earth's thermal radiation conversion has been theoretically predicted. A method of evaluation of the Kullback's measure of voltage fluctuations in small amounts of electrolyte has been proposed. Using a simple model of the Earth's surface heat transfer to the upper atmosphere, the effective Earth's thermal radiation temperature has been determined. A comparison between the theoretical values of the Kullback's measure derived from the fluctuating physical time model and the experimentally measured values of this measure for two independent electrolytic cells showed a good qualitative and quantitative concurrence of predictions of both theoretical model and experimental data.

Fluctuation of Information Entropy Measures in Cell Image

A simple, label-free cytometry technique is introduced. It is based on the analysis of the fluctuation of image Gray Level Information Entropy (GLIE) which is shown to reflect intracellular biophysical properties like generalized entropy. In this study, the analytical relations between cellular thermodynamic generalized entropy and diffusivity and GLIE fluctuation measures are explored for the first time. The standard deviation (SD) of GLIE is shown by experiments, simulation and theoretical analysis to be indifferent to microscope system “noise”. Then, the ability of GLIE fluctuation measures to reflect basic cellular entropy conditions of early death and malignancy is demonstrated in a cell model of human, healthy-donor lymphocytes, malignant Jurkat cells, as well as dead lymphocytes and Jurkat cells. Utilization of GLIE-based fluctuation measures seems to have the advantage of displaying biophysical characterization of the tested cells, like diffusivity and entropy, in a novel, unique, simple and illustrative way.

Eigenfunction statistics of Wishart Brownian ensembles

We theoretically analyze the eigenfunction fluctuation measures for a Hermitian ensemble which appears as an intermediate state of the perturbation of a stationary ensemble by another stationary ensemble of Wishart (Laguerre) type. Similar to the perturbation by a Gaussian stationary ensemble, the measures undergo a diffusive dynamics in terms of the perturbation parameter but the energy-dependence of the fluctuations is different in the two cases. This may have important consequences for the eigenfunction dynamics as well as phase transition studies in many areas of complexity where Brownian ensembles appear.

Estimation of Pst indicator values on the basis of voltage fluctuation indices

Power quality is described by voltage fluctuation measures. Voltage fluctuation is understood as “a series of voltage changes or a continuous variation of the rms or peak value of the voltage.” Voltage variation is most often manifested by flicker, which might become obnoxious at a high enough intensity. One of the standard measures of voltage fluctuation is $\boldsymbol {P}_{st}$ indicator. One of its major flaws is its limited diagnostic capabilities. Voltage fluctuation indices are the measure, which provides much bigger range of diagnostic capabilities. However, it has not been acknowledged as a standard measure. The initial part of this paper includes the description of the accepted method of reproducing voltage variation. It also presents general characteristics of the $\boldsymbol {P}_{st}$ indicator and voltage fluctuation indices. The next part of this paper describes the methods of converting voltage fluctuation indices into $\boldsymbol {P}_{st}$ indicator and vice versa. The capability of estimating the $\boldsymbol {P}_{st}$ indicator on the basis of the indices has been confirmed. Three examples of measurement results of both these measures in low-voltage (LV) power grids have been presented. These results have proved the connection between the estimated values (on the basis of voltage fluctuation indices) and the results of the $\boldsymbol {P}_{st}$ indicator measurements.

Statistical moments in superposition models and strongly intensive measures

First, we present a concise glossary of formulas for composition of standard, cumulant, factorial, and factorial cumulant moments in superposition (compound) models, where final particles are created via independent emission from a collection of sources. Explicit mathematical formulas for the composed moments are given to all orders. We discuss the composition laws for various types of moments via the generating-function methods and list the formulas for the unfolding of the unwanted fluctuations. Second, the technique is applied to the difference of the scaled multiplicities of two particle types. This allows us for a systematic derivation and a simple algebraic interpretation of the so-called strongly intensive fluctuation measures. With the help of the formalism we obtain several new strongly intensive measures involving higher-rank moments. The reviewed as well as the new results may be useful in investigations of mechanisms of particle production and event-by-event fluctuations in high-energy nuclear and hadronic collisions, and in particular in the search for signatures of the QCD phase transition at a finite baryon density.

Comparison of methods for the identification of mesoscale wind speed fluctuations

Mesoscale wind speed fluctuations influence the characteristics of offshore wind energy. These recurring wind speed changes on time scales between tens of minutes and six hours lead to power output fluctuations. In order to investigate the meteorological conditions associated with mesoscale wind speed fluctuations, a measure is needed to detect these situations in wind speed time series. Previous studies used the empirical Hilbert-Huang Transform to determine the energy in the mesoscale frequency range or calculated the standard deviation of a band-pass filtered wind speed time series. The aim of this paper is to introduce newly developed empirical mesoscale fluctuation measures and to compare them with existing measures in regard to their sensitivity to recurring wind speed changes. One of the methods is based on the Hilbert-Huang Transform, two on the Fast Fourier Transform and one on wind speed increments. It is found that despite various complexity of the methods, all methods can identify days with highly variable mesoscale wind speeds equally well.

Sustained attention to a predictable, unengaging Go/No-Go task shows ongoing development between 6 and 11years.

Response time variability (RTV) is a useful measure of sustained attention; however, little is known about developmental changes in RTV at different temporal frequencies. Thirty-five 6-year-olds, 31 8-year-olds, and 37 10-year-olds completed the fixed-sequence Sustained Attention to Response Task on three occasions, six months apart. Fast Fourier Transform and ex-Gaussian analyses of response time (RT) data assessed momentary fluctuations in RT, gradual changes in RT, and very long responses, thought to reflect attentional control fluctuations, slow-shifting arousal, and infrequent lapses in attention, respectively. A half-by-half analysis measured within-occasion time-on-task effects. The 10-to 11-year-olds performed with less momentary fluctuations in RT, fewer long responses, and fewer commission and omission errors than the younger groups. This group performed well in the first half of the task but showed time-on-task effects on measures of momentary fluctuations in RT, very long responses, target sensitivity (d'), and commission errors. The 6- to 7-year-olds performed less well than the older groups, and showed time-on-task effects, on almost all measures. The 8- to- 9-year-olds mostly performed at an intermediate level compared with the other groups; however, this group performed with a similar level of momentary fluctuations in RT and very long responses as the 6- to 7-year-olds. These findings indicate that there is ongoing maturation of various aspects of sustained attention on a predictable task, with a period of relative stability in performance between 8 and 9years of age.

Conserved charge fluctuations using the D measure in heavy-ion collisions

We study the net-charge fluctuations, $D$-measure variable, in high energy heavy-ion collisions in heavy-ion jet interaction generator (HIJING), ultrarelativistic quantum molecular dynamics (UrQMD) and hadron resonance gas (HRG) models for various center-of-mass energies (\sqsn). The effect of kinematic acceptance and resonance decay, in the pseudorapidity acceptance interval ($\Delta\eta$) and lower transverse momentum ($p_{T}^{min}$) threshold, on fluctuation measures are discussed. A strong dependence of $D$ with the $\Delta\eta$ in HIJING and UrQMD models is observed as opposed to results obtained from the HRG model. The dissipation of fluctuation signal is estimated by fitting the $D$-measure as a function of the $\Delta\eta$. An extrapolated function for higher $\Delta\eta$ values at lower \sqsn is different from the results obtained from models. Particle species dependence of $D$ and the effect of the $p_T^{min}$ selection threshold are discussed in HIJING and HRG models. The comparison of $D$, at midrapidity, of net-charge fluctuations at various \sqsn obtained from the models with the data from the ALICE experiment is discussed. The results from the present work as a function of $\Delta\eta$ and \sqsn will provide a baseline for comparison to experimental measurements.

Quantum Fluctuations along Symmetry Crossover in a Kondo-Correlated Quantum Dot.

Universal properties of entangled many-body states are controlled by their symmetry and quantum fluctuations. By the magnetic-field tuning of the spin-orbital degeneracy in a Kondo-correlated quantum dot, we have modified quantum fluctuations to directly measure their influence on the many-body properties along the crossover from SU(4) to SU(2) symmetry of the ground state. High-sensitive current noise measurements combined with the nonequilibrium Fermi liquid theory clarify that the Kondo resonance and electron correlations are enhanced as the fluctuations, measured by the Wilson ratio, increase along the symmetry crossover. Our achievement demonstrates that nonlinear noise constitutes a measure of quantum fluctuations that can be used to tackle quantum phase transitions.

Ultrasensitivity and fluctuations in the Barkai-Leibler model of chemotaxis receptors in Escherichia coli.

A stochastic version of the Barkai-Leibler model of chemotaxis receptors in Escherichia coli is studied here with the goal of elucidating the effects of intrinsic network noise in their conformational dynamics. The model was originally proposed to explain the robust and near-perfect adaptation of E. coli observed across a wide range of spatially uniform attractant/repellent (ligand) concentrations. In the model, a receptor is either active or inactive and can stochastically switch between the two states. The enzyme CheR methylates inactive receptors while CheB demethylates active receptors and the probability for a receptor to be active depends on its level of methylation and ligand occupation. In a simple version of the model with two methylation sites per receptor (M = 2), we show rigorously, under a quasi-steady state approximation, that the mean active fraction of receptors is an ultrasensitive function of [CheR]/[CheB] in the limit of saturating receptor concentration. Hence the model shows zero-order ultrasensitivity (ZOU), similar to the classical two-state model of covalent modification studied by Goldbeter and Koshland (GK). We also find that in the limits of extremely small and extremely large ligand concentrations, the system reduces to two different two-state GK modules. A quantitative measure of the spontaneous fluctuations in activity is provided by the variance in the active fraction, which is estimated mathematically under linear noise approximation (LNA). It is found that peaks near the ZOU transition. The variance is a non-monotonic, but weak function of ligand concentration and a decreasing function of receptor concentration. Gillespie simulations are also performed in models with M = 2, 3 and 4. For M = 2, simulations show excellent agreement with analytical results obtained under LNA. Numerical results for M = 3 and M = 4 are qualitatively similar to our mathematical results in M = 2; while all the models show ZOU in mean activity, the variance is found to be smaller for larger M. The magnitude of receptor noise deduced from available experimental data is consistent with our predictions. A simple analysis of the downstream signaling pathway shows that this noise is large enough to affect the motility of the organism, and may have a beneficial effect on it. The response of mean receptor activity to small time-dependent changes in the external ligand concentration is computed within linear response theory, and found to have a bilobe form, in agreement with earlier experimental observations.

Statistical and fractal features of nanocrystalline AZO thin films

In this paper, We investigate the morphology effect of Aluminum-doped zinc oxide (AZO) thin films on the physical properties such as conductivity and grain size. The AZO thin films are prepared by spray pyrolysis at different thicknesses in the range 100–400 nm. Height fluctuations obtained from atomic force microscopy (AFM) analysis are applied to the statistical and fractal analysis of thin films. We show that the conductivity of thin films is proportional to the roughness parameter as σ∼Wm which m=6.42±0.50. Calculating the nonlinear measures (skewness and kurtosis) of height fluctuations demonstrates the isotropic nature of AZO rough surfaces. Fractal analysis of the mentioned thin films using two dimensional multifractal detrended fluctuation analysis illustrates the multifractality scaling and the strength of multifractality increases with thickness. Our results show that the reason for the multi-affinity is the existence of different correlations in the height fluctuations of the thin films. Calculating the contour loops features of the height fluctuations reveals that the radius, length, and area of loops increase with thickness enhancement and the radius of contour loops is introduced as a new statistical parameter which is linearly related to the grain size and could be useful to calculate it.